Det medisinske fakultet

Strain rate imaging.

Myocardial deformation imaging by ultrasound / echocardiography

Tissue Doppler and Speckle tracking

by 

Asbjørn Støylen, Professor, Dr. med.

Department of Circulation and Medical Imaging,
Faculty of Medicine,
NTNU Norwegian University of Science and Technology

Contact address: asbjorn.stoylen@ntnu.no

Introduction for the novice researcher and curious clinician. Now with tables of normal values and reproducibility for tissue Doppler and strain/strain rate from the HUNT study


Website updated: August 2015.     This section updated:August  2015.    
Follow updates on twitter:  @strain_rate

Link to what's new.
Link to website index.
Link to tables of normal values
Link to Why strain and strain rate?
Link to "How to use deformation imaging clinically"



Cardiac ultrasound:



Ummanaq (the heart shaped mountain), national mountain of Greenland Snøhetta (Mount Snow Hood), by many regarded as the national mountain of  Norway. Not quite as heart shaped, but at least situated at the heart of both Norwegian geography (grensen mellom det Nordenfjeldske og Søndenfjeldske - Gerhard Schøning) and history (enig og tro til Dovre faller).


Welcome

The internet is free, so feel free to use the examples found on this website in demonstrations and lectures. However, ordinary ethics dictates that credit should be given to the author (using the address: from: http://folk.ntnu.no/stoylen/strainrate).  For publishing, I and the Norwegian University of Science and Technology retain the copyright to all material published here. (For written publication, the acknowledgment should thus be: reproduced with permission from: http://folk.ntnu.no/stoylen/strainrate).
I do not consider the fact that a signature is embedded in some pictures sufficient acknowledgement, without the website address.
Even if the images are taken from other websites that do acknowledge the source, I still require acknowledgment of this website as the principal source, the fact that there are publications with permission/acknowledgement available on the net, does not alleviate the duty to acknowledge the original source.

Using the material in papers without
acknowledgement, and for published material without permission, I consider academic misconduct in addition to being copyright violation.

The most extreme example of this kind I have seen so far, is a paper by the authors Dagianti A, Regna E, Laurito A, Malaj A, Gossetti B, Fedele F, that I recently came across in some journal called "Prevention and research". The paper had used nine figures coming from this website without copyright permission and with no acknowledgement. Repeated inquiries to the journal have elicited no response.





Recent updates:



May 2015: Mainly extending the chapter on evidence based diagnostics.

June 2015: Slight extension of the discussion of segmental interaction in this section. A new and better integrated illustration of the integration/derivation relation between velocity, displacement, strain rate and strain. The somewhat tedious introduction about usefulness and methods in the general comments chapter have been abbreviated.

I have also added an example showing how assessing motion on B-mode may result in erroneous diagnosis. The case illustrates eminently the difference between motion and deformation as shown below, and the advantage of assessing strain rate imaging as shown in the clinical use section.

As diagnostics is technology driven, I have added a short chapter on how technology driven diagnostics may lead to over diagnosis to the evidence section.

July 2015: Added a new paragraph on the mechanics of the apex beat.
The chapter on peak systolic indices of myocardial performance, being the closest measures of contractility, has been revised, for a more integrated understanding of the relations between peak systolic annulus velocity, peak systolic acceleration (which so far is rather undefined and not proven ery useful), peak systolic strain rate and peak LVOT flow velocity.
I have also added a short introduction to the chapter on how motion and deformation can be displayed, for pedagogic reasons so to improve the  understanding of curves and colour for novices.

August 2015: Added a discusssion on "high risk", in the sense of risk profile, vs high pretest risk in diagnostic testing to the "utility" section. The two must not be confused. Also added some new images of how to use velocity, strain rate and CAMM, and extended the paragraph on pre clincal studies in the strain rate evidence chapter). 

Added a case where all segments have post systolic shortening simultaneously, which means there can be no segment interaction as the mechanism. in that case, the mechanism is wall-cavity interaction (tension pressure), due to trapping of blood.



Website index:

List of tables of normal values


This section:

Deals with understanding the basic concepts, the geometry of deformation, understanding the display modes of deformation and the relation between imaging and physiology.


Other sections:


Basic ultrasound, echocardiography and Doppler for clinicians

A basic explanation of the fundamental physics and technology of ultrasound for the medical profession. Technical or mathematical background is not necessary, explanations are intended to be intuitive and graphic, rather than mathematical. Thus, technologists will find it embarassingly simple. This section is important for the understanding of the basic principles described in detail in the section on measurements of strain rate by ultrasound. Especially in order to understand the fundamental principles that limits the methods.The priciples will also be useful to gain a basic understanding of echocardiography in general, and may be read separately even if deformation imaging is not interesting.


Measurements of strain and strain rate by ultrasound - technology and limitations
The section deals with the fundamentals of the different methods for measuring strain and strain rate by ultrasound, and their limitations. It it may be seen as a continuation of the basic ultrasound section, which only deals with deformation imaging in a cursory way. However,
the understanding of the basic principles of ultrasound will add to the understanding of the methods as described in detail in the measurements section.

Is deformation imaging useful? - Clinical use and scientific evidence.

The section deals with the approach to using deformation imaging by ultrasound in a practical way, as well as the accumulating clinical evidence for the utility of the methods. 



Mathematics of strain and strain rate:

A more in depth treatment of some of the concepts, for specially interested. However, still on a basic level intended for medical personnel, higher mathematical background is not required, and again people wioth technical / mathematical background may find it embarassingly simple.

References for all sections





About the website:

Some of the animations may upload slowly or not at all by the first try, and remain motionless. Usually, just clicking the view: reload /refresh button will correct this. The animations and video examples are all in *.gif animation format, so no special software in the form of various media players will be necessary for the animation. Also if downloaded (with due credits, of course), it can be embedded in a power point presentation and will run in all versions from office 2000 and onwards. It should then be treated as "picture", not a video, meaning that it is inserted in the file as a picture, and will then run without the media player. It also means that it will not be necessary to keep the loop separate outside the presentation, the animation is fully embedded in the powerpoint file, just like any other picture, and will run in a continuous loop when the picture is shown.
The text is riddled with links. Following the links to see the reference, just click on the "back" button in your browser, and you return to the point in the text where you were
.


I have received some requests for the website in *.pdf format. This of course is now feasible, and a pdf version have nor been added for your convenience. However, the pdf will of course not include videos, and may lag behind in updating. Also, converting from html to pdf will not, of course, result in very well edited page divisions. Editing this will require too much work. And I warn you, the document is large, and will download veeryyy sloooowly. The present pdf version is the March 3 2015 update, which can be downloaded here.


The website is divided into sections to allow quicker downloading. Every section can be read separately and are accessible by links, or the complete website index above.

This first section deals with understanding the basic concepts, the geometry of deformation, understanding the basic principles for measurement and display modes of deformation and the relation between imaging and physiology/pathophysiology. All methods can give the information as numerical traces, parametric (colour) images (in 2D or Colour M-mode). 3-/4D reconstruction has some limitations using segmental strain, however.

The introduction deals with the  advantages of using deformation measurements in certain situations, as well as discussing why deformation imaging is somewhat underutilised despite the advantages. The general comments about the methods (speckle tracking and tissue Doppler), some comments on nomenclature and some comments on unfounded presumptions and controversial issues have also been moved to the introduction.

  1. The differences between motion (displacement and velocity) and deformation (strain and strain rate) is discussed in the first chapter,.
  2. As functional imaging is display, the different methods for display are given in the second chapter, in order to being able to interpret the displays used here.
  3. Strain is geometrical changes, so the main point of strain rate imaging is understanding geometry, which is discussed in the third chapter.
  4. It is important to realise that any kind of imaging does only measure deformation. Deformation is the result of tension (contractility) and load, deformation alone tells only half the truth about global contractility, as discussed in the fourth chapter. However, due to myocardial segment interaction, segmental deformation will tell about regional reduced contractility.
  5. The relation of deformation parameters to the heart cycle, the new information that has been gained by new methods, and the events in the heart cycle is discussed in the fifth and main chapter which also discusses the relation to different pathophysiologic states.
    1. in relation to start and end systolic and diastolic timing
    2. Global systolic function
    3. Regional systolic function
    4. Asynchrony
    5. Diastolic function
    6. atrial function.
The next section: Basic ultrasound, echocardiography and Doppler for clinicians gives a basic explanation of some of the fundamental physics and technology of ultrasound for the medical profession. Technical or mathematical background is not necessary, explanations are intended to be intuitive and graphic, rather than mathematical. Thus, technologists will find it embarassingly simple. This section is important for the understanding of the basic principles described in detail in the section on measurements of strain rate by ultrasound. Especially in order to understand the fundamental principles that limits the methods.The principles will also be useful to gain a basic understanding of echocardiography in general, and may be read separately even if deformation imaging is not interesting.

The third section: Measurements of strain and strain rate by ultrasound - technology and limitations, deals with  the technical fundamentals of the different methods for measuring strain and strain rate by ultrasound, and their limitations. It is a continuation of the basic ultrasound section, which only deals with deformation imaging in a cursory way. However, the understanding of the basic principles of ultrasound will add to the understanding of the methods as described in detail in the measurements section. In this section, the basis for deformation measurement by different ultrasound methods, as well as the limitations of the various methods are discussed in more detail.

Basically, however, irrespectively of method, the fundamental indices of motion (velocity and displacement) and of deformation (strain rate and strain) are the same. Also, the display of the indices can be used irrespectively of the method for acquiring them. However, some of the methods set limits for how the display can be made.

The fourth section: Is deformation imaging useful? Clinical use and documentation is under revision at present. The aim is to present first an introduction to using strain and strain rate in the clinical situation, illustrated  by examples. Also, how to assess the effects of artefacts to avoid pitfalls and to get additional information out of the methods. This is an integrated approach, using both velocity curves and colour SRI, in addition to strain rate and strain curves.

In the second part, the clinical evidence for the use of deformation imaging will be reviewed.


The last section: Mathematics of strain and strain rate is for the specially interested. It is dedicated to a more in depth treatment of some themes the mathematical basis of strain and strain rate imaging (and a little other things, like derivation of the Doppler equation). However, still on a basic level intended for medical personnel, higher mathematical background is not required out over what is obtained by a general high school education. The emphasis is on graphic illustration, and mathematicians and engineers will find this embarrassingly simple.



Introduction


The method of strain rate imaging by tissue Doppler was developed here at the Norwegian University of Science and Technology in Trondheim, Norway. It was the subject of two doctoral theses, one in technology (1) and one in medicine (2), and was a result of a successful cooperation between technical research (in strain and velocity gradients) and medical research (in long axis function of the left ventricle). One of the important point of my work with long axis function, was that this lead to Strain Rate Imaging being applied to longitudinal velocity gradients, thus making the rough method more robust, as well as all segments of the ventricle available for analysis. The method was originally validated in a mechanical model, in cooperation with the university of Leuven, Belgium (3) and described in a method article from Trondheim in 1998 (4) and 2000 (5). The basic publications dealt with feasibility (1998) ( 4), clinical validation by comparison with echocardiography (6) and with coronary angiography (7). Validation of strain measurements (from integrated strain rate) was done at Rikshospitalet, Oslo, Norway by comparison with ultrasonomicrometry (8)  and MR, in cooperation with Johns Hopkins Hospital (9). Early work on the feasibility of the method in myocardial infarction was also done at the university of Linköping and later at Leuven (10). An excellent early review paper was published by the Leuven group (11).

Now, it is important to emphasize that both motion and deformation imaging are no longer simply tissue Doppler derived modalities. Both can be derived by tracking the motion of the myocardium in grey scale pattern, speckle tracking. The basic concepts are the same; general principles of motion (velocity and displacement) vs. deformation (strain rate and strain) apply, irrespective of method but the limitations may differ between the methods.

The terms: - Velocity imaging, - Displacement imaging, - Strain rate imaging, - Strain Imaging, should not be taken synonymous with tissue Doppler, but should be used irrespectively of the method employed, and the term "by tissue Doppler",  "by speckle tracking" or whatever application is used should be added, if studies are cited.

Some general comments:



Why use strain and strain rate?

  1. The strain and strain rate subtracts motion due to the effects of neighboring segments (tethering). Tethering may both mask pathological deformation and impart pathological motion to normal segments and deformation imaging and is necessary to locate and show the true extent of pathology. And in some situations exclude regional pathology. This means that motion parameters (displacement and velocity) reflects global function, and should be applied to the mitral ring, while deformation imaging (strain and strain rate) shows regional function within the myocardium.
    1. However, strain and strain rate are more susceptible to noise, both by tissue Doppler and speckle tracking ( the weaknesses of the last being masked by smoothing), and a rough qualitative assessment of regional function can be done by assessing the offset between velocity curves, as well as by colour M-mode.
    2. Even if velocity curves indicate abnormal motion, the deformation parameters are necessary to localise the area of abnormal deformation.
    3. Deformation parameters are useful in doing a more comprehensive assessment of local contraction and relaxation, such as initial stretch, hypokinesia, post systolic shortening, both in infarcts / ischemia and in electrical asynchrony.
  2. Strain and strain rate are deformation per length, and thus are normalised for heart size, also in global deformation, meaning that it reduces biological variability due to size differences. Clinical evidence for the advantage of this is emerging, at least in children where variability in heart size is greatest. The advantage in adults is still uncertain.
  3. However, Strain and strain rate only describe the part of the myocardial work relating to volume changes (i.e. ejection), not to pressure, and both systolic and diastolic deformation itself is load dependent, as is the case with all volume based measures of ventricular function. This, it appears, cannot be emphasized enough. But as the main value is in diagnosis of regional dysfunction, the segment interaction in combination with the load dependency enables us to make inferences about uneven contractility, i.e. regional dysfunction, even if the contractility cannot be measured directly. Thus, regional deformation imaging shows regional relative contractility.
  4. In addition, in different inotropic states, the changes in contraction will be caused by changes in contractility, and thus the measures are valid measures of contractility changes.
Deformation imaging has added a lot of knowledge of the regional myocardial properties, and the fundamental physiological knowledge gained from deformation imaging is method independent. Thus, the basic principles and the relation to pathophysiological knowledge comes first, in this section.

But of course, even with the fundamentals of physiology, an understanding of the technical aspects of the methods and especially the limitations and propensity to artefacts is important, as reviewed in the second and third sections.

Also, methods are not useful unless knowing how to use them and what to look for. In addition, of course even with fundamental basic knowledge, the scientific evidence for the methods should be present. Both these aspects are reviewed in the fourth section.

However, it is a main point that deformation imaging is about added value, on top of a basic echo.

Why is deformation imaging underutilised?



The number of publications is enormous, but the use in daily clinic is still limited despite giving additional information, as shown in "How to use strain and strain rate clinically", the method, especially tissue Doppler seems to have gone into a partial eclipse:


Partial solar eclipse, March 20. 2015. Picture taken from Trondheim


This has some historical reasons:

Tissue Doppler derived deformation

When tissue Doppler derived deformation (strain rate imaging) arrived (4), we concentrated on semi quantitative assessment with colour M-mode (4, 6, 7). The colour WMS seemed to equivalent with B-mode WMS both in feasibility and accuracy (6, 7), but no better. This is hardly be surprising, as the expert WMS is a fairly precise method, an colour WMS is still semi quantitative. However, with increased understanding, it beacme evident that the colour M-mode offered additional information, both on the time course of the deformation (like initial akinesia and post systolic shortening), as well as being very robust against noise.

noise

However, the possibility to go from semi-quantitative assessment of regional function to quantitative measurement, seemed interesting. And with objective measurement, the experience dependency might be bypassed. So objective measurement became the goal. And principally peak vaues. But as strain rate is the result of a derivation, it is much more noisy than  velocity curves. Even if smoothing and the integration to strain took care of much of the random noise, non random noise (especially clutter) remained a problem.


Thus, curves and especially peak values seemed to be difficult to interpret, as it was difficult to see whether the curves were due to pathology or artefacts. In addition the fact that tissue Doppler was angle dependent, and that strain rate derived from a set of velocities was even more angle dependent, lead to a lot of erroneous speculation that it could for instance not be used in the apical segment, which of course is nonsense. And in this setting, it became evident that using tissue Doppler with reliance was just as experience dependent as B-mode.

Thus, inherent weaknesses in the tissue Doppler method, especially angle dependency and vulnerability to noise, especially to clutter, made the method little approachable, and this  led to the method being little used.

And in all this, colour tissue Doppler was not reinstated, despite it's ability to:
  1. Give information as wall motion score similar to B-mode, and
  2. Give additional information on timing beyond the B-mode information (also due to higher temporal resolution), and
  3. Visualise clutter artefacts in a way that makes timing information still available, and hence,
  4. Might guide the placement of the ROIs to extract reliable curves.
Thus, interpretation of artefacts, as well as timing is easy with colour M-mode. The curved M-mode will then give the possibility of assessing both if regional shortening is normal, and to look at the timing. Actually, the curved M-mode has better spatial resolution that strain rate or strain curves.

Also, in the user interface provided, all difficulties were eminently visible, but instead of being considered an advantage, it disgusted a lot.
The problem being both the experience dependency, initially poor user friendliness, and variability of results. The limitations of the methods may scare potential users as well. 

One of the main points about assessing regional function by deformation parameters, however, is that peak values is not the most important thing at all. As seen below, the colour M-mode and the shape of the curves gives almost all information qualitatively in a quick and easy way:

Both initial delay in shortening of a segment, reduced peak values and post systolic shortening are all phenomenons that tells about the relative reduction in rate of tension development (strain rate) and total tension, all measures of relative reduced contractility of a segment or region, as well as delay in relaxation, another assessment of both ischemia and contractility.

In my opinion, however, tissue Doppler seems to be able to fly, although it is a rather heavy bird:


Wandering albatross is heavy in taking off from water. Drake Passage. However, this bird is fully able to take off and fly.



Speckle tracking derived deformation

When speckle tracking was launched, it seemed to solve some of the problems from tissue Doppler.

 
The challenger. Musk oxen, Grønnedal, Greenland.

  1. It came with an alluringly user friendly interface which actually had nothing to do with speckle tracking per se). Especially for deriving peak values, which is attractively easy, but poor use of data, as it discards additional information about timing. 
    1. In addition, the low frame rate makes it less suited for timing, especially in the spline smoothed versions.
  2. Also, it was maintained that speckle tracking was angle independent, and able to track in all directions,
    1. Which is a half truth at best, as
      1. the axial resolution of B-mode is so much better than the lateral, this means that tracking is better in the axial direction.
      2. The line density decreases with depth, and so, of course do the  lateral resolution and
      3. With increasing frame rate of B-mode, the line density is reduced, and especially in 3D speckle tracking, where line density is severely reduced.
  3. There was an apparent reduction in noise, (which again did not have anything to do with speckle tracking per se, but with the applications using a generous amount of smoothing), and the smoothing made the effects of clutter less visible, and the method apparently more robust.
    1. It is true that speckle tracking is done in harmonic mode, while tissue Doppler is done in fundamental, removing some of the clutter, but
    2. Most of the clutter is smeared out due to the spline smoothing, which may lead to absurd examples as seen here
    3. The only method free of this that I know of, is the segmental tracking application developed by NTNU, described elsewhere, which can track segmental deformation by speckle tracking alone, or in combination with tissue Doppler.
  4. Thus, the segmental values obtained by this kind of speckle tracking are not true segmental values, results of a spline (or similar) function taking into account not only the tracking of speckles in the actual segments, but the over all tracking as well as the global deformation.  the segmental values are then partly splines of the global function. Given the obvious curvature dependency in addition, the method has a serious sensitivity issue for reduced segmental function. Thus the apparent lower vulnerability and better reproducibility of speckle tracking over tissue Doppler is due to more smoothing. When the same smoothing is applied to tissue Doppler. results become near identical.


Thus, for regional function, the flight capability of speckle tracking is low:


Molting gentoo penguin, Port Lockroy, Antarctica.
Jumping penguins. Paradise Harbour, Antarctica.

A direct comparison between speckle tracking and tissue Doppler in clinical examples can be seen here.


It is thus no surprise that the publications on speckle tracking lately, has been about global strain, which is a global function parameter. (Thus, a method that started out as a method for regional function, has devolved to being a global measure, due to the inherent weaknesses in the speckle tracking application). Here, it may prove useful, especially when compared with the most used and poorest method of them all; ejection fraction. It has been instrumental in shifting emphasis from ejection fraction (which in fact doesn't work in small ventricles), to long axis function. However, so far it has not been proven that global longitudinal strain adds information to that of simple longitudinal shortening . However, the value of long axis function was shown early in the 90ies (31, 32, 33, 34, 35, 64, 65, 66) by mitral annular plane displacement(MAPSE). It has not been definitely proven that normalising for LV length (which is global strain), is advantageous in adults, although of value in children (159, 214, 288).

Also, global strain is not load independent, and do not measure contractility.


The different advantages and disadvantages, which is extensively discussed in a separate section on measurements of strain and strain rate by ultrasound. It may also be a surprise to some, but spectral Doppler has a fairly low temporal resolution. Even if sampling rate can be as high as 1000, the spectral analysis requires a long sequence of frames, thus reducing the effective frame rate, the temporal resolution of both pulsed Doppler flow and tissue Doppler is usually around, and may even be below 100 FPS. This is described in slightly more detail in the basic ultrasound section.

Modern ultrasound technology utilising the ability of new probes being able to transmit more data, as well as increased computing speed and capacity for more advanced post processing, has increased both line density and frame rate of B-mode, and this development will continue. This means that some of the reservations towards speckle tracking in terms of frame rate and lateral resolution will become less important in time. This, however, do not lend more validity to earlier results. And so far, it does not apply to 3D speckle tracking


The fundamental concepts relating to geometry, pumping and physiology, however, are independent of methods (except where the methods relate differently to geometry), so even if examples are taken from one method, the underlying pathophysiology should be the same with other methods. The sensitivity for specific changes may vary in different situations according to the strengths of each method .

In the ideal world, any measurement would give the diagnosis once correct cut off an normal values are established. But this is not the ideal world, and image quality is far from perfect in most cases, which is a fundamental property of ultrasound. Thus, no single measurement is perfect, an echocardiographic examination always consists of using all the available, more or less circumstantial evidence, weighing findings against each other and arriving at a conclusion. This will usually be fairly certain in the hands of an experienced clinician, even if single measurements are not. This is a fundamental property of all echocardiography. With the limitations inherent in basic ultrasound and in the specific methods, clinical ultrasound will partly be a craft, not pure science. The careful weighing of the evidence in terms of the methods limitations is thus an integral part of the examination, and a knowledge of the methods themselves and the method specific limitations is essential.

This is also the case with deformation imaging, and this should be the basic approach, deformation imaging being part of the total evidence, and can serve as an aid to diagnosis, as shown in the last chapter on how to use deformation imaging clinically.

Concerning nomenclature:


There is still a need for standardisation of nomenclature in the field. Especially for newer measures relating to deformation imaging, which are not covered by The ASE standards (146). The systolic mitral annular excursion is a useful measure of global systolic function. It has had various names, the term AVPD (atrioventricular plane descent) is unfortunate, as it don't separate beteen mitral and tricuspid excursions, event though they are different, the term MAE has been used from the beginning, but as TAPSE has been firmly established for the right ventricle, I think the term MAPSE (mitral annular plane systolic excursion) should be used in order to harmonise. The text and figures in this website have been adjusted accordingly.

The nomenclature about positive and negative deformation has been a mess.The original definition of strain makes shortening and shortening velocity negative values. For the longitudinal and circumferential functional measures, this means that the more the contraction, the lower the negative values. Then "increased" strain and strain rate would mean "less contraction", which is absolutely counter intuitive. Also, the literature has through all the time strain and strain rate has been evident, talked about "peak values" strain and strain rate. Consistent with the usage of negative values, that actually should have been "trough values". For transmural strain, the case is opposite, wall thickening is positive strain and peak values are really peak values. The new definitions paper (287) recommends the use of absolute numbers, which will make the discussions more intuitive, and I wholeheartedly concur.

However, as we have two reference systems for strain and strain rate: Lagrangian and Eulerian, I'm no fan of the term "natural strain" for Eulerian strain, I can't see why one reference system is more "natural" than another. Also using mathemathician's names should be symmetrical.

There are still controversial issues, as well as unfounded presumptions in the field.


An academic discussion. Northern fulmars in New Ålesund, Spitsbergen Professor and student.  Blue eyed shag and adelie chick- Peterman Island, Antarctica

I'd like to comment on some of them:
  1. Strain and strain rate are not load independent. 
    1. This is because shortening as seen by imaging does not equal contraction. What we measure with imaging by any method, is deformation of the ventricle, whether we measure shortening fraction, ejection fraction, annular displacement, annular velocity, strain or strain rate.
    2. Active contraction happens only during pre ejection, where there is no deformation (in fact about 80% of the systolic work is done during that phase), and first part of ejection, ejection and systolic deformation (chamber shortening, length and volume reduction etc), continues well into myocyte relaxation due to the inertia of the blood as discussed below. thus the cellular systole as seen in isolated myocytes is shorter than the cardiac systole, and the celluar diastole in fact corresponds to late systole and early diastole as defined by the cardiac cycle.
    3. Even deformation during active contraction is the result of interaction between contractility (developed force) and load. Strain rate is NOT load independent as discussed below. (Nor is strain of course, but this is more evident as this is the cumulated work during systole). On the other hand strain and strain rate are size independent measures of contraction, as opposed to annular motion and velocity.
    4. Thus: Strain rate do not measure contractility. As discussed below, strain rate shows changes in contractility better than strain, and this is the reason for the confusion in studies. But also, strain rate shows regional differences in contractility, actually due to the fact that it is load dependent.
  2.  Using tissue Doppler, there does not seem to be any gradient of longitudinal strain rate from base to apex, as has been maintained by some. This may be an artefact due to the curvature dependency of 2D strain, as it has not been found by tissue Doppler in the HUNT study, and looking at the spatial distribution of longitudinal velocities, it seems fairly improbable.
  3.  Understanding of Geometry is crucial.
    1. It is important to understand that the effects seen by strain rate imaging has geometrical explanations. This means that over all geometry governs the changes and relations between strain components. This is true both of transmural and circumferential and area strain, as well as the strain gradient across the wall seen both in longitudinal and circumferential direction. Thus, it also becomes important in dealing with regional function when measured by circumferential strain, especially in non transmural situations.
    2. There is no such thing as "radial function". Radial strain means wall thickening, but there are no myocardial fibres going in the radial direction. Wall thickening is a function of wall shortening, as the heart muscle is incompressible. Also the term "radial" is unfortunate, as it is also taken as meaning "in the direction of the ultrasound beam", ie. axial direction.
    3. Increased "radial function" measured by fractional shortening as compensation for reduced longitudinal function, is  a conceptual error, due to misunderstanding of geometry as seen below.  Thus, it is doubtful also that increased "radial function" (meaning wall thickening) as compensation for decreased longitudinal function actually exists, it seems theoretically impossible.
    4. Circumferential strain do NOT reflect circumferential fibre contraction. There would have been circumferential shortening even without circumferential fibres.
      1. Circumferential strain is mainly the circumferential shortening due to inward movement of midwall or endocardial circumference as the wall thickens (inwards - as described by the eggshell model), as discussed below. This means that circumferential strain is a function of transmural strain, and thus also of longitudinal strain.
      2. Also, the global circumferential strain is the same as the negative value of fractional shortening as explained below.
      3. As different vendors use different definition of circumferential strain (midwall or endocardial), there is no standard circumferential strain.
    5. Area strain is neither the sum, nor the product of circumferential strain. A slightly simplified modelling will give the formula A = L * C + L + C . Thus, area strain is a function of longitudinal and circumferential strain, not a "new" parameter.As different vendors use different definition of area strain (midwall or endocardial), there is no standard circumferential strain.
    6. Atrial strain during ventricular systole do NOT reflect atrial function (reservoir or otherwise). Atrial expansion is a function of the descent of the mitral annulus, (being a measure of systolic ventricular function) divided by atrial size (being a function of chronic filling pressure). Thus reduced atrial strain is a composite of reduced ventricular function and filling pressure, nothing else see here.
  4.  Local measures of annular motion (displacement or velocity) do NOT give information about regionally reduced function. Any regional hypo- or akinesial will affect all ponts on the mitral ring according to the degree of contractility reduction and amount of affected myocardial tissue as described here..
  5. Longitudinal layer strain is dubious, even though analysis software will produce values at request. Layer strain separation depends on line density, line width, direction in relation to the wall (in order to avoid pericardial echoes), and focussing. Number of lines is again dependent on frame rate. It is difficult to achieve a sufficient line density as well as narrow enough lines. This is discussed here.
  6. The pre ejection positive velocity spike of the ventricles is NOT isovolumic, it comes before mitral valve closure and thus before start of isovolumic contraction period, as discussed here. There is no such thing as isovolumic acceleration! The concept is nonsense.
  7. The post ejection negative velocity spike before early filling, is NOT isovolumic,  it comes before aortic valve closure, and hence beofre start of isovolumic relaxation period, as discussed here.
  8. Preserved ejection fraction in heart failure do not reflect "diastolic heart failure". The whole point is that ejection fraction (or fractional shortening) do not measure systolic function in concentric geometry, All principal systolic strains can be reduced and still the EF may be preserved. In eccentric hypertrophy, it is opposite, the EF may be reduced despite completely normal myocardial function. All this is due to the faulty use of EF in altered geometry.
  9. Left ventricular compliance is not a measure of ventricular diastolic function. Compliance is an end diastolic passive property, LV diastolic function in it's most commonly used  meaning, reflects early filling, being an active property of the ventricle. As discussed here.
  10. It seems that the number of segments of the left ventricle still is an issue for discussion. However many of the reasons for choices are historical. The present ASE/EAE guidelines (146) do NOT explicitly recommend 17 over 16 segments, it's optional (287). 
  11. Segment interaction within the AV-plane leads to the specific patterns of regional dysfunction. This includes both delayed onset of shortening/intitial stretch, systolic hypo-/a-/dyskinesia, and post systolic shortening, which all are part of the same mechanism. This also shows that which has be shown in studies, mitral annulus motion will not give information about regional function. Post systolic shortening is thus not an isolated event, but part of the total pattern in ischemia, but on the other hand is not limited to ischemia, being seen both in left bundle banch block and hypertrophy.

Basic concepts in  strain and strain rate.


Motion and deformation:



Motion. Floating iceberg in hurricane, Antarctic sound.
Deformation. Calving glacier in Marguerite Bay, Antarctic peninsula.


When considering the different modalities of echocardiography, the distinction between motion and deformation imaging is important. Displacement and velocity are motion. A stiff object may move, but not deform. A moving object does not undergo deformation so long as every part of the object moves with the same velocity. An object that deforms may not move in total relative in space, but different parts has to move in relation to each other for the object to deform. The object may then be said to have pure translational velocity, but the shape remains unchanged. Over time, the object will change position – this is displacement. Velocity is a measure of displacement per time unit.

,Strain and strain rate are deformation measures. If different parts of the object have different velocities, the object has to change shape. This is illustrated below.


Motion imaging.  Parametric (colour) image. A train staring, running and stopping.  The engine starts first, the connection between carriages has to stretch, before the next carriage is brought into motion. When all carriages are in motion, the train runs evenly. In stopping, the engine stops fist, then the connection between carriages has to be compressed before the next carriage stops, until all carriages are motionless. In this parametric image all carriages that are in motion are coloured red. However, both at standstill (the whole train is white) and running evenly (whole train red), there is no deformation, only motion. The engine keeps the connectors between the coaches stretched to a fixed length by pulling at constant speed, so the engine and coaches remain in the same position relative to each other.  The deformation occurs when any two carriages are moving with different velocities. This is shown below.



Deformation imaging.  Parametric (colour) image. This is the same figure as above, but in his image, the two carriages between which deformation occurs are shown in either cyan (stretching) or orange (compression), while the other carriages where no deformation occurs are shown in green. When the train is immovable, there is no deformation, the whole train is green. AS the engine starts, there is stretching between that and the first carriage (cyan). Once the first engine is at the same velocity as the engine, no further stretching (deformation) of that connection occurs, while the stretching has moved backwards in the train to the next connection. The stretching can be seen as a wave of deformation (cyan) moving backwards in the train. (Another example of this is given below). Once all carriages move with the same velocity, no further deformation occurs, and the whole train has even motion, and is coloured green again. When all parts of the object have the same motion, there is no deformation.  In stopping the opposite occurs, there is compression between engine and first carriage, then between first and second carriage, and so forth.  Again the compression can be seen as an orange wave moving backwards through the train.  When the train is at standstill, no further deformation occurs. When different parts of the object have different motion, there is overall deformation of the object.  Deformation is thus differential motion.

Comparing the two images above, one thing is evident. As the carriages have acquired a motion, even if this is the same as the neighboring carriage, they are all visualized in the same colour. In this case, the passive moving carriages is tethered to the carriage in front. The deformation image below is able to separate those carriages that move with different velocities, where there is stretching or compression of the connection between them, and those that are passively moving along. Thus there is an additional spatial resolution in deformation imaging compared to that of motion.

The images below shows how the impression from motion may be erroneous, while deformation gives the correct answer:



Short axis view. The inferior wall shows systolic outward motion, thus apparent pathological motion; dyskinesia.
Reconstructed M-mode through the inferior wall from the same loop. The inferior wall shows systolic thickening, thus normal deformation, normokinesia.

This example is more discussed in detail here.


The passive motion due to active contraction of other parts is called tethering, the passive parts being tethered to the active. In the heart this is where akinetic segments are pulled along by other active segments.


Strain and strain rate.

Strain, in daily language means, “stretching”. Basically, the strain is the deformation itself, not the force that cause stretching, this is "stress". The relation between the stress and the strain is the compliance.



Strain. Thingvellir, Iceland is situated on the rift between the Eurasian and American continental plates, which are sliding apart. Thus the area is expanding (positive strain), which can be seen by the ground cracking up.

In scientific usage, the definition is extended to mean “deformation”. The concept of strain is complex, but linear strain can be defined by the Lagrangian formula:
  which describes deformation relative to baseline length.

Where  is strain, L0 = baseline length and L is the instantaneous length at the time of measurement as shown below. Thus strain is deformation of an object, relative to its original length. By this definition, strain is a dimensionless ratio, and is often expressed in percent. From the formula, it is evident that positive strain is lengthening or stretching, in accordance with the everyday usage of the term, negative strain is shortening or compression, in relation to the original length. By using this definition, however, when an object is stretched from Lo, strain will remain positive during compression as long as the object remains longer than Lo, and vice versa after compression, strain will be positive during stretching so long as the object remains shorter than Lo.  (This is treated in more detail here).

The strain rate is the rate by which the deformation occurs, i.e. deformation or strain per time unit. This is equivalent to the change in strain per time unit.
The unit of strain rate is /s, or s-1. The strain rate is negative during shortening, positive during elongation. Thus, two objects can have the same amount of strain, but different strain rates as shown below:


Strain
An object undergoing strain. In this case there is a 25% elongation from the original length (L0). The Lagrangian strain is then:
Thus, according to the Lagrangian formula there is positive strain of 25% or 0.25.
Strain rate. Both objects show 25% positive strain, and both corresponds to the object to the left, but with different strain rates, the upper has twice the strain rate of the lower.  If the period is one second in the upper object, the strain rate is 25% or 0,25 per second, giving a strain rate of 0.25 s-1. The lower object has twice that period, i.e. half the strain rate, which then is 0.25 / 2 seconds = 0.125 s-1 . In these cases, the strain rate is constant.


The main point is that there may be motion without deformation, and deformation without much motion, the deformation is due to the differential motion within an object:

This means that there can be motion without deformation, but no deformation without motion - differential motion:

Strain rate. In these four cases there are different instances of deformation and motion. Object A does not move, none of the end points has motion (V1 = V2 = 0), and thus, there is no motion and no deformation (SR = 0). Object B has motion, but the two points 1 and 2 move with the same velocity. Thus there is motion, but no differential motion, and thus no deformation. (SR = 0). No elongation of the object can be seen. In object C point 1 has no velocity (V1 = 0), but point 2 has velocity, thus the two velocities are different, the object has differential velocities and motion, and thus there is deformation (SR does not equal 0), elongation is very visually evident. There is little motion, although one might argue that the midpoint does move a little. Object D shows velocities at both end points, thus there is definitely motion, and in addition V1 and V2 are different. Thus there are differential velocities and differential motion, and there is deformation, visually, elongation in addition to the motion is evident.
Looking at displacement instead of velocity, the change in length of the objects is the difference in displacement of the two end points:

L = L0 + (D2 - D1), L = D2 - D1,  and  = (D2 - D1)/L0


Thus, the strain rate is equal to the differential velocities of the object, strain is equalt to the differential displacement, in the examples above the difference between points 1 and 2.

All of the derivations can of course be reversed by integration, so velocity, displacement, strain rate and strain are all inter related:




Relation between strain rate, strain, velocity and displacement. From one dataset (e.g. a velocity field), all three other parameter sets can be derived.




Velocity gradient

As we have seen the strain is the differential displacement of the object, while strain rate is the differential velocities of the object.

In the heart, the apex is stationary, while the base of the ventricles move towards the apex (ventricular shortening) in systole. If the velocities are distributed evenly, it means that there will be a velocity gradient along the wall. The spatial derivation of velocities can be approximated:


i.e. change in velocity over a finite distance. If (and only if) velocities are evenly distributed, i.e. the velocity gradient is constant along the wall, this resolves into:

i.e. velocity difference per length unit.

