Det medisinske fakultet

Strain rate imaging.

Myocardial deformation imaging by ultrasound / echocardiography

Tissue Doppler and Speckle tracking

by Asbjørn Støylen, Professor, Dr. med.

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: December 2014.     This section updated: December 2014.



Ummanaq (the heart shaped mountain), national mountain of Greenland Snøhetta (Mount Snow Hood), by many regarded as the national mountain of  Norway. Not 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).


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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 shold thus be: reproduced with permission from: http://folk.ntnu.no/stoylen/strainrate). Using the material in papers without acknowledgement, I consider academic misconduct in addition to being copyright violation.


Still preaching my personal agenda: Strain is geometry. Cormorant seen in Galway, Ireland



Some comments:
Strain means relative deformation, strain rate means the rate of relative deformation. This website is mainly about deformation imaging by ultrasound, although both in relation to physiology, pathophysiology, other ultrasound modalities (motion imaging) and technology.

  1. Shortening does not equal active contraction.What we measure with imaging by any method, is deformation of the ventricle, wheter we measure shortening fraction, ejection fraction, annular displacement, annular velocity, strain or strain rate.
    1. Active contraction happens only during 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.
    2. 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.
    3. 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. Understanding of Geometry is crucial. 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 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.
  3. 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 ultraound beam".
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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..
  9. 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.
  10. 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.
  11. 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 pincipal 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.
  12. 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.
  13. 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 do NOT explicitly recommend 17 over 16 segments, it's optional. 



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


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
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The website is divided into sections to allow quicker downloading, this section shows the full website index for this section and all other sections.

Recent updates:

December 2014: The section on strain geometry has been extended, both the discussions of the relation between longitudinal strain and circumferential strain and the relation between circumferential strain and fractional shortening (C = ÷ FS) i.e. Circumferential strain is nothing more than fractional shortening of the cavity, and especially in relation to   area strain , emphasizing that the different strain components are inter related thorough the incompressibility. The derivation of the area strain formula is given in the mathematics section. The paragraph on 3D ultrasound in Basic ultrasound has been extended, also incorporation a description on stitching. Also, two short paragraphs on angle deviation have been added to the same section, as it seem to be surprising to many that while M-mode derived motion overestimates the displacement by the cosine to the insonation angle, the Doppler derived velocity measurement (and hence also displacement measured by integration of tissue velocity) underestimates the velocity (and motion) by the cosine of the angle.

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 at around or below 100 FPS. I've just added this to the relevant paragraphs in the basic ultrasound section.



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 principles of ultrasound and scanner technology.

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
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?

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

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.


Why 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. 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.
  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 is method independent. I now give basic knowledge first, and a review of methods later. The chapter on clinical evidence and how-to come last, as clinical evidence is method specific, and the how-to presupposes knowledger of the fundamental priciples of the methods as well at the limitations.

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 interpret findings.

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.  Paramteric (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.

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


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 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”. 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:

Where e 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 instantaneous strain (or 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:


An object undergoing strain. In this case there is a 25% elongation from the original length (L0). The lagrangian strain is then: = (L - L0)/L0 = L / L0 (The Eulerian strain rate is E = (L - L0)/L = L / L as explained in detail here)Thus, according to the Lagrangian formula there is positive strain of 25% or 0.25. (The Eulerian strain is then 20%). The strain can, however happen at different rates as shown to the right. 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.




We have seen that deformation of an object is present when there is differential motion within the object. Thus spatial derivation of velocity will yield strain rate (velocity differences per time unit), and spatial derivation of displacement will yield strain (i.e. motion differences per length unit). Temporal derivation of displacement gives velocity (displacement per time unit)
and of strain gives strain rate (deformation per time unit). Integration is the process of summing differences, so temporal integration gives displacement from velocity and strain from strain rate. Spatial integration (summing deformation along a segment) will give displacement from strain and velocity from strain rate. In principle there is one dataset which can produce all four measurements. This will be explained in more detail elsewhere.


As strain rate is equal to velocity gradient, in fact deformation can be described as motion gradient, strain rate being the velocity gradient (spatial derivative of of velocity), and strain the displacement gradient (spatial derivative of displacement)
.
Velocity
Temporal integration



Temporal