Then, the longitudinal velocity gradient, velocity per length unit is a measure of longitudinal strain rate, but this is only valid if velocities are evenly distributed, i.e. if the velocity gradient is constant. If not, this is an approximation, which becomes more precise the shorter the L. However, Longer L improves signal to noise ratio as described here, especially if strain rate is derived by linear regression of velocities along the whole of the L. However, the longitudinal velocity gradient seems to be fairly constant:






Systolic velocity plot through space, from the septal base to the left through the apex in the middle to the lateral base to the lateral base to the right. The velocities seem to be distributed along  fairly straight lines, i.e. there seems to be a fairly constant velocity gradient (in space, but not in time).
Longitudinal velocity gradient, where v1 and v2 are two different velocities measured at points 1 and 2, and L the length of the segment between those points.

(In fact: this might be so in the longitudinal direction. However, transmurally, there is a gradient of strain, and thus strain rate across the wall, as shown below. This means firstly, that the transmural velocity gradient is not constant, and secondly that the transmural endo- to epicardial velocity gradient only gives the average strain rate across the wall).

Still, longitudinally the velocity gradient is:



Then strain rate equals the velocity gradient:


However, this is only partially true.

Lagrangian and Eulerian strain


There are two different ways of describing strain and strain rate: Lagrangian and Eulerian (named after the two mathematicians Joseph-Louis Lagrange and Leonhard Euler, respectively.

Lagrangian strain is the strain defined above;   the change in length divided by the original length, while Eulerian strain is the strain divided by the instantaneous length; .

Some prefer to use the term "Natural strain" instead of "Eulerian", however, I fail to see how one reference system is more "natural" than another. Using both mathematicians' names, the nomenclature will at least be more symmetrical.



Lagrangian strain (top) and Eulerian strain (below). Visually, it is evident that both objects undergo the same strain at the same strain rate. Thus, the physical reality is the same, but the two figures show the two different ways of describing the deformation, as the Lagrangian strain shows an increasing deformation relative to the constant baseline length, while Eulerian strain describe the deformation (in this case constant, as the strain rate is constant, but this is not a condition), relative to the continually changing length.
Lagrangian strain (top) and Eulerian strain (bottom). Only four point in time is shown, to illustrate how this means that by Lagrangian strain at any time is the sum of all length increments up to that time, divided by the baseline length, while Eulerian strain at any time is calculated as the sum of all ratios of length increments and the instantaneous length up to the actual time.

Then, as described above left, Lagrangian strain is the cumulated deformation, divided by the initial length, Eulerian strain is the cumulated ratios between the instantaneous deformation and the instantaneous length:
Lagrangian strain is:                                   while Eulerian strain is:                

This is described in details in the mathematics section, but the point is that the two formulas will result in slightly different values. The positive Lagrangian strain of 25% in the example above, will be equivalent to 22% Eulerian strain (and not 20%, as one might believe).

The customary use is Lagrangian strain, but eulerian strain rate. This has historical reasons; Lagrangian strain was first used by Mirsky and Parmley in describing myocardial strain (12). Strain rate was first measured by tissue Doppler velocity gradient (4, 14) which is equal to the Eulerian strain rate (as can be seen by the formula, the denominator is L, not L0). This is explained in more detail here. Then, integrating strain rate to strain, gives Eulerian strain, the value has to be converted in order to derive Lagrangian strain. 

With speckle tracking, the relation to the two reference systems is more complicated, and might vary.





If speckle tracking is used to track the relative positions of two kernels, the strain will be derived form the relative displacement, divided by the distance between the kernels. If the denominator is the initial (end diastolic) distance, this gives the Lagrangian stran, if it is the instantaneous distance, it will be the Eulerian strain.
Segmental strain by speckle tracking, applying the principle shown to the left. In this application, it uses the instantaneous distance, so in order to acquire the Lagrangian strain, the conversion below has to be used.

Other applications, using the whole 2D field, may use the tracking to acquire a velocity field by dividing by the FR-1, thus starting with the velocity field as in tissue Doppler, which means deriving strain rate, and then integrating to strain. Again, however, it will be possible to divide by the initial (end diastolic) length, which gives Lagrangian strain rate and strain, or by the instantaneous length (as material points are tracked), giving Eulerian strain and strain rate.



The point is that the two formulas will result in slightly different values:



Lagrangian versus Eulerian strain. Lagrangian strain will give slightly higher values, i.e. negative values are lower in absolute values, while positive values are higher.
Lagrangian and Eulerian strain curves. As myocardial strain in general is negative, the Eulerian strain curve lies below the Lagrangian.


In general, peak strain may be up to 4% higher (absolute values but a relative difference of up to about 20%) by Eulerian strain than by Lagrangian strain, but the two references can be easily converted:
          and           

Lagrangian and Eulerian strain rate

The relation between Eulerian and Lagrangian strain rate is:
       and       

.

Lagrange vs Eulerian strain rate. As Eulerian peak systolic strain is lower (more negative) than Lagrangian, the peak Eulerian systolic strain rate has to be lower (more negative) too, in order to reach lower strain values. In diastole, however, the peak strain rate has to be higher (positive), in order to return from deeper negative values.

In this case, the difference in peak systolic and diastolic strain rates are smaller, about 12% relative.

Conversion is simple and can be applied by the scanner and analysis software instantly.

This means that any scanner or analysis software need to report which reference is used (287).


How to display (and understand) cardiac motion and deformation?


Most of what follow is about longitudinal motion and deformation. This is because the longitudinal shortening of the ventricle describes the whole of the ejection work (but not the pressure vork) as discussed below. The most important measures are thus measures of longitudinal motion and deformation. Looking at a beating heart:

AS we seen the systole results in a longitudinal shortening. This means that the basal parts of the heart has motion towards the apex, while the apex is stationary (almost). Thus, the whole ventricle shortens - deforms.
Lookng at an M-mode of the ventriculoar base (the mitral annulus), the systolic motion of the base can be displayed as a motion curve, and the peak systolic displacement of the base (the MAPSE - Mitral Annulus Plane Systolic Excursion) can be measured.

The term Mitral Annular Plane Systolic Excursion (MAPSE) (31, 35, 37, 40) should be used. Atrioventricular plane descent (AVPD) (30, 32, 34, 36) is incorrect, as the term also comprises the tricuspid part, and while tricuspid displacement and velocity can be measured (and is higher than in the left ventricle) , it is usually measured only in one point, and the relative weights for the whole of the AV-plane is unclear.

It is also evident, that as the apex is stationary, there is no displacement, and the whole of the ventricle is deformed, as there is differential motion:


Thus, the MAPSE divided by the end diastolic length L0 (which, in fact is a spatial derivation),  is the Lagrangian strain of the ventricle, and divided by the instantaneous length, is the Eulerian strain.
The deformation ois evident when looking at the M-mode in the septum, the tissue (speckle) lines  moves more, the more basal they are, and thus the convergent lines shows the differential motion (deformation).


It's important to realise that both motion and deformation parameters can be derived in a variety of ways. M-mode and pulsed tissue Doppler records the motion (displacement and velocity, respectively) at one point at a time. Tissue Doppler gives the motion velocity of the tissue.

Pulsed tissue Doppler of the mitral ring.  These are the velocity traces of the longitudinal motion.  As motion decreases from apex to base, velocities have to as well. Thus there are differential longitudinal velocities, decreasing from maximal at the base to zero (almost) at the apex. The differential velocity also described as thevelocity gradient, is equivalent to the rate of deformation; the strain rate.




Colour tissue Doppler and speckle tracking can derive the velocity field across the whole image (more or less - dependent on the sweep speed) simultaneously. Thus, the point values for displacement and velocity, strain and strain rate can be extracted in the form of numerical traces, or displayed semi quantitatively in a parametric image analogous to the colour flow of blood velocities. The basic principles, basic physiology and relation to load, the shapes of curves apply irrespectively of which methods are used, as this relates to coronary physiology, and not tho the methods. However, as the methods  have differences, the values obtained (and the normal values), as well as the applicability, sensitivity to dysfunction and relation to the various ultrasound artifacts may differ, as will be discussed below and in other sections. 

Numerical traces



Displacement

Strain

Displacement (motion) curve (derived by integrating the velocity curve from colour Doppler). The curve shows the motion upwards (towards the apex) during systole, and downwards (away from the apex)during early and late filling phases in diastole, and the similarity to an M-mode curve is evident.
Strain (deformation curve. The curve describes the shortening of the myocardium in systole, meaning that as the length becomes less, the strain is negative. This follows from the definition above.Then, there is lengthening again in diastole, mainly during early and late filling phases.  However, the curve remains negative, as all lengths are shorter than the end diastolic, which is maximum length. Looking at the M-mode curves above, the curve describes the difference between two M-mode or displacement lines, which is a spatial derivation. However, the curve is actually obtained by temporal integration of the strain rate curve below, and then converting from Eulerian to Lagrangian strain.



Colour Doppler derives the velocity data from the Doppler effect, and generates a velocity field over the whole image. Thus, the velocities are the primary data, from which displacement, strain and strain rate are derived as described above and ilustrated in more detail below.


Tissue velocity

Strain rate
Normal tissue velocity curve. The curve is the derivative of the displacement curve above, or oposite the displacement curve is the integral curve of this velocity curve. The similarity of this cirve to the pulsed Doppler curve shown above is evident. There is systolic velocity towards the apex (upwards) during systole (S), and downwards (away from the apex) during the early (E) and late (atrial A) filling phases.
Normal strain rate curve processed from the same acquisition by spatial derivation of velocity gradient. Again, the strain rate is negative during systole, as there is shortening, and then positive strain rate during early and late filling phases, as there is lengthening. 

Thus, the velocity and displacement curves decrease in amplitude from base to apex, while the strain rate and strain curves in general do not (constant velocity gradient).




Relations between systolic motion and deformation measurements




Thus, there is a relation between motion and deformation parameters as shown in the figure in the introduction. Below is an illustration of the same, this time with the relation between the curves:



The spatial derivation process can be seen applied to velocity curves (top) and displacement curves (bottom), in the horisontal direction from left to right. In both cases the derivation is between two points, and the spatial derivative is the instantaneous difference in velocity or displacement between the two points, divided by the instantaneous distance between them. Thus, the strain rate derived from the two velocity curves is the deformatin rate of the area between them, demarcated by the red ROI top left. (The offset between the two curves is marked in red, but in this case do not mean that the derivative is the area between the curves, each value is the instantaneous distance. ) This is equal to the velocity gradient or displacement gradient, and results in strain rate and strain, respectively. The curves are shown to the left.

The temporal integration is shown in the vertical direction, applied to velocity (left) and strain rate (right). The integration is applied to one curve at a time, but both curves are shown to the left. The integrstion amounts to the sum of (all velocity or strain rate values times the sampling interval). This process results in the area under the curve. The value can be expresses as a new curve. The value of this curve increases when the original velocity or strain rate curve is positive, decreases when they are negative.



But this, of course means that strain rate and strain can be visually assessed by the offset between the curves.

Strain rate assessed by offset between velocity curves


Segmental strain rate from velocities: Left: velocity curves from four different points of the septum. The image shows the decreasing velocities from base to apex. Middle, the areas between each curve has been shaded, showing the strain rate of each space between the measurement points (segments). Left: Strain rate curves, from the same segments; colours matching.



Segmental strain from displacement. Left: displacement curves from four different points of the septum. The image shows decreasing displacement from base to apex. Middle, the areas between each curve has been shaded, showing the strain of each space between the measurement points (segments). Left: Strain curves, from the same segments; colours matching.

Thus, it is evident that the strain rate and strain can be visualised (qualitatively) by the spacing of the velocity and displacement curves, even without doing the derivation.






A patient with an apical infarct, especially evident in the inferolateral wall.
By colour M-mode initial akinesia apically, hypokinesia in the middle segment and basal normal shortening.


Reduced strain rate in an infarct visualised by tissue velocity. The systolic velocities can be seen to decrease normally in the basal segment (white to lilac curve, red interval), while the middle segment (lilac to orange curve, cyan interval), and almost no difference in the apical segment (orange to green curve, yellow interval). The intervals correspond to the strain rate, showing normal shortening in the basal segment, hypokinesia in the middle segment and akinesia in the apical segment In fact, inital systole, shows reversal of velocity curves, thus signifying positive strain rate (initial dyskinesia).
Strain rate curves from the segments between the measurement points in the left image. Thus, the amplitude of the strain rate curves correspond to the width of the intervals between the measurement curves, and for clarity, the curves have the same colours as the intervals to the left.

Here is apical: initial dyskinesia, reduced peak strain rate, but also post systolic shortening, midwall hypokinesia and basal normal strain rate.

Thus, no offset between velocity curves means zero strain rate (no deformation). Another example can be seen below.


Normnal vs. alrge apical infarct, see the lack of distance between the two apical velocity curves.

This is important as the velocity/displacement curves have more favourable signal/noise ratio than the derived curves, as can be seen by these examples from early days of strain rate imaging, with little smoothing:





Velocity and displacement curves with some noise in the velocity curves, the integration in obtaining displacement curves tend to eliminate random noise.
Top: strain rate curves obtained by spatial derivation of the velocity curves to the rigth. Bottom, strain curves by integration of the strain rate curves above. Again, integration tends to smooth the random noise. However, that makes it especially vulnerable to non random noise (clutter).

The problems with random noise and clutter in tissue Doppler and in speckle tracking are discussed further in the measurements section.



The displacement, velocity, strain and strain rate curves can be displayed separately for each point in the image (or at least those points corresponding to points in the myocardium). Thus gives fully quantitative data, and the curves give the data for the whole heart cycle, but is limited to one or a few points at a time. Too many curves in the same image are unfeasible.



This reflects the difference between motion and deformation on a fundamental level, that deformation in the heart is motion normalized for heart size. This is important both in evaluating regional differences as well as global function, and is one of the main advantages in using deformation imaging.



For systolic measurements, the peak values are the most commonly used measures. This means peak systolic velocity and peak systolic strain rate, which are relatively early systolic measures, and peak systolic displacement and strain, which are close to end systole. (And in fact, end systolic strain and displacement are reasonable substitutes). MAE is the peak systolic displacement.


The fundamental difference between motion and deformation is that while deformation is local, the motion of any part of the myocardium is influenced by overall motion (translational effects) and tethering. It can also be said that the deformation measures subtracts motion due to translation and tehtering, by the simple subtraction algorithm. .

Translational effects:

Overall motion of the heart will reflect in each and every segment the translational motion added to the local measurement.


In this video the rocking motion of the left ventricle is evident, the whole heart rocks toward the left in systole. (However, this is NOT due to conduction delay). However, looking at deformation (wall thickening - transmural strain) in this cross sectional recording, the wall thickening can be seen to be normal and symmetric in both onset and extent.

In fact, wall thickening in the cross section seems to supplement the impression from the four chamber view, that the rocking motion is not regional dyssynergy. Wall thickening is transmural strain.




Apparent asynchrony: Looking at mitral valve velocities, the lateral wall (cyan) seems to have a delayed contraction compared to the septum (yellow), both looking at onset and peak velocities, indicating either asynchronous activation or initial akinesia of the septum Looking at multiple sites in the lateral wall, it seems that the delay in early ejection phase corresponds to positive velocity in the base (yellow), zero velocity a little more apical (cyan), and increasingly negative velocities toward the apex, i.e. possible apical initial dyskinesia (which might be ischemia). The curved M-mode from the base of the septum through the apex to the base of the lateral wall shows the same effect, normal timing of the velocities in the septum, inverted velocities in the apical two thirds of the lateral wall.







Comparing tissue velocity with strain rate in the base and apex, however, , we see that the apparent delayed motion in the lateral wall has no corresponding delay in deformation, wheteher looking at onset of, or peak negative strain rate.  All four parts shortens synchronously and normally. Thus, it illustrates that the rocking motion velocities are added to the velocities, the subtraction algorithm of the velocity gradient subtracts these velocities again, showing the true timing of regional deformation.


In this case, the motion (velocity imaging) is mis informing, giving the appearance of dys synchronous function of the left ventricle, while deformation shows this to be untrue. Thus, asynchrony is in some cases better characterised by deformation. In this case the patient's diagnosis was not clear. The cause might be reduced contraction of the right ventricle, despite the normal TAPSE. Part of the TAPSE might be due to the rocking as well, as shown below. However, there was no adequate registrations with tissue Doppler from the right ventricle, and the speckle tracking method would incorporate the full TAPSE in the smoothing.


The TAPSE is the displacement of the lateral part of the tricuspid annulus, and is often used as a marker of right ventricular function. There is an apparent normal TAPSE of 3 cm, but this is solely due to tethering,  the rocking motion of the heart adds motion to the lateral tricuspid annulus, so the TAPSE is misleading. Deformation measures were not available, but here it is visually evident that the right ventricle is dilated and stiff, poorly functioning.

Tethering

The point of tethering it that a passive segment is tethered to an active segment, and thus is being pulled along by the active segment, without intrinsic activity in the passive segment. This means that a passive segment may show motion, but without intrinsic deformation, and the deformation imaging will discern. This is evident both in systole and diastole. tethering effects may show diverse results. It has three important consequences:
  1. Infarcted segments may be totally akinetic, but still being pulled along by active segments, showing motion without deformation. In this case, no offset between displacement curves, means no strain. This is usually evident in the inferior wall. A perfect example of a totally passive, tethered segment moving close to normally, can be seen below, and in more detail here. It may also be pertinent to the basal part of the right ventricle. In both cases, the annular motion may be near to normal due to hyperkinesia in the neighboring segment, as this segment is offloaded as explained here.  

    Tethering: The basal and midwall segments are infarcted, and are being pulled along by the active apical segment. The whole inferior wall seems stiff.



     


    The stiffness is evident in velocity and displacement curves. All of the wall has motion, which must be due to the apical segment, but as all curves lie on top of each other, the whole wall moves as a stiff object, i.e. there is no deformation below the apical point, and thus akinesia.
    Strain rate and strain curves, however, show that the findings are more differentiated, showing akinesia basally (yellow), hypokinesia in the middle (cyan) and hyperkinesia in the apex (red).

  1. Thus; in this case, the passive segment is tethered, showing motion and masking the pathology to some degree. Deformation imaging will show this.
  2. If there is pathological contraction at some time in the heart cycle (e.g. post systolic shortening), the shortening of a pathological segment may impart motion to a whole wall.


    Velocity images showing motion towards the apex in red,  away from apex in blue.  Left, systolic 3D reconstructed image, showing normal motion in the septum and inferior wall, and paradoxical motion in the inferolateral, lateral and anterior wall. Right, o top are bull's eye from systole, showing the same, as well as early diastole showing inverse motion during the e-phase, i. e motion of the whole wall towards the apex in diastole. Apparently, the whole anterolateral half of the ventricle is ischemic .
    Strain rate images from the same recording, left systole, right early diastole, showing that the ischemia is due to a smaller ischemic area in the inferolateral, lateral and anterior apex, where there is stretching during systole (blue).  This stretching, results in the midwall and basal segments moving away from the apex, despite contracting normally. In early diastole there is recoil in the ischemic area (yellow), resulting in anterior diastolic motion in the whole of the wall.  In this case, the ischemia is obviously limited to a part of the apex, the rest of the motion abnormalities being due to tethering.
In this case, the normal segments in the midwall and base of the affected wall has abnormal motion due to being tethered to the pathological segments in the apex. Another, similar example of this in ischemia, can be seen below. Thus, it may mistakenly be taken ass asynchrony between walls. Deformation imaging shows the true location and extent of the pathology. 

In phases where parts of the myocardium is active, other passive, due to differences in timing, the tethering of passive to active segments may make the whole myocardium move throughout the whole phase, even if each segment is active only part of the time. This is evident in diastole, where elongation occurs at different times in the different levels of the myocardium.



  1. (Motion (velocity), The diastolic phases of early and late relaxation are seen as being simultaneous from base to apex. Protodiastolic downward motion can be seen befor AVC (aortic valve closure) in the tow basal segments.
    Deformation (strain rate) shows both early and late relaxation to be biphasic, and in addition the peaks are not simultaneous in the different levels of the myocardium. Protodioastolic elongation can be seen to be present in the midwall segment only, the protodiastolic motion of the basal segment being a tethering effect.
    This is explained in more details here.
The tethering effects is the cause why motion imaging mainly shows global function, and deformation imaging shows regional function. This has also been shown in a clinical study (40).


Apex to base differences


As the apex is stationary, while the base moves, the displacement and velocity has to increase from the apex to base as shown below.

As the apex is stationary, while the base moves toward the apex in systole, away from the apex in diastole, the ventricle has to show differential motion, between zero at the apex and  maximum at the base. Longitudinal strain will be negative (shortening) during systole and positive (lengthening) during diastole (if calculated from end systole). M-mode lines from an M-mode along the septum of a normal individual. These lines show regional motion. It is evident that there is most motion in the base, least in the apex. Thus, the lines converge in systole, diverge in diastole, showing differential motion, a motion gradient that is equal to the deformation (strain).  This difference in displacement from base to apex is also evident in the displacement image shown above.


Velocity gradient



AS motion decreases from apex to base, velocities has to as well. Thus, there is a velocity gradient from apex to base, which equals deformation rate. Spatial distribution of systolic velocities as extracted by autocorrelation. This kind of plot is caled a V-plot (247).  It may be usefiul to show some of the aspects of strain rate imaging. The plot shows the walls with septal base to the left, apex in the middle and lateral wall base to the right. As it can be seen again the velocities are decreasing from base to apex in both walls. There is some noise resulting in variation from point to point, but the over all effect is a more or less linear decrease. The slope of the decrease equels the velocity gradient. (Image courtesy of E Sagberg). However, this shows only one point in time, and all values are simultaneous. 
Thus there is a velocity gradient in systolic velocities, from base to apex. This is equal to strain rate as it is shown here. In fact, the strain rate is displayed by the slope of the V-plot. However, the V-plot itself, has been shown to be vulnerable to especially drop outs, and by colour Doppler the the drop out and infarct looks similar. Clutter is less of a problem, as there will be variations in the velocities as each pixel will have variations between the weight of true velocities and clutter (284).  Thus, the V-plot may be useful to show the effect of stationary reverberations on velocities (247).

However, the V-plot is the instantaneous velocity gradient, which may differ from the peak strain rate, if peaks are at different times in different parts of the ventricle.


The systolic motion of each myocardial segment from the apex to the base is the result of the segment's own deformation, added to the motion that is due to the shortening of all segments apical to it. Thus, as the apical segments shortens, this segment will pull on the midwall and basal segments ( this is passive motion - tethering), the midwall segment also shortens, and pulls even more on the basal segment, which is shortening as well.  As the apical parts of the ventricle pulls on the basal, the displacement and velocity increases from apex to base (25). This means that some of the motion in the base is an effect of the apical contraction - tethering. In fact, completely passive segments can show motion due to tethering, but without deformation. (4, 6, 7), as also demonstrated above. This means that the velocity (and displacement) are position dependent, if not normalised while strain rate (and strain) are much more position independent, if the velocity gradient is evenly distributed.

This is illustrated below.

Velocity, displacement, strain rate and strain from three different points, apex, midwall and base, in the septum of a normal person. These curves all represent the same data set. It is evident that motion (velocity and deformation) increases from apex to base, showing a gradient, while deformation (strain rate and strain) is more constant, in fact a direct measure of the motion gradient.  Diastolic deformation is far more complex, and is discussed below.


Motion (velocity and displacement - left) and deformation (strain rate and strain - right) traces from the base, midwall and apex of the septum in the same heart cycle. It is evident that there is highest motion in the base (yellow traces), and least near the apex (red trace), and this is seen both in velocity (top - actually both in systolic and diastolic velocity) and displacement (bottom). The distance between the curves are a direct visualization of strain rate and strain, but the curves are shown to the left, showing no difference in systolic strain rate or strain between the three levels.



Is there an apex to base gradient in strain / strain rate as well?

If systolic displacement and velocity decreases evenly from base to apex, the systolic deformation (strain) and velocity gradient (strain rate) is evenly distributed throughout the myocardium. Some of the earliest studies seem to indicate this (10, 19, 341), although later studies seem to find differences with lowest values in the apex (124). However, the angle error is also greatest in the apex (206). In the comparative study between methods in HUNT (153) there was lower values in the apex, but only using the longitudinal velocity gradient, and only when the ROI did not track the myocardial motion through the heart cycle. Thus, it seems fairly reasonable to conclude that this finding is artificial.

With 2D strain, some authors have found a reverse gradient of systolic strain as well, highest in the apex, lower in the base (207). However, in that application, measurements are curvature dependent, the apparent curvature being highest in the apex and lowest in the base, and the discrepancy between ROI width and myocardial thickness being greatest. In addition, the strain values The HUNT study (153) found no such gradient with the combined speckle tracking -TDI method, nor in the subset of 50 analysed for comparison of the methods.


Basal
Mid ventricular
Apical
Strain rate (s-1)
-0.99 (0.27)
-1.05 (0.26)
-1.04 (0.26)
Strain (%)
-16.2 (4.3)
-17.3 (3.6)
-16.4 (4.3)
Results from the HUNT study (153) with normal values based on 1266 healthy individuals. Values are mean values (SD in parentheses).  Differences between walls are small, and may be due to tracking or angular problems.  No systematic gradient from apex to base was found.


In addition, in the  comparative study
, there was no gradient using the 2D strain application, in this case care was taken to align ROI shapes as much as possible.

MR studies have also found various results. Although some MR studies have found a gradient, Bogaert and Rademakers (171) found lowest longitudinal strain in the midwall segments, higher in both base and apex, but no systematic gradient from base to apex. MR tagging may have some processing issues also, which may account for some of the findings when curvature and angle varies long the wall from base to apex. Thus, the presence of a base to apex gradient in deformation parameters has so far not been established.


Looking at the V-plot, the curve seems fairly straight, i.e. the velocity gradient seems fairly constant along the wall:




Good quality V-plot shows velocities as near straight lines, and thus, a constant velocity gradient. This seems to exclude that there is a strain rate gradient from base to apex.
A nearly straight line. Blue eyed shags (cormorants) at Cabo de Hornos (Cape Horn), Chile.
 

Why are the systolic shape of velocity and strain rate curves different?

From the examples above, it seems that velocity curves have different shapes with earlier maximum than strain rate curves. Both should in principle represent the peak rate of volume reduction and thus ejection rate, but this cannot be entirely true.


Left: Real velocity curves from two points at a distance of 1.2 cm, right strain rate calculated from the velocity traces as the velocity gradient SR= (v(x) - v(x+x))/x. It is evident that both velocity curves have a much steeper initial slope, an earlier maximum and a steeper decline. Thus, peak myocardial velocity is not simultaneous with peak strain rate (rate of shortening).


Looking at velocity curves at different levels, it is obvious that the myocardium has parallel velocities around the peak:
Strain rate is the difference between the curves. Here the difference between the two velocity curves is calculated in excel (red) without the length correction, (which then is equal to SR*1.2). As can be seen, the early steep slopes of both curves (orange) will result in a much less steep slope in the difference curve. From the peaks of the velocity curves the two curves seem almost parallel, despite both dipping sharply, this results in a near horisontal strain rate curve, and finally the slow convergence of the curves give a much slower reduction of the difference.


The differences in the shape are thus not due to differences in Lagrangian and Eulerian strain, as I have mistakenly maintained before, it is simply because the strain rate curve is the value of differences.
But then, the velocity components that are subtracted are translation velocities, without deformation as explained above. Thus, there is a velocity peak during early ejection that is only translation.

This basically means that there is an initial translational velocity of the whole heart towards the apex. The mechanism for this is most probably the recoil from ejection, creating (most of) the motion towards the chest wall, the apex beat (ictus cordis).

This also has implication for the relation to global ejection parametrers, which will be examined under global function



Differences between walls

Although Höglund did not find any difference in systolic mitral annular displacement between different walls (30), other authors have found such differences, with lateral displacement higher than the septal (167). In the large HUNT study, the same differences were found in systolic annular velocities (165), with differences between septum and lateral wall was of the order of 10%, but not in deformation parameters (153), where the same difference was on the order of 4% in strain rate and only 1% (relative) in strain.


Anteroseptal
Anterior
(Antero-)lateral
Inferolateral
Inferior
(Infero-)septal
PwTDI S' (cm/s)

8.3 (1.9) 8.8 (1.8)

8.6 (1.4)
8.0 (1.2)
cTDI S' (cm/s)

6.5 (1.4)
7.0 (1.8)

6.9 (1.4)
6.3 (1.2)
SR (s-1)
-0.99 (0.27) -1.02 (0.28)
-1.05 (0.28)
-1.07 (0.27)
-1.03 (0.26)
-1.01 (0.25)
Strain (%)
-16.0 (4.1) -16.8 (4.3)
-16.6 (4.1)
-16.5 (4.1)
-17.0 (4.0)
-16.8 (4.0)
Results from the HUNT study (153, 165) with normal values based on 1266 healthy individuals. Values are mean values (SD in parentheses).  Velocities are taken from the four points on the mitral annulus in four chamber and two chamber views, while deformation parameters are measured in 16 segments, and averaged per wall.  The differences between walls are seen to be smaller in deformation parameters than in motion parameters, although still significant due to the large numbers.

This is illustrated below.





Top: Pulsed wave recordings from the mitral ring, peak systolic velocity can be seen to be highest in the lateral wall.  Below; the same can be seen in the M-mode recordings of the left ventricle, lateral systolic annular displacement is seen to be higher than in the septum.
Top: Colour tissue Doppler recordings from the same subject. Mark how colour Doppler recordings are analogous to, but slightly different from the pulsed wave recordings to the left.  This is discussed more in detail in the ultrasound section. The difference is also evident from the normal values of the HUNT study. Below: Motion of the mitral ring, can be shown by integration of the velocity, and both peak systolic velocity (top) and displacement (bottom) can be seen to be higher in the lateral wall than in the septum.  The effect seen in motion measurements may vary, due to the difference of insonation angle.
Deformation of the walls, both peak systolic strain rate (top) and strain (bottom) can be seen to be equal in the two walls (the small peak in the strain of the septum is post systolic, and in addition only amounts to 1% absolute or 5% relative).  Thus the higher motion of the lateral wall is not reflected to the same degree in deformation. The shape of the heart. As can be seen in the top image, and is illustrated in the bottom, the curved lateral wall is longer than the septum.  Thus,  strain rate (velocity difference per length) and Strain (shortening per length) is more similar between the walls than just the total shortening or velocity of the wall.

What is the difference between using strain and strain rate curves?

1. Strain rate has better temporal resolution than strain. Strain rate shows changes in the deformation status of a segment in each time point, while strain in any time point is the cumulated             strain rate up to that frame, compared to the start. Thus peak values of the rate of change in deformation can only be measured by strain. This means also that strain is only used as a systolic             measure, strain rate gives information also about diastole.



Normal subject. Strain rate (top) shows the changes in deformation, while strain (bottom) shows the deformation statur at any given point in time. Thus, quick changes will only show up in strain curves as changes in the direction of the curves. This is especially evident when looking at the diastole.
In this case with a large antero apical infarct, changes in segmental deformation from stretch to shortening during ejection is evident with strain rate (top), but not in the strain curves (bottom). Peak rate of change  in any phase can be measured by strain rate, not by strain.   Changes in strain (i.e. strain rate) can be puzzled out qualitatively, if one looks at the changes in direction of the curves (which in fact is strain rate). The main impression from strain, however, is the systolic stretch in the two apical segments.

2. Peak strain rate is less sensitive to load (although not load independent), and more closely related to contractility as an early measure of maximum (rate of) systolic shortening. Peak strain is the end systolic measure of the maximal shortening. This means that peak train is more sensitive to load through systole, i.e. especially afterload.





Parametric imaging

Parametric imaging is based on colour display as described in the ultrasound section on colour Doppler. This means that numerical data are colour coded, and displayed semi quantitatively, in order to visualize semi quantitative data simultaneously over the whole image. Thus, the image gives access to more generalized information, in exchange for less quantization. It is customary to image:
Strain is little suited for parametric imaging. Looking at the diagram above, it is evident that strain is negative throughout the heart cycle. In addition, there is little difference between the different heart cycles, thus, differences between regions is little evident. Finally, the strain is actually best visualized in the images of end diastolic displacement shown below.

However, it must be emphasized that the information contained in a colour couded image remains numerical, and can be extracted again from combined images like 3D or bull's eye, among other thing for purposes of area measurement.

2D parametric images.




Velocity imaging. Velocities toward the probe is coded red, away from the probe is blue.  Thus the ventricle is red in systole, when all parts of the heart muscle moves toward the probe (apex) and blue in diastole. Strain rate imaging, strain rate is coded yellow to orange for shortening, cyan for lengthening but green in periods of no deformation, and is thus yellow in systole, cyan in the two diastolic phases early and late filling and green in diastasis.



End systolic displacement, imaged in a different colour for each range of 2 mm displacement.  This is shown for comparison in the curves to the right, the colours of the curves corresponds to the colours of the points, i.e. the position of each point. As only the end systole is of interest, there is no need for looping the image. Displacement is highest in the base, smallest in the apex. The spaces between curves is shown to the roght, coloured correspondingly to the 2<D image. The width of each coloured band in 2D as well as the space between curves gives the deformation in the area.  As long as the bands are of relatively even width, the strain is evenly distributed. From this image, the base to apex gradient in displacement is very evident.

Curved anatomical M-mode.

Looping the parametric images in general will show the changes too quickly to be of any interest. In order too see differential colours, it is more useful to use the curved anatomical M-mode (CAMM), developed by Lars Åke Brodin and Bjørn Olstad showing the whole time sequence in one wall at a time. (18). By this method, a line is drawn in the wall, and tissue velocity data are sampled for the whole time interval (e.g. one heart cycle) and displayed in colour along a line in a time plot, as shown below.


Curved M-mode. The line is drawn in the wall, in this case from the base of the septum through the apex and back to the base of the lateral wall, and then straightened Meaning that only the distances along the line are incorporated into the final information. Along the y-axis is thus the distances along the line. The velocity data re then displayed through the whole time sequence (which is the x-axis), giving a two-dimensional time-space display of velocity.

This has the advantage of displaying the whole sequence in a still picture, giving a temporal resolution like the sampling frequency. Curved M-mode .



Curved M-mode showing velocities.  In this case, the curve is drawn from the apex to the base, showing one wall. The shifts between positive (red) and negative (blue) velocities are clearly demarcated.
Curved M-mode showing strain rate ( the curve is the same as in the image to the left, but the mode is shifted to display strain rate).  The pattern is different, due to the better spatial resolution when deformation is imaged, as shown above, and discussed in details below.



Curved strain rate M-mode drawn from base of septum through apex to base of lateral wall. This display is most often used to compare different walls, and is especially useful in assessing left bundle branch block. However, in the apex, there is both angle distortion as well as nearfield reverberations, which has to be excluded. The most useful method for identifying nearfeild reverberations from pathology, is to look at the distasis period. Fields with high colour intensity (meaning a lot of  deformation), has to be artefacts.


Strain rate CAMM has better spatial resolution than segmental curves.

The curved M-mode will, in fact, give a better spatial resolution than using Strain rate or strain curves. Using numerical traces from each segment, the effective spatial resolution in depth, will be one segment, or about 3 cm, despite the good axial spatial resolution inherent in the ultrasound beam.







In the strain rate CAMM; there is evidence of an early shortening before MVO, the MVO can be timed, the pre AVC stretch is visible, the apical lengthening during IVR, and the propagatopn of stretch waves are all visible in  the curved M-mode- Although the events can be seen in the curves as well, the space-time resolutions are much easier to discern in the CAMM.
The strain CAMM (it's the same line as in the SR CAMM to the left, only reprocessed into strain) doesn't give much information at all. Looking at the curves, it is evident that the whole course of the curves lies below zero, thus showing a red colour, although there is a colour cut off around -10. The blue lines is reverberations, but with low intensity, as they don't even disturb the SR CAMM.


Top, strain rate curves from septum of a patient with a large anteroapical infarct. The three segments are covered by one ROI each and the curves are thus the average for that segment. The CAMM and traces have the same temporal resolution, and thus are able to show all phases. There is initial stretch at start ejection (1), hypokinesia during ejection (2), and post systolic shortening after ejection (3). I addition there is reduced recoil after atrial systole (4) (as compared to the more healthy region), which may indicate some stiffening in the infarct area. the CAMM shows intioal stretch to be present even partway into the basal segment, hypokineasia to be preent in the apical half (i.e. the apical plus half the midwall segment, and post systolic shortening also in half the wall. Thus the extent of the different abnormal strain rates is better discriminated by the CAMM.
Strain curves and CAMM from the same wall / segments. This illustrates
1:first that the temporal resolution of strain rate disappears when converted to strain, as strain in each point is the cumula
ted deformation up to that timepoint. In this case  only stretch during the whole of ejection is seen in the apical and midwall segments.  The remaining hypokinesia is nor evident.
Changes in strain (i.e. strain rate) can be puzzled out qualitatively, if one looks at the changes in direction of the curves (which in fact is strain rate). Then, secondly even post systolic shortening disappears in the CAMM image, because parametric display shows only that the curve is above or below the zero point. Thus the colour display becomes rather featureless regarding time curves, even compared to strain curves.



There will be averaging in colour strain rate as well, but not in defined ROI's, and despite a fairly long strain distance (offset). this will be equivalent to using a sliding window, and the loss of spatial resolution will be less.




Strain ratecurves and CAMM from Normal left and large apical infarct. Both show initial dyskinesia, systolic akinesia and post systolic shortening, but the extent of each phenomena is better discernible by CAMM.







The curved M-mode will also give the additional option of new quantitative measures, i.e. additional information of space-time relations:


Curved M-mode from base of the inferolateral wall through apex and back to base of anterior septum. In this image it is evident asynchrony, the septum having anterior motion (red velocities before the inferolateral wall). Here the point is comparison of walls, but the difference in onset of motion can be measured quantitatively.
Strain rate curved anatomical M-mode from one wall only, of a normal person. The point in thois image is the measurement of the propagation velocity of the stretch waves during early relaxation and atrial systole that only can be measured in the parametric image, due to it's display of distance-time relations..

This means that the CAMM display is a two dimensional display, one dimension in time, and one dimension in space, but in addition displayeing the velocity or strain rate values. (Which are displayed qualitatively, but might be displaued numerically in a 3D graphic display.)

The curved M-mode is superb in showing the time-phase relations, and inequalities in timing between different parts of the wall.

In addition, strain rate CAMM is suited to detect the presence of reverberations:


All the phases of the cardiac cycle can be seen and the timing seems normal.
In this case there is left bundle branch block, with reverberations in the lateral wall. Still the septal flash with lateral stretch, the lateral wall shorteining with early and late septal stretch and the septal post systolic shortening (recoil) can be seen. The image can guide the placement of ROIs, but the information should still be used only qualitatively.

Heavy reverberations will show up, and the Colour M-mode will tell about timing parameters, and say if the quality is good enough to extract  deformation curves, and the CAMM will still show the timing.



The curve can be drawn through both ventricle and atrium to compare the walls of two chambers as shown below, and also from base to apex to base to compare walls as shown below.  In fact, I find the curved M-mode the most useful application of parametric imaging of all.

Thus.
  1. Strain rate curves give the rapid changes in deformation, and peak values of those changes in all phases of the heart cycle, but with reduced spatial resolution.
  2. Strain rate CAMM gives the rapid changes in deformation qualitatively, but with better spatial resolution.
  3. Strain rate CAMM is excellent to discover the presence of clutter.
  4. Strain curves gives less temporal information, mainly peak systolic strain, but strain rate can be seen in the curves qualitatively, and is thus comparable to Colour SRI, but with lower spatial resolution.
  5. Strain CAMM is of little use whatsoever. 




Displacement can also be colour mapped. As shown above, colour mapping shows gradual decreasing systolic displacement in colour bands. As each band shows a limited range of displacement, the width of the band displays the strain directly.




The same curved M-mode showing displacement during the heart cycle. However, In order to display data for the whole ventricle. one need to display an array of CAMM recordings. 4-cnamber plane (top), 2-chamber plane (middle) and apical ong axis (bottom). For each plane the curved M-mode is drawn from the base through the apex and back to the base in the opposite wall, thus displaying the base at the top and bottom of each M-mode, apex in the middle.In this display, all six wall are displayed.






However, for a simultaneous display of the whole ventricle in one image, the Bull's eye plot may more useful. This shows a geometrically distorted image of the curved left ventricular surface (similar to a map displaying the curved surface of a globe), but only in one point in time.

Bull's eye plot

The bull's eye plot is a well known metod of display, and is often used to display segmental values of wall motion score from standard segments, or measured values as f.i. emd systolic strain:

The principle of bull's eye projection; a planar map projected from a polar view of the curved surface of the left ventricle. It is analogous with the construction of maps from the curved surface of the earth. Some distortion has to be accepted. In this case, the apical area is under represented, and the basal area is over represented.  Thanks to Mr. Bong who pointed out an inconsistency in this figure. Bull's eye plot of segmental end systolic strain. Each wall is shown to be represented by a slice of 60°, corresponding to a wall in three standard 2D acquisitions.




Bull’s eye projection is a 2 - dimensional map of the entire surface of the left ventricle. Like the CAMM, it is a two dimensional display, but with two spatial and no temporal dimensions, meaning a display on a plane, at only one point in time. With numerical values from three planes, and an assumption of the angle between the planes,

From 2D acquisitions, the 3D image has to be reconstructed from more than one plane, customary from the three standard apical planes. Thus, the model includes an assumption about the angle about the planes, as well as the heart rate being reasonable similar:



it is possible to do an interpolation of values between the recorded planes, thus displaying the Bull's eye as a continuum:

Bull's eye plot of velocities in systole (left) showing velocities toward the apex in red, and early diastole (right) showing velocities away from the apex in blue. Strain rate data from systole (left) showing longitudinal shortening in yellow, and early diastole showing longitudinal elongation in blue/cyan. Systolic strain rate data from two different patients with an apical (left) and inferior (right) infarcts, respectively. The area of dyskinesia is shown in cyam, contrasting with normal shortening in the rest of the ventricle. Data are interpolated.

With intelligent interpolation (f.i. spline) between values at the same level, this might give an idea of the extent of the area of interest. However, bull's eye recontruction will result in distortion of the areas. It is analogous to displaying the curved surface of the earth on a flat map, which always results in distortion of area, angles, or usually both. In bull's eye, the display is a polar projection with apex in the center, the base in the periphery, resulting in a diminishing of the apical area and an increase of the basal area as shown below.






Three dimensional display - area measurement

However, drawing a curved M-mode, one part of the information is discarded, both in the CAMM and the bull's eye. The curved M-mode is a line that curves through the two dimensional plane, containing information about the spatial relations between the point on the line in the plane, or said in another way, the curvature of the line. Using that information, it is possible to make three dimansional surface:

The curved M-mode is a line (one dimensional) that curves through the two dimensional plane (left). The curvature gives information about the spatial relations between the pints on the line.
Keeping the curvature information enables the mapping of the points of the line in two dimensions (middle).
Using three standard planes, it is possible to reconstruct a grid with the true curvature of the surface, in this case a curved plane, that curves through three dimensions (left).

This enables a correct area representation. With the same interpolation as described above, the data can be displayed in a three dimensional figure:
Combining information from three apical planes, or in the future, analyzing motion and deformation from 3D ultrasound, it is possible to display the data in 3D (22):



3D velocity display in systole and diastole, the same dataset as in the bull's eye above.
3D strain rate display in systole and diastole, the same dataset as in the bull's eye images above.

The difference between area mapping in bull's eye view and 3D area measurement becomes eviden when looking at the infarcts below, comparing the bull's eye views with the 3D displays where the figurte is rotated with the infarct area towards the spectator. 




Apical


Inferior

The area distorsion in bull's eye is evident comparing these strain rate images of the same infarcts in bull's eye and 3D. All images are from mid systole, the infarcted area is shown in cyan, showing a- to dyskinesia, while normally shortening myocardium is shown in yellow.

In the measurements section, this has been extended to show how that can be used for direct infarct size measurement.

Fundamentally, both stationary 3D view and bull's eye are views of the left ventricle at one point in time, giving the 3D information.

Four dimensional data sets

But the Curved M-mode shows the time dimension as well.

Thus, incorporating the curvature data, the time space relation can be mapped on a curved plane curving thropugh two spatial dimensions.

CAMM reconstruction. It is the same process as above, but with obne more piece of information added: the curvature. This means that the file contains information not only about velocity or deformation values and their relation to each other in a 2 dimensional flat time space, but also the curvature of that plane thorugh three dimensions, meaning that this is in fact a three dimensional dataset.

If the three planes are combined, like in the 3D reconstruction above, we arrive at a four dimensional dataset, where there are data on a curved surface, in reality a 3-dimensional figure, and a time sequence, the dataset is in fact four dimensional. As the reconstructed dataset is really 4-dimensional (22), three spatial dimensions and time as well (through one heart cycle), the image can be scrolled in time and space as shown below. But again, as in 2D, in order to see details, the scrolling has to be stopped for visual inspection.
Strain rate 3D mapping. The 3D image can be rotated in space showing that it contains a full reconstructed 3D dataset. Stopping the scrolling will allow closer inspection, but scrolling in space will show only one instance in time.  (In this case it's mid systole). (Image courtesy of E. Sagberg.) Strain rate 4D mapping. The image can also be scrolled in time, showing the full time course of the data. Stopping the scrolling will allow closer inspection.  The problem with the moving loop is the same as in 2D display, and in addition it won't show all of the surface simultaneously.  (Image courtesy of E. Sagberg.)

The four dimensional dataset cannot be intelligibly displayed, but three dimensional infromation must be extracted at a time:

In this case, the data are extracted as velocities (left), displacement (middle) and strain rfate (right). Top: Bulls eye views, middle CAMM array, in this case arranged as a series of six, from each wall with apex on top, base at the bottom of each M-mode, and below 3D firgures.

As the basis for colour display is numerical, the curves from one point can also be extracted (22).


Myocardial strain


Geometry of myocardial strain


Still preaching my personal litany: Strain is geometry. (Cormorant seen in Galway, Ireland).



Strain in three dimensions

Three dimensional objects  can deform along all three axes. Thus, there may be more than one component of strain.
In a three dimensional object, there is the possibility of deformation in three directions. Normal strain is the deformation components along the main axes of a coordinate system. To complicate matters further, there are also shear deformations, which means displacement of the surface borders relative to each other. In fact, 3-dimensional strain is a tensor with three normal and six shear components (11). This is further explained in the mathemathics section. As all strain components are interrelated, one component may be representative of all of the regional function (7), but the 3-dimensional nature of the strain tensor is important to understand the specific problems of insonation angle in strain rate imaging compared to velocity imaging.

The basic direction in three dimensions are given by the coordinate system given. In a Cartesian coordinate system, the directions are x, y, z, somewhat randomly chosen. In relation to the ultrasound system the coordinates of the ultrasound system are often used: Axial (depth - i.e. along the ultrasound beams also often called radial), lateral (In-plane angle or distance - i.e. across the beam; also called azimuth) and elevation (out of plane distance or angle), while in relation to the ventricle, the coordinates are longitudinal, circumferential and transmural (also confusingly called "radial").





Strain in three dimensions. All three-dimensional objects can be deformed in three dimensions (along all three axes).  In this case there is deformation along the X axis,, the strain  is:
Shear strain. In this case the cube is deformed along the X axis, and the shear strain is:




The three main deformation components are :
 .


Thus, linear strain is deformation along the main axes.

Shear strain along one axis measured relatively to an orthogonal axis.In principle there may be six shear strain components, as described in more detail in the mathemathics section. There are three shear deformations, but each can be measured relative to two different orthogonal axes, thus giving six shear strains.

This elaborated in the mathematics section.


Incompressibility.



The cylinder shows strain (compression along its long axis) , which can be described as Lagrangian strain from L0 to L. However, the figure also shows simultaneous thickening or expansion in the two transverse directions. This also illustrates the principle of incompressibility. An incompressible object must maintain an unchanged volume, thus compression along one axis has to be balanced by extension along at least one other. In this case both diameters increase simultaneously. Incompressibility in the XYZ coordinate system. Usually this comprises simultaneous strain inall three directions:
The cube is stretched along the x axis, and compressed along the y and z axes, the three strains musc be interrelated so:

If  the object is incompressible, the volume (not mass!) remains constant during deformation as shown in the illustrations above.This is the true definition of incompressibility. Thus, compression in one dimension has to be balanced by expansion in others as shown in the figures above, i.e. strain in the three dimensions in a coordinate system cancel out, in way described in more detail here. This means that strain in three dimensions are interrelated, so strain in one direction is representative of regional deformation in more than one direction, as has been shown for heart muscle where wall thickening and wall shortening gives the same information about regional function (7).


It can be shown that in an incompressible object:


in order to maintain a constant volume.




The eggshell model

In order to see which consequences the incompressibility of myocardium has for cardiac mechanics, it is important to look at the eggshell model of left ventricular function.

The concept that the heart functions as a double pump, with the atrioventricular plane as a piston, is indeed a concept dating back to Leonardo da Vinci (57).In 1951 Rushmere was able to show by means of implanted iron filings in dog hearts inserted in the wall of the ventricles, that the pumping action of the right ventricle was predominantly in the long axis direction, while the left ventricle apparently pumped by an inward squeezing action (58). The inward motion of the markers, however, is dependent on how deep into the myocardium (close to the endocardium) the markers are placed. The concept of inward squeezing motion has been confirmed by innumerable ventriculographies (59), blinding the viewers to what happens the outer contour of the heart during systole.

Already in 1932, Hamilton and Rompf (59) argued from experimental studies that the heart worked mainly by the movement of the atrioventricular plane toward apex in systole, away from apex in diastole, while the apex remained stationary and the outer contour of the heart relatively constant. The heart will the work by the principle of a reciprocating pump, alternately expanding the atria and the ventricles, without moving the surrounding tissue.  Their hypothesis was confirmed by Hoffman and Ritmann in CT studies in dogs in 1985 (60), showing a stationary apex, constant outer contour and motion of the AV-plane. They also stressed that this mode of action minimised the energy expenditure by moving blood into the heart rather than moving the surrounding tissue during systole. If the heart should be pumping by inward squeezing, reducing the outer contour of the heart this would be extremely unfavourable energetics, as this means moving the surrounding tissue (lungs and mediastinum) inward by each heartbeat, without regaining this energy in diastole. Mitral ring movement was first demonstrated by echocardiography from the apical position by  Zacky in 1967 (61). Working before the time of MR and second harmonic 2D echo, Stig Lundbäck, in a series of elegant human studies  using both  gated myocardial scintigraphy, echocardiography and coronary angiography (Demonstrating the outer heart contour by tangential cine angiograms of the LAD), documented the invariant outer contour and the AV-plane mode of working (13).
It has been established that the longitudinal shortening of the left ventricle, and thus the longitudinal measures is closest related to the stroke volume and EF, i.e. to the total left ventricular volume change (30 - 35, 56, 59, 60, 64 - 67, 116). A comprehensive study of both the apex movement and the long axis function by echocardiography was published by Jones et al in 1990 (33), also demonstrating the very slight displacement of the apex toward the probe in systole. This is easy to demonstrate in modern imaging such as MR or high quality echocardiography as f.i. above.



The radial motion of the septum in diastole is determined by the differences in filling pressure of the left and right ventricles. In systole, If the filling pressures are reasonably similar, as in the normal situation, the septum has little radial displacement in diastole.  In systole, the pressure induces a circular cross section, as the most energetically feasible shape. Thus, during systole, the ventricle operates without much change in the outer contour.

Looking at the ventricular volume curve shown below left, it is evident how much the volume curve reflects a longitudinal strain curve, showing the close relation between longitudinal deformation and pumping volume. (The volume curve shows the remaining volume in the ventricle). Looking at the figure above, given the invariant outer contour, the whole of the stroke volume is described by the longitudinal shortening, as wall thickening is simply a function of wall shortening. The total volume in diastole is the sum of the blood inside, and the muscle wall. When the left ventricle shortens in systole, the total volume is reduced by the volume of the cylinder  shown in grey: . But the myocardium, comprising a part of this volume is incompressible, thus maintaining a constant volume.  Thus, the whole volume reduction  is the reduction in blood volume, in other words the stroke volume:  Thus, the stroke volume is given by the outer diameter and the systolic longitudinal ventricular shortening (56). But as the myocardium is incompressible, the wall shortening and thickening, and thus the internal diameter reduction have to be interrelated (7), and thus both would be valid measures of stroke volume. In a newer study, the correlation between MAE and stroke volume in healthy adults was seen to be about 90%, corresponding to an explained 82% of the stroke volume compared to the reference (Simpson). Thus, an outer contour systolic reduction should be present to explain the rest of the stroke volume (158).



This model has been slightly modified, showing that the total stroke volume implies an outer contour change of about 3% (158), or theoretically around 5%, this is little compared to wall thickening, showing that the main inner contour diameter reduction is due to longitudinal shortening and incompressibility, as discussed above. Thus, the eggshell model is fairly accurate, and the long axis function describes most of the pumping action of the heart.

M-mode as well as short axis cross sections, may sometimes show greater inward motion of the outer contour, due to the out of plane motion of the base of the heart as shown below:


Apparent exaggeration of inward epicardial motion, due to the motion of the base of the heart. As the base of the heart moves towards the apex in systole (red ventricle), the M-mode line is situated more basally in the narrower part of the heart. The enlarged section shows that this leads to a near doubling of the inward motion (cyan) compared to the real (blue).

There is no reason to believe that the eggshell model holds for volume loaded ventricles!

As shown theoretically and in studies, the eggshell model seems to be accurate within about 5%. However, this is in normal ventricles.
The reasoning above is limited to situations where both ventricles fill with a reasonable similar volume. If one ventricle is volume loaded, as in mitral or aortic regurgitation, the different volumes will cause a septal shift during diastolic filling, so the outer contour changes more. And in dilatation there may be a different geometry. Thus the relations between the strains and volumes may be different.

The eggshell model and atrial filling.

In the eggshell model, the atrioventricular plane has to be the piston of a reciprocating pump as discussed ), expanding the atria while the ventricle shortens and shortening the atria while the ventricle expands. This is energetically feasiblel, as the work used to decrease the volume, in additon to ejection, also moves the blood from the veins into the atria. If the heart had worked by squeezing changing outer contour to a high degree, the work would have been used to shift the rest of the thoracic contents especially lungs inwards in each systole, work that would have been waisted. Thus, most of the filling volume to the ventricles, is a function of the AV-plane pumping, as also discussed it the section of strain in the atria.

The eggshell mechanism

But how is this possible, even if energetically favorable, the pericardium is not stiff, and the surrounding lung tissue is highly compliant. The muscle forces would tend to reduce both inner and outer contour, as the circumferential fibres contract. If the pericardium had been stiff, this would generate a pressure drop, and the vacuum would hold the myocardium against the pericardium. But as the pericardium is pliable, this would not work. And Smiseth et al has shown that pericardial pressure actually increases during systole, if measured by proper techniques (63).

The answer may lie in the recoil forces. The pericardium is soft, but non-compliant. During ejection, the ventricle impels a momentum to the blood volume being ejected, generating a momentum of similar magnitude, but opposite direction according top Newton's third law (mv = - mv where m is mass and v is velocity). The recoil, pressing the heart toward the chest wall as can be felt by the apex beat and demonstrated by apexcardiography and has been demonstrated by echocardiography as well (33). And the pericardium, although pliant, is not elastic, and pressing the heart into the pericardial sac will give a constraint and pressure increase as previously shown (63). A recent study demonstrates the importance of the pericardium in accordance with the above arguments in an elegant way (122). Following the velocity and strain rate by TEE during an operation, they show that when the apex was dislodged from the pericardium, the basal velocities changed direction, so the base and apex moved toward each other in systole, without any change in strain, i.e. the myocardium still shortening at the same rate. The motion of all basal regions toward the apex was reestablished after the heart was repositioned within the pericardium.



The volume (and mass) being ejected, is equal to the volume being moved towards the apex as shown here. 
Recoil forces.  The momentum away from the apex is ejection of the stroke volume. The displacement of the ejected volume is equal to the stroke velocity integral (measured by Doppler flow in the left ventricular outflow), which is about 15 to 20 cm. The motion of the opposite momentum is displacement of the annular plane, which  is between 1 and 1,5 cm (30) at the same time, and the mass being displaced also equals the (mass of the) stroke volume. The mass is the same. The mean velocity, and thus, the momentum, being mv, being generated by ejection is at least ten times the momentum pushing in the other direction, thus generating the forces pushing the heart into the pericardium, which is non compliant.
This can be felt as the apex beat, shown here in an apexcardiogram demonstrating that the beat is a systolic event. (Image modified from Hurst: The Heart).


However, the septum is not contained in the pericardial sac. But the motion of the septum is small compared to the wall thickening, and some of the motion may be apparent as shown above. Thus, the pumping action of the left ventricle can be described by the long axis changes, and is a measure of  the systolic pumping function. Even so, much of the ventricular work is not taken into account by this, namely the work that is used for increasing the pressure from low filling pressure to high ejection (aortic) pressure. However, this is true whether measures of cavity size such as stroke volume, ejection fraction, shortening fraction. or measures of longitudinal shortening such as mitral annulus displacement, systolic annulus velocity, longitudinal strain or longitudinal strain rate is used.

Myocardial dimensions

Strain in the heart also has three main components, but the directions are related to the most common coordinate system used in the heart: Longitudinal, circumferential and transmural. (The term "radial" is often used to describe transmural direction, but as this in ultrasound terms also means in the direction of the ultrasound beam in the ultrasound specific coordinate system, "radial" strain is ambiguous and should be avoided. Transmural strain is unambiguous).






Strain in three dimensions. In the heart, the usual directions are longitudinal, transmural and circumferential as shown to the left. In systole, there is longitudinal shortening, transmural thickening and circumferential shortening. (This is an orthogonal coordinate system, but the directions of the axes are tangential to the myocardium, and thus changes from point to point.) This video shows how the apex is stationary, while the base moves toward the apex in systole, away from the apex in diastole. This ,ans the ventricle shows strain between apex and base. Longitudinal strain will be negative (shortening) during systole and positive (lengthening) during diastole (if calculated from end systole).  Wall thickening . The relatively constant outer contour and inward moving endocardium, shows clearly a displacement gradient (strain)  gradient across the wall.The wall thickening is equivalent to transmural strain.



As shown in the figures above, deformation of a three dimensional object is in all three dimensions simultaneously.
In relation to the heart, the directions are longitudinal, transmural and circumferential. In relation to the ultrasound beams, the directions are axial (along the beam), lateral (across the beam in the imaging plane) and elevation (out of the imaging plane), the coordinate systems are described in the mathematics section. Thus the terms "radial" should be avoided, as it can mean both axial in  relation to the ultrasound beam and transmural in relation to the heart, "lateral" can mean both transverse and transmural (although those may be the same in the apical views.)

It is evident that Lagrangian strain is well suited to describe systolic deformation. Diastolic thinning or elongation, however, is not so well described by Lagrangian strain as Lo is defined in end diastole.

Thus:

Longitudinal strain



Longitudinal shortening can easily be demonstrated in apical echo images as shown above, as well as measured as shown below. Transmural thickening is equivalent to wall thickening, but from the images below, it is evident that the wall has to thicken as it shortens in order to conserve volume (NOT MASS!!!).



Ventricular strain. Diastolic and systolic images of the heart. Systolic shortening of the left ventricle relative to diastolic length, is the systolic strain of the ventricle.  The longitudinal strain during systole is thus:

However, it is also evident that as the wall shortens, it also thickens, to conserve the volume. Heart muscle is generally assumed to be incompressible.
Strain being (L - L0) / L0 may still not be unambiguous, as shown below. Both the strain length, L0 and the shortening (L - L0) will be different when measured along a skewed line (red) and even longer along a line following the wall curvature (blue).  As both strain length and shortening increase when the curved line is used, the ratio will not be as affected,  but still, L0 will increase more than than the shortening.

It's important to realise that different applications may measure strain in different ways as indicated in the above right figure, and as shown below. 2D strain measures along the curved line following the wall, the M-mode method as well as Tissue Doppler will measure along the ultrasound beam, being a straight line, while segmental strain will measure along a straight line in each segment, thus being somewhat in between, as shown by this figure. Also, there is a slight difference between longitudinal stain measured in the midwall compared to endocardial measurement, due to the inward shift being more pronounced in the endocardium as discussed below, as well as due to the fact that the midwall line is slightly longer than the endocardial, thus giving a larger denominator in the strain expression.

Thus, global longitudinal strain will vary with processing software (vendor).

Now, the EACVI?EAE task force has recommended that for speckle tracking, the denominator should be the line following the myocardial wall, whether it is is the endocardial or midwall, and also that the level should always be reported by the software (287).



The longitudinal fibers are responsible for the longitudinal shortening, and any process that mainly affect longitudinal shortening (f.i. sub endocardial ischemia), will result in reduced longitudinal shortening. It is also true that the ejection work (stroke volume and ejection fraction) is closely correlated with longitudinal strain as discussed in long axis function. In fact, the longitudinal shortening can explain most (but not absolutely all (158)) of the stroke volume. This is mainly the work of the longitudinal fibers (or the longitudinal component of the spiral fibers) both in the endo- and epicardium and represents mainly isotonic work. This is what we measure by longitudinal displacement, velocity and longitudinal deformation measures.

Transmural strain

Transmural strain is simply relative wall thickening as shown below.



Transmural strain. In short axis view,  the septum and inferior wall can be imagined in cross section. Here displacement and velocity can be measured across the wall, meaning that deformation imaging with tissue Doppler can be done in only those two areas in real time. The most accurate measurement being the M-mode. Wall thickening can be measured around the wall by manual scrolling, but this reduces the accuracy. Automated measurement, for instance by 2D strain is feasible, but still gives a lower frame rate and are less accurate i the transverse direction, as the lateral resolution is lower.  Strain by  tissue Doppler is also only feasible in the two walls perpendicular to the ultrasound beam as indicated by the arrows. Systolic wall thickening can be measured, and the wall thickening is the transmural strain:
 


The concepts transmural displacement and transmural velocity are in reality meaningless in a physiological sense. The displacement and velocity in the transmural direction is dependent on where across the wall it is measured, i.e. the transmural depth of the ROI placement. Different data sets from tissue Doppler in the transmural direction is thus not comparable, and the measurements have little clinical value. Some applications like 2D strain will give the segmental average value for transmural velocity and displacement. They may have a clinical meaning, in that they may separate normal from reduced function, but the use of clinical measurements that are physiologically unsound, is doubtful.

As the ventricle shortens, the wall has to thicken in order to maintain the wall volume, as the myocardium is incompressible. Thus, one source of the wall thickening is simply that the volume has to be conserved when the walls shorten. Inward motion of the whole wall, would also cause the wall to thicken, as the reduced circumference would necessitate the wall to thicken instead. However, there is very little inward motion of the outer contour in a normal ventricle (13, 59, 60, 116) as discussed above. Thus, the only source of volume for increased wall thickness is the concomitant wall shortening, as the total wall thickening must be a function of wall shortening. As the outer contour changes little during systole, this means that as the ventricle shortens, the wall has to thicken inwards.

This has two important consequences:
  1. There is no such thing as transmural function. This is hardly surprising, as there are no transmurally directed fibres. Wall thickening reflects the thickening of the individual muscle fibers inn all directions as they contract.
  2. Transmural strain is in the eggshell model simply a function of longitudinal shortening, as shown below.




Simultaneous strain in three dimensions. Relation of long axis shortening and wall thickening.  As the heart muscle is generally considered incompressible, longitudinal shortening must give trensmural thickening.. Thus as the ventricle shortens, the wall has to thicken correspondingly in order to preserve wall volume, the thickening shown in blue. In this case, the outer contour of the left ventricle is assumed fairly constant, as described below. Transmural strain is wall thickening. Wall thickening is a function of longitudinal strain (longitudinal strain given in negative values; i.e. wall thickening increases as THE VALUE of longitudinal strain increases) in a half-ellipsoid model of the left ventricle with a length of 9.5 cm, outer diastolic diameter of 6 cm (reduced by 5% in systole as discussed below and in  the math section), and a wall thickness of 9 mm.

Wall thickness and cavity diameter are also geometric determinants of wall thickening. However, in any given ventricle with a given cavity diameter and end diastolic wall thickness, the transmural (radial) strain is a function of longitudinal strain, not an independent measure. However, transmural strain will be very much influenced by processing, especially ROI size (276), as discussed here.

There will be a gradient of transmural strain from the epi- to the endocardium. As the wall thickens, the endocardial layers expand in a space with a smaller circumference, and thus they have to thicken more for the same volume increase. But this is due to geometry, not to any gradient in layer function, as discussed below.



As in longitudinal strain, it is important to realise that as different applications use different assumptions, the values measured may vary. This is also true of different views of the same region:


Different  measures of the wall thickness and thickening. As the ventricle shortens, it will thicken. myocardium, being thinner in the apex, will thicken less absolutely, but probably as much relatively. (Black, gray.) However, looking at a cross section, (as in parasternal views, or measuring thickening in the horizontal direction (As in many MR tags) , will give a distortion, the measures a thicker wall and a greater absolute wall thickening. (Blue.)  The effects of relative wall thickening may vary, depending on the angle and the change of angle during systole. Assuming equal wall (ROI) thickness throughout the length of the wall (as in som e speckle tracking applications), will overestimate the wall thickness in the apex. If inward displacement at the same time is taken from tracking data, the measure of wall thickening will be unpredictable as compared to the  real wall thickening. 



Circumferential strain


Circumferential strain is an ambiguous term.

The circumferential strain has no meaning except as a shortening of a defined circumference. And this is dependent on which circumference, as circumferential shortening increases from the epicardium (being fairly close to zero - see below, to the endocardium (being maximal), as shown in the figure. Thus, again, there is a gradient of circumferential strain from the outer to the inner contour, due to geometry, NOT to layer specific function.

Thus, in order to talk about circumferential strain, first, the question has to be answered: Which circumference?

Different software today use different definitions, some measuring endocardial, others midwall circumferential shortening. Thus, there is no standard circumferential strain, it is is method dependent.

Secondly: The circumferential strain in a normal ventricle is the shoshortening of a circumference due to the inward shoft caused by the wall thickening. Even if there had been no circumferential fibres, there would have been wall thickening and thus circumferential strain as shown in the figure below. If shortening of the circumferential fibres had been a contributor to circumferential shortening, this would imply reduction in outer circumference, which have been shown to be negligible (13, 59, 60, 116), discussed in more detail below. The main function of the circumferential fibres is to balance the intracavitary pressure by muscle tension.

  1. Firstly, this means that the circumferential shortening is mainly due to the inward shift caused by wall thickening, not a measure of circumferential function, as also discussed in relation to fibre dicection below.
  2. Secondly, the level of measurement is more important than longitudinal shortening, leading to large differences in circumferential strain between different software.
  3. Finally, as the circumference is simply a function of the diameter (C = * D), circumferential strain can be computed directly from the diameter fractional shortening (i.e. midwall or endocardial, respectively): C = (C - C0)/C0 = ( * D - * D0) / * D0 = (D - D0) / D0 = ÷ FS
Thus, global circumferential strain equals fractional shortening!
(I.e. either endocardial or midwall)

Of course, this is in the absence of regional dysfunction. With regional dysfunction, the mean circumferential strain is of less interest, it is differences in regional circumfernetial strain that is the main objective.








Relation of wall thickening (transverse or transmural strain) and circumferential strain.  As the wall thickens in systole (blue), the midwall line moves inwards half the distance of the endocardium. Endocardial circumferential shortening is greater than midwall circumferential shortening, which is greater than epicardial circumferential shortening  (which is close to zero).  (although a small reduction in outer contour will contribute slightly).
Endocardial and midwall circumferential strain in the same half ellipsoid model as above, as a function of wall thickening (transmural strain), given an end diastolic outer diameter of  60 mm, and end diastolic wall thickness of 10 mm and assuming a systolic outer contour reduction of 5%  (Circumferential strain given in negative values; i.e. as wall thickening increases, THE VALUE of circumferential strain increases). As wall thickening increases, end systolic diameter decreases, leading to a decreased end systolic circumference, hence, increased circumferential strain. Using endocardial strain shows the same relation, but higher absolute strain values.  Circumferential strain in the same ellipsoid geometrical model, showing circumferential strain as a function of longitudinal strain.

But as wall thickening is dependent on wall shortening, and circumferential shortening is a function of wall thickening, this means for any given ventricle (diameter and wall thickness), circumferential strain is also a function of longitudinal strain:
 


Thus, neither transmural nor circumferential strain are independent measures of ventricular function. However, the relations will change not only with longitudinal strain, but also with ventricular size and wall thickness, still dependent on the geometry of the ventricle.

They may also behave slightly differently in regional function assessment as discussed below.

As strain measurements are software dependent, inter vendor consistency is low, although best for global longitudinal strain (277, 278), as might be expected as the sources of differences are smaller.

Area strain


Strain area. The Thingvellir Rift Valley in Iceland is the rift between the North American and the Eurasian continental plates. The plates are diverging, so the rift is expanding and the area undergoes positive strain.


Hypothetically, with the advent of 3D echocardiography, it would also be possible to measure simultaneously in all direction, enabling the measurement of composite measures. One candidate for such composite measures is  area strain. However, as discussed elsewhere, there are serious shortcomings in 3D speckle tracking, due to low frame rate and line density.

Both area strain as well as transmural and circumferential strain can in principle be assessed by 2D acquisitions, if they are processed into a 3/4D reconstruction.
This, however, requires tracking in both longitudinal and transverse directions, ans thus has to be done with either speckle tracking alone , or combined tissue Doppler and speckle tracking, as shown below. It also includes some assumptions about the angle between the planes and simultaneity of events in the loops that are acquired sequentially, but processed into a simultaneous image.




3D strain rate mapping. Reconstructed 3/4D image with longitudinal tracking from tissue Doppler. (This is described in detail below). Yellow represents shortening, blue elongation and green no strain. In this case only longitudinal strain is tracked and displayed, as can be seen from the diameter circumference of the grid, it doesnt change during the heart cycle.
Apical four chamber view with B-mode and tissue Doppler data. Longitudinal shortening is tracked by tissue Doppler. In this image both sides of the LV wall are marked and tracked,  thus the wall thickening is tracked as well, by speckle tracking. In this analysis both longitudinal and transmural strains are available, but for circumferential strain 3/4D reconstruction is necessary, and requires three planes.
3/4D reconstruction from three sequential planes to a thick walled model analysed as shown in the image in the middle. In this case, the endocardial and midwall circumferences are given in the grid, and circumferential and area strains can be calculated. (The colours in this image, however, are tissue Doppler derived strain rate, i. e. longitudinal strain rate).

Giving the present sorry state of 3D speckle tracking, this may still be an option, especially as B-mode has improved substantially with new computing techniques, giving both higher line density and frame rate.


However, as area strain is not part of the original Lagangian definition, the concept needs a definition, one reasonable candidate is simply the systolic relative reduction in area, giving an analogous definition to the one concerning one dimensional strain:









Area strain. As the one dimensional strain is relative change in length, the area strain should have the same definition: relative change in area.

However, just as circumferential strain, the area strain is dependent on which level of the wall it is measured. Epicardially, there is very little circumferential shortening at all, and the area strain would be equal to the longitudinal strain, as the area will shorten by length only.



Area strain. As the ventricle contract, the end diastolic area of the selected region (red) would be reduced in both the longitudinal and circumferential direction. Assuming a cylindrical shape of the segment, the area will be equivalent to a flat geometry. In the apex, the shape would be more triangular, which means the area is only half that. Both the cylinder and triangle will underestimate the true area, as the surface is curved, but the underestimation will be similar in end systole and end diastole, so the area strain approximation will be closer to the real area strain.
Area strain is a function of longitudinal strain.


Simple geometry will then show that the area strain is a function of circumferential strain, and that the relation is: A = L * C + L + C  the derivation of this expression can be seen here.
As area strain is a function of circumferential and longitudinal strain, and circumferential strain again is a function of longitudinal strain, area strain itself can be seen as a function of longitudinal strain:


Thus, for global function, area strain does not seem to add new information. Also, for area strain, the 3D speckle tracking technique may render it inferior to single measures from 2D or tissue Doppler.


Where there is regionally reduced function, however, the situation may be different. The circumferential shortening may be reduced in a sector, and the area strain would then be a compound of reduced longitudinal and circumferential shortening. However, it could still be computed to  certain degree, as endocardial circumferential shortening can be computed from the fractional shortening through the hypokinetic area. The limitations in area strain, however, will still persist.

However, in a recent study (279) of myocardial infarcts, 3D strain did not show incremental diagnostic value to the other modalities. 3D longitudinal strain was inferior to 2D longitudinal strain, and 3D Circumferential, longitudinal and area strain did not add information, as opposed to infarct area by tissue Doppler (243).

Myocardial shear strains

As explained above, there may, at least theoretically be shear strains in the myocardium as well. In the myocardium the principal deformations should be as for the principal strains, longitudinal, circumferential and transmural. (this is evident, force being a vector can only have three spatial components). But as measured relatively, there will be six different shear strains. If shear strains will be avalilable for measurements, some may have more practical implications than others. Measuring shear strains means that one will be able to measure differential strain across a cross section of the image. This is related to measurement of layer strains as discussed below.

Is there layer specific strain, and can we measure it?

The advance of speckle tracking have enabled analysis of deformation in all directions, although with severe limitations inherent in ultrasound itself as well as due to the specific applications for analysis Speckle tracking also gives the possibility of measuring smaller regions of the myocardium. This may be subject to severe restrictions, however.

Longitudinal layer specific strain:

The longitudinal layer strain will of course still be governed by the length tension relation, meaning that the systolic shortening is a function of tension and load. And as tension differs, the longitudinal tension from adjacent segments will be part of the load of each segments. Thus: Reduced tension in one segment will result in increased shortening in other segments as dicussed above. However, as fibre directions vary across the wall, the longitudinal tension has to be unequally distributed; specifically it will probably be lowest in the middle layer, where the fibre direction is mostly circular. It is customary to discern between three layers, defined by anatomy: The endocardial, the middle and the epicardial layers. The layer structure is well establshed (62, 256, 257). Due to different fibre direction (62, 257), they may have different longitudinal tension also in the natural situation. If the layers had been able to deform independently, this would result in inequal strain across the wall. However, this is improbable for several reasons:

Thus, there will be considerable dependency between layers, both due to the framework and the interconnection between layers.

Transmural gradient of longitudinal strain.

As the wall is curved also in the longitudinal direction, there will be a strain gradient across the wall, even if there are no tension differences. This is partly due to:




Simplified diagram of how curvature may affect longitudinal strain, showing the wall divided into two layers. In this diagram, only the effect due to wall thickening is shown isolated, to avoid confusion with the effects of longitudinal wall  shortening. As the outer layer (grey) thickens, both the mid layer (thin black lines) and inner contour (thick black lines) of that layer shifts inwards (dotted lines).  In a curved wall, this inward shift of the midwall line (average for the layer), will shorten it, this is an effect that is added to the wall shortening itself. Thus, longitudinal strain has some effect of wall thickening, like circumferential strain.

But as the outer layer thickens inwards, the inner layer not only thickens, but also is displaced inwards. This adds tothe inward shift of the midwall line, this midawall line is thus displaced inwards both by the layer displacement and the layer thickening. And this effect is even greater, as there is less room for the inner layer as it is displaced inwards, forcing it to thicken even more, displacing the midwall line even more. This is equivalent to the effect on circumferential layers, and this effect is most pronounced in the inner layers.

In longitudinal strain the wall shortening is the most important for the over all strain, however, the layer effect may be responsible for the gradient, or else there would be torsion of the mitral ring. In circumferential strain this effect is the mechanism for both overall strain and the strain gradient.

Global longitudinal strain. This diagram shows how it can be measured in different ways, giving different results.

The effect illustrated to the left will be mainly if strain is measured alng the curvature of the wall, while straight line shortening as measured by B-mode, M-mode or tissue Doppler will not show this effect. Measuring along a curved wall will increase this gradient even more, as the denominator shortens due to curvature as well.



This makes longitudinal strain to some degree curvature dependent (measured by speckle tracing) as explained elsewhere, although the effect of curvature may differ between applications



Hypothetical model of equal tension (orange lines), equally distributed  along the layers as well as acros the wall will result in normal shortening (orange) across the wall layers and along the wall regions. Approximation to the normal tension distirbution of the tension, with least longitudinal tension in the middle layer. With a deformable mitral ring and independent layers, the deformation would be unequal as well, causeing the mitral ring to buckle in the middle (A). As discussed above, this is undocumented as well as improbable, the more probale model being homogeneous deformation across the wall, as a resultant of the different forces.




A: Unequal distribution of tension (red: high , orange: medium and yellow: low - reduced) across the wall. If this should result in differential deformation, (A1), there would be torsion of the mitral ring, which is improbable, and indeed undocumented. As in the discussion and example above, the more probable would be a more homogeneous deformation due to the transmural resultant force (A2). B: Unequal distribution of tension along the wall, but not across the wall will cause the segments to behave differently, the weakest may be akinetic, or even stretch (cyan) due to the pull from adjacent segments  while the strongest may shorten excessively due to the reduced pull of the weaker segments, as discussed later). The total wall shortening is reduced due to reduced total force, but the mitral ring does not move less locally, but globally, as discussed later, and shown empirically (40). Hypothetical model of unequal distribution both across and along the wall, in a model where there is some freedom for the layers to slide past each other. A; in the base and B; in the apex. This corresponds to various situations of ischemia with varying transmurality. This may cause the layers to behave differently, layers with very reduced tension in one segment may be akinetic or even stretch in that segment due to the pull from the stronger layer segments, and the reduced pull in weaker segments thus causing extra shortening in normal segments as shown here.

Thus, with some degree of layer independence, and differential tension both across as well as along the wall, there may be differential layer strain. The difference in longitudinal strain across the wall is will then be longitudinal shear deformation, and measured relatively to wall thickness, it will be longitudinal/transmural shear strain.

The shear strain has been demonstrated experimentally by applying differential stress to isolated tissue (i. e;. passive strain), showing that the tissue strains most easily in the direction l  the myocardial layers (258). Differential tension restricted to regions in the myocardial wall is what is expected from non transmural ischemia. Thus, shear strain might be demonstrable in these situations, and has been demonstrated experimentally (259).

Hypothetically, measuring sub endocardial longitudinal strain selectively, if possible, might increase sensitivity for non transmural infarcts / ischemia, as the endocardial layer will be the most affected. However, this remains to be proven. Also it may hypothetically be a method for differentiating transmural and non transmural akinesia, in the acute situation demonstrating transmural ischemia. Transmural ischemia in the acute situation may be an indication of coronary occlusion as opposed to non transmural ischemia.


However:

In order to be able to measure this in three layers, the lateral resolution has to be so high as to allow three lines within one wall. This is dependent on both

The main point is that studies of longitudinal strain in full sector is dubious, even if the analysis software produces layer strain values at will.



Speckle tracking has the advantage of a higher line density of B-mode, at the cost of a lower temporal resolution.  The very low lateral resolution used in tissue Doppler in order to achieve a high frame rate, results in a low line density, and in practice limits the measurement in the beams in the longitudinal (and tangential - for circimferential measures) direction to the entire wall thickness, for a standard set up. Layer specific measures may be possible using either narrower sectors (typically one wall) while at the same time keeping frame rate at the same level.


Contamination by epicardial signals, averaging  non moving structures into the deformation analysis may be possible, and this tendency might be highest in the outer layer, decreasing inwards. This might also account for an apparent transmural gradient of longitudinal strain, increasing inwards.


If analysing longitudinal layer strain from apical positions should make sense, it should probably be done with ,
Frame rate, line density and focus positions should always be reported in studies.

The newest hardware has improved B-mode line density as well as frame rate. Thus, layer strain findings may be more credible in the future than in the past.

However, studies of longitudinal layer strain from apical full sectors older than about 2012 may be dubious, and if focus and line density is not reported, actually valueless.




Circumferential layer specific strain:

In the transmural and circumferential directions speckle tracking is not limited to the direction of the ultrasound beam, while tissue Doppler, due to angle dependency, can only measure anterior and inferior transmural strain, and (at best) lateral and septal circumferential strain as discussed in the measurements section. Also, the need for a certain strain lenghth, measuring transmural strain in different layers of a wall need higher frequencies in a low noise set up to be reliable. In standard probes the best quality measures are obtained by measuring transmural strain through the whole of the weall. (Which again is unnecessary, as this is the wall thickening can be measured more reliable by M-mode).

However, in the circumferential strain, geometry again raises it's ugly head. As the wall thickens, the endocardial layers expand in a space with a smaller circumference, and thus they have to thicken more for the same volume increase. But this is due to geometry, not to any gradient in layer function.




As shown above, circumferential strain is the reduction of a circumferential line as it is shifted inwards by the wall thickening. The endocardial circumferential strain is higher in value than the midwall circ strain.
If we add another layer with the same diastolic thickness, it becomes more complicated as shown in this simplified model of two layers. The outer layer is identical to the layer shown to the left. Thus, outer contour of the inner layer is identical with the inner contour of the outer layer. The inward displacement of the inner contour of the outer layer, displaces the outer contour of the inner layer inwards the strain are identical. But this means that the wall thickening of the inner layer has to be greater, in order to conserve volume, as there will be less space for the layer in systole. This means again that both midwall and endocardial strain in the inner layer will have a greater value, not only as the wall thickening of the inner layer is added to that of the outer, but also because the wall thickening itself is greater due to the lack of space. I e. there vill be increasing both transmural and circumferential strain form the epi- to the endocardium.

This means that there is a gradient of both transmural and circumferential strain across the wall, with increasing values towards the inside. This has been confirmed emprically (255).  However, this har nothing to do with layer function in the symmetric ventricle, only with geometry. In regional dysfunction where there is loss of substance or loss of force, the situation may differ between layers.

Strain and fibre direction


It has been a popular misconception that strain in the different directions have to do with the actions of different muscle fibers, i.e. circumferential and transmural (radial) strain reflects the action of circular fibers, while longitudinal shortening reflects the function of the longitudinal fibers. It seems to be something almost "everybody knew". While the latter is partially true, the first is not.  There would have been circumferential shortening even if there had been no circumferential fibres. Mean circumferential strain must be taken to mean midwall circumferential shortening. As shown above, the midwall circumferential shortening is almost entirely the function of diameter shortening, which again is a function of wall thickening. This is due to the finding that the LV outer contour is nearly invariant from diastole to systole (13, 59, 60) as shown in the example above, the diameter reduction being a function of wall thickening inside a virtual "eggshell". The reduction in outer contour contributes only to a small part of the circumferential strain.


The fibre directions are diverse, and varies throughout the thickness of the heart, the middle layer being more circular, while the endo- and epicardial layers being more longitudinal, although helically ordered (62, 257). In dealing with the principal strains, the wall is treated as isotropic, which it is not. Thus, there may be differential strain as well as shear strain.


Differences in longitudinal strain across the wall, as has been described by some authors, would necessitate a torsion of the mitral annulus , and thus is geometrically unfeasible, except to a very minor degree allowed by the small change to the saddle shape in systole. The studies finding large differences, are probably describing artifacts, as the lateral resolution is low, and the angle deviation may vary.


The concept "radial function" is somewhat meaningless, as there are no fibres running in the radial direction. What is called "radial function" is either wall thickening, which is a function of fibre thickening, and circumferential shortening, and the term radial function means that the transmural strain, or wall thickening is used, the term circumferential strain means that circumferential shortening is used as parameter.

Only the small contribution from circumferential shortening that results in outer diameter reduction, is the independent radial function. Fractional shortening is the reduction in cavity diameter, and is equal to * endocardial circumferential shortening.

 
Thus the three principal strains are totally interrelated and does not convey separate information about different fibre function. The information is about the myocardial volume deformation in ejection phase.

The concept maintained by some authors that radial function and longitudinal function independently contribute to the stroke volume, is thus totally erroneous. So is the assumption that the circumferential and longitudinal strain directions reflects function of different layers.

Thus, circumferential shortening is related to wall thickening, which is due to the thickening of the individual muscle fibres.
In addition, as the inner circumference decreases, the longitudinal fibers gets less room, especially in the endocardial parts, and thus the longitudinal fibers have to shift inwards during systole.  This also contributes to the wall thickening as illustrated below. Wall thickening is thus greater than the sum of the individual fibre thickenings.

Transmural strain is not only due to wall thickening, but also of inward displacement of the inner layers. Simplified and exaggerated diagram showing the relation between fiber thickening and wall thickening. As the fibers shorten, they thicken. Thus, the sub epicardial  longitudinal fibers will thicken, displacing the circular fibers in the mid wall inwards. In addition, as the fibre become thicker, they will need more room, thus necessitating some rearrangement of the fibres, making the layer thickening even more than the individual fibres. They will also displace the circular fibres inwards, thus making the shorten and also thicken as they contract. Finally the sub endocardial longitudinal fibers will be displaced inward. The sub endocardial fibers will also, thicken. But the circumference has been decreased at the same time due to the thickening of the outer fibers,  and thus there has to be an extra inward shift of longitudinal fibers for them to have room. Assuming a systolic reduction in outer diameter will only enhance this effect. By this, it's evident that wall thickening is not equivalent to the sum of fibre thickening alone. The circumferential strain is thus mainly the shift of the midwall line inwards due to wall thickening.


The circumferential fibers,  mainly contributes to the pressure increase, i.e. isometric work, which takes place mainly during the  isovolumic contraction phase, as discussed below. Isometric contraction cannot be measured by deformation along the fibers. As they contract, however, there will also be a slight inward shift, due to the displacement of the fibres, which also results in a shortening and thickening of the fibres. In addition, the circumferential fibers may be responsible for whatever there is of outer contour diameter reduction . If so, they contribute to the ejection work, and in addition slightly to wall thickening, as the wall has to thicken even more in order to retain wall volume with a reduced outer diameter. If there is loss of longitudinal contractile function, either regionally (typical ischemia) or globally as in cardiomyopathia with sub endocardial affection (e.g. Fabry), there may be a shift toward circumferential pumping, with an increase in the variations of outer circumference. Then there will be true radial compensation for loss of longitudinal function. But in hypertrophic states, there is usually loss of longitudinal function and circumferential function both, but due to the increased wall thickness the fractional shortening may be increased. This has been called "radial compensation", but as explained belowthis is a total  misunderstanding of geometry.

It is also extremely important that if longitudinal and "radial function" are compared, care should be taken that the measurements are comparable. To compare for instance fractional shortening of the LV diameter with longitudinal strain (wall shortening), is comparing two different measures, and may lead to completely erroneous conclusions as shown below, where fractional shortening increases but wall thickening decreases.


In regional dysfunction, there is an inter dependence of the segments in both directions, that will alter regional deformation, in addition to the loss of tissue, that will be described below.



Thus, the pumping action of the heart, i.e. the ejection volume can be described by the long axis function.


However, considerable energy is used to build up the ventricular pressure from the low filling pressures of the left atrium to the high ejection pressures of the aorta in systole. In a simplified model, the work can be described as an isometric (mainly isovolumic) component, and an isotonic part, being ejection at a much more stable pressure. This may be described in terms of energetics:

The potential energy that is stored in the blood pool in the ventricle during isovolumic contraction is P x V. The kinetic energy in the blood being ejected is 1/2 m v2, which is less than 20% of the potential energy. Thus, almost 80% of the work is pressure buildup, and this is done by tension increase, not necessarily with simultaneous shortening (deformation). I.e. the work is mainly isometric.


Pressure work

Even is both longitudinal and circumferential fibres will contribute to ejection, the fact that 80% of LV fibres are circumferential, (62) It may seem that the circumferential fibres are the main contributors to the pressure work. And mechanical arguments show that circumferential forces are the most effective for pressure increase. Some of the ejection energy, however, results from conversion of pressure energy, intraventricular pressure being higher that aortic during first part of ejection. Longitudinal deformation work on the other side also comprises moving the AV - plane toward the apex, moving a volume equivalent to the stroke volume, but with a velocity of only about 10 cm/s (37, 38), i. e. a fraction of the ejection work. 

This may not be as energetically unfeasible as it may seem at first glance. The pressure is transmitted to the aorta, where much of the systolic pressure is stored as elastic energy, with a slow recoil during diastole. Thus, the aorta is the pump driving the blood flow in diastole, and the energy is the stored pressure energy from the ventricular systole.

Thus, deformation analysis, whether it is factional shortneing, EF, longitudinal shortening, or deformation, all measure myocardial deforrmation in one way or other, and thus only a fraction of the work done by the heart. The greatest  great part of the ventricular work - the isometric work, cannot be described by deformation analysis (or any imaging modality) at all as all functional analysis by cardiac imaging is about deformation.

The full description of LV work need to incorporate a measure of load, either by invasive measures, or by externally measured pressure (eventually pressure traces) in combination with mathematical models.

Most of the pressure work is isometric (isovolumic), as most of the pressure build up happens during isovolumic contraction time. AS pressure results in ejection, and as ejection results in deformationm, however, some of the pressure work will reflect in the global deformation.



What does cardiac imaging actually show?

The relation between function imaging and physiology.

It is evident that any kind of cardiac imaging is based on visualisation of either
The first derivatives of these parameters are

Any kind of functional inference from imaging thus is based on the motion or deformation, which is neither contraction, nor contractility. Deformation is definitely NOT contractility. In comparison with the cellular physiology, it is a huge difference between the contraction - relaxation cycle and the ejection - filling cycle. Basically, it can be said that contraction generates tension or force, while deformation is the result of force and load.


Thus the notion that deformation indices can be load independent, is self contradictory, although different parameters may relate differently to load as discussed here. And the notion that different imaging methods (like MR) are less load dependent than others, is simply ridiculous.


Thus, any imaging modality, including strain and strain rate only tells half the truth about contractility. Moon near third quarter.



To explain this in a little more detail, it is necessary to go into the contraction mechanisms, and the relation to mechanics:

The fundamental stimulus for contraction is the action potential, which triggers release of calcium to the cytoplasm, which again triggers the coupling of cross bridges between actin and myosin, and the release of energy from ATP resulting in shortening of the sarcomeres.



Excitation-tension diagram. After Cordeiro (234). The Action potential triggers the influx of calcium, which triggers further release of Ca2+from sarcoplasmatic reticulum. Calcium binds to troponin, and allows activated (by ATP) myosin heads to bind to troponin sites on actin (cross bridge forming) and release energy, causing the filaments to slide along each other, as long as there is a high calcium concentration in the cytoplasm.  As the cell membrane repolarised, this triggers the removal of calcium from the cytoplasm, mainly by the SERCA pumping it into the sarcoplasmatic reticulum again.  Thus, the forming of new cross bridges is inhibited, and relaxation starts. The pumping of calcium is energy dependent, and is the energy requiring part of the relaxation cycle. In energy depletion (f.i. ischemia), there will be less shortening in systole, but also slower relaxation.
Image of beating isolated myocyte. The myocyte is treated with an agent that fluoresces in the presence of free calcium in the cytosol. We see that the cell lightens and shortens simultaneously; stimulation causes an increase in free calcium (released mainly from the sarcoplasmatic reticulum), causing the cell to become lighter. The free calcium is the trigger for the binding of ATP, and the formation of activated ("cocked") cross bridges between actin and myosin, and the subsequent release, which leads to tthe buildup of tension in the cell. In the unloaded isolated myocyte, (as in previous studies in isolated papillary muscle), this will correspond almost directly with the shortening, as virtually no energy is used to overcome load. However, a small part of the energy needs to be stored for diastolic lengthening, even in isolated myocytes, as discussed below. Thus, even an isolated myocyte is not entirely unloaded. Image courtesy of Ph.D. Tomas Stølen, cardiac exercise research group (CERG), Dept. of Circulation and Medical Imaging, Norwegian University of Science and technology.


(The opposite process is the removal of calcium from the cytoplasm, and the uncoupling of the cross bridges, releasing tension. The removal of calcium is energy demanding, thus relaxation as well as contraction is energy dependent. However, there is no mechanism in the molecular contractile apparatus that leads to elongation of the cell. Thus, the elongation of the cell is dependent on energy stored from systole, which is released as contractile tension decreases. However, in energy depletion, there will also be less shortening in systole, and thus also slower recoil, so energy depletion slows recoil in more than one way. Even isolated myocytes in nutrition solution elongates back to their original shape, so the main or at least part of the recoil mechanism may actually be in the cytoskeleton itself.)
Basically, an isolated myocyte is under no load (at least externally). In that case, the tension developed corresponds to shortening. In this case, contraction equals contractility. And the relaxation corresponds to elongation. However: as the heart reverts to its original shape on relaxation, there is no mechanism in the contractile apparatus that causes this, so the elongation has to be elastic recoil stored in shortening, released as the cell relaxes. (This goes to show that even a single cell develops increasing internal load as it shortens. This may be disregarded for practical purposes, and the isolated cell being cionsidered the unloaded condition.)

In the intact heart, however, there is external load as well.

The normal mechanical sequence vill then be as follows:
After mechanical activation, there is an intial shortening seen in the velocity traces as a positive spike of short duration - the pre ejection spike. This initial contraction gives a small pressure rise which closes the mitral valve (236) about 30 ms after initial septal contraction (268). The lateral wall starts slightly later,  but within 40 ms (maximum duration of the normal Q-wave - septal activation). 

AS the walls contract in parallel, they will give rise to isovolumic contraction where there is pressure increase without deformation, and then ejection when ventricular pressure exceeds aortic, the ejection phase is characterised by longitudinal shortening and wall thickening.

However, active contraction is in terms of force, and cannot be seen by deformation, as the continuing ejection will result in continuing shortening despite tension decrease. The development of active contraction do not continue during the whole of the ejection, tension decrease starts around mid ejection, probably at the time of peak pressure / peak strain rate, after this there is tension release. Thus, the tension buildup is an event of much shorter duration than ejection. After this there is still tension, although decreasing, during the last part of ejection the ejection is partly driven by inertia.
The main load, however, is from pressure, and the interaction between ventricle and pressure. Deformation (shortening - elongation) is the relation between tension and load.

The contraction relaxation can be visualised either in stimulating isolated myocytes in a nutrition solution, or by measuring tension, or length in muscle preparations suspended in measuring apparatus. Looking at an isolated muscle cell, stimulation will cause the cell to shorten, and then to elongate. This is the contraction relaxation cycle of the cell. However, this is not equivalent to the ejection-filling cycle of the intact heart. Even excluding the phases of diastasis and late filling (where the ventricular myocardium is in a passive state), the ejection and early filling do not correspond to myocyte contraction and relaxation, and thus the contraction - relaxation in a cardiological sense, at least when viewed by imaging, is different from the physiological sense, as argued by Brutsaert et al (224, 225).  

In the isolated cell, elongation starts at start of tension release (- decrease). In the intact heart, tension decrease starts at the start of pressure decrease, this means before mid ejection. But as blood is still being ejected, the ventricle will continue to eject, and thus reduce its volume, and we measure systolic deformation in the meaning volume reduction/wall shortening all the way to end ejection. This is due to the blood being accelerated to ejection velocity, meaning that the inertia will cause it to flow for a time even as pressure drops.This means that myocytes are still shortening as well,despite tension release;still shortening as volume decreases due to continuing ejection, as mentioned above. Also, any imaging modality will show continuing systolic deformation (i e longitudinal and circulferential shortening, volume decrease and wall thickening), despite myocyte relaxation, all the way to end ejection.

I.e.

  1. In the normal heart, there is active contraction (building up of force) only during pre ejection and first part of ejection.
    1. During isovolumic contraction, there is pressure buildup without volume changes, and hence, no deformation.
    2. Ejection results in volume decrease, and thus there is deformation (ventricle shortening and wall thickening). During first part of ejection, this deformation is active contraction
    3. Peak tension is reached about the time of peak ventricular pressure, near peak ejection velocity or peak systolic annular velocity, although the ejection rate may be slowed slightly before peak pressure, due to arterial impedance.
  2. After this there is still tension, although decreasing, during the last part of ejection the ejection is partly driven by inertia
    1. As there is still volume decrease, there will still be volume decrease, and hence, wall thickening and shortening. This continuing decrease, however, is passive, and the muscle is in fact relaxing at the same time.
 



It has been shown that the re ejection tissue velocity spike in the septum styarts about 35 ms after start ECG (268), thus corresponding to the electromechanical delay on the cellular level (234) shown above, so the start of the pre ejection spike marks the onset of the active contraction in the septum, startring slightly before the mitral valve closure as discussed below.
The pre ejection spike terminates with the mitral valve closure and the start of isovolumic contraction, wherte there is tension development, but no deformation. Ejection starts with the aortic valve opening (AVO), after this there is ejection and volume decrease, but much slower pressure increase. The peak ejection rate may be a little before peak contraction, (tension), as the ejection rate may be slowed slightly because of arterial impedance. However, the ejection persists both due to the tension being reduced gradually, and due to the inertia as the blood pool is accelerated.



The peak velocity of annular plane motion may differ at different sites, The earlyt peak often only present lin the lateral wall) and the early peak during ejection will often be earlier than the peak ejection, this is also true for the mean velocity cyrve between eptal and lateral annulus. 
Peak rate of deformation is later, as the early peak is translational motion.


The main point is that active contraction is an event with much shorter duration than the ejection. This has consequences for the mechanics in left bundle branch block.


The consequences for the physiology of diastole is discussed in more detail under diastolic function.

Thus, deformation is not even contraction in the cellular sense.

This is dicussed more below.

What is contractility?

The elephant test:

"It is hard to define an elephant, but you know it when you see it."

Looking at various definitions:

"the intrinsic ability of a cardiac muscle fibre to contract at a given fibre length."
"the intrinsic ability of the heart/myocardium to contract"
"changes in the ability to produce force during contraction"
"capacity for becoming shorter in response to a suitable stimulus"
"a measure of cardiac pump performance, the degree to which muscle fibers can shorten when activated by a stimulus independent of preload and afterload"

Thus we see that contractility definition varies in terms of force generation and shortening. But force and shortening is interrelated through load.

Fundamentally, contractility should thus be the ability to generate force (tension). The higher the tesion that can be developed, the higher the contractility. In the isolated myocyte (in general considered an unloaded situation), they may be taken as equivalent. The generation of force, however, has been studied in isolated muscle preparations, mounted in a set up where they cannot shorten, but where force can be measured by a tensiometer. This isolates the tension from other measures.


Fundamental length-tension diagram in an isometric preparation.  AS the muscle is pre stretched, the tension that develops with stimulation increases up to a certain point, and then decreases. This is due to the fact that the force is related to the number of cross bridges that can be formed between actin and myosin. The optimal sarcomere length is the situation where each myosin head can bind to a troponin head. If sarcomeres are too short, there will be overlap between the myosin chains themselves, meaning that there will be shortage of troponin sites, and thus fewere cross bridges can be formed. If the sarcomeres are too long, there will be myosin heads that cannot bind to troponin sites. Howeveer, passive stretch willl also store some elastic energy by stretch of the elastic element of the sarcomere, and thus add to the initial length tension relation.

In general, it has been established that maximum tension developed:

The length-tension relation is the load dependent part, and thus not a measure of contractility. Contractility is always defined as an "intrinsic", meaning load independent  property.

However, in these isometric experiment models, there is no change in length during contraction, hence the implications for imaging are limited, except as the framework for understanding the physiology.

The fact that tension develops without shorteneing, shows that the cell has to have both contractile and elastic elements in series for this to take place. In order to develop tension, the contractile element has to shorten, as given by the molecular basis for contraction, and thus another part of the cell has to stratch. This role seems to be taken by the protein anchoring myosin to the Z-plates; titin (274, 275). Thus as the contractile element shortens, the elastic elelent of the sarcomere stretces as a spring. But this also means that the force that is generated is stored as elastic force. It also means that passive pre stretch may lead to some storage of elastic energy even before start of contraction, which will add to the contractile force being generated. And this again will be part of the length tension relation.


Any imaging measurement (As Ultrasound, MR, MUGA etc), will measure shortening. But the shortening is the result of force versus the load that force has to overcome. Thus, shortening in images is always load dependent, at least in the intact heart.

Force and tension are interchangeable concepts relating to the state of the muscle, i.e. the force developed by the muscle.

How does tension relate to shortening?

In isolated myocytes, tension and shortening may be considered equivalent as they are unloaded.


In loaded situations, however, the shortening is the result of tension versus load. However, the relation is not simple even here. Due to the Frank starling effect, The preload will stretch the muscle, and thus increase contractilion (up to a certain length).

What is load?

The concept of load is useful, in understanding complex issues, even if they are difficult to define in an operational measurable sense in the intact heart. Fundamentally, load is the force acting on, or generated by the heart muscle. In the heart we usually talk about preload and afterload.

Preload is the force acting the muscle before the start of contraction, i.e. the force stretching the muscle before contraction, and thus determines the passive tension of the muscle, as well as the initial length which again is related to the tension development.  But the preload is also part of the total load the muscle must overcome in order to shorten.
Afterload is the force added to the preload that offers resistance to the muscle shortening.
Total load is preload + afterload. This is the force the muscle must overcome ( e. the tension the muscle must develop) in order to shorten.
This is illustrated below.




Pre- and afteroad: The concepts of pre and afterload are easily defined and studied in isolated muscle preparations, as illustrated in a simplified diagram to the left:.The preload is attatched to the muscle, stretching the muscle to equilibrium (passive tension). The table is then placed under the preload weight to prevent further stretching. Then the afterload is added, (this doesn't stretch the muscle, due to the table). As the muscle starts to contract, the contraction is isometric until tension equals total load (pre + afterload), then it starts to shorten. As the afterload is lifted, the load is constant, and the muscle shortens as an isotonic contraction, as shown right. The dotted line illustrates the maximum shortening rate (actually this is an over simplification, the maximum tension resulting in shortening is at the time when tension ovecomes load, i.e. start of shortening, but the peak rate of shortening is a little later, due to the time it takes to accelerate muscle and weight) . Shortening velocity (= strain rate) and total shortening (Strain) decreases with increasing load (after 208).

Muscle shortening physiology were also primarily studied in isolated preparations, often similar to the set up illustrated above, including a tensiometer as in isometric experiments. In an isolated muscle preparation in such a set up, there will first be isometric tension development, after the tension equals total load there will be shortening at constant load. From this, it is evident that the time before the muscle starts to shorten, and hence, the total shortening, will depend on both the load and the contractility. However, as shown in the early sixties (208, 209), also shortening velocity is load dependent. This also contributes to the reduction of total shortening with increasing load.

However, the concepts of pre- and afterload remains simplyfied explanatory models, as we move to increasingly complex situations.



When doing imaging, the parmeter is always shortening, and shortening is the result of both contractility and load:




In contraction, the muscle will increase tension, but resulting in no shortening as long as the tension is below the total load (isometric contraction). When tension equals load, further contraction will result in shortening at constant tension (isotonic contraction). This is what we see in imaging.
However an increasing  load will both delay onset of shortening, as the development of higher tension takes longer time, but will also result in less shortening, as well as a lower initial rate of shortening.  The effect of increased load in slowing relaxation (224) is not shown in this simplified diagram. This would have shown up in slowing the tension downslope, but the lengthening would still be shortened by increased load.
Reduced contracility will give a slower tension development and lower peak tension. However, this has the same effect as increased load on shortening, resulting in delay in onset of shortening, lower rate of initial shortening and less total shortening. The relative incr4ase in load due to reduced contractility, would still slow relaxation, (224), but this is not shown here.

Thus, imaging alone cannot measure contractility directly.

How is this in the complete ventricle?

Once we move from isolated myocytes to a full ventricle, the situation is no longer linear, and the situation becomes far more complicated.
  1. The load is related to the intraventricular pressure. This is the pressure the muscle has to overcome in order to shorten. The higher the volume, the more tension the muscle has to develop in order to shorten.
    1. Preload may be taken as related to end diastolic pressure, the initial pressure filling the ventricle (stretching the muscle), and the terms are often used interchangeably.
    2. Afterload may be taken as the systolic pressure, the resistance during shortening
  2. The load is also related to the chamber volume. The bigger the volume, the larger the surface area the force has to act on, for any given pressure. Thus, the greater the area, the greater the force that must be developed to overcome any given pressure any given pressure. (In fact this follows from the definition, as pressure is force per area unit).
  3. Finally, the force is related to the wall thickness. Wall stress, is the tension per cross sectional area unit. Thus is varies inversely with the thickness of the muscle.


The law of Laplace states that the wall stress is proportional to a function of pressure, radius and wall thickness as shown below right. The actual formula is dependent on the shape of the chamber that is assumed in the model.



Relation of force to surface area. Assuming that the two balloons have the same intracavitary pressure, the total load on the wall (as illustrated by the larger number of arrows in the larger balloon) is proportional with the surface area, and thus a function of the radius
(F = P × A = P
× (4/3)  × pi × r3).
Wall stress.  A force acting on a segment is distributed across the cross section, thus a bigger cross section gives a smaller force per square unit as illustrated by the wider segment with smaller arrows on each half.

Thus, the concepts of load, tension and wall stress can be described, and used for explanatory  purposes, although the measurements in intact ventricles are only model approximations.

And looking at regional longitudinal function, the concept of load is not limited to the simple model of Laplace, as it should include the effect of segment interaction (forces), as discussed under regional function.

Thus, contractility may be seen as the ability to overcome load. The Frank starling mechanism describes how contractility is a function of volume, by the same mechanism as the length force relation shown above:

The Frank Starling curves. Increasing EDV increases contractility, through the length-force relation. However, as increased diameter also increases total load, the effect on stroke volume may be somewhat less than the effect seen in isolated muscle. Contractility increases with inotropic stimuli (sympathetic tone, drugs or increased stimulus frequence), and decreases with heart failure, having effect on contractility.



In the complete ventricle, there is also a separation between the filling pressure (being the mean atrial pressure, which partly determines preload), and the ejection pressure, being the systolic aortic pressure, which is the main determinant of afterload. So in the complete ventricle, there is pressure volume relations, which are the equivalents of tension length relations decribed above. Also, the complete heart cycle is more than the contraction relaxation cycle as described above.

The heart cycle can basically be described in terms of volume changes, which in turn are the function of ejection and filling:

Classically, the changes during the heart cycle can be described in terms of either the volume changes, or the pressure changes and -differences during the heart cycle. The flow is basically a function of pressure differences, and the volume changes are a direct result of flow, (the volume is the integrated flow rate). Pressure are the result of filling pressure and myocardial contraction and - relaxation, resistance, elasticity and compliance. Thus, it might be said that the myocardial changes are the primary mover. But this is at the cellular level.



The Wiggers cycle. The pressure changes are shown in relation to the heart cycle. The filling pressure is the atrial pressure, and the total filling determines the end diastiolic pressure (and volume). The contraction starts with isovolumic contraction (IVC), which raises the ventricular pressure to the level of the aorta. This is the isometric phase of conmtraction, i.e. tension (pressure) increase without volume (muscle length) decrease.The ejection phase is during aortic opening.  From the pressure curves it it evident that the tension decline (i.e. relaxation) starts around mid ejection, and the last part of ejection is during relaxation. But as there is ejection, there is still volume reduction. Relaxation continues into the isovolumic relaxation (IVR) phase, where there is further pressure (tension) release, and then into early filling (E) phase of mitral opening. The rest of the heart cycle, the diastasis and late (atrial -A) filling phase are phases where the ventricular myocardium is passive.
Volume change and flow rates related to the heart cycle.
Top,  Ventricular volume curve, with the different phases demarcated. IVC starts with  mitral closure (MVC). Then, there is pressure increase as shown to the left, but no volume change. During ejection, there is volume decline, corresponding to muscle  shortening. Peak ejection rate, corresponds more or less to maximal tension. After that, there is ejection, due to the inertia of blood, but simultaneous tension decline as shown by the pressure traces (left).  After end ejection there is further decline in pressure, but no volume change in IVR, and then further relaxation creating early (E) filling. In diastasis, there is little filling, and then there is further filling of teh passive ventricle due to atrial contraction.
Below, composite Doppler flow velocity curve showing both LVOT outflow and mitral inflow to the left ventricle. The flow velocity curve is an approximation to flow rate, and hence, similar to the temporal derivative of the volume curve, or, conversely, the volume changes are the integrated flow rate.


PV-loops

The pressure volume relations are traditionally visualised in a pressure volume loop, which takes both load and volume into consideration:


Schematic diagram of pressure-volume relations. Pressure-Volume (PV-) loops. Isovolumic contractio(IVC) is pressure increase, without volume change. Ejection is volume reduction, during ejection. IVR is pressure drop, without volume change. The filling isperiod is volume increase at low prerssure. With increasing volume load (preload), there will be increased contraction through the Frank-Starling mechanism. However, the end systolic pressure-relation (ESPVR) will basically remain along a straight line (239). Inotropy will increase the slope of the line (fine line).  Heart failure will decrease the slope of the line (dotted line). Thus the slope of that line is a preload insensitive index of the contractile state. This has been termed ventricular elastance. The end diastolic pressure volume relation (EDPVR), on the other hand, has been taken as a measure of left ventricular compliance. (Some has even erroneously taken this as a measure of diastolic function).





Thus, both contractility, end diastolic volume and load will affect the stroke volume, and hence, the deformation:


From this, it is evident that contractility cannot be measured by shortening alone, and hence, not by imaging alone, without a measure of load.

Contractility can be inferred, but from assumptions about load. On the other hand, changes in contractility are more evident by imaging. Change in stroke volume and/or end diastolic volume, wil generally increase all imaging parameters, although the early systolic velocity measures are less affected by a subsequent rediction in EDV. as discussed below. Early global systolic measures are Peak ejection flow velocity measured in LVOT, peak systolic mitral annular velocity and mean peak systolic strain rate.

End systolic global measures , on the other hand, are stroke volume, ejection fraction, end systolic strain and mitral annular displacement. They are all a measure of the total work done by the ventricle in systole. However, thic can be acheved at a lower force, if done over longer  time, so they are farther from contractility (78, 79), being closer related to the stroke volume and EF, i.e. to the total left ventricular volume change.

Longitudinal systolic strain of the left ventricle is shortening, normalised for diastolic length (similar to EF, which is volume decrease (stroke volume) normalised for end diastolic volume). As longitudinal shortening describes most of the actual ejection work (13), , there is a strong relation between EF and longitudinal strain.Thus, it may seem that the longitudinal fibres (or force components) are the main contributors to the ejection work, i.e. the isotonic part of the work.

But even so, early systolic measures during ejection are also load dependent.

Flow is pressure driven and the flow velocity measurements are the real indices of pressure differences.  It has thus been hypothesized that as deformation is the generator of pressure differences, and flow the result, flow is the indicator of pressure differences while tissue velocities and hence, strain rate is load independent. This belief about systolic performance indicators has also been reinforced by the apparent load independence of diastolic velocities compared to diastolic flow. It has been assumed that the deformation and velocity parameters are load independent, but this is not the case, the load independence of diastolic velocities is also only partial (160).  The mechanism for diastolic load dependency may be partially different as discussed here. Still, the early diastolic tissue velocity is less load dependent than flow velocity, making the ration (E/e') useful in assessing ventricular filling pressure as discussed below.

Left ventricular elastance.


The slope of the end systolic PV relation line is called ventricular elastance and has been proposed as a definition of contractility, as it reflects the different contractile states independent of load (239).


The end systolic pressure volume relation, is the slope of the straight line through pressure volume loops for a given inotropic state. As it can be seen, the slope is the pressure volume relation, the change in pressure for a given volume.

The general definition of elastance is given by:

E = P / V

It is usually taken to mean the measure of the ability to recoil in terms of unit of volume change per unit of pressure change, i.e. for an elastic object, the recoil force generated by a certain volume expansion. In the actively contracting ventricle, however, it becomes a measure of the force that generates a certain volume reduction by the contractin, and hence, a measure of contractility.





 PV loops are often erroneously shown with horizontal pressure during ejection, and equal pressure at start and end ejection, but the pressure at start ejection, bein equal to the end diastolic aortic pressure, and the arterial pressure dropping during diastole, the start ejection pressure has to be lower than the end ejection. Also, the true pressure curve shows an increase at start ejection and drop at end ejection. The filling period is complex. It is often erroneously shown as horizontal  or gradually rising,  but as there is pressure drop simultaneous with volume increase during early filling, and may be slow filling during diastasis, and finally  concomitant pressure and volume increase during atrial contraction, the filling phase has to be a curve more or less as shown. Also, it is a trend to describe the filling as passive, while it actually consists of active relaxation and atrial contraction, only during the last, is the ventricle passive. The dynamics of filling are discussed below.
The effect of end diastolic volume, load and inotropy on the PV loops. Black: Normal PV loop. Yellow: effect of increased end diastolic volume or preload, (e.g. volume load, or increased RR interval) without increased afterload. The contraction will increase through the Frank Starling mechanism, and the stroke volume will increase somewhat, partially restoring the end systolic volume. Blue;the effect of afterload increase. Increased afterload will close the aortic valve at a higher pressure, and higher end diastolic volume, reducing the stroke volume (blue dotted line). This, however, will increase end diastolic volume (through reduced emptying) if filling is unchanged, increasing end diastolic volume, which partially will redice the effect on stroke volume. Green: Inotropy increases contractility, and thus, the end systolic pressure volume relation line, and thus increases stroke volume by reducing end systolic volume. However, even if increase in contractility may increase cardiac output somewhat, if filling remains unchanged, the end diastolic volume will decrease again, offsetting some the effect of inotropy in normal ventricles (green dotted line). Thus increased contractility without increased venous return may lead to the ventricle mainly workingat somewhat lower volumes, with only a slight increase in stroke volume. Orange, in heart failure, contractility is depressed. Venous return will cause the PV loop to move out on the end diastolic slope, but in time reduced stroke volume will also reduce venous return..


However, pressure-volume relations in the intact heart in situ, however, are more complex than shown above.
Thus, it can be discussed whether ventricular elastance is sufficient to define the term "contractility" in absolute terms. In fact, even pressure volume loops remain simplified explanatory models only.

The main point here is the term: "contractile state", which defines the contractility in relative terms, higher and lower contractile state, while being load independent.  Ventricular elastance fulfils this.

Pressure work

A considerable part of the energy from myocyte contraction is not used directly for ejection, but to to build up the ventricular pressure from the low filling pressures of the left atrium to the high ejection pressures of the aorta in systole as shown by the pressure curves above. In a simplified model, that work can be described as isometric (isovolumic). This may be described in terms of energetics:

The potential energy that is stored in the blood pool in the ventricle during isovolumic contraction is P x V, where P is the pressure increase, and V is the volume (end diastolic) of the blood pool.

Thus, from the viewpoint of deformation, some of the work in tension development is in order to overcome pressure, without deformation. This work does not result in deformation, and thus is not shown by imaging.


Only part of the work results in deformation, which is what is shown by imaging. It is important to realise that  imaging measures only deformation. And the deformation is thus still a result of interaction between tension (contractility) and load.

The heart in situ

Moving from a model of the whole heart as seen in open chest experiments or in Langendorf preparations, the situation increases more in complexity.

Firstly, the mechanics of the heart changes. In an open chest, the apex and base moves towards each other, while in the intact heart, the apex is stationary, and the longiotudinal shortening is due to the motion of the base (249). The longitudinal strain, however, remains unchanged.

Secondly, as the transmural pressure is completely different, this may affect both transverse deformation and diastolic suction.

Thirdly, the afterload is a complex function of the aortic compliance, peripheral resistance and even reflected pressure waves. This is obviously dependent on the total characteristics of the vascular bed in the intact body.




Ventriculo arterial coupling

The concept of ventriculo arterial coupling is closely related to the concept of afterload. All may be rather difficult to define in an operational (measurable) sense, but the concepts may still be valuable for the understanding of complex issues.  The ventriculo arterial coupling is simply an extension of the  load dependency of  LV performance, as  shortening (strain), EF or  stroke volume decreases as load increases, in the absence of compensatory  mechanisms. (LV stroke work being the same). Thus, the arterial resistance is important for all measures of LV systolic function obtained by imaging. However, this will also mean that the diastolic function is dependent on afterload, as some of the energy for diastolic suction is the stored energy from systole (recoil).

Thus, the afterload being dependent on the systolic arterial pressure, the afterload (the pressure part of it) may be taken as central aortic systolic pressure (CAP). But this again, is dependent on more factors:
  1. 1: Peripheral resistance. The peripheral resistance determines the run off through the whole of the heart cycle, i.e. both systole and diastole. The resistance is usually given by the simplified concept of the Ohm's formula:   P = Q x R, where P is the the mean arterian pressure, Q the cardiac output and R then defined by R = MAP / Q. However, this is the mean pressure during the heart cycle, while the afterload is related specifically to the pressure during ejection, which depends not only on the mean pressure, but the balance between systolic and diastolic pressure. Basically, the resistance is the arteriolar function.As diastole is longer than the systole during rest, the main effect is on the diastolic arterial pressure, especially as the aortic compliance may compensate for the peripheral resistance during systole.
  2. The elasticity (compliance) of the arterial (especially the aortic) wall. During ejection, the volume ejected into the aorta distends it. The distensibility of the aorta is called the compliance, and this is defined as: C = V / P, which means how much the volume will increase for a given increase in pressure. As can be seen, the compliance is the inverse value of the elastance, but in this case the aortic elastence, and in this case the elastance means the ability to generate recoil (force or pressure) from a given expansion (volume). This means that the systolic distension of the aorta will lead to diastolic recoil, in other words the aora acts as a diastolic pump, maintaining flow durinbg diastole. i.e. some of the ejection energy is taken up in the aortic wall (and delivered again to the blood during diastole, providing the energy driving the blood out into the arteries during diastole and maintaining central diastolic pressure, being higher that the diastolic ventricular pressure). The more distensible the aortic wall, the less the pressure in the aorta will rise, and the lower the CAP. The stiffer the aorta, the less it will be distended (the less the compliance) for a given pressure increase, or conversely the more the pressure has to be increased in order to inject a certain volume (stroke volume) into the aorta. Thus, increased arterial stiffness will increase the systolic pressure, and hence, the afterload.  Arterial stiffness increases with disease and age, and thus the systolic pressure will increase, increasing the afterload.
  3. Pulse wave propagation. The pulse wave leads to an increase in pressure and arterial diameter. This will propagate as a wave along the arterial wall, faster the stiffer the wall is. (Not to be confused with flow velocity, which is far slower). As the stiffness of the arterial wall increases with age and disease (as well as with pressure itself), the pulse wave propagation will increase too. But as the pulse wave travels along the arterial bed, at various levels the waves will be reflected backfrom the periphery, and thus there are two waves traveling back and forth during each heart cycle. Where the outgoing and the reflected (from previous pulse wave) pressure peaks coincide, there will be augmentation of peak pressure, where the reflected peak coincides with the through, there will be neutralisation of the peak of the reflected wave. Thus, the faster the pulse wave propagation the faster it returns toward the central aorta, and the earlier it will meet the next wave. Thus, with increasing pulse wave propagation velocity, the more it will augment the peak systolic central aortic pressure (253). This means that the central systolic pressure may be higher than the peripheral as measured by the manometer cuff or radial catheter.


The effect of pulse wave propagation on aortic waveforms through interaction between forward wave and reflection of previous wave. On top (A)  is illustrated the forward pulse wave and the reflection of the previous wave travelling in the opposite direction. Bottom left (B) with a low wave propagation velocity, the two eaves can be seen to meet in the aorta with the peak of the reflected wave coinciding with the through of the forward wave, thus no increase in systolic pressure. To the right, with a higher wave propagation velocity the two peaks meet, peak of reflected wave adding to peak of forward wave (which may be higher already due to reduced aortic compliance),  creating a higher peak systolic pressure, thus increasing afterload.


Thus, the arterial stiffness and resistance are factors contributing to the afterload, but the compexity of the issue, (especially #3 above) means that the central aortic pressure may vary from the peripheral arterial pressure, and thus the real afterload may not be assessed directly by peripheral blood pressure measurement, but will need invasive measurement or complex modeling.

Interaction with the body

Finally, of course, the body regulates both the cardiac performance and load in relation to the needs of the body:
  1. The contractile state as well as heart rate is a function of the total autonomic balance of the body
  2. The afterload is regulated both by the autonomic balance as well as the other blood pressure regulatory mechanisms affecting the peripheral resistance
  3. The preload is a function of both blood volume (which again is regulated both by the kidneys (and fluid regulatory hormones) and the tissue capillary filtration/resorbtion
  4. And the venous tone is the main regulator of venous return as well as balancing the fluid volume

Thus, of course, all factors of cardiac performance in the intact body may change in relation to the body's needs. But this may be a very complex regulation of the contractile state (by variations in inotropy), preload (by variations in venous return - venoconstriction; giving load dependent increase in contraction) and afterload by varying arterial tone (which again is often balanced by inotropy).  The final variable is the cardiac output, which may be seen as the stroke work (ejection work) times the heart rate.

Ejection work

The ejection phase is the phase where the stroke volume is ejected, and the volume is reduced. Thus, the active contraction during this phase is used for deformation, and it may be said that imaging shows the ejection work either directly (by flow as shown above), or by imaging the volume reduction as shown below.





Left ventricular volume curve from MUGA scan (gated blood pool imaging  by 99Tc labelled albumin. The total volume is proportional to tne number of counts, thus making MUGA a true volumetric method, but averaged from several hundred beats.) It is evident that there is volume reduction corresponding to ejection, then there is early and late filling. Thus this might seem to corresond to contraction - relaxation. The temporal resolution of MUGA is low, and the isovolumic phases are poorly defined.
(Longitudinal) strain (shortening) curve from left ventricle. Note the close correspondence to the volume curve on the left, but due to higher temporal resolution, the isovolumic phases are visible.  Again the shortening might seem to be contraction, and the (early) elongation relaxation.

In terms of energetics, the ejection work may be described as The kinetic energy in the blood being ejected is 1/2 m v2, which is less than 20% of the potential energy (P*V). Thus, almost 80% of the work is pressure buildup, and this is done by tension increase, not necessarily with simultaneous shortening (deformation).

However, this relation is not simple. Active contraction is, as have been dicussed only the first part of active contraction, while the last part is inertia driven. (In fact, there is very little, or even negative pressure gradient from LV to aorta in this phase). During the systole, there is active contraction only during isovolumic contraction and the first part of the ejection period, starting with isovolumic contraction, and ending with peak ventricular pressure. I.e. the work is mainly isometric. And only a part of this is converted to velocity (and thus ejection and volume decline), as most of the work is used for overcoming the aortic pressure (afterload) and will not be reflected in deformation. Some of the ejection energy, however, results from conversion of pressure energy, intraventricular pressure being higher that aortic during first part of ejection. Longitudinal deformation work on the other side also comprises moving the AV - plane toward the apex, moving a volume equivalent to the stroke volume, but with a velocity of only about 10 cm/s (37, 38), i. e. a fraction of the ejection work.  But, as the velocity is built up by the active contraction, this means that the whole ejection (and deformation) is the result of active contraction.

After peak pressure (and flow), there is active relaxation, the force declines, and the left ventricular pressure drops slightly below the aortic. The continued ejection is due to the inertia of the flowing blood, the kinetic energy is sufficient to overcome the small pressure difference. (By the simplified Bernoulli equation, 1m/s = 4 mm Hg). As the ejection continues, the ejection of blood volume causes the ventricle to diminish, LV volume, LV length and diameter decreases, stroke volume, EF and absolute strain increases, and strain rate remains negative during the rest of EP while the myocytes relax. Thus there is continuing systolic shortening (even of the myocytes), although the myocytes are relaxing. It is evident that in this phase, deformation does not describe contraction at all, and the situation is completely . +

This may not be as energetically unfeasible as it may seem at first glance. The pressure is transmitted to the aorta, where much of the systolic pressure is stored as elastic energy, with a slow recoil during diastole. Thus, the aorta is the pump driving the blood flow in diastole, and the energy is the stored pressure energy from the ventricular systole.




Load dependency of strain and strain rate


Thus, strain rate and strain are not load independent, as explained above. One would almost say of course. Force is the primary effect of contraction. Deformation is secondary to force, and depends on load. Motion is the summation of deformation. The systolic volume change of the ventricle is related to the resistance, which again is a function of both pressure and vascular resistance. What we measure with deformation parameters, is only the changes in shape, thus the resulting volume changes.It is well established that increased pre- and afterload decreases both dL/dT of shortening, and amount of shortening (208, 209), and thus, physiologically the rate and amount of longitudinal shortening should decrease with increasing load. Anything else would be counterintuitive.


The strain rate and strain relation to load should be equivalent to the shortening and shortening velocity.  (after 208)


Invasive (161) and non invasive (162) clinical studies has shown the load dependency of systolic annular velocities. The simplest test being the supine versus sitting position, where the person doesn't use their legs as on a bicycle. This has been shown conclusively that both LV systolic annular velocity and displacement decreases, concurrent with mitral flow indices of filling pressure and LVEDV (160). This study also showed load dependency of diastolic velocities.

In symmetric ventricles, the velocity and displacement values are evenly distributed from the base to the apex, and thus the annular peak systolic velocity and peak annular displacement are global measures of strain and strain rate when normalised for LV length. Thus it's nonsense to assume they are different, although some differences may arise form the velocity being equivalent to Lagrangian strain rate rather than Eulerian, and the performance of the indices across a wide range of body sizes may vary as well, as discussed later. Thus all evidence showing that systolic tissue velocities are load dependent, is pertinent to strain rate as well. Already the first experimental works did show load dependency of strain (8, 163). This has been repeated in newer experiments (164, 216).

 Peak velocity and strain rate are early systolic measures, and thus ought to be more closely related to contractility, during active contraction, while displacement and strain are end systolic measures related to the total stroke volume. This was confirmed by an experimental study by Weidemann et al (78, 79), with pacing, beta blocker and dobutamine, showed strain rate to be most closely related to dP/dt, i.e. contractility, while strain (and thus by inference displacement) is more closely related to stroke volume and EF. It did not, however do pressure/volume loops. The finding, however, has been confirmed in arecent experimental studies in mice (254) and healthy normal human subjects (223)

The study by Greenberg et al (80), did do pressure volume loops, and seemed to show that s strain rate was better related to end systolic pressure volume relation during different inotropic states (esmolol, baseline and dobutamine) than systolic velocities, but did not compare with end systolic measures.


Also, this will be independent of the method used for measuring strain / strain rate, and in fact all of the B-mode and M-mode echocardiography is actually about imaging wall motion and deformation.

What do Strain and strain rate actually measure?

It is important to realise that  strain and strain rate measure only deformation.

Thus, as deformation is a result of tension, or rather tension versus load, strain and strain rate do not measure function directly. In principle, velocity and displacement measures the effect of contraction of the whole ventricle apical to the point of measurement. Thus, annular plane displacement and velocity measures the global function of the left ventricle (13). This has been demonstrated in several studies, both for systolic annular displacement (30 - 36) and velocity (37 - 40). This will be the same for global strain and strain rate, which are only shortening and velocity normalised for ventricular size. Basically, longitudinal strain and strain rate are methods to measure regional deformation, the basic algorithm subtracts the motion due to contraction of neighboring segments (tethering effects).

Even so: Early systolic measures such as peak annular velocity or peak systolic strain rate, will be less load dependent, as they are reached in a shorter time, and thus will not be subject to load during the whole of systole (226).  (As contractility in fact is the development of force, the most direct measure should have been strain rate acceleration, acceleration being directly related to force.  However, as strain rate is a fairly noisy method, derivation to strain acceleration have so far been shown to be prohibitive because of noise. And still, it would only be the force leading to deformation, not pressure build up.) In addition, imaging will measure deformation  during the first part of myocyte relaxation. This is true of MR, ultrasound, MUGA.

Strain and strain rate measure relative regional contractility


But taking regional function into the concept of load, deformation imaging can be used to infer force, or at least inequalities in force development, as shown below. n fact, this is the basis for much of the findings in regional dysfunction, as the load is relative, in part determined by the action of neighbouring segments in regional dysfunction. The slowing down and prolongation of shortening will also be the basis for the post systolic shortening observed in regional dysfunction. Thus, strain rate images shows gradients of relative contractility in the ventricle, even if one does not measure absolute contractility.

And that is the main point in regional diagnosis.

Strain and strain rate measure size independent shortening


Although strain and strain rate are just as load dependent as aother systolic measures, in global function, the main point is that as the total muscle (wall) shortening is the sum of the shortening of the parts (segments) of the same muscle. Thus, the longer the muscle, the greater the shortening. However, strain and strain rate are shortening and shortening rate per length of muscle, i.e. they measure size independent shortening. This means that they are more position independent as discussed here, the length of the wall as discussed here and also more independent of the size of the ventricle as discussed here.

Strain and strain rate measure motion independent shortening

Strain and strain rate subtracts the effect of overall (translational) motion of the whole heart, as well as the motion due to tethering from other segments as will be further explained below.


Events of the heart cycle






The Wiggers cycle: Heart cycle in terms of pressure changes
                                             
Volume and flow

Classical Wiggers cycle, where events during the heart cycle is related to pressure changes in atrium and ventricle. The flow is a direct result of the pressure differences, and thus the volume changes are the result of flow. It is evident that pressure decline (relaxation) starts long before end ejection when comparing with the image to the left. Top,  Ventricular volume through one heart cycle, with the different phases demarcated. Below, composite Doppler flow velocity curve showing both LVOT outflow and mitral inflow to the left ventricle. If the orifice remains constant, the flow velocity will be similar to the flow rate curve. Thus, the flow velocity curve is an approximation to flow rate, and hence, similar to the temporal derivative of the volume curve, or, conversely, the volume changes are the integrated flow rate. The isovolumic phases are exaggerated.
Displacement and velocity

Strain and strain rate

Top, mitral annular displacement curve, being the curve showing the longitudinal shortening of the left ventricle. Below, the tissue velocity curve, which is the temporal derivative of the displacement curve. Comparing to the volume/flow curve, it is evident that there is more complex motions, especially n elation to the isovolumic phases, than is evident from the mere volume diagram to the left. Top, strain curve from mid septum, showing the deformation, below the strain rate (temporal derivative). The curves seem to be very similar to inverted motion and velocity curves, however, deformation will show more regional detail as discussed below. Remark also how the strain curve is similar to the volume curve, showing the same pattern, while the strain rate (temporal derivative of strain) is similar to the flow curve (temporal derivative of volume).



It has been established that the longitudinal shortening of the left ventricle, and thus the longitudinal measures is closest related to the stroke volume and EF, i.e. to the total left ventricular volume change (13, 30 - 35, 56, 59, 60, 64 - 67, 116). Thus, the longitudinal strain is the most important measure, and it is also closely related to the wall thickening and thus internal shortening as discussed above.

Looking at longitudinal motion, the phases can be displayed by tissue Doppler:


The phases of the heart cycle shown as basal velocities (top) and motion by integration of velocity traces (bottom). The velocity curve crossing the zero line corresponds to a shift in the direction of motion. Thus, positve velocities are motion toward apex, negative velocities are motion away from the apex. The heart cycle in the ventricle starts with start of QRS in the ECG (provided the scanner ECG is properly aligned with the disrection of the initial vector of activation (across the septum).
  1. The first period until ejection is the Pre Ejection period (PEP), starting with the start of QRS, and ending with the aortic opening. (and start of flow and volume reduction). During PEP there is a positive velocity spike. This is before the mitrav valve closure, but the MVC cannot be seen in the TDI traces.
  2. The ejection period (Ej) starts with an abrupt onset of positve velocity, due to the volume reduction and hence, motion of basis toward the apex. The positive velocities during ejection are often termed S'.
  3. At end ejection there is a short negative velocity spike,
  4. followed by the isovolumic relaxation (IVR), defined by the period between mitral valve closure and aortic opening.
  5. After IVR, there is the period of early filling E - the negative velocity spike is often termed e'
  6. Then the diastasis
  7. And finally the late filling phase due to atrial contraction (A), vlelocity spike called a'

Systolic events

The precise timing of events, like the valve openings (start of flow), as well as valve closures (which may be a little later than end of flow, but can be timed with valve clicks as shown below (168)), may be most reliably timed as global events by Doppler flow (289). However, this presupposes that heart rate is fairly constant, as tissue Doppler/B-mode recordings are taken as separate aquisitions.

End ejection can be reliably identified by Tissue Doppler tracings from the septum, both in relation to Doppler flow and Phono (168), to very high frame rate B-mode (169) in both normal ventricles, ventricles during high heart rate and ventricles with ischemia infarct sequelae (170). This can thus be done in the same acquisitions as the tissue Doppler recordings, without having to transfer from a different recording. However, in mechanical asynchrony from other causes, this is more dubious (289)

By experience, this is probably not feasible in conduction abnormalities nor pacing, as discussed below. That has also recently been shown (289). The main point in the studies (168, 169, 170), however, was mainly to elicit the mechanisms for aortic valve closure, and to correct much cited, but mistaken suppositions that the IVC was the initial negative velocity of the tracings, i.e. to elicit the physiology.

The pre ejection period

To start with: There is no such thing as isovolumic acceleration!
Even if this has been describes as such (330), the concept is nonsense. During isovolumic contraction there is no volume change, and thus no real deformation. What happens in the pre ejection phase is discussed below.


The pre ejection period (PEP) is defined as the period from the start of the first deflection of the QRS, to the start of ejection, as defined by the aortic valve opening, or the onset of flow in the LVOT (235).


Pre ejection period, from onset of ECG (provided the ECG is properly aligned) to start of flow out of LVOT. There is a short flow into LVOT during PEP. THis may be due to delayed vortex formation from mitral inflow. The early inflow into LVOT during PEP can also be seen by colur M-mode, but stops above the annulus.




The first thing to be aware of, is that as the first ventricular activation is the septum, in normals from the left to the right side, the start of QRS might be seen as much as 40 ms delayed if viewed in a lead with direction parallell to the septum (i.e. at 90° angle to the electrical vector).

The PEP shows a series of events than may affect imaging.

First, there is the electromechanical delay (EMD), which at the cellular level consist of the action potential generating Calcium influx, again generating release of more calcium form the SR, resulting in onset of cell shortening as shown above. This process takes about 30 - 40 ms (234), and leads to onset of local shortening. Simultaneously, there is propagation of the action potential over the whole ventricle, this is the propagation that is seen as the QRS potential, and the time it takes is the duretion of the QRS (about 80 - 110 ms, although the last part may be activation of the right ventricle).

Early experimental and invasive studies seemed to show that there is initial endocardial activation almost simultaneously in mid septum and mid lateral wall, after 10 - 15 ms after onset of ECG (350, 351).

Theoretically, this should be followed by a similar wave of mechanical activation of contraction, with a standard EMD. However, due to the effects of tethering, the velocities during initial contraction, may not reflect the wave of electromechanical activation, active contraction in one segment may result in motion in another.


Spatial distribution of pre ejection velocity spikes. A: comparing different levels in the septum, B comparing sepum and lateral wall and C: comparing different levels in the lateral wall. (Colours on ROI and velocity curves correspond). Areas at this frrame rate (ca 100 FPS), there is no evident timindifferences of the pre ejection spike, showing that this is a global event, and that the spike does not show propagation of electromechanical activation.



Active contraction has been seen to start before the mitral valve closure (MVC) (236). This is intuitive, the initial contraction being the force for increased LV pressure that closes the mitral valve. Thus, the isovolumic contraction phase, defined as the period from MVC to aortic opening, is shorter than PEP (235), and also the duration from onset of contraction to start ejection (236).

The pre ejection velocity spike is due to active contraction, as has been verified experimentally in simultaneous pressure - tissue doppler recordings (173). The spike is present in atrial fibrillation (173), and is thus not any kind of "recoil" after atrail systole, as has been suggested. Even if these facts were known, it seemed that everybody "knew" that the first spike was isovolumic contraction, as seen in a lot of publications.

However, this is counterintuitive given previous knowledge of physiology (236), which should logically mean that the initial pre ejection spike should start before mitral valve closure, as can be demonstrated below, by phonocardiography:

In this recording, the pre ejection spike (middle vertical marker line) is seen to start after the onset of ECG (left vertical line), but before the onset of the first heart sound (right line). In the Doppler recording, the ECG can be seen to precede the first heart sound, which precedes the start of ejection.

Now it can also be easily demonstrated by the conventional method of transferring the opening and closing events from Doppler recordings to the worksheet of analysis software, to be used in other quantitative analysis: ,

 
Recordings from LVOT (bottom left - 62 FPS) and mitral annulus (bottom right - 60 FPS)) with closing and opening of aortic and mitral valves marked and measured. The analysis software has then transferred the events to the tissue Doppler analysis (63 FPS), and the basal pre ejection spike can be consistently seen before MVC.

However, this is slightly less accurate as events are transferred from separate recordings (different cycles) and thus are vulnerable to heart rate variability.


In the initial situation, with open mitral valve, the left ventricle is close to unloaded, and active contraction should lead to shortening rather than pressure increase. This would mean that the PEP motion would give a very small volume decrease, before the mitral valve closes, but without any regurgitation, as the valve moves within the stationary blood volume. But this, again would give a small volume reduction in the pressure - volume loop, before the true isovolumic phase, as has been shown experimentally (237), and is illustrated below (right).



Volume reduction due to pre ejection shortening. This movement can also be seen in displacement traces (below). This motion of the nitral ring would tend to displace the mitral eaflets towars the middle, and thus be a part of the closing mechanism. The mitral leaflets move towards the middle, and thus the displacement of the ring towards the apex is far less than the motion of the leaflets towards the base.
During isovolumic relaxation there is no filling, as both valves are closed, and hence, no downward motion. When relaxation (tension decrease) has progressed to the point where atrial and ventricular pressures equalise, the mitral valve opens, and the two filling phases follow. At the end of late filling (atrial systole), there is again equal pressures in atrium and ventricle, and no flow. The start of contraction will then lead to closure of the mitral valve, as they move in a stationary  blood column, they will be pushed toward the base and toward the middle. The motion of the leaflets is mainly lateral, i.e. towards the middle, and thus may be greater than the longitudinal displacement of the annulus.
This means that there should be a small volume decrease at end diastole, not due to any regirgiation, but due to the mitral annulus sliding along a stationar column of blood that then is "atrialised". Pressure volume loop with a small pre ejection or protosystolic volume reduction before IVC (P) according to this model. This shape of the pressure volume loop is in accordance with experimental data (173).

Thus, the initial velocity spike should be termed "pre ejection" or "proto systolic" spike, instead of "isovolumic".


This shortening would then stop abruptly at mitral closure. But this also may mean that the peak pre ejection velocity is dependent on the MVC closure, and thus be load dependent.


 During the IVC, there is no shortening, and hence, no velocity or acceleration. This is solely a function of the difference between the preload and the afterload, without afterload, there would be no IVC, the initial shortening would just continue into ejection, instead of taking time to increase pressure. This was shown experimentally by Remme et al (237), by stenting of the mitral valve, the initial velocities coninued directly into ejection- i.e. volume reduction. Thus, the MVC that causes a stop in the initial shortening, i.e. MVC does not cause the initial velocity spike per ce, but rather the drop in velocities after this spike.




Pre ejection period seen with tissue Doppler velocity (left) and motion (right). The start of ECG (grey vertical line) is seen to be slightly earlier than the start of the spike. This corresponds to the electromechanical dely, although the alignment of the elecrode may be less than perfect. The initial positive velocity line crossing the zero point and the corresponding onset of motion toward the apex is shown by the first vertical white line. This event precedes the mitral valve closure, markin gthe start of active contraction that generates the pressure increase closing the MV. (The MVC might correspond to the point where the motion line becomes horizontal, but the temporal resolution of this imagee may be too low). The ejection marks the next onset of positive velocity / motion (second white vertical line).



The true isovolumic contraction time (IVC)  is defined from MVC to the start of ejection. In this phase, there is no volume change, and, hence, should be no deformation. This phase it on the other hand, the period of most rapid pressure rise, peak dP/dT, which occurs during IVC (241). This represents the most rapid rate of force development (RFD), as there is no volume change, and may also be one correlate of contractility. However, as seen fom the length force relation above, this maximal force measure is not preload independent.



With ultra high frame rate tissue Doppler (268), this can be demonstrated. Both tissue Doppler and M-mode can be generated from RF data from the same cine loop, and by comparing them, the timing of MVC can be seen to come after the pre ejection spike. In a study of ten healthy subjects, time intervals from start of ECG to start of the initial pre ejection velocity spike in the septum was 22.7 ms, and from this to MVC was 29.6 ms (268). In the septum, there was actually two pre ejection spikes, in the lateral wall only one, and both were present also in atrial fribrillation without any atrial activity, showing both to be ventricular in origin. The presence of the double spike in the septum has been shown before in experimental equipment with high frame rate (270), but only in a figure, without any comments as the focus of the paper was different.


Ultra high frame rate tissue Doppler (about 1200 FPS) from the base of the septum a normal subject. The timing is evident, with ECG starting first, then the pre ejection velocity spike starting about 23 ms later, and then the mitral valve closure about 30 ms after this. This recording is from the septum, and as can be seen, in the septum there is a second spike before ejection starts. It can be seen to repeat from beat to beat. This was not present in the lateral wall. Image modified from (268).

It can be demonstrated by tissue Doppler, provided the frame rate is sufficiently high:

Tissue Doppler from basal septum of healthy subject. at 93 FPS, only ione pre ejection spike can be seen. By using narrow sector and maximum frame rate, it is possible to achieve 250 FPS, and here the pre ejection spike is evident. (That this is not a phenomenon of random noise can be seen, as the double spike is reproducible at the start of the next cycle.

It has been argued that the first velocity spike may represent recoil from atrial activation, and not ventricular contraction. But as the finding is present also in atrial fibrillation, it seems to be of ventricular origin, although with some modifications. But there may well recoil from atrial activity as well, as the following examples show:




Ultra high frame rate tissue Doppler  from the base of the septum a  subject with atrial fibrillation. Even with no atrial activity, there is the same pattern of double velocity spikes, showing them to be ventricular in origin. Image modified from (268). Ultra high frame rate tissue Doppler  from the base of the septum a  subject with 2nd degree AV block, as seen by the second P-wave following the first heartbeat, with no QRS nor ejection velocities. The atrial recoil can be seen as three velocity spikes (arrows), indicating that the mitral ring bounces. However, this is in a situation without LV myocardial tension. At start of the first heart cycle, there may be some fusion between atrial recoil and vetricular contraction as seen by the timing. this may be due to longer PQ time. Image modified from (268). Ultra high frame rate tissue Doppler  from the base of the septum a  subject with 1st degree AV block. (This is a highly trained, healthy subject, the AV block is physiological)Three spikes are seen before ejection (arrows). Here, the initial spike must be atrial recoil, coming before start of the the QRS, it cannot be ventricular i origin. Even the second spike may be atrial, or a fusion of an atrial bounce and ventricular contractioncontraction. Both middle and left images shows that there is atrial activity i the pre ejection phase, but that the visibility of this may be dependent on the PQ interval. in shorter PQ interval, the presence of ventricular tension may modify or abolish the atrial component. Image modified from (268).

The second spike is isovolumic, and present only in the septum:

Simultaneous recirdings with UHFR TDI from the septal (top) and lateral (bottom) base. Each recording consists of two velocity curves from two points along the Rx beam, with a distance of 1 cm. Green is the most basal. Thus, the offset between the curves represent the strain rate. The second spike seen in the septum, is not present in the lateral wall.

Thus the second velocity spike occurs during IVC, but most probably represent a rocking motion, possibly originating from interaction with the MVC, or with the right ventricle.

Another point is that the pre ejection spikes in the septum and lateral wall can be seen to be absolutely simultaneous. This is also in accordance with early electrophysiological studies that demonstrated simultaneous activation of the mid septum and mid lateral wall (350, 351).


In summary:

In conclusion:
  • The pre ejection spike represents start of active ventricular contraction, before the MVC. 
  • The pre ejection velocity spike is not isovolumic, it precedes MVC, and is probably the mechanism for the MVC itself.
    • The height of the pre ejection spike is probably preload dependent, as this will influence the point of MVC, and thus
    • The "isovolumic acceleration" is probably not a measure of left ventricular function at all.
  • There should be no velocities during IVC, as there is no volume change
  • The pre ejection spike is a combination of events.
    • There is some late effect from atrial contraction, as seen in 1. and 2. degree AV-block above, but this is not the full explanation, as the double spike is still present with atrial fibillation.


Thus, the sequence of events in the pre ejection phase should be somewhat like:

Normal electrical activation starts in mid septum. The whole of the left ventricle is then activated within 80 - 100 (120) ms (the duration of a normal QRS). Electromechanical delay at the cellular level is 20 - 30 ms (234, 268). Intitial contraction gives a small pressure rise which closes the mitral valve (236) about 30 ms after intial septal contraction (and thus without help of the lateral wall), and then the lateral wall will have to start contraction less than 40 ms after the septum. Thus, the start of the contraction of the lateral wall should be within 40 ms after start of septal contraction (the maximum duration of a normal Q-wave - septal activation before start of the R-wave - lateral activation). The electromechanical dely is assumed to be the same in all walls.


When is aortic valve opening in relation to tissue Doppler?






The geyser Strokkur at Haukadalir, Iceland at  pre eruption (pre ejection). In a geyser, the water is heated deep below the surface, at high pressures. Thus the water becomes superheated before it boils. when boiling, the column of steam will rise through the water, causing the water above to bulge (no isovolumic, then). To the left, the steam can be seen within that bulge, steam just beaking through the surface at one point. To the left, the steam breaks through, and the water is driven out both by the steam and the pressure below, resulting in the start of an eruption (ejection).



As ejection in fact is synonymous with volume reduction, this is basically trivial. AVO is at start ejection, and start ejection is at the start of rapid volume reduction, which corresponds with start of rapid AV-plane motion:







Aortic valve opening is at start of the outflow ...corresponding to the start of rapid reduction of ventricular volume as seen by the annulus velocity. 


The ejection period


Strokkur at start ejection, where water and steam is accelerated.


The ejection phase is the most visible phase of left ventricular systolic work, and thus the

As has been discussed above, only the first part of ejection is active contraction, the rest is actually relaxation. The normal mechanical sequence is as follows:
After mechanical activation, there is an intial shortening seen in the velocity traces as a positive spike of short duration - the pre ejection spike. This initial contraction gives a small pressure rise which closes the mitral valve (236) about 30 ms after initial septal contraction (268). The lateral wall starts slightly later,  but within 40 ms (maximum duration of the normal Q-wave - septal activation). 

AS the walls contract in parallel, they will give rise to isovolumic contraction where there is pressure increase without deformation, and then ejection when ventricular pressure exceeds aortic, the ejection phase is characterised by longitudinal shortening and wall thickening.

However, active contraction is in terms of force, and cannot be seen by deformation, as the continuing ejection will result in continuing shortening despite tension decrease. The development of active contraction do not continue during the whole of the ejection, tension decrease starts around mid ejection, probably at the time of peak pressure / peak strain rate, after this there is tension release. Thus, the tension buildup is an event of much shorter duration than ejection. After this there is still tension, although decreasing, during the last part of ejection the ejection is partly driven by inertia. Also, from the argument above, the rate of force development has to be declining from the point of peak dP/dt, although not as much as the rate of pressure increase. This means that the initial rise of velocities is the most active part of ejection, and indeed, the highest ejection force should be immediately after aortic valve opening (AVO). However, the acceleration of the blood volume takes some time, thus the peak velocities are delayed somewhat into the ejection phase. But peak ejection velocity and peak LV shortening velocity (S') is both seen to be very early events in ejection phase.

The ejection phase shows a rapid rise in both ejection flow and tissue velocities, with an early peak, and the slower decline. The peak ejection flow velocity is the the maximal rate of of shortening,  after the AVO. This should be the peak rate of volume decrease, although it is difficiult to align completely with peak systolic strain rate. The peak rate of annular displacement (annular velocity) is usually earlier, at least in the lateral wall, due to the early over all motion towards the apex.

Thus, the initial ejection / deformation velocity is closest to the maximal rate of force development. As force is related to acceleration, the initial rate of velocity increase might be a measure of contractility. However, not only shortening, but also rate of shortening is load dependent, and in this dynamic situation load is a function of both resistance and aortic compliance.


It is obvious that the LV shortening and the ejection are interrelated. In fact, the LV systolic shortening * the circumferential area should be aproximately equal to the stroke volume.


Stroke volume by Doppler flow velocity integral (VTI) and LVOT diameter. The diameter gives the area, and the velocity time integral gives the distance that an object travels if it follows that velocity curve (v =ds/dt, means that s =  v dt. Multiplied with each other, the area and VTI gives the volume of a cylinder, equal to the stroke volume.
Relation of stroke volume and LV shortening. The volume reduction is LV shortening * LV area at the mitral plane. As area is far higher, the distance is far smaller than the VTI.




Strokkur during ejection and immediately after. During ejection there is a water column that is ejected due to the pressre. At peak height, all the pressure is converted into potential energy. Afterwards, the height of the column decreases, water is still flowing due to inertia, but decelerating, and the flow rate and height decreaseing, at the end there is only the remaining steam column, active ejection is finished.


The apex beat



The apex beat is well known as a clinical event. The apex is pressed forwards and collides with the chest wall during systole, and marks the location of the cardiac apex on clinical examination.


The apex beat, shown here in a normal apexcardiogram demonstrating that the beat is a systolic event. (Image modified from Hurst: The Heart). AS can be seen, in this case the impiulse wave starts before the 1st heart sound, i.e. before MVC and the start of IVC.
The collision. Musk oxen, Grønnedal, Greenland


The apex beat has been characterised by apexcardiography, placing a pressure transducer above the apex, and recording the pressure trace, which then will be a function of the movement of the chest wall. The contraction, however, results in ventricular shortening. Unbalanced, this should logically tend to pull the apex away from the chest wall, being kept in place either by tethering or suction. In both cases this would result in an inverted apex curve.  This is discussed above. Thus, it seems that the main force responsible for pressing the apex toward the chest wall is the recoil from ejection, as discussed in the eggshell concept.



The systolic motion of the apex towards the chest wall, even displacing the tissue overlying the apex is visible in this normal echo.
....and can be visualised by the reconstructed M-mode from the same loop. The shape of the curve resembles the apexcardiogram above.


Using tissue Doppler, the initial velocity of the apex towards the chest wall, and the end systolic velocity away from the chest wall are both evident. Forward velocities can be seen to start about at the peak of QRS.
...and the integrated displacement curve shows the same shape as the M-mode above.

However, timing makes the situation more complex. As the anterior apical motion starts before ejection, the recoil mechanism cannot be the full explanation.

The apical motion starts at the same time as the pre ejection spike. At this point, however, there is no ejection, and hence no recoil (unless there is mitral regurgitation, of course). And midwall activation, would tend to pull the apex the other way. Thus, the initial apical motion must be due to some external impulse, probably the impact of the late filling wave from atrial contraction.




Doppler LVOT flow from the subject above. The ejection starts later than the QRS, and thus later than the start of apex beat.   Doppler mitral flow. The apex motion starts close to the end of the A-wave.
Reconstructed colour M-mode from the same person. The inflow during atrial systole can be seen to propagate all the way to the apex, and may be assumed to deliver an impact to the apical myocardium.

Thus it seems that the initial impetus for the apical anterior motion may be atrial filling. Thus, the effect may vary according to the atrial part of the total filling volume, the PQ-time, and factors affecting the flow propagation of the A-wave. However, as the atrial impetus is an event of short duration, the recoil of ejection may still be the main force that presses the apex towards the chest wall as seen below:



Combined image from another patient. In this patient apical motion starts before the QRS, and stops abruptly when the apex is pressed into the chest wall as far as it can go. The apex then stays pressed to the chest wall during the whole of the ejection phase.






Resolving the motion, we see that the anterior motion in this case starts even before the start of QRS (A). (The motion seen in the displacement curve starts below zero because the tracking is set at zero by the ECG marker). Peak forward velocity (B1) is just after the QRS, while the motion stops in systole (B2), but the apex remains in the anterior position. At end systole (by T-wave in ECG), there is the start of backward motion (C), and the apex returns to the diastolic position at D.
Comparing the apex tissue velocity with LVOT flow (aligned by ECG), both start and peak apical velocity occurs before start ejection, but continues into ejection. In this case, even a second peak may be seen starting at start ejection, indicating a second impetus from ejection recoil.
And for illustration the relation between apical displacement and ejection. Apical displacement starts before ejection, and then continues into ejection, and maximal apical displacement is close to peak ejection velocity. The apex remains pressed to the chest wall during most of ejection, until the flow velocity is so low as to not generate sufficient recoil pressure, while the full return to diastolic position is somewhat later.

The pre ejection spike in the base and midwall,  is active, the mechanics ot the pre ejection spike are discussed here.

But this means that while there is initial pre ejection contraction in the base and midwall, resulting the MVC as discussed above, this would tend to pull the apex away from the chest wall as there is no recoil force at that point. However, there is an impact from the blood coming nto the ventricle, which pushes the apex towards the chest wall already before the ejection as seen by the tissue Doppler. In stretch, this should mean that there has to be initial stretch of the apex during the pre ejectioon, simultaneous with shortening of the midwall and base.





Comparing this with basal velocities, we see that the anterior motion of the apex starts in the pre ejection phase. The basal pre ejection spike, however, reaches peak before the apex velocity, which peaks close to the time of start ejection (B), by the tissue Doppler curves. Backward apical motion starts a little before end ejection (C), while end of backward apical motion is well within the early filling phase (D)
Relation between apical and basal  displacement shows the same. Looking at strain rate, at the time of pre ejection, there is maximal apical velocity and there seems to be positive strain rate (stretch) in the apex, but negative strain rate (shortening) in the midwall and base, consistent with there being active pre ejection shortening, but the apex being stretched due to the A-wave impact.




Recordings from two different normal subjects, showing basal and midwall shortening during the pre ejection velocity spike, consistent with active contraction during this phase, while the apex shows stretch, consistent with passive motion of the apex, which may originate from the impact of the A-wave as suggested above. Looking at the early ejection phase, there is an early velocity spike which probably is due to recoil force as discussed above. The early ejection velocity spike can be seen to be progressively dampened from base to apex, as the apex of course cannot be accelerated, being already in contact with the chest wall. But this means higher (absolute) strain rate during early ejection (not to be confused with peak strain rate).


Colour M-modes shows the same, with pre ejection stretch in the apex, and highest absolute early compression in the apical part.

During early ejection there is thus an acceleration of the ventricle due to recoil from ejection. But as the apex is in contact with the chest wall, and cannot be accelerated by this. thus, the apex has to be compressed as shown above, meaning that there is passive compression in addition to active contraction in the apex. This means the shortening during the early ejection (not pre ejection) velocity spike is highest in the apex. However, this is before peak strain rate, and do not necessarily reflect the distribution of peak strain rate.

Delayed and prolonged apex beat can also be demonstrated by tissue Doppler:

Delayed and prolonged (heaving) apex beat in a patient with hypertrophy due to hypertension.

Global systolic function measures

As has been emphasised above, myocardial function is characterised by force (tension), while imaging is about shortening, which is force versus load.

In muscular physiology, it is customary to measure performance mainly in relation to two measures:
  • Rate of force development (RFD) and
  • maximal force
In resting heart examination, however, the myocardial performance is not necessarily maximal, so for physiological understanding, it will be more useful to speak about peak values:
  • Peak rate of force development and
  • Peak systolic force
The force/tension is mainly measured by the pressure that is developed, (although volume plays a role too, for any given pressure, the force is proportional to the surface area).

Still that means that myocardial function is closely related to:
  • Peak rate of pressure increase (which is peak dP/dt) and
  • Peak systolic pressure

Peak dP/dt

As force is related to pressure, peak rate of force development is at the time of peak rate of pressure increase; peak dP/dt. Peak dP/dt is before aortic opening (241), i.e. in the true isovolumic contraction phase. Thus, the force development is isometric. This also means that peak RFD is at a time where there is no shortening, and thus nothing can be seen by imaging at this point in time. There thus has to be a decline in the rate of force development already before aortic opening.



Exaggerated and simplified diagram of the pressure rise in IVC. The pressure curve in black is seen to be sigmoid. This follows by necessity, as the peak pressure rise (shown as the red tangent to the pressure curve (dotted line) as well as the thick red curve), is before the end of IVC.

Peak dP/dt will still be preload dependent, as the rate of tension development is load dependent. Also, however, preload has an opposite influence as contractile force increases with increasing myocyte length due to the Frank-Starling mechanism.

Peak pressure

However, the force continues to increase after Aortic valve opening, as aortic pressure increases as volume is ejected into the proximal aorta. This happens at a decreasing rate of force development. Peak pressure (and tension) is reached during ejection. The peak pressure is the maximal tension that the ventricle has to develop, to overcome the maximal impedance. Thus, it is dependent on the total load, but it is still a measure of the peak force, but not necessarily the contractility.


In imaging, however, the myocardial performance must be assessed from the volume changes, and thus from indices that occur during ejection. These, in one way or other relate to either:
  • Peak rate of systolic performance, which is related to peak rate of volume change, or
  • Total systolic work, which is related to end systole, and basically to stroke volume.
In both groups, the imaging indices disregard the load.


Peak systolic versus end systolic measures of ventricular function.

Peak systolic measures are the measures of peak ventricular performance, and are basically
  • peak ejection velocity in the LVOT,
  • peak annular systolic velocity, and
  • peak global ventricular strain rate.
These occur early in systole, and may be less load dependent, as maximum afterload is reached later in systole. They all occur during the first part of systole, and thus are more closely related to contractility, and especially to contractility changes, as shown in studies (78, 79, 80, 223).

All such studies are really studies in contractility changes, and thus, useful to separate contractile states, rather than measure contractility direct.

However, they are not completely load independent, as increased load will result in a delayed and blunted development of force and velocity, as opposed to the pressure/volume relation.


End systolic measures on the other side, are measures of the total work performed by the left ventricle during ejection. This is influenced not only by force, but also by load (resistance), and the ejection time (HR). They are
  • stroke volume,
  • Ejection fraction (and fractional shortening)
  • annular displacement and
  • global strain

There is, however, little evidence directly comparing displacement / strain to velocity / strain rate at varying load, and the few and small studies that are published seems to indicate a very similar load response. However,  increased contractility will not to the same degree lead to increased stroke volume, if there is no concomitant increase in venous return, as in inotropic stimulation. Thus stroke volume wil be maintained, but at a lower end diastolic volume. This means end systolic measures will be less sensitive to  contractility increase as discussed above (223).


Peak systolic annular velocity (S'), which is early systolic,  compared to peak annular displacement (MAPSE), which is end systolic. S' is actually the peak rate of annular displacement, and is thus closer to contractility, while MAPSE is end systolic and thus closer to ejection fraction.  Peak strain rate, being early systolic,  compared to peak strain, which is mainly end systolic, and closer even, to ejection fraction.


Most of the indices above have been studied, and are established as indices of ventricular function. However, in addition to they all being only imaging indices, they have different shortcomings, and to some degree slightly different interpretation physiologically.

Even LV elastance is an end systolic measure, although it is taken as the real contractility. This may be only in relation to volume, in fact.

Peak systolic measures - contractility indices

Even though contractility per se cannot be measured by imaging alone, the measurement can be approximated, but early systolic measures come close (78, 79, 80, 223).

Peak annular systolic velocity

Peak systolic velocity (S') was early validated as a measure of systolic function (37, 38, 39, 40). Peak annular velocity occurs early in systole, and may be less load dependent, as maximum afterload is reached later in systole. The peak velocity is taken as an average measure of two or four points around the mitral ring.



Pulsed tissue Doppler of the mitral ring.  These are the velocity traces of the longitudinal motion, while dividing by the end diastolic length results in the Lagrangian strain rate .
Age dependent peak systolic, early and late diastolic velocity in normals from the HUNT study (165). The early diastolic velocities are higher than the systolic, and the decline is thus steeper, but the relation is evident.

The peak systolic annular velocity is useful in that it is a better marker of systolic function than EF, and that it offers a measure that allows direct comparison of systolic and diastolic function.
as they are measured by the same method.

But there are some slight limitations:

1: Peak systolic velocity is not a direct measure of peak rate of shortening.

Even though it seems intuitive, the comparison with peak strain rate shows that there is a velocity component in the peak that is a global translational motion toward the apex as discussed above. This is due to the recoil force.


Peak velocities from the myocardial wall are shown in blue and green, showing parallel velocity curves at peak, thus identifying the velocity as translation, which do noe show in the difference (strain rate) curve (red).
Peak velocities along the septum, showing a slight blunting of the velocity peak in the apex. Even if there is a translational velocity, this will decrease in the apex where the myocardium is pressed into the chest wall. The strain rate curves corresponding to the regions between the velocity curves are shown below, indicating the this velocity is not the true deformation rate.


It might be argued that the recoil velocity is also generated by myocardial contraction, and represents a liberation of the work done during IVC. From this argument, peak velocity might be considered a fully legitimate measure of myocardial performance, maybe even more legitimate that peak rate of volume decrease.


2: Peak systolic velocity is not always simultaneous in all segments of the mitral annulus. 

The normal pattern of annular velocities varies in the normal subjects:




A fairly common pattern is a sharp peak in the lateral annulus (cyan), and a more rounded curve with a later peak velocity in the septum (yellow). Thus, the divergence of the curves in the initial ejection phase may represent a light tilting (rocking) of the apex toward the septum. A slightly different normal pattern where the initial peak in the lateral wall decelerates slightly, the accelerates again, giving a later second peak. The septum shows an even curve, but with peak velocity between the two peaks of the lateral wall.
In this case peak annular velocity is early and simultaneous in both walls.

The varying timing of the peaks is most probably due to different impact of the recoil force from ejection, creating a slight rocking motion of the whole heart. AS in the example to the left, this will mean that the lateral peak is exaggerated due to rocking, while the early septal velocity is blunted, and the later peak is due to this blunting.



The impact of the recoil momentum on the septal and lateral annulus will, of course, depend on the angle between the momentum vector (velocity vector), and the ventricular long axis. As the aortic opening is situated in the septal part of the LV base, the angle deviation, if any, can be expected to be towards the septum, delivering the highest impact laterally. This is in accordance with clinical observation, the peak is most consistently present in the lateral wall. However, the ejection from the right ventricle must also be taken into consideration, being nearly simultaneous, and with the same stroke volume (mass), only the difference in velocities will account for the difference in momentum. The pulmonary ostium is also situated medially, in front of the aortic, but often with less of an angle deviation. However, the angle will be opposite, and may counteract the aortic momentum.

Thus, both the actual value and the timing of peak systolic velocity can be dependent on the site where it is measured as shown above. This, of course means that the peak annular systolic velocity which is used as a systolic functional parameter, measured either as one site, or as an average, is an approximation, as the timing may differ between sites.

The correlation with EF is weaker than for MAPSE, which is not unsurprising, EF and MAPSE being end systolic measures, and as such measures of the total systolic work, S' is peak systolic, measuring peak systolic performance.




One of the main advantages of tissue velocities is that systolic and diastolic function are measured by the same method. From the beginning, systolic function by EF was compared to diastolic function by mitral flow, equivalent to comparing apples with bananas. This lead to the concept of pure diastolic dysfunction, which has later been shown to be erroneous (202).

The correlation between systolic function S' and diastolic function e* was found in an early study to be 0.6 over a wider range of ventricular function (201), and in the HUNT study (165)with a large number (N=1266) and limited to healthy subjects, the correlation was found to be 0.59.

The correlation reflects among other things, the physiological mechanism that much of the diastolic recoil is due to elastic stored energy from systolic contraction (restoring forces), but also, and most important: that systolic and diastolic function are closely related.




In another study (202) it was found that the systolic function by S' was reduced in patients with heart failure with normal ejection fraction. This led to a renaming of the state that up to then was called "diastolic heart failure" to "heart failure with normal ejection fraction". This, of course corrects the implied, but mistaken assumption that there existed a pure diastolic failure. However, it does not address the fundamental problem, which is one of methodology, that EF should not been used in normal sized or smaller ventricles.


The S' has been shown to be sensitive for reduced function in relatives who are mutation positive, of patients with manifest hypertrophic cardiomyopathy, despite having normal EF and no hypertrophy (203). The diastolic function by tissue Doppler was similarly decreased. It also correlates better with BNP in heart failure than the fractional shortening (204).

Thus, the peak systolic annular velocity is useful in that it is a better marker of systolic function, and that it offers a measure that allows direct comparison of systolic and diastolic function.
Where and how should measurements be done?



As the peak velocities are more often higher in the lateral than the medial, it is evident that the measurements are different if different sites are chosen. This can be seen from the HUNT study (165). This study consisted of  673 women with a mean BP of 127/71 ,mean age of 47,3 years and BMI of 25.8 and 623 men, with mean BP of 133/77, mean age of 50.6 and BMI of 26.5. Both sexes were normally distributed with an SD of 13.6 and 13.7 years, respectively. 20% of both sexes were current smokers. Basic echo findings  are in accordance with other studies, like the findings of Schirmer et al (156, 157), so the study population may be assumed to be representative.


Anterior
(Antero-)lateral
Inferior
(Infero-)septal
PwTDI S' (cm/s)
8.3 (1.9) 8.8 (1.8)
8.6 (1.4)
8.0 (1.2)
cTDI S' (cm/s)
6.5 (1.4)
7.0 (1.8)
6.9 (1.4)
6.3 (1.2)
Results from the HUNT study with normal values based on 1266 healthy individuals. Values are mean values (SD in parentheses). 

The maximal differences can be seen to be about 10% relative, with the highest values in the lateral wall, lowest in the septum. The reason for this, can be partly explained by the differences in length of the walls, seeing that the peak strain and strain rate varies much less.

The initial studies (37, 38, 39) used the average of four sites as a measure of global systolic function. In the HUNT study, however, there were no difference between the peak systolic velocity (S') mean of lateral and septal, and the mean of all four points. However, Thorstensen et al (154) did show that reproducibility was about 35% better using four point average (p<0.001), in line with what was found earlier (40), even if the mean values were the same.


The common method of measuring peak velocity at each point and then average the peak values from two or four point, is methodologically slightly unsound, as they may not be simultaneous:

Septal (yellow) and lateral (cyan) velocity curves from the fisrt subject above. Peak velocities are 6.25 cm/s septally and 7.6 cm/s laterally. Mean of peak values are thus 6.93 cm/s. The averaged curve of the two is shown in red, and the peak of the average is 6.67 cm/s. Difference here is small, but this may not always be the case.

The point from a puristic view is that if the peaks are not simultaneous, the mean peak velocity doesn't exist in real time (cfr. the peak-to-peak gradient of invasive aortic stenosis measurement). Still, the method has been established as useful, and normal values for the averages has been established (165). And, as in the example above, while the early peak in the lateral wall is exaggerated due to the rocking, the early septal velocity is blunted. The true peak translational velocity is seen in the average curve, and the true peak velocity is the peak of the average curve, not the average of the peaks.

The varying timing of the peaks is most probably due to different impact of the recoil force from ejection, creating a slight rocking motion of the whole heart. AS in the example to the left, this will mean that the lateral peak is exaggerated due to rocking, while the early septal velocity is blunted, and the later peak is due to this blunting.

In some cases, the rocking of the apex, even if the ventricle is normal may become completely misleading.





Rocking heart with normal ventricular function.
Peak velocities have totally different timing, and much of both of the peak components are due to translation.The septal peak has a component of rocking to the right, the lateral peak a component of rocking to the right, both may be overestimates.
As discussed above. In this case, the peak velocities should be viewed with skepticism as functional measures. The mean curve might give a more correct estimate, although this is not validated, and is not available in standard analysis software.

Using pulsed wave tissue Doppler, this is not an option, and curve averaging is not standard analysis software.

Normal values for systolic velocities of the right and left ventricle from the HUNT study.



Left ventricle, mean of 4 walls
Right ventricle (free wall)

S' (pw TDI)
S' cTDI
S' (pwTDI)
Females



< 40 years
8.9 (1.1)
7.2 ( 1.0)
13.0 (1.8)
40 - 60 years
8.1 (1.2)
6.5 (1.0)
12.4 (1.9)
> 60 years
7.2 (1.2)
5.7 (1.1)
11.8 (2.0)
All
8.2 (1.3)
6.6 (1.1)
12.5 (1.9)
Males



< 40 years
9.4 (1.4)
7.6 (1.2)
13.2 (2.0)
40 - 60 years
8.6 (1.3)
6.9 (1.3)
12.8 (2.2)
> 60 years
8.0 (1.3)
6.4 (1.2)
12.5 (2.3)
All
8.6 (1.4)
6.9 (1.3)
12.8 (2.2)
Annular velocities by sex and age. Values are mean (SD).  pwTDI: Pulsed Tissue Doppler recorded at the top of the spectrum with minimum gain, c TDI: colour TDI.  Normal range is customary defined as mean ± 2 SD.

The study is based on 1266 healthy individuals from the HUNT study by Dalen et al (165). The age dependency of values is evident. Colour tissue Doppler gives mean values, which are consistently lower than pulsed wave values, as discussed here. It is evident that the systolic values decline with age, as do the early diastolic.

It is important to realise that the peak values obtained by pw tissue Doppler are higher, due to the breadth of the spectrum, while colour tissue Doppler gives mean velocities, thus being modal velocities in the middle of the spectrum. However, peak values by spectral Doppler are affected by gain settings (increased gain - broader spectrum - higher peak values), while colour Doppler are affected by clutter (stationary reverberations - zero velocity - reduced average).



Same tissue Doppler recording with two different gain settings. We see that peak systolic velocity differs by 2 cm/s, and the lowest gain setting is closest to the modal velocity. However, the modal velocity itself, remains unchanged by the gain setting.
There is a band of clutter close to zero velocities, but as seen here, the spectral modality makes it very easy to separate the true and clutter velocities. However, the clutter affects the autocorrelation velocity (red line), giving lower velocities, but with clutter filter this effect is removed (blue line), and the peak value is substantially higher. Image modified from (268).


Peak acceleration (??)


As acceleration precedes velocity, and is at the time of peak rise of velocity, this should be slightly earlier than peak velocity, and thus even less load dependent, - at least afterload, preload dependency will still be present. Acceleration is also more closely related to peak force by Newton's second law (F = ma). In addition, if taking the peak velocity to be partly a function of the recoil, it is also caused by the pressure buildup, even more so than the peak velocity. Thus there are hypothetical advantages in relation to physics and physiology.

However, the concept is ill defined. Also, the temporal derivation of acceleration from velocity will result in a less favourable signal-to-noise ratio than the velocities.



Velocity curves from a normal subject. The initial peak acceleration may be defined by the slope of the tangent to the initial velocity curve. As illustrated, as the two curves from septum and lateral walls are different, this will result in different acceleration values. In addition, there can be different ways of defining the tangent:
  • A: The steepest slope of the lateral curve
  • B: The slope from nadir to the lateral curve peak
  • C: The steepest slope of the septal curve
  • D: The slope from nadir to the septal curve breakpoint
  • E: The slope from nadir to septal curve peak
All of them reasonable, but resulting in wildly different values (This is equal to a noise component as shown right)
Real-time temporal derivation of the two velocity curves. Due to the derivation, the curves are fairly noisy, especially taking into account the the velocity curves was somewhat smoothed at the outset. It is obvious that the peak values may be affected by the noise,  incorporating noise spikes. Averaging the septal and lateral points, still doesn't solve the noise problem. Also averaging can be done in two ways:
  • Mean of peak values, which in this case will be 186, and
  • Peak of mean curve, in this case 163
And in addition, curve derivation and averaging is not standard issue in analysis software.

At present, the peak acceleration is less useful, being
  • Closely related to peak velocity, as the peak velocity is determined by the rate of velocity rise,
  • In need of definition of concepts
  • Dependent on heavy post processing, and not standard analysis software
- while especially pw Tissue Doppler in the standard mode is a quick, robust and online method.


Peak systolic strain rate

Peak systolic strain rate is the peak rate of shortening. As explained above, this peak occurs later during the ejection phase than peak velocity, as the strain  rate algorithm subtracts the initial velocty peak, being translation, not deformation:





Examining one normal subject with early velocity peak in the lateral annulus:
Looking at velocities within the wall in base an apex, the biphasic pattern with an early peak can be seen in both points in the lateral wall.
Examining the strain rate from the entire walls between the apical and basal points no sign of a biphasic shortening can be seen, indicating that the lateral peak is only due to translation, the peak being subtracted. The peak strain rate is much later than peak velocity in both walls, as discussed above.


The slight rocking motion affecting the timing of peak velocities, means that there is no fixed relation between the timing of peak strain rate and peak velocity:




Early peak velocity on both sides. Slightly later peak strain rate in both walls.
Early lateral peak velocity. late septal; early septal peak strain rate, later lateral, mean peak strain rate later than mean peak velocity
Early lateral and later septal peak velocity, earlier lateral than septal peak strain rate, mean peak strain rate later than mean peak velocity.



Thus, peak strain rate is the true measure of peak deformation rate, i.e. peak rate of shortening. However, this does not mean that it is a truer measure of peak systolic performance, as the peak velocity incorporates the ejection recoil due to the isovolumic pressure buildup.

But basically, as volume change is generally are related to longitudinal shortening as discussed above, peak strain rate must be close to peak rate of volume reduction, i.e. peak emptying rate.

For global strain rate measures, the strain length as well as the ROI should be as long as possible to reduce noise (331) as shown in the above examples and discussed in the measurements section.

Thus, the peak strain rate should be more related to peak force than to peak rate of force development. However, in an experimental invasive study, Greenberg (80) found a stronger correlation between both dP/dt and LV elastance with strain rate than with systolic annular velocities.

Normal values are necessary if measurements are to be used diagnostically. In addition, they will give additional information about physiology. In the north Tröndelag population (HUNT) study, 1266 subjects without known heart disease, hypertension and diabetes were randomly selected from the total study population of 49 827, and subjects with clinically significant findings on echocardiography (a total of only 30) were excluded. (153) This is the largest normal population study of echocardiographic strain and strain rate rate to date. End systolic strain and peak systolic strain rate was measured by the combined tissue Doppler / speckle tracking segmental strain application of the Norwegian University of Science and Technology, but the results were compared to other methods in a subset of subjects, showing small differences. The study consisted of  673 women with a mean BP of 127/71 ,mean age of 47,3 years and BMI of 25.8 and 623 men, with mean BP of 133/77, mean age of 50.6 and BMI of 26.5. Both sexes were normally distributed with an SD of 13.6 and 13.7 years, respectively. 20% of both sexes were current smokers. Basic echo findings  are in accordance with other studies, like the findings of Schirmer et al (156, 157), so the study population may be assumed to be representative.

While differences between septum and lateral wall was of the order of 10% in velocities, in deformation parameters (153), the same difference was on the order of 4% in strain rate and only 1% (relative) in strain.


Anteroseptal
Anterior
(Antero-)lateral
Inferolateral
Inferior
(Infero-)septal
SR (s-1)
-0.99 (0.27) -1.02 (0.28)
-1.05 (0.28)
-1.07 (0.27)
-1.03 (0.26)
-1.01 (0.25)
Strain (%)
-16.0 (4.1) -16.8 (4.3)
-16.6 (4.1)
-16.5 (4.1)
-17.0 (4.0)
-16.8 (4.0)
Results from the HUNT study (153, 165) with normal values based on 1266 healthy individuals. Values are mean values (SD in parentheses).  The differences between walls are seen to be smaller in deformation parameters than in motion parameters, although still significant due to the large numbers.

Normal values for global strain and strain rate


Female
Male

End systolic strain (%)
Peak systolic strain rate
End systolic strain Peak systolic strain rate
< 40 years
-17.9% (2.1)
-1.09s-1 (0.12)
-16.8% (2.0)
-1.06s-1 (0.13)
40 - 60 years
-17.6% (2.1)
-1.06s-1 (0.13) -18.8% (2.2)
-1.01s-1 (0.12)
> 60 years
-15.9% (2.4)
-0.97s-1 (0.14) -15.5% (2.4)
-0.97s-1 (0.14)
Over all
-17.4% (2.3)
-1.05s-1 (0.13) -15.9% (2.3)
-1.01s-1 (0.13)
  Values are given as mean ( SD). The customary definition of normal values as mean ± 2SD, giving about 95% of the normal population, results in wider normal limits than previously shown as cut off values in small patient studies. The values were normally distributed, and with no clinically significant differences between levels or walls. Values decline with age, as does the velocity.



Normalised velocity(?)

As seen later, peak annular displacement can be normalised for left ventricular length to derive a measure of global longitudinal strain. But this doesn't necessarily mean that normalising velocity in the same way gives global strain rate. Assuming that annular velocity was the peak rate of ventricular shortening, normalising for end diastolic length would give peak Lagrangian strain rate, normalising for instantaneous systolic length would give the Eulerian strain rate. However, giving the difference in riming between the two curves, due to the translational velocity, this is not the case.



Basal velocity traces, and the velocity traces normalised for end diastolic ventricular length (Lagrangian normalisation), results in curves that resemble inverted velocity curves, with the same shape.
Comparing this with the real velocity / strain rate plots from the same subject, it is evident that strain rate curves have a different shape. (In fact, in this case the lateral strain rate curve is more rounded, the septal with an earlier and more defined peak, opposite of the velocity curves).

This means that in terms of curve shape and timing, there is no point in normalising the velocity curves, and the normalised velocity curves is still a slightly different measure than strain rate.


However, where there is a large variation in ventricular size, as in children it makes sense, giving age independent measures  (159, 214, 288). Strain rate is one form of size normalising, but using pulsed tissue Doppler, normalised velocity will make the velocity measurements useful in children of all ages.


Basically, peak strain rate is most useful for assessing regional function, where the motion due to tethering to neighboring segments needs to be subtracted n(although the effect of segment interaction remains). With uneven segmental contractility, the peak strain rate in different segments also becomes non simultaneous.

Peak ejection velocity

LVOT ejection velocity must be proportional to flow, as the LVOT diameter is considered constant. But this means that peak systolic velocity is actually a direct measure of peak volume reduction rate or peak emptying rate. And, as peak shortenoing rate (strain rate) is very close to peak emptying rate, this means that both measures are very close to measuring the same thing. THis was evident in a study where both measures did show a very similar change with chenges in contractile states (223).







In all four subjects, the peak velocity of LVOT flow seems to be relativelt simultaneous with peak strain rate, consistent with theory. Averaged curves might be even closer.

Thus, both theoretically, empirically and experimentally, the peak LVOT flow and peak global strain rate seems to be measuring very much the same event, even though indifferent measures.

But should peak LVOT velocity be normalised for heart size? Probably not, AS strain arte already is a norlmalisation for heart size, the flow velocity is dependent on LVOT diameter, whic increases with heart sise. So, the LVOT velocity is in a way a normalisation of peak flow.

Normal peak ejection velocities

From the HUNT study (165)



Females
Males
< 40 years 1.01 (0.17)
0.99 (0.17)
40 - 60 years 1.02 (0.16)
0.99 (0.18)
> 60 years 1.01 (0.17)
0.96 (0.18)
Over all 1.01 (0.16)
0.98 (0.18)
Values are given as mean ( SD). The customary definition of normal values as mean ± 2SD, giving about 95% of the normal population, results in wider normal limits than previously shown as cut off values in small patient studies.

The only difference is that peak values of peak ejection velocity do not decline with age. AS stroke volume gpoes down with ventricular volume by age, this must mean a corresponding reduction in LVOT diameter.



With the appearance of new methodology, a number of new methods for measuring left ventricular global function has emerged. Older measures has traditionally been measurements of the cavity function: Stroke volume, ejection fraction (and the M-mode equivalent shortening fraction). Newer methods include longitudinal measures of wall function, as annular displacement and velocity, as well as mean strain/strain rate, either based on segmental measurements, or a global averaging (as global strain form speckle tracking 2D strain). It should be of general interest to comment on the relationship between the methods. It is also important to realise that while strain and strain rate are measures of shortening per length unit, the annular velocity and displacement are also measures of the same, but in absolute values (i.e. not normalised for ventricular length). However, all measures that measure relations to changes, i.e. in paired experiments of load alterations, the normalisation will cancel out, and displacement will behave as strain, strain rate as velocity (more or less see difference between Eulerian and Lagrangian strain rate). Thus all experiments with systolic displacement and velocity in relation to global changes, will pertain also to strain and strain rate.

End systolic measures - systolic work indexes.


End systolic measures on the other side, are measures of the total work performed by the left ventricle during ejection. This is influenced not only by force, but also by load (resistance), and the ejection time (HR). They are
  • stroke volume,
  • Ejection fraction (and fractional shortening)
  • annular displacement and
  • global strain

There is, however, little evidence directly comparing displacement / strain to velocity / strain rate at varying load, and the few and small studies that are published seems to indicate a very similar load response. However,  increased contractility will not to the same degree lead to increased stroke volume, if there is no concomitant increase in venous return, as in inotropic stimulation. Thus stroke volume wil be maintained, but at a lower end diastolic volume. This means end systolic measures will be less sensitive to  contractility increase as discussed above (223).

Wall measurements - long axis systolic function.

Wall thickening is a measure of systolic deformation. It can be assessed semi quantitatively in B-mode. Wall motion score index (WMSI) by B.mode, being the  average of wall motion score  of all evaluable segments becomes a measure of  global function, and has been shown to correlate with EF in infarcted ventricles (40). It has also been shown to be similar in sensitivity to reduced function (and infarct size) to global strain (189). However, the index is useless unless there is regional differences. Any dilated cardiomyopathy will show hypokinesia in all segments, giving a WMSI of 2, regardless of EF.
Wall thickening measured in M-mode, however, is only available in limited segments, and can only be generalised to global measures if the ventricle is symmetric. In addition, as discussed above, the wall thickening is mainly a function of the long axis shortening, due to the incompressibility of the heart muscle.




Systolic long axis shortening

The systolic long axis function is measured by any means of any longitudinal motion or deformation. I.e. Long axis shortening measured by mitral annulus motion or global strain, or shortening velocity / rate by mitral annulus velocity or global strain rate.






It has been established that the longitudinal shortening of the left ventricle, and thus the longitudinal measures is closest related to the stroke volume and EF, i.e. to the total left ventricular volume change (30 - 35, 56, 59, 60, 64 - 67, 116).
Longitudinal systolic strain of the left ventricle is shortening, normalised for diastolic length (similar to EF, which is volume decrease (stroke volume) normalised for end diastolic volume). As longitudinal shortening describes most of the actual ejection work, , there is a strong relation between EF and longitudinal strain. Thus, it may seem that the longitudinal fibres (or force components) are the main contributors to the ejection work, i.e. the isotonic part of the work.

Mitral annular systolic displacement




Long axis shortening of the ventricle equals the mitral annular systolic displacement. Longitudinal M-mode through the mitral ring, displaying the displacement of the mitral ring. The total systolic displacement (MAPSE; mitral annular plane systolic excursion) can be measured.  If  the MAPSE is divided by the end diastolic length of the ventricle (which, in fact is a spatial derivation), it will give a measure of the strain of the wall. The global strain of the left ventricle is an average of more points of the wall. The longitudinal (Lagrangian) strain during systole is thus MAPSE /LD.



Mitral annular plane systolic displacement or excursion (MAPSE), and mitral annular systolic velocities, are measurements of total ventricular shortening and shortening velocity:





The annular measurements reflect the total shortening of the ventricle, and are thus measures of global longitudinal function.

The mitral annular systolic descent has had many names: The mitral annular excursion (MAE) (31, 35, 37, 40) has been used for a long time. Atrioventricular plane descent (AVPD) (30, 32, 34, 36) is incorrect, as the term also comprises the tricuspid part, and while tricuspid displacement and velocity can be measured (and is higher than in the left ventricle) , it is usually measured only in one point, and the relative weights for the measurements is unclear.

However, the term TAPSE for the tricuspid systolic annular excursion has been firmly established. In order to remain consistent in nomenclature, the corresponding term MAPSE for Mitral Annular Plane Systolic Excursion is in increasing use. Thus, it might be the best term, and it still retains the specificity that AVPD lacks.

The longitudinal shortening has been shown to be very closely related to ejection fraction when comparing different patients with normal or reduced left ventricular function (30, 31, 32, 34, 35, 36, 40, 64), as illustrated below:


When the left ventricle dilates, the volume increases, and the stroke volume can be maintained by a smaller fraction (Ejection fraction) of the total (end diastolic) volume. At the same time, the cross sectional area increases, so the volume can be maintained by a smaller stroke length. 

The relation between MAPSE and EF has shown a correlation of 80 - 90%. However, the relation only holds in dilated ventricles. In normal ventricles, the MAPSE is related to the stroke volume (59, 60, 116). In left ventricular hypertrophy, the MAPSE is reduced despite preserved EF, and there is no correlation (190).

In addition, the MAPSE is reduced in ventricles with normal ejection fraction , the so-called HFNEF (191), i.e. despite normal ejection fraction. 

The annular displacement has been shown to be more sensitive than EF in predicting events in heart failure (36, 192) and hypertension (193), indicating that it is a more precise measure of systolic function, that the cavity measurements. This may be due to the shortcoming of EF in small ventricles / hypertrophy. There is also a trend towards a better correlation with infarct size than EF (150).

Also, the MAPSE correlates better with BNP in heart failure, that the fractional shortening (204).

Thus, the MAPSE is a more all round useful measure of longitudinal function than EF.

There has been some arguments for measuring MAPSE only during ejection, i.e. excluding the isovolumic phases (194). The value will be a little lower, and the main advantage seems to be that post systolic shortening, not being part of the systolic work, will be eliminated.


Systolic annular displacement of the septal point. There is a small shortening in the isovolumic contraction phase (IVC), and post systolic motion (PSM) after AVC, so the systolic MAE is lower than the total MAE.

However, the total shortening is probably related to the total ventricular size. This means that small ventricles has a lower MAPSE, even if similar in relation to the total length. This also means a lower stroke volume, of course, from a smaller ventricle. So the relation MAPSE x cross sectional area = SV still holds. However, this means that some of the variations in MAPSE are due to heart size, not heart function, which mans that the relation with heart function has a reduced explained variance. Theoretically, this means that the annular displacement should be normalised for heart size, which also is the case when using global strain instead, being relative shortening. This is definitely necessary in children (159, 214, 288), where the varation in heart size is great, the advantage in adults, where variation in heart size is less (and less than the difference betweeen normal and pathological) is not documented.

Where should measurements be done?
As the displacement is higher in the lateral than the medial, it is evident that the measurements are different if different sites are chosen. All studies have used the average of four points: septal and lateral in the four chamber view, and anterior and inferior in the two-chamber view. Thus the average is fairly robust, representing a global average. However, the main reason for using four points would be to reduce variability (which is reduced by about 25% by using four points instead of one (40). In addition, regional differences due to regional dysfunction may be evened out,, however, we found that ring motion was reduced in all points in localised infarcts (40).



Global strain

Global strain and strain rate, may be taken as global measures of ventricular function. This can be achieved simply by measuring and averaging the strain/strain rate in all segments of the ventricle.  However, there is one caveat:
Commercial software may give segmental values for six segments in each  imaging plane, resulting in a total of 18 segmental values. However, this results in equal weight given to all myocardial levels, despite there being much less myocardium in the apical level. In order to ensure that the average value gives similar weight to all parts of the myocardium, only four segments in the apical level should be included, as recommended by ASE/EAE (146). If not, the global measures may be misleading. (This is doubtful in the global strain measurement by 2D strain). The global strain by this application also is somewhat processing dependent, as discussed below.

Strain and strain rate, however should not be normalised for body size. Both measures are deformation per length, i.e. in fact normalised already for the size of the ventricle. Further normalisation for body size (which in fact is a correlate of healthy heart size), will then be erroneous. This is analogous to the fact that EF, which is stroke volume normalised to end diastolic volume, is never normalised again for BSA.

Global strain by speckle tracking has been introduced as a new measure of global left ventricular function (147). This compensates for the shortcomings of ejection fraction, being both more correct in the case of small or hypertrophic ventricles, and more sensitive (149). In the 2D strain application, it should be noted that the application relies heavily on the AV plane motion, and then distributes the motion along the wall as explained and shown above. By this method, regional artifacts as drop outs and reverberations will have less impact, which is an advantage in measuring global function. (As it may be a disadvantage in regional function, as the same smoothing may reduce the sensitivity to regional reduced function).

It is unclear whether this application actually corrects for the reduced amount of myocardium in the apex, giving at the outset 6 segments per view, or 18 segments in total. Bull's eye plots seem to show 17 segments, but whether this is carried over to the calculation of global strain is uncertain.

Global longitudinal strain by this method, has shown a trend to be more sensitive to infarct size and correlate better with infarct mass than EF. Global longitudinal strain is thus a measure of wall shortening, normalised for the length of the wall, as length is measured along the curvature. Whether this allows sufficiently for the reduced amount of myocardium in the apex, seems unclear, as the referred study included 33 anterior and only 7 inferior infarcts. Annulus displacement had a slightly less diagnostic accuracy than global strain, but whether this was significant is less clear. Normalising the annular displacement for LV length (see below), did not show ovious improvement in diagnostic ability, in this group (150). However, annular displacement normalised for LV length IS a measure of longitudinal strain. Recent studies in children has shown normalised displacement to be an age independent measure of systolic performance (159, 214, 288), i.e. in the instance where the variation in LV size is greatest in the normals.

Thus, it is emerging evidence that global strain, adds incremental value to the simple AV-plane motion (159). This is credible, some of the variability in MAPSE will be due to differences in LV size, and normalising will remove this variability and give a tighter relation to pumping parameters normalised for body size, and thus a higher diagnostic discriminatory value. This probably has most importance when normal variations in body and heart size is biggest (as in children) and least importance where normal variability is lower, and variation between normal and pathological is great (as in dilated heart failure). None of the methods for normalisation, however, have established superiority.


Normal systolic strain values

Normal values are necessary if measurements are to be used diagnostically. In addition, they will give additional information about physiology. In the north Tröndelag population (HUNT) study, 1266 subjects without known heart disease, hypertension and diabetes were randomly selected from the total study population of 49 827, and subjects with clinically significant findings on echocardiography (a total of only 30) were excluded. (153) This is the largest normal population study of echocardiographic strain and strain rate rate to date. End systolic strain and peak systolic strain rate was measured by the combined tissue Doppler / speckle tracking segmental strain application of the Norwegian University of Science and Technology, but the results were compared to other methods in a subset of subjects, showing small differences. The study consisted of  673 women with a mean BP of 127/71 ,mean age of 47,3 years and BMI of 25.8 and 623 men, with mean BP of 133/77, mean age of 50.6 and BMI of 26.5. Both sexes were normally distributed with an SD of 13.6 and 13.7 years, respectively. 20% of both sexes were current smokers. Basic echo findings  are in accordance with other studies, like the findings of Schirmer et al (156, 157), so the study population may be assumed to be representative.





Normal values for left ventricular strain and strain rate from the HUNT study



Female
Male

End systolic strain (%)
Peak systolic strain rate
End systolic strain Peak systolic strain rate
< 40 years
-17.9% (2.1)
-1.09s-1 (0.12)
-16.8% (2.0)
-1.06s-1 (0.13)
40 - 60 years
-17.6% (2.1)
-1.06s-1 (0.13) -18.8% (2.2)
-1.01s-1 (0.12)
> 60 years
-15.9% (2.4)
-0.97s-1 (0.14) -15.5% (2.4)
-0.97s-1 (0.14)
Over all
-17.4% (2.3)
-1.05s-1 (0.13) -15.9% (2.3)
-1.01s-1 (0.13)
 
Values are given as mean ( SD). The customary definition of normal values as mean ± 2SD, giving about 95% of the normal population, results in wider normal limits than previously shown as cut off values in small patient studies. The values were normally distributed, and with no clinically significant differences between levels or walls. Values decline with age, as does the velocity.


Normalised displacement.



Both annular displacement (MAPSE) and annular systolic velocity can be normalised for (divided by) the length of the ventricle.  


Systolic strain is normalised MAPSE. The normalised MAPSE for this ventricle with an end diastolic length of 9.2 cm and an MAPSEE of 15 mm is 15 / 92  = 16.3. THis corresponds to a longitudinal strain of -16.3%. Compare with global strain, in this case the global strain was 16.1%, giving a good comparison. However, the two methods are different, as this method normalises for the length of the curved wall, and the actual values are dependent on the curvature (especially in the apex) of the segments.






Mitral annular dexcursion can be measured by B-mode, M-mode or tissue Doppler:



MAPSE by M-mode. In this case the MAPSE was 14 mm in the septal site and 16 mm in the lateral, giving an average of 15.
MAPSE by tissue Doppler showing an MAPSE of about 15 mm.






Diastolic and systolic images of the heart. Systolic shortening of the left ventricle relative to diastolic length, is the systolic strain of the ventricle.  The longitudinal strain during systole is thus:

However, it is also evident that as the wall shortens, it also thickens, to conserve the volume. Heart muscle is generally assumed to be incompressible.
Strain being (L - L0) / L0 may still not be unambiguous, as shown below. Both the strain length, L0 and the shortening (L - L0) will be different when measured along a skewed line (red) and even longer along a line following the wall curvature (blue).  As both strain length and shortening increase when the curved line is used, the ratio will not be as affected,  but still, L0 will increase more than than the shortening.


It's thus important to realise that different applications may measure strain in different ways.





The normalised annular displacement will be a measure of the global strain, making it less dependent on ventricular size (and thus, body size). Recent studies in children has shown normalised displacement to be an age independent measure of systolic performance (159, 214, 288), i.e. in the instance where the variation in LV size is greatest in the normals. The study in children (159) did show better correlation with EF over a wide range of pathology and age. In a small study in normal adults, it has shown better correlation with EF (217), which may be an indication that it removes variability due to LV size. However, introducing another measure (LV length) will increase the measurement variability of the composite parameter, and thus, the advantege is still unclear.

Thus, it is emerging evidence that normalisation of MAPSE, adds incremental value to the simple AV-plane motion. This is credible, some of the variability in MAE will be due to differences in LV size, and normalising will remove this variability and give a tighter relation to pumping parameters normalised for body size, and thus a higher diagnostic discriminatory value. This probably has most importance when normal variations in body and heart size is biggest (as in children) and least importance where normal variability is lower, and variation between normal and pathological is great (as in dilated heart failure). None of the methods for normalisation, however, have established superiority, and whether normalisation in adults gives better results, remains to be proven. (Firstly, because it increases measurement variability, and secondly because the differences in pathology may be greater than the differences in ventricular size in adults.







Cavity measurements of systolic function


Fractional shortening

As M-mode was the first echo modality, the fractional shortening of the LV cavity was the first LV systolic functional measure by echo. The fractional shortening is defined as FS = (LVIDD - LVIDS)/LVIDD thus, in fact being an one-dimensional version of EF. Diameter is conventionally measured to the endocardium, so the fractional shortening is more precisely the endocardional fractional shortening. It's less accurate than the EF when there is regional dysfunction, as the measured fractional shortening will be generalised to the whole ventricle. It is quite common to measure longitudinal strain, i.e. wall or segment shortening as a measure of longitudinal function. On the other hand the fractional shortening of the chamber diameter is a well established measure of global and radial function. But in the case of hypertrophy, this may lead to completely erroneous conclusions about the changes in radial versus global function, as shown in the theoretical treatment below.

The relation between wall thickening and fractional shortening is ilustrated below:


In this theoretical M-mode of the LV, a normal ventricle has a wall thickness of 1 cm, an internal end diastolic chamber diameter (EDD) of 4 cm, resulting in an external diameter of 6 cm. As most of the wall thickening is inward, with little change in outward diameter (except in the case of differing filling pressures on the two sides), an end systolic wall thickness of 1.5 cm will result in a diameter shortening of 1 cm and an end systolic chamber diameter of 3 cm. Thus, wall thickening (WT, transmural strain) is (1.5 cm - 1 cm) / 1 cm = 50%, chamber diameter reduction is 1 cm, fractional shortening (FS) is (4 cm - 3 cm) / 4 cm = 25%. Thus, if wall thickening decreases due to reduced myocardial function, so do fractional shortening as seen in the middle figure. And if there is dilation as well, the denominator will increase, resulting in further reduction in FSas an inverse function of the diameter. In LV dilation, there is usually a combination of increased diameter and reduced wall thickening.


The erroneous comparison between longitudinal strain and fractional shortening:

The incompressibility principle tells us that as the wall shortens in the longitudinal and circumferential direction, it has to thicken in the transverse direction, and the relation is geometrically determined. Thus the longitudinal and transverse function as measured by strain should be interrelated. Reports about radial compensation of reduced longitudinal function is in direct opposition to the incompressibility principle.  The problem arises if we do not measure the same values for longitudinal and radial function.

Compared to the normal example to the left,  in the case of concentric hypertrophy as in the middle, the chamber diameter is reduced due to increased wall thickness.  A hypertrophy leading to a wall thickness of 1.5 cm, will give an EDD of 3 cm. A systolic wall thickening of  0.5 cm will then be (2 cm - 1.5 cm) / 1.5 cm = 33%; i.e. a clear reduction in radial function. But 1 cm diameter shortening  is FS = (3 cm - 2 cm) / 3 cm = 33%, an apparent  increase in radial function, due to geometrical misconception! In concentric remodelling (right), the diameter is reduced. In the case of heart failure with reduced myocardial function, (reduced wall thickening), the diameter reduction may cause the FS to be normal, despite the reduced radial function.

From the reasoning above, any conclusions about radial function based on fractional shortening in the presence of hypertrophy may be erroneous, and the term radial function needs to be defined. The conclusion that there is radial compensation for reduced longitudinal function should be reserved to the cases where WT is increased (If this is possible, it seems theoretically impossible, as the reduced longitudinal shortening should correspond to reduced wall thickening due to incompressibility).

It is extremely important that if longitudinal and "radial function" are compared, care should be taken that the measurements are comparable. To compare for instance fractional shortening of the LV diameter with longitudinal strain (wall shortening), is comparing two different measures, and may lead to completely erroneous conclusions as shown above, where fractional shortening increases but wall thickening decreases.

 as the same erroneous results will be obtained by the fractional shortening as of EF, as shown below.

And this shows that fractional shortening is not a true measure of "radial function".


Patient with concentric hypertrophy. Looking at the cavity, the systolic function may appear fair.





Wall thickness 17 mm, EDD 40 mm, Fractional shortening was 35%, however, wall thickening only 28%





Ejection fraction

Based on Nuclear or X-ray contrast studies, the first measures was measurements of cavity reduction in systole, i.e. the stroke volume. While this may be the most important result of cardiac pumping, it confers little information about the state of the heart itself. A dilated ventricle can maintain stroke volume, but it is reduced in terms of the left ventricle volume, and may have a severely reduced contractility. Thus stroke volume should be normalised for end diastolic volume, to obtain Ejection fraction:

Ejection fraction is still the most widely used measure of systolic left ventricular function today. This is mainly due to the vast amount of prognostic information from earlier studies, and the prognostic interventions that are geared to a cut off point in EF. Even so, EF has been shown to be a poor prognosticator even in heart failure, when patients without dilation is included (227). In assessing EF, it should be emphasized, however, that EF is not a direct measure of myocardial function, as it measures the cavity, not the myocardial deformation. At best, it could be characterised as an indirect measure. Does this matter? Yes. If we look at a few examples:

Again, the cavity approach works very well in dilated hearts, but not in eccentric hypertrophy:


Classic view of ejection fraction. In a dilated ventricle (right), with thin wall, both wall thickening and longitudinal shortening are reduced. The cavity volume is increased, so the EF is reduced, even if the stroke volume may be maintained. As the ventricle dilates crosswise, the stroke volume is maintained with a shorter MAPSE, thus the longitudinal strain is also reduced, as shown below.

As we see, in dilated ventricles, there is a correlation between longitudinal shortening and EF, as explained below. However, this correlation is not present in hypertrophic ventricles (190). But this is due to the fact that in concentric geometry (hypertophy or remodelling) EF doesn't measure systolic function at all.

The erroneous use of EF in concentric geometry.

concentric geometry, EF will not give true measures of systolic function at all!


In concentric hypertrophy (middle), as often seen in pressure overload, the wall may be thickened, and the cavity volume is usually reduced.

Concentric hypertrophy reduces the cavity volume. Absolute wall thickening may often be preserved, while relative wall thickening is reduced as in the example of rectional shortening above. Then the longitudinal shrtening will also be reduced. I have pointed this out concerning fractional shortening as seen above, the reasoning was taken further into three dimensions by MacIver (228). EF has been shown to be more related to absolute than relative wall thickening (229), and  may be unchanged or even increased, but stroke volume is reduced, which also indicates systolic dysfunction. This is the same finding as above.


The same patient as above. EDV about 100 ml, EF about 55%. Again the systolic function may appear normal, looking only at the cavity. However, looking at long axis shortening, it appears severely depressed.


- which is confirmed, systolic mitral annular excursion is 5 mm and peak systolic annular velocity is < 3 cm/s


In concentric remodelling, as in the atrophy of ageing, where LV mass is unchanged. but ventricle size is reduced, the EF will fare just as poorly. Wall thickness may be unchanged or increased, but as the myocardial mass/volume is reduced less than cavity size, the myocardial wall / cavity volume ratio is decreased. Again, stroke volume is reduced, EF may be normal. Absolute wall thickening may be reduced, but relative wall thickening more, and the longitudinal shortening is reduced in proportin to relative wall thickening.

The annular displacement has been shown to be more sensitive than EF in predicting events in heart failure (36, 192) and hypertension (193).
But alas, interventional studies using echocardiography as secondary outcome, persists in using only EF, instead of including newer measures for direct comparison of the ability in predicting clinical outcome as well as establishing cut off values for intervention, as studies are driven by investigators with little knowledge of echocardiography. This is illustrated below.


Normal left ventricle
Dilated left ventricle
Concentric hypertrophy
Concentric remodelling

Diastole
Systole
Diastole Systole Diastole Systole Diastole Systole
LV length (cm) 9.5
7.7
11
9.8
11
10.6
8.5
7.8
LV outer diameter (cm) 6.0
5.7
7.5
7.1
6.5
6.18
4.5
4.2
Wall thickness (cm)
0.95
1.43
0.6
0.7
1.7
2.0
0.95
1.2
LV Inner diameter (cm) 5.1
4.1
6.3
5.7
3.1
2.1
2.6
1.9
LV cavity volume
123
78
228
167
55
24
30
15
Stroke volume (ml)

45

61

31

15
Ejection fraction (%)

62

27

56

51
Fractional shortening (%)

30

10

32

27
Wall thickening (%)
50

20

20

25
Longitudinal shortening (%)

21

10

3

8


15

7

14

13
All measures are calculated from a geometrical model of a half ellipsoid with wall thickness in the apex being half of the sides, all measures are calculated from the input measures of LV length, outer diameter, wall thickness and wall thickening.

While cavity parameters are preserved or even increased in the concentric geometry, all systolic wall deformation measures (longitudinal, circumferential and transmural strain)are reduced.

It has been shown by speckle tracking observational studies in various hypertrophic states, that all three pricipal strain may be reduced, whil ejection fraction is preserved (230, 231, 232, 233).


Thus, the EF or FS is a measure that actually only works with dilation of the ventricles and becomes erroneous in the cases of reduced EDV. EF is a geometrical concept, and only works in some geometries.  Asd both the modelling and the sudies cited above shows, the systolic finction may be reduced in all directions despite a normal EF. Because this has been poorly  recognised, it has lead to some fairly bizarre results. As systolic function has been measured by EF, and diastolic function with mitral flow parameters, the hypothesis of "isolated diastolic heart failure" has been proposed. At the outset, measuring systolic and diastolic function by different measures with different sensitivity, is methodological nonsense in any case.

This has been realised, ad the term is now substituted with the term "Heart failure with normal  or prteserved ejection fraction" (HFNEF or HFPEF).

But as EF as a measure of systolic function in the case of small, hypertrophic ventricles is meaningless, the concepts are still dubious, the emphasis of an erroneously normal EF remains.

The problem with both strain AND EF in eccentric hypertrophy

In eccentric hypertrophy, the problem reverses, but in this case it even affects strain. Basically, in eccentric hypertrophy, the VV mass increases, but hte wall cavity ratio remains normal (146). This means that the ventricle enlarges mainly outwards, but as a more or less normally thick wall (at least relative) surrounds a much larger cavity, the mass has to increase. This is seen in different states:

  1. As compensation for volume load in valvular regurgitation. In this case, the end diastolic volume increases, but so does the total stroke volume. In this case the EF remains normal or even super normal. The strains can thus also be expected to remain normal as long as myocardial function is.
  2. In athletes heart. In this case there is eccentric hypertrophy in response to endureance training, i.e. the demands on the ventricle during near maximal performance. The ventricle increases both in diameter and length, and hence, in end diastolic volume.

Diagram illustrating how eccentric hypertophy, with a larger ventricle with normal wall thickness, will show reduced shortening fraction due to the larger denominator, even if wall thickening is normal. (Same wall thickening, larger end diastolic diameter, same absolute, but less relative diameter shortening). The finding will be the same in three dimensions, a larger ventricle with normal strains will still show reduced EF, even if stroke volume remains the same (Larger EDV, same stroke volume = same absolute, but less relative  volume reduction; i.e. lower EF). This, however, is an over simplification, unchanged stroke volume in a larger ventricle will show reduced strains as discussed below.

As long as stroke volume remains constant, the absolute wall thickening and shortenings (strains) will also remain constant, but the relative wall shortening will be less due to a longer ventricle (i.we. lower longitudinal strain). As relative wall shortening decreases, this may be seen to give a lower wall thickening as well, as the two are interrelated due to the incompressibility principle. If the wall thickening is unchanged in terms of absolute amount of wall thickening, the thickening is spread over a larger surface of a longer and wider ventricle, and thus is reduced in terms of relative wall thickening. And in fact in a larger ventricle, even absolute wall thickening may be reduced, as a lower amount of wall thickening wil result in the same volume reduction when spread over a larger surface.

Thus; in eccentric hypertrophy, the strains will decrease, even with unchanged stroke volume.






Eccentric hypertrophy with unchanged stroke volume. In the larger ventricle to the left, the same stroke volume as to the right, can be maintained by a smaller longitudinal shortening (MAE) due to the wider ventricle as explained here. This will result in a lower longitudinal strain. And the strain is even more reduced as this smaller MAE is relative to a greater LV length.  But less longitudinal shortening will also result in less wall thickening, thus all strain are reduced. However, even this is still an over simplification, as this is reasoned without the compensatory regulatory mechanisms.
Thus, with an increased EDV and unchanged stroke volume, the EF and FS may be reduced, and so may strains, due to the larger ventricle.


However, athletes usually have downregulated heart rate as well,  which increases diastolic filling, and thus the stroke volume. In the intact body, the cardiac output is regulated according to the circulatory need, by both autonomic balance and other vasoactive and volume regulatory mechanisms affecting both filling and resistance, contractility and heart rate simultaneously.

This means that athletes at rest (having no need of increased resting cardiac output - only of increased cardiac output reserve) will have unchanged cardiac output, a larger LV, with lower heart rate and increased stroke volume. But as this is a result of a lower sympathetic tone, the ejection fraction and strains may still be reduced, although to a lesser degree than if HR was unchanged, and may be unpredictable.

For evaluation of systolic myocardial function in eccentric hypertrophy, myocardial systolic velocities or strain rate would be more appropriate, although the litterature is fairly scarce, at least in comparing with normals. At least, the rate of shortening should be less affected by the total stroke volume, but afterload may still be a confounder, in general athletes may have lower blood pressure, but also a lower sympathetic tone.



When is aortic valve closure in relation to the events seen in echo?

The timing of end systole is crucial to defining end systolic strain, especially in the cases of post systolic shortening. End systole is often defined as end ejection, as defined by the aortic valve closure (AVC), as shown in the diagrams above. The end ejection is easily seen in Doppler flow recordings from the LVOT, by the aortic valve click, as described here, and shown below.


Recordings from LVOT (bottom left - 62 FPS) and mitral annulus (bottom right - 60 FPS)) with closing and opening of aortic and mitral valves marked and measured. The analysis software has then transferred the events to the tissue Doppler analysis (63 FPS), and the basal protodiastolic spike can be consistently seen before AVC.




Parasternal recordings of the aortic valve can also identify the AVC, but due to the longitudinal motion of the heart, the aortic valve often moves out of the M-mode line in end systole. However, at the present stage of technology, Doppler flow recordings must still be taken separately from B-mode recordings, with or without tissue Doppler data. By transferring the AVC from a Doppler flow recording the heart rate variability may lead to errors in the estimate of the AVC, as the ejection time is proportional to the total cycle length (RR - interval) (29).  The ECG has a low precision in timing end systole, and regression equations based on heart cycle length has limited validity as the relation between RR interval and ejection time is not linear, at least not over the full range of heart rates (29). By interfacing a phonocardiograph with the scanner, the timing of valve closures can be done in all recordings. However, low level noise may lead to small errors in detecting the earliest part of the first heart sound, and so the phono should be calibrated by Doppler.

Apical recording of Doppler flow of the LVOT. At end ejection, the valve click can easily be seen as the short spike. This is coincident with the start of the phonocardiographic first heart sound as seen by the phonocardiogram.  However,  in the last heart cycle, there can be seen  a small oscillation earlier in the others, a small noise spike (red arrow). Thus the Doppler is the gold standard, and the phono has to be calibrated.

Or by M-mode of the aortic valve, as seen below, although this is less feasible due to out-of line-motion as we have shown (168), and which is evident from the images below.



Parasternal long axis of the aortic valve, Due to the longitudinal motion of the base of the heart, the valve has moved out of the M-mode line at end ejection, and the AVC cannot be seen.
But this recording was done with tissue Doppler superposed, and turning on the colour reveals the valve click as a vertical blue line (marked by the yellow arrow). The visibility in tissue Doppler is due to the broader beams and different filter setting of tissue Doppler compared to the B-mode.

But for the purpose of timing tissue Doppler events, all of these methods depend on transferring the event from one recorded heart cycle to another, and heart rate variability reduces the accuracy of this method for timing. Thus, for tissue Doppler analysis, the timepoint should be identified in the same heart cycle as the analysis is done.

Tissue velocity can also identify the valve closure in the aortic valve if the valve is present in the image itself. This is due to the fact that the valve moves with the velocity of the blood during opening and closure, which is ten times higher than the tissue velocity, as seen here.


Aortic valve closure seen by tissue Doppler in long axis view. The AVC is identified by the start of rapid positive velocities (toward the probe/apex) in the sample volume in teh LVOT. (Blood velocites are filtered out by the low amplitude as explained here. (The rapd upstroke is not an aliasing of the high downward velocities seen imidiately before, this can be seen as the shift from negative to positive occurs at lower velocities than the peak negative velocity in the a' wave, which doesn't aliase)


Thus the problem seems trivial, but only in apical long axis views. (In five chamber views as well, but not in proper four chamber views). But this still necessitates transferring the AVC timing from one cycle to another for analysis in other views.

The event of aortic valve closure in other views, however, could be identified from the tissue velocity waveforms themselves, if they are related directly to the event.


The tissue velocity traces shows a small and short negative spike at end ejection. This was early assumed to be the isovolumic relaxation resulting in a shape change of the left ventricle. In fact, it was something "everybody" seemed to know. The AVC was thus assumed to be at the start of this spike by various authors. This negative event can also be seen in colour M-modes of tissue Doppler, both in the mitral ring and the mitral leaflet. The negative spike will then correspond to a narrow blue (negative colour) band, and the AVC was assumed to be at the start of this band. This has even been published as a method for determining the timing of AVC in tissue Doppler images. This is illustrated below.



Short, negative velocity spike at end ejection. This has erroneously been assumed to be isovolumic relaxation, and hence, AVC at the start of the spike.
The negative spike corresponds to the vertical narrow blue band (blue = negative velocity) and perpetuating the mistake, the AVC would be at the start of this blue band as marked by the black arrow.


However, as one knows that the relaxation, meaning decline in tension during the last half of ejection, as discussed above, (the last half of ejection flow/volume reduction/longitudinal shorterneng being due to inertia of the blood) it is evident that at the point of no ejection flow, there has to be some elongation of the ventricle as well. In an early observational study (16) of high frame rate, we saw that this took place in mid septum before the valve click of aortic closure.

Locating the AVC by this assumption, the method of tracing an M-mode across the anterior mitral leaflet has been published. However, still with AVC as the onset of the early diastolic negative spike. Colour strain rate M-mode from the septum of a normal subject. It is evident that there is an elongation in mid septum, resulting in initial negative velocities in mid and basal septum before closure of the aortic valve. Notice also how the initial elongation of the mid septum occurs before the closure of the aortic valve, i.e. the initial negative velocities in the basal and mid septum are protodiastolic.




It is thus conceivable that there is a small elongation at end ejection that stops abruptly with the AVC, which is a sharp, mechanical event. This can be seen in both parasternal m-modes of the septum, as well as longitudinal M-modes of the mitral ring and mitral ring displacement traces.




Well known finding of a systolic "notch" in the septum in systole. This corresponds to a slight thinning of the septum with an abrupt stop.
Displacement curve of the septal mitral ring. (The same can be seen in septal M-mode). It can be seen that there is a short motion away from the probe, corresponding to the negative velocity spike at end ejection. The motion stops abruptly, and there is a slight "bounce" before mitral opening leads to another downward motion.

Using first phono that was calibrated by Doppler, we were able to show that the observation by strain rate imaging was actually true. AVC was in fact at the end of the negative spike, where velocities crossed back from negative to positive, i. e. corresponding to the "notch" in the mitral ring motion (168). Although for practical purposes, the automated algorithm identifies the point of maximum acceleration, which is very close. Later we used a 
scanner that was modified to acquire B-mode and tissue Doppler alternating in an 1:1 pattern, and in narrow sector of the septum giving a frame rate of close to 150, imaging both the base of the septum and the aortic valve at the same time  in 5-chamber and long axis views.  Here, the  actual closure of the AVC could be identified  with a temporal resolution of about 7 ms. The study confirmed the previous findings (169), and, repeating the study in infarction patients and in high frame rate during stress echo, showed the finding to hold true (170) also outside the normal range.


Thus, end ejection can be reliably identified by Tissue Doppler tracings from the septum, both in relation to Doppler flow and Phono (168), to very high frame rate B-mode (169) in both normal ventricles, ventricles during high heart rate and ventricles with ischemia infarct sequelae (170). This can thus be done in the same acquisitions as the tissue Doppler recordings, without having to transfer from a different recording. However, in mechanical asynchrony from other causes, this is more dubious (289)

By experience, this is probably not feasible in conduction abnormalities nor pacing, as discussed below. That has also recently been shown (289). The main point in the studies (168, 169, 170), however, was mainly to elicit the mechanisms for aortic valve closure, and to correct much cited, but mistaken suppositions that the IVC was the initial negative velocity of the tracings, i.e. to elicit the physiology.
Thus, the initial negative spike is a protodiastolic event, the continuation of relaxation into the phase after the final shortening, as shown below. It is not a measure of isovolumic relaxation. However, this still means that the AVC can be identifies as a mechanical event without recourse to the flow curves or direct visualization of the aortic valve.


Correct positioning of the AVC by tissue Doppler of the septal mitral ring is where the protodiastolic negative velocity spike crosses zero, and becomes positive.





The AVC should preferably be located from the basal septal traces, as the closure of the aortic valve is a mechanical event that propagates through the myocardium, and thus will be slightly later with increasing distance from the aortic valve (towards apex and in the lateral wall), as shown by high frame rate TDI (172).







Placing the AVC event marker, shows the protodiastolic negative velocities to be present in the basal and midwall segments (yellow and cyan curve), but not in the apex (red curve).  Converting the dataset to a curved M-mode, the spike corresponds to the narrow blue band, and the zero crossing to the shift from blue to red.
Keeping the event marker, but converting to displacement, wee see the "notch" in the basal (yellow) curve, and the AVC is the bottom of the notch where there is an abrupt change from downward to upward motion, thus the change from negative to positive velocities.


Using ultra high frame rate tissue Doppler, however, we have been able to show that the AVC as measured by the acceleration of tissue velocities, are not simultaneous through the wall. The point of peak acelleration has a definite propagation velocity of ca 5 m/s (268), corresponding to the propagation velocity of a shear wave in similar tissue, and with a delay of about 8 ms from septum to lateral wall (172).



Propagation of mechanical wave along septum, as visualised by ultra high frame rate TDI. The wave is identified by the peak positive acceleration in each point, showing this to be earliest in the base, lowest near the apex. The orange frame shows the velocity curves, the blue frame the acceleration curves. Image courtesy of Svein Arne Aase, modified from (172). Point of peak acelleration can also be shown by this method to be later in the lateral wall than in the septum. Image courtesy of Svein Arne Aase, modified from (172).



The propagation velocity can be measured by colour M-mode. In this case, positive acceleration is shown in red, negative acceleration in blue. Left are the relation of acceleration visualisation in colour M-mode to the heart cycle, right an magnification of the end ejection, illustrating how propagation velocity  can be measured, in the same way as strain rate propagation. Image modified from (268).

This propagation has been demonstrated earlier (269), but not with commercial equipment.

How do this correspond to strain rate?


Keeping the event marker in place, but converting to strain rate and strain. Now it can be seen that there is an elongation only in the midwall (cyan curve). The finding of negative velocities in the base as well, is due to tethering, and shows how deformation imaging has a better spatial resolution in separating events in space. The protodiastolic phase cannot be seen in the traces from the base, only in the mid wall and in the M-mode as seen below. Strain rate traces shows a generally complex pattern and are little suited to location of AVC. In strain curves, however, AVC can again be seen as a "notch" (as in displacement), most evident in the midwall (cyan) trace.
Strain rate M-mode. If AVC should be placed by strain rate traces, it can only be located from the M-mode or the midwall trace, just after the initial elongation, but strain rate traces shows a generally complex pattern and are little suited to location of AVC. M-mode is far better.

Thus: three things are evident:
  1. Looking at elongation, there is an initial elongation in the midwall before the AVC. This has some bearings on the mechanism for the aortic valve closing as shown in the illustration below. This results in negative velocities in the basal half of the septum.
  2. The AVC can be located in most traces (provided a sufficiently high frame rate), without transferring data from a Doppler or phono recording, preferably in the septum, and most easily in the basal segments of motion traces or the midwall segments of the deformation traces.
  3. The midwall elongation (resulting in the post ejection negative spike) is not "strain during IVR", and deformation is mainly present in midwall, and the amplitude is position dependent.



Proposed mechanism for the aortic closure. During ejection the ventricle can be seen to shorten, and there is ejection (arrow), keeping the cusps open. Ejection is  decreasing towards the end of the ejection period, as shown by the decreasing length of the arrow. At end ejection, there is no flow, and the relaxation that started during ejection as a reduction in tension, leads to a slight elongation (blue arrows). The aortic cusps then are closed due to the valve motion in the now stationary blood column, similar to what happens if a scoop is put into the water (opening forward) from a boat that is moving forward. In this case, the motion of the cusps are mainly lateral, i.e. towards the middle, and thus may be greater than the longitudinal displacement of the annulus.

The annulus motion stops when the cusps close, there being no further room for backward motion. This leads to an abrupt stop in the motion of the base of the heart, and a small "bounce", which is what's seen in the motion traces above. (The "bounce" is not depicted in the animation.)
But this mechanism also should lead to there being a small volume increase of the LV at end ejection, protodiastolic volume increase (P); due to the motion of the AV plane. This, again is not due to regurgitation, just the point that the aortic annulus "grabs" a small volume by moving around a immobile column of blood. This shape of the pressure volume loop again is in accordance with experimental findings (173).





This model of early relaxation was later confirmed by a combined experimental and theoretical analysis (173), although the interaction with the blood column was not specified, and the load dependency of early diastolic tissue velocity was taken to mean that the load (filling pressure) was part of the mechanism for ventricular elongation (enlargement), although this is doubtful, considering that the pressure in the ventricle actually drops during early diastole as discussed below.




The complete pressure volume curve as shown above.
The full heart cycle according to this model. During ejection the ventricle can be seen to shorten, and there is ejection (arrow), keeping the cusps open. Ejection is  decreasing towards the end of the ejection period, as shown by the decreasing length of the arrow. At end ejection, there is no flow, and the relaxation that started during ejection as a reduction in tension, leads to a slight elongation (blue arrows). The aortic cusps then are closed due to the valve motion in the now stationary blood column. The annulus motion stops when the cusps close, there being no further room for backward motion. This leads to an abrupt stop in the motion of the base of the heart.

During isovolumic relaxation there is no filling, as both valves are closed, and hence, no downward motion. When relaxation (tension decrease) has progressed to the point where atrial and ventricular pressures equalise, the mitral valve opens, and the two filling phases follow. At the end of late filling (atrial systole), there is again equal pressures in atrium and ventricle, and no flow. The start of contraction will then lead to closure of the mitral valve, as they move in a stationary  blood column, they will be pushed toward the base and toward the middle. Motion again will stop when the valve is closed, and the isovolumic contraction follows untill aortic valve oipens and ejection starts.
Thus, the complete heart cycle as seen with tissue Doppler. The pre ejection period statrs with electromechanical delay, and then early shortening which close the mitral valve. Mitral valve closure (MVC) would then, according to this model at the abrupt stop of the initial apical motion, i.e. where the pre ejection spikke crosses the zero line. The isovolumic contraction is then the period till massive apical motion when there is ejection. Protodiastolic lengthening closes the aortic valve closure, which then is at the abrupt stop at the basally directed motion, i.e. when the velocity spike crosses zero.




Regional systolic function

The regional systolic function is traditionally shown as wall motion score:
  1. Normal
  2. hypokinetic
  3. Akinetic
  4. Dyskinetic
Wall motion score index (WMSI), being the  average of wall motion score  of all evaluable segments becomes a measure of  global function, and has been shown to correlate with EF in infarcted ventricles (40). However, the index is useless unless there is regional differences. Any dilated cardiomyopathy will show hypokinesia in all segments, giving a WMSI of 2, regardless of EF. Thus, wall motion score is useful only in regional dysfunction. 

Segmental division of the left ventricle. The segments are related to different vascular territories, as shown by the colours. After Lang et al (146).  However, in the figure given in that paper, the apicolateral segment is given as Cx or LAD, while the apical inferolateral is not, despite the model is only giving four segements in the apex.  Thus, there is a slight inconsistency.



This segmental model gives a longitudinal resolution of the model of about 3 cm, and a circumferential of 60°, which may be considered low. However, in relation to vascular territories, it seems sufficient, and deformation rate measurements with higher resolutions (which are possible with both speckle tracking and tissue Doppler) have not so far demonstrated added clinical value.

16, 17 or 18 segments?

It has been an issue of discussion how many segments the left ventricle should be divided into. As there are different recommendation, and the reasons for the recommendations are partly historical, they are reviewed. The original ASE recommendation was six segments in the base and midwall, but only four in the apex (239). The reason for this was that the three standard planes were visualised as the apical four- and two-chamber planes, but the parasternal long axis. AS apical segments were not seen in most parasternal windows, there was only four segments, and the lateral and inferolateral and likewise the septal and anteroseptal segments were considered the same.

In an attempt to harmonise nuclear and echo imaging terminology (240), an apical "cap" segment was added, giving a total of 17. This, however is due to the thickness that is vuisualised in nuclear myocardial images, while the wall in the apex in reality is very thin, and is in fact only useful in perfusion studies.

In the present ASE/EAE consensus recommendation (146), this is commented on, and there is no direct recommendation on using 17 segments. On the contrary, it says explicitly: "When using this 17-segment model to assess wall motion or regional strain, the 17th segment (the apical cap) should not be included. A 16 segment model can be used, without the apical cap, as described in an ASE 1989 document."

The present standards paper for deformation imaging (287), specifically states that 17 segments, (including an apical cap) "is not recommended for functional imaging as the apical cap does not contract".

At present, using three standard apical planes, the approach will result in 18 segments. For segmental analysis, this doesn't matter, and we have used that approach in the HUNT study (153), giving normal values for each wall and level. However, for global function calculated as an average of segmental values, 18 segments is incorrect (146). the amount of myocardium in the apical level is less, and should be weighted less, as the 16 segment model will do automatically. For this we have reduced the number of segments by averaging the the lateral and inferolateral segmental values and likewise the septal and anteroseptal segmental values before calculating the global average of 16 (153, 223).



It is regional systolic dysfunction the deformation imaging has it's main use, as it makes it possible to differentiate between passive motion due to tethering and active contraction. Longitudinal strain can give the wall motion score by parametric imaging . It has been shown to give about the same infrmatin as wall thickening by B-mode (6, 7).


Segment interaction

To fully appreciate the deformation patterns in regional dysfunction, the concept of segment interaction (meaning that segments pull on each other) must be considered.


Brown skua, Deception Island, (South Shetland Isles), Antarctica.

The segment interaction is important to understand all kinds of deformation patterns showing, not only in ischemia, but also in other kinds of asynchronia as well.


Thus Segment interaction within the AV-plane leads to the specific patterns of regional dysfunction. This includes both delayed onset of shortening/intitial stretch, systolic hypo-/a-/dyskinesia, and post systolic shortening, which all are part of the same mechanism. This also shows that which has be shown in studies, mitral annulus motion will not give information about regional function. Post systolic shortening is thus not an isolated event, but part of the total pattern in ischemia, but on the other hand is not limited to ischemia, being seen both in left bundle banch block and hypertrophy.


1: Segments interact within the framework of the AVplane.

The mitral ring is stiff, each segment does not move independently.Not only are the segments around the mitral ring closely bound together, thus excluding the possibility of each segment moving independently, but the mitral ring itself is part of the whole AV plane, consisting of the connected rings of the pulmonary artery,  the aorta, the mitral and the tricuspid valves. There is no isolated mitral ring, the ring is simply part of the much bigger fibrous AV plane, and thus even  the possibility of the ring tilting as each wall functions differently, is severely restricted. :





The AV plane. It consists of a fibrous plane connecting the rings of the pulmonary artery (PA),  the aorta (Ao), the Mitral (MV) and the tricuspid (TV) valves, and surrounded by the muscular base of the heart. The sections of the mitral ring cannot be seen as indepndently moving structures. Thus, segments will interact within this framework. And both ventricles move the AV plane. (It might seem to be slightly flexible, as the motion of the tricuspid corner (tapse) is higher than the mitral motion, but still the palne will move as a whole, even if there is some deformation. The velocities of the lateral left wall are higher than the septum, but this is due to the longer wall, as discussed above. The overall systolic motion is not so different.

From the understanding that the AV plane is a rigid frame, the segment-segment interaction is necessary to understand the effects of regional function measured by deformation imaging.

2: Load is more than pressure, segment interation forces is part of segmental load.

Looking at longitudinal function, the concept of load is not limited to the simple model of Laplace, as it should include the effect of segment interaction (forces).


Diagram of longitudinal segment interaction. the longitudinal shortening of one segment results in shortening of the segment itself (orange arrows), but also in motion (red arrows) of the segments basally to it. (In this illustration, the red arrows show the motion of the middle of the segment, meaning that it also included the effect of the shortening of the apical half of the segment itself.)and the motion of each segment is equal to the summation of the shortening of the segments apically.  However, the primary effect is force generation. And this means that contraction in one segment results in a force applied to the neighboring segments. This force has different effects, as the apex is considered anchored (by the recoil force), while the midwall segment has force applied from both sides, and the basal segment is freely movable.  The main point is that the force from neighboring segments may be considered part of the load of each segment, and that motion is secondary to deformation, but deformation is secondary to force and load.

Thus segments can be seen pulling at each other, and the relative shortening (sgtrain) is dependent on the relative strength.


When doing imaging, the parameter is always shortening, and shortening is the result of both contractility and load:




In contraction, the muscle will increase tension, but resulting in no shortening as long as the tension is below the total load (isometric contraction). When tension equals load, further contraction will result in shortening at constant tension (isotonic contraction). This is what we see in imaging.
However an increasing  load will both delay onset of shortening, as the development of higher tension takes longer time, but will also result in less shortening, as well as a lower initial rate of shortening.  In these diagrams, the effect of load in slowing relaxation(224) is not shown. This effect would show up in prolanged duration of the downslope in the tension diagram. However, the lengthening phase would still be shortened by the load.
Reduced contracility will give a slower tension development and lower peak tension. However, this has the same effect as increased load on shortening, resulting in delay in onset of shortening, lower rate of initial shortening and less total shortening. Thus, reduced contractility would also have effect on relaxation (224), seen in the tensin curves, but this is not shown here.



Thus, differences in contractility will affect both normal and pathological segments, but differently:






Symmetrical forces in all segments, will result in symmetrical shortening. Thus, all segments shorten equally (orange colour), which means that the base moves most (the sum of shortening of all segments), as the apex is stationary.
Loss of contractility in a basal segment (smaller black arrows in the left basal segment), results in less shortening in the affected segment. However, this means that the load on the more apical segment is reduced, and thus, this segment will shorten more Red colur9 , not due to hypercontractility, but to less load. Also, the total force acting on the base is reduced, resulting in reduced total shortening (smaller red arrows in the base).
Even more reduced tension in a basal segment will result in the segment actually stretching, while the apical segment shortens even more in response to the basal segment stretches. This will not result in reduced motion of the regional mitral ring point, mainly a shift in the distribution of shorteningbetween segments, and a reduced global shortening.
Reduced tension and stretch of an apical segment may result in increased shortening of the opposing wall, as well as the basal segment, but this may result in a rocking of the apex toward the healthy wall. 
Symmetrical weakening of the apical segments, may result in increased shortening of the basal segments, but as the apex stretches, the motion of the AV-plane is more reduced.


3: Thus, annular measures do not give regional information.

As strain and strain rate are noisy methods, it is an attractive thought thay annular measures (annular systolic displacement or velocity) will give some regional information, in that points on the mitral ring close to a hypo- or akinetic area will show reduced motion, while remote points will not.

 However, this is definitely not the case, as we showed already in 2003 (40).

In a study of 19 infarct patients versus 19 control subjects, we found that while global function was reduced in patients, the variability between the difference between annular points was not:


Mean

EF (%) WMSI
MAE(mm)
S' (cm/s pwTDI) S' (cm/s cTDI) Segmental SRs (s-1)
Patients: 41
1.6
1.2
7.7
4.8
1.0
Controls: 55*
1*
1.6*
9.9*
7.6*
1.4*


Mean intra subject variation (max - min)
Patients:

0.41
2.8
2.5
1.6
Controls:

0.41
3.4
2.8
1.0*

Thus, no ring measures showed increased variability in infarct patients who had regional dysfunction. Only the segmental measure of strain rate did show that, despite having the highest variability. Moreover, in the patients; there were no differences between the magnitude of ring measures close to the infarct, compared to the measures remote from the infarct:


MAE(mm) S' (cm/s pwTDI) S' (cm/s cTDI) Segmental SRs (s-1) Mean SRs (s-1) per wall
Close:
1.2
7.7
4.9
0.8
1.0
Remote:
1.2
7.2
5.1
1.1*
1.1

The mitral ring motion were reduced in infarct patients compared to controls, and more reduced in anterior than in inferior infarcts due to the difference in infarct size.Thus, it can not be inferred that the point on the ring close to the infarct can identify the affected wall.Oonly the segmental measure did show difference between close and remote points, while the ring measures did not. And finally, averaging all three segments in a wall, resulting in a wall measure equivalent to the ring measures, made this difference disappear. This means that ring measures all are global measures, local reduction of contractility will affect segmental shortening, but not local ring motion. The global systolic motion of the ring is a measure of the infarct size (32), being reduced in proportion to the total amount of longitudinal fibre loss (210). Segmental reduced function will not cause the ring to lag in part of the circumference, however, the total ring motion will be reduced as a function of the reduced total shortening force. This may explain why the global strain is just as useful as regional strain in assessing the infarct size (205).

Motion is global function, only deformation can be regional.

As shown above, motion parameters will thus always reflect global function, only deformation parameters can show regional function.

In studies of the course of infarcts (92, 188), it has been shown that as there is initial hypo- to akinesia in infarcted segments, there is corresponding hyperkinesia in neighbouring non infartcted segments. As contractility in infarct segments improve due to recovery of the stunning part of the injury, the resiproke hyperkinesia will regress as illustrated below.



Strain rate of an inferior infarct at day 1, showing akinesia in the basal segment (yellow curve) and hyperkinesia in the apex (blue curve). The hyperkiesia can be explained by the load reduction due to the lack of force from the infarcted segment. (Image courtesy of Charlotte Björk Ingul). The same patient at day 7. Function in the basal segment (yellow curve) can be seen to be nearly normalised, and the shortening of the apical segment (blue curve) is correspondingly reduced.  (Image courtesy of Charlotte Björk Ingul).


The hypothesis of the regional effects on the mitral ring is thus disproved by anatomy, by the load dependency of regional deformation and by studies (40, 92, 188)


There is no regional reduction of mitral motion in regional dysfunction.
Only global reduction of mitral motion, and segmental hypokiesia with resiprocal hyperkinesia.



This can be seen both in systolic and diastolic function. The myocardium moves within the stiff framework of the annular plane and the "eggshell", but within this, there are differences in deformation, both in amount and timing, which will lead to segments deforming differentially.

Thus, as deformation is a result of tension, or rather tension versus load, strain does not measure function directly. But the effect of the force from neighbouring segments is part of load. Taking regional function into the concept of load, deformation imaging can be used to infer force, or at least inequalities in force developmen. This means that regional deformation is closer to contractility than global measures, which are dependent on absolute load. And that is the main point in regional diagnosis.


4: Regional circumferential and transmural strain

Regional circumferential and transmural strain may be sensitive indicators of infarct, but as discussed earlier, they will to a great degree be affected by geometry, not only layer function.

As discussed earlier, the circumferential strain is a funcrtion of wall thickening, causing the midwall line to shift inwards and thus shorten, not a measure of circumferential fibre function. At least in ischemia, if there is differential myocardial function, the reduction will always be most severe in the endocardial layer. However, in the case of reduced endocardial function, there will mainly be reduced transmural and circumferential strain due to reduced thickening (and hence, reduced circumferential shortening because of reduced inward circumferential shift, and not to the same degree due to reduced circumferential force. In that case reduced endocardial circumferential strain is a function of geometry. If there is reduced circumferential strength as well, as in more transmural ischemia which will affect the midwall circumferential fibres, resulting an an imbalance of forces equivalent to what is seen in the longitudinal direction. Thus there will be decreased load on the normal segments which may shorten more, stretching the affected segment, depending on the degree of stiffness. This is illustrated below:







Circumferential strain in a symmetrical ventricle model. For simplicity, the wall is divided into two layers. As the wall thickens, there is thickening and inward shift of the midwall line of both layers, but the innermost layer is in addition shifted inwards, cusing both a greater wall thickening (due to lack of room), and a greater midwall circumferential strain, both due to this, and due to the inward displacement of the innermost layer due to thickening of the outer layer. Akinesia of the inner (sub endocardial) layer. In this case there will be normal wall thickening and cicumferential shortening of the outer layer, and almost no thickening of the inner layer. Still, there will be inward shift of the inner layer due to thickening of the outer, this will reduce the space and may cause some thickening even without function. Mainly due to inward shift, there will still be midwall circumferential shortening of the inner layer. Reduced circumferential strength in a segment, will result in the normal segments contracing more (due to reduced regional circumferential load, and the affected segment may stretch. In that case this will also result in thinning, as the segmental volume stretches.


Thus circumferential and transmural strain will be much more profoundly affected by the transmurality of the infarct, as shown in an observational study (262), as in this case the circumferential tension is recuced. Some authors have found a higher sensitivity for transmurality by circumferential than longitudinal strain (221), which may be in accordance with this model. The interesting thing is that for identifying non-transmural infarction, the accuracy was highest for endocardial circumferential strain, and lowest for epicardial strain, with total wall thickness circumferential strain was in between (263). For identification of transmural infarcts, epicardial circumferential strain was more accurate, while accuracy of endocadial and total wall circumferential strain was lower and similar (263). This is in accordance with the model, but also confirms that circumferential strain analysis seems to be  feasible in clinical analysis. Whether layer strain will increase over all accuracy, compared to over all strain, needs to be confirmed by more studies.


5: Differences in segmental function changes segmental interaction and timing of segmental deformation

This results in specific patterns seen in ischemia.
There are fundamental anatomical and physiological reasons for this

The load dependency of deformation parameters, as well as the understanding of load as partly the global load (determined by the radius of curvature and the intracavitary pressure), and the regional load, being dependent on the force from neighbouring segements, is the basis for the differences in systolic deformation. Thus the main point is that deformation parameters are load dependent. But this means that if the contractility in one segment is reduced, the part of the load of neighbour segments that is caused by the contraction from that segment, is reduced.  This lead to increased deformation of neighbouring segments, due to reduced load - without any increase in contractility, and, concomitantly, the affected segment will show reduced deformation.  The global loss of contractility by a regional process (as ischemia or infarction) will reduce the global deformation, and within the ventricle the regional deformation will reflect the inequalities of force development (contractility). Thus, regional loss of contractility may be inferred from the reduced regional deformation.



The full deformation pattern in acute ischemia was shown early in the experimental work of Tennant and Wiggers (46):


Figure modified from (46), the time course of segmental myocardial deformation after acute LAD occlusion. The deformation (myogram) curves have been inverted to orient them as customary for strain curves today. Thus, the sequence starts at the bottom with A, and progression of ischemia is upwards, following the letters to the left. The numbers to the right, denotes the number of heartbeats after occlusion. As we see, in A there is a normal strain curve, the first change is an abbreviation (B) of the duration, and then delayed onset and reduction of the magnitude systolic strain (D), followed by initial systolic stretch and an increasing post systolic shortening peak (E-G). At the end, the systolic stretch lasts through systole - i.e. holosystolic stretch, but with post systolic shortening that exceeds the amount of systolic stretch )H-J), and finally there is virtually only passive stretch and recoil (K). Myocardial ischemia in the LAD area during dobutamine stress echo shown by the strain curves. The different colours of the curves correspond to differently placed ROIs in the lateral apex (cyan), septal apex (yellow) and basal septum (red). To correspond to the image to the left, the time course of ischemia is from bottom to top, so the four panels are baseline (bottom, then 10ug dobutamine/kg/min, then twenty, and finally 30 at the top.  The different regions have different degree of ischemia during the stress. At baseline there is slight post systolic shortening in the apical lateral part, increasing ischemia at 10 ug where there is initial akinesia (even a little stretch), reduced systolic shortening and finally post systolic shortening. This is similar to stage F at the left. At 20 ug there is initial stretch, systolic akinesia and post systolic shortening in the apicolateral segment, increasing to holosystolic stretch and post systolic shortening at peak, corresponding to stage G-H to the left. The two other segments showing less ischemia, although the septal apex shows hypokinesia and post systolic shortening at 20 ug awhich is increasing at peak, while the basal septum shows slight ischemia at peak.








It is evident that in a segment being stretched in systole, if there is any elasticity at all, the segment will recoil in diastole, i.e. as a function of the elastic force stored in the segment. (also, if the segment had not returned to the original shape, the whole heart would have been turned inside out in the time of a few minutes. Thus, stretch /  recoil is a mechanism for post systolic shortening. In ischemia, post systolic shortening develops before there is systolic stretching (46, 100 ), i.e. while there still is systolic shortening as shown in the stress example. This this can be explained by the timing of the tension interaction between segments.

As a segment becomes ischemic, there will be reduced energy (ATP) available, this will lead to:
  1. Slower tension buildup
  2. Lower total tension
  3. Slower tension devolution:
    1. The removal of calcium from the cytoplasm by the SERCA complex is necessary for releasing the actin myosin cross bridges, and this calcium removal is an energy demanding process, the release of the cross bridges, and hence, tension release is slowed (296). Thus, the tension remains longer in an ischemic segment. 
    2. Increase in load itself slows onset of relaxation (224). Weakening by ischemia may be considered a relative increase in load, and thus itself may be a contributing factor to reduced relacation rate.
But the deformation pattern of the ischemic segment is then a result of this process in interaction with non-ischemic segments. A mathemathical model describing the segment interaction was published by the Leuven group (298). The focus on the segment interaction, to explain the deformation patterns is important, but the model is erroneous. The model errs in the timing of tension, as they confuse the time of active tension with the time of active buildup of tension, thus considering the period of tension devolution as a period without any muscular tension at all, which is wrong. During late systole and post systole, the model then is concentrating solely on the elasticity / active force interaction. And finally the model do not include the ischemic slowing down of relaxation (296).

Below is a sequence of diagrams of segment interaction where slower tension buildup, lower total tension and slower tension devolution is illustrated in terms of interaction with normal segments.





1: Two segments with equal tension (red and blue) will shorten equally and symmetrically.
2: If one segment becomes ischemic, this will lead to:
1: slower tension buildup, leading to initial stretch,
2: lower total shortening, and concomitant increased shortening of the healthy segment as the load on this is reduced
3: prolonged tension in the ischemic segment, leading to increased shortening as the two tension curves cross, the ischemic segment shortens as the healthy relaxes. This is post systolic shortening.
3: As ischemia progresses and tension becomes lower, the initial stretch increases, and shortening becomes less and later, while post systolic shortening remains.
4: At one point, there will be only stretch during systole. However, the remaining post systolic shortening after normal contraction,  is a sign that there is still active tension remaining.
5: Finally, with total loss of tension, there is only stretch. The post systolic shortening is still present, but only as a recoil phenomenon, with no sign of active tension.


In a totally passive segment, without any systolic shortening, the post systolic shortening may be simply passive recoil, as in the theoretical instance 5 above. However, even if there is holosystolic stretch, if the segment shortens more than it is stretched (instance 4), this is an indication of remaining tension, although too little to withstand the tension of healthy segments. This was demonstrated by Lyseggen et al (299).

An example of progressive iskemia during dobutamine stress echo can be seen below:

Stress echo from a patient devolving apical ischemia. From a fairly normal pattern at baseline, there is increasing contraction at 10 ug/kg/min, but mainly in the base, some apical hypokinesia at 20 ug, and the protocol was terminated at 30 ug because of pronounced apical akinesia.







Baseline shows slightly reduced strain rate and post systolic shortening in the apicolateral segment (cyan) already at rest.
At 10 ug/kg/min, there is initial stretch in the apicolateral segment, reduced systolic strain rate and strain, as well as post systolic shortening.
At 20 ug/kg/min there is prolonged initial stretch, near zero systolic strainrate and strain and extensive post systolic shortening in the apicolateral segment. In addition there is reduction in systolic strain from 10 ug, and initial post systolic shortening in the apicoseptal segment (yellow).
At peak stress (30 ug/kg/min) there is holosystolic stretch in the apicolateral segment,but with some post systolic shortening indicating that the segment is not completely passive. There is also extensive hypokinesia with post systolic shortening in the apicoseptal segment.
In fact, these curve is very similar to the curves in the original work of Tennant and Wiggers from 1935 (46).

The same can be seen in strain rate colur CAMMs from the differennt stages:



Thus initial delay of shortening (tardokinesia) has been seen as a component of ischemia from early experiments (46) as well as in late experimental (304) and semi-clinical (305) work. It is commonly used as a method for assessing B-mode WMS i stress echo (tardokinesia - 306)

Post systolic shortening in ischemia


1: PSS is not only seen in ischemia.

It is important to realise that post systolic shortening is not only a phenomenon of ischemia, it can be seen both in left bundle branch block and hypertrophy. The mechanism is also in those cases asynchronous interaction between segments, but with different causes of asynchrony. While ischemia results in prolonged relaxation, LBBB results in delay of the whole activation relaxation sequence, and, surprisingly, PSS in not in the delayed wall, as the final mechanism for PSS is stretch - recoil, it occurs in the earliest wall (septum). Thus, the mechanics are different.

2: PSS in ischemia is only a part of a set of specific deformation changes in ischemia.

As seen above, PSS is part of a complex change in deformation pattern, which is the delayed evolution of tension, reduced absolute tension and delayed relaxation in acute ischemic segments interacting with normal segments that causes the pattern of initial stretch, systolic hypo-, a-, or dys kinesia, with post systolic shortening. 

3: Without normal segments there will be no PSS

Without any normal segments to interact with, there will in fact be no PSS, as shown by the following example where there is total ischemia, and hence, no normal segments and (almost) no PSS in the ischemic segments:


Severe ischemia in all walls in a patient with severe three vessel disease (among other things stenosis left main, occluded LAD filled from RDP, even with occluded RCA filled from collaterals) .  Visually, the most striking finding is fall in EF with increasing stress.



Strain rate colour M-mode.  No significant PSS can be seen (Except possibly apicolaterally). Thus at first glance, the M-mode looks normal, at least concerning synchronicity.
Strain rate  curves (top) and strain (botom) of the ventricle at peak stress. Again, no significant PSS can be seen (Except possibly apicolaterally), demonstrating clearly that there are little PSS  when there are no segments with normal contraction-relaxation cycles.  The AVC is evident from the phono traces. The strain curves show delayed and prolonged shortening, but more or less in all segments. This is equivalent to the balanced ischemia of scintigraphy.

Post systolic shortening (PSS) means that the segment continues shortening after the aortic valve closure, often after a short relaxation giving one or two peaks a systolic and a post systolic, or a single peak after AVC as shown in the figure below, left. The definition of shortening as post systolic is dependent on the location of AVC, which can be done by TDI as described above. This holds even in the presence of iskemia (with PSS) and in high HR (170).



Normal strain rate curves. Note that there is a little shortening of the lateral wall (cyan curve) after AVC (green vertical line). This is normal, and related to the shape change in IVR. Initial systolic stretch, reduced systolic shortening and presence of post systolic shortening in the apical segment (cyan curve), with normal systolic shortening and no post systolic shortening in the basal segment (yellow curve). Two different instances of post systolic shortening. Apicolaterally, there is stretching and then recoil after AVC (cyan curve), with possibly a little overshoot as indication of a remnant of tactive tension.  Apicoseptally there is systolic shortening and then further post systolic shortening (yellow curve), which thus has to be active. It also shows the mechanism for PSS to be different than recoil.  


The phenomenon of post systolic shortening in acute ischemia was demonstrated already by Tennant and Wiggers in 1935 (46), although it was not discussed explicitely in the paper. Already in the eighties, however, it was recognised that post systolic thickening and post systolic shortening was the same thing, due to the incompressibility as discussed above, and that the PSS in acute ischemia was a marker of active tension, and thus a possible predictor of functional recovery (297). 


Inferior infarct (yellow), showing both reduced strain rate and strain, with shortening after the normal shortening of the healthy segments (post systolic shortening). In this case, there is both systolic (although reduced) and post systolic shortening, thus the PSS has to be tue to active tension, as in instance 2 above.

The presence of PSS in acute ischemia in the clinic was shown with M-mode by Henein (300), and later with strain rate by Jamal in 1999 (185) and Kukulski (99, 100).

Post systolic shortening has been proposed to an additional diagnostic criterion for ischemia in stress echo (113), but other studies has not shown additional diagnostic value of this (128).

As seen by the colour M-mode below, the presence of post systolic shortening in a segment, leads to a delay in the onset of segmental lengthening compared to the normal segments, so the finding is equivalent to the delayed compression/expansion crossover described by some authors (186).




Apical myocardial infarct in the inferolateral wall. Inward motion after systole can be seen in the apex.
In this case we see systolic stretch in the apex, and with PSS as in instance 4 above, midwall initial stratch and then systolic shortening with further PSS as in instances 2 and 3 above, and then normal shortening and relaxation in the base. That post systolic shortening in the infarct area is simultaneous with elongation (relaxation) in the normal basal part, is very evident from the colour M-mode.


Looking at tissue Doppler, there is post systolic motion of the borders of the midwall segment (lilac and orange curves), but very little in the apex (green) or the mitral annulus (white).
But this of course means that post systolic deformation happens in the apical segment (yellow coloured interval between green and orange curve).




The post systolic shortening is thus in the infarcted apical segment (yellow cirve, negative deflection) as seen from the strain rate .....
.... and strain curves.
Also, comparing strain and strain rate curves, with the velocities, it can be seen that post systolic shortening only reslts in relative motion, without much over all effect on the motion of the mitral ring.









The post systolic shortening of the apex can in this instance be seen to cause an ejection of blood from the apex towards the base after normal ejection.
This is evident in the still frame from early diastole (top), and from the colour M-mode where the duration and extent of the jet cab be seen (arrows) just before onset of early filling.


As in the example above, the area of a- to dyskinesia is the area most affected by ischemia (instance 4 -5 above), while the surrounding area will have systolic and post systolic shortening as in instance 2 - 3 above showing a lesser degree of ischemia. 3D starin rate mapping will show this, the area of dyskinesia being smaller than the area of PSS:


Strain rate bull's eye and three dimensional reconstructions of a ventricle in systole (top), showing an area of dyskinesia (blue) in the apex, and diastole (bottom), showing a larger area of post systolic shortening (yellow). Strain rate bulls eye from systole and early diastole (top, left) , below 3D reconstruction (bottom, left) in systole and M-modes from all six walls (right), showing an inferior infarct with slight dyskinesia and more extensive akinesia in systole and post systolic shortening in a larger area also around the infarcted wall.



Duration of post systolic shortening after infarct

In acute ischemia, the prolonged tension / delayed relaxation is due to a reduced rate of removal of cytoplasmic calcium due to energy depletion. As shown in experimental ischemia, as well as in PCI studies, this reverses quickly with normalisation of flow ( 99, 100, 299, 300). However, longer duration of ischemia, or repeated ischemia will lead to a prolonger stunning of the myocardium, affecting both contraction and relaxation (301). Normalisation of systolic function would be expected to be paralleled by a reduction of PSS, as seen below:



Strain rate of an inferior infarct at day 1, showing akinesia in the basal segment (yellow curve), but with pronounced PSS during systolic relaxation. (Image courtesy of Charlotte Björk Ingul). The same patient at day 7. Function in the basal segment (yellow curve) can be seen to be nearly normalised, and the PSS is correspondingly reduced.  (Image courtesy of Charlotte Björk Ingul).

Thus, PSS as well as systolic dysfunction is expected to be present for some time during the acute phase of infarction (92, 174, 188). Those studies showed that systoic function in affected segments normalised mainly within the first two days, with little improbvement during later obervation, thus reduced systolic function seen later would be permanent (loss of myocytes / scarring). PSS decreased concomitant with increase in systolic function. The post systolic shortening was about the same in border zone segments and infarct segments, despite infarct segments having lower absolute value of peak systolic strain rate. The PSS diappeared in the border zone segments in a week, but continued to decrease somewhat in the infarcted segments during a longer observation period (92), indicating that the diastolic stunning might last somewhat longer. However, some PSS remained also after 3 months.







Small acute apical infarct showing delayed onset of shortening, hypokinesia and post systolic shortening in the apicoseptal segment.
Same infarct 1 month after successful revascularisation of LAD, showing still some hypokinesia and post systolic shortening, although the PSS have decreased in amplitude.



In a cross sectional study (47) Voigt et al found PSS to be present in normals as well as infarcted hearts, in normals it was present in up to about 30% of segments, but then associated with normal systolic strain, and being both less in magnitude and earlier in the peak than in infarcted segments. It was present both in acute infarctions and in chronic infarcts. In acute infarcts, it was seen in 78% of ischemic segments, in older infarcts in 79% of scarred segments (which may presumably be fewer than in acute ischemia as seen above). Thus, the ischemic relaxation dysfunction is not the only explanation for PSS.

Loss of longitudinal fibres in myocardial infarction (210) will lead to loss of contractile force in the longitudinal direction. This is equivalent to a local increase in the load/contractility relation. Thus, reduced muscle mass will result in increased relative load from healthy segments, and this alone may be a mechanism for delayed relacation in affected segments (224), although without the additional delay from hypoxia. So, the PSS in infarcts would be expected to decrease in magnitude with time as shown (92).







Large apical infarct in the acute phase. Initial stretch (1), pronounced apical hypokinesia (2) and pronounced PSS (3).
Same infarct after 3 months, evidently some recovery of stunning, less tardokinesia, less hypokinesia, and the PSS is far less in magnitude.

Thus, post systolic shortening can be expected to decrease with the normalisation of ischemic stunning, but may partly remain where there is noticeable loss of fibres leading to reduced regional contractility.



Post systolic shortening and diastolic filling will interfere, as we see a delay in mitral annulus e' wave in walls with PSS:



Asyncronous motion.
Showing initial stretch, systolic hypokinesia and post systolic shortening in the apical half, PSS can be seen to be simultaneous with lengthening in the base, thus interfereing with the filling phase. THese effects may be real, as seen above, PSS can actually affect flow. 
Looking at annular velocities and comparing with mitral flow, onset of mitral flow in this case can be seen to be earlier than onset of annular elongation (e'), even in the lateral wall, but especially in the septum. This might indicate increased atrial pressure.

Diastolic effects of PSS are discussed further below under diastolic function. However, some authors have suggested that PSS is actually the cause of diastolic dysfunction. This is really putting the cart before the horse, to say it mildly. From the discussion above, it is really the other way around, delayed relaxation in ischemia that is the cause of ischemic PSS.

It must be emphasized that the presence of PSS is mainly a measure of inhomogeneity of force development, due to differences in activation, load or contractility, and not as specific marker of ischemia. While ischemia results in prolonged relaxation, LBBB results in delay of the whole activation relaxation sequence, and, surprisingly, PSS in not in the delayed wall, as the final mechanism for PSS is stretch - recoil, it occurs in the earliest wall (septum). Thus, the mechanics are different.

Asynchrony:

Asynchrony may arise from various mechanisms.

Left bundle branch block




Typical pattern of tissue velocity in the septal base, in a case where LBBB induces mechanical asynchrony.

left bundle branch block may have  very different mechanical effects. This is due to the very large variability in how much, and which parts of the left bundle that are affected, and to what degree.

Basically, left bundle branch block means a reduced conduction velocity in the left bundle, below that of the right bundle, causing the septum activation direction to shift from left-right to right-left, but also meaning that parts of the left ventricle are activated later than the right, and later than normal, causing a widening of the QRS. The mechanical effects of the LBBB may be quite various, however:

  • The Left bundle fans out in a mesh of fibres, and the conduction velocity may vary in different parts. (Most typical left anterior vs. left posterior hemi block)
  • The width of the QRS reflects the delay to the latest activation area. However, this may not be the mechanically most important parts. Thus, the width of the QRS have some bearing but not closely to the mechanical delay.


Thus, the mechanical manifestations are various:
  • Some patients display an apparent normal activation pattern
  • Some patients display normal pattern at rest, but shows mechanical asynchrony at higher heart rate, due to the relative conduction delay that may manifest with increasing HR.
  • Some patients display mechanical asynchrony at rest.


The bundle branch block may cause
  • Inter ventricular asynchrony, with LV activation after RV activation. However, the onset of ejection is a poor marker of this, as ejection onset comes after IVC, and IVC is dependent on the load of the actual ventricle, as well as the contractility. Thus, a poor LV, will have a longer IVC, and ejection starts later, if the RV is more normal, this will cause delay in onset of LV conduction. If ejection should be used as a marker, it should use MVC compared to TVC.
  • Selective AV block to the left ventricle, causing shortening of the LV filling time
  • Intraventricular asynchrony in the left ventricle, due to the delay in lateral wall activation compared to the septum (even if the septum is activated right-left, this doesn't affect the time to activation of the septum to any noticeable degree.


Mechanics of asynchrony in left bundle branch block

The pattern of deformation in left bundle branch block is also due to interaqction between walls, as they interact differently when the activation sequence interact.


If there is intraventricular asynchrony, this is usually very evident, and the most typical marker is the "septal flash".

Septal flash

The most typical pattern, originally called "septal beaking"(as it was origially described in M-mode), was described early (251). Later, it has been termed "septal flash" (252).




Patient with "septal beaking" in M-mode, seen as a short inward motion starting at the peakof QRS, and peaking at exact the same time as the onset of inward motion of the inferolateral wall. The contration of the lateral wall is the force terminating the septal flash, so the time from onset of septal flash to onset of inferolateral wall thickening is the true mechanical delay between the walls.
The septal flash consists of a short inward and then outward motion of the septum, the outward motion start about simultaneously with inward motion of the lateral wall.
The   "septal flash" evident in both parasternal long axis and short axis.


What we see is a pattern of septal flash, shortening during ejection, late systolic stretch and post systolic shortening.


Typical pattern of tissue velocity in the septal base, in a case where LBBB induces mechanical asynchrony.The septal flash can be seen early, then the ejection, then late systolic stretch of the septum, which is due to the continuing tension in the lateral wall (being delayed), and then post systolic shortening of the septum due to recoil from the previous stretch, simultaneous with the relaxation of the lateral wall..
The M-mode shows the same. (Another patient, but the pattern is similar). The septal inward motion starts early during QRS (first vertical line). The peak is when the lateral wall thickening starts (second yellow line). During lateral wall thickening there is much less thickening of the septum, which actually seem to move outwards. Then at peak lateral wall thickness (i.e. when lateral wall starts thinning), inward motion and thickening of the septum starts again (third yellow line - post systolic thickening) and then peak septal thickening is simultaneous with the end of the steepest part of lateral wall thinning. 

Looking at strain rate imaging, the interactin between walls is visible, corresponding to what can be seen in M-mode:


The pattern from the septum can be seen in this SRI M-mode (this is another patient). But here the delay between walls, as well as the phases being result og interaction between the walls is mode visible. This is explained below.


Rocking apex

The septal flash has also been called "rocking apex" (285), as the asynchrony induces a rocking motion of the apex as seen in the four chamber view. The rocking apex is equivalent with the septal flash, as it is the initial contraction of the septum without simultaneous contraction in the lateral wall that results in the rocking towards the septum. The rocking due to septal flash, is always toward the septum, while the rocking apexes shown above (not due to conduction anomalies), is more often towards the lateral wall. The rocking is also evident in the tissue Doppler images, although with a complex pattern:

The four chamber view shows both septal flash and rocking apex.
"Rocking apex" as seen by tissue Doppler. The apex moves first towards the left. This is evident as the left side of the apex moves downwards (yellow curve - initial downward velocity) and the right side moves upwards (cyan curve, initial positive velocity). After this initial rocking, the apex stays in the new position for a period as seen by the two curves lying close together. the there is slow motion towards the lateral wall, and then an abrupt reverse rocking (negative cyan peak - downwards motion of the lateral apexand positive yellow peak - upwards motion of the septal apex). Finally, there is even another reverse of the rocking after end systole.
However, looking at the B-mode above, the motion is far more complex than this. The initial inwards motion of the septum is reversed, the rocking of the apex towards the septum, however is not reversed before the end of the systole, where the apex rocks back.



To understand the mechanisms of the asynchrony, the normal pumping physiology has to be considered. Normal electrical activation starts in mid septum. The whole of the left ventricle is then activated within 80 - 100 (120) ms (the duration of a normal QRS). Electromechanical delay at the cellular level is 20 - 30 ms (234, 268). Thus, the start of the contraction of the lateral wall should be within 80 - 100 ms after start of septal contraction. The normal mechanical sequence vill then be as follows:
After mechanical activation, there is an intial shortening seen in the velocity traces as a positive spike of short duration - the pre ejection spike. This initial contraction gives a small pressure rise which closes the mitral valve (236) about 30 ms after initial septal contraction (268). The lateral wall starts slightly later,  but within 40 ms (maximum duration of the normal Q-wave - septal activation). 

AS the walls contract in parallel, they will give rise to isovolumic contraction where there is pressure increase without deformation, and then ejection when ventricular pressure exceeds aortic, the ejection phase is characterised by longitudinal shortening and wall thickening.

However, active contraction is in terms of force, and cannot be seen by deformation, as the continuing ejection will result in continuing shortening despite tension decrease. The development of active contraction do not continue during the whole of the ejection, tension decrease starts around mid ejection, probably at the time of peak pressure / peak strain rate, after this there is tension release. Thus, the tension buildup is an event of much shorter duration than ejection. After this there is still tension, although decreasing, during the last part of ejection the ejection is partly driven by inertia.


Delayed intraventricular conduction, on the other hand, will lead to delayed activation of the lateral wall.

Thus, the septum will contract for a longer time alone, with no balancing tension in the lateral wall, meaning that the septal contraction is free to stretch the initially passive lateral wall as seen by the rocking apex. This again means that the initial contraction of the septum actually results in shortening and thickening of the septum, asnd simultanelos stretch of the lateral wall, with no pressure increase (A). If so, there will presumably be no MV closure. Thus, there is septal deformation (shortening) earlier than in the normal ventricle.

At the time of initial lateral wall contraction, there will be tension of both walls, leading to pressure increase, which presumably will be the time of mitral closure (MVC). After this, contiuing tension in both walls will increase pressure (IVC). The increase in pressure will start to push the septum back (as seen on M-mode, but not longitudinal shortening), thus the peak of the septal beak is the start of the lateral contraction (B).

Then there will be shortening of both walls, but with uneven tension, as the septum will start tension decrease while lateral wall tension is increasing. There has to be some remaining tension in the septum, or else, with a totally passive septum, lateral contraction would simply stretch the septum, resulting in only rocking with no real ejection work . However, ejection will lead to volume decrease, and thus shortening of the left ventricle. Once ejection is under way, there will be shortening of the septum even if it is largely passive (C).

When the septum is relaxed, the delay in the apex will also affect the relaxation, thus there is still tension in the lateral wall. This will lead to stretching of the septum (D).

Post systolic shortening in LBBB


And finally, there will be relaxation of the lateral wall, when this is passive, there will be elastic tension in the septum, and it will recoil in a post systolic shortening  (E).






Septal activation alone. leading to septal shortening and thickening, with concomitant lateral stretch - the septal flash. No pressure increase.
Lateral wall activation, ending the septal flash which peaks) with remaining septal tension (or else there would be only rocking, no pumping). In this case there is pressure buildup, MVC, IVC and probably start ejection.
During most of the ejection there will be shortening, but part of this may be passive due to volume decrease, especially in the septum.
In the last end of the ejection there will be little or no remaining tension in the septum, which then will stretch, due to the remaining tension in the lateral wall (which have been activated later). Thus, there will be stretch og the septum and shortening of the lateral wall.
Finally, there is no tension in the lateral wall, which relaxes. In this phase there will be elastic tenbsion in the septum due to the previous stretch, which will shorten in post systolic shortening, whil the lateral wall stretches (both due to septal shosrtening, but also in the course of normal early filling).

All of this can be summed up by strain rate colour M-mode:



The phases wall interactions above, visualised in colur SRI.


Thus, while ischemia results in prolonged relaxation, LBBB results in delay of the whole activation relaxation sequence, and, surprisingly, PSS in not in the delayed wall, as the final mechanism for PSS is stretch - recoil, it occurs in the earliest wall (septum). Thus, the mechanics are different.

This can be further analysed in detail by tissue Doppler:




The ejection period timed by Doppler flow from LVOT.
The phases are visible by tissue Doppler. This is the same image as above, but with two more sample volumes added in the base. (the differences in amplitude of the apical curves is due to autoscaling). Deformation is visible by the offset between the velocity curves; there is septal shortening when the red line lies above the yellow, and lengthening when yellow is above the red. Likewise in the lateral wall there is shortening with green above cyan, and lengthening with cyan above green. During QRS there is shortening of the septum (yellow to red), and stretching of the lateral wall (green to cyan). This is the septal flash. With onset of lateral shortening, the septal flash reverses, resulting in the peak of the septal flash (yellow vertical line), which also marks the MVC and onset of IVC. At start ejection, there is abrupt apical velocities of both basal points, marking shortening of the whole ventricle, as seen byt the velocity offset, there is shortening in both septum and lateral wall. before end ejection, however, the septum starts to stretch due to end of relaxation, as seen by the yellow/red crossover. This continues after end ejection, while the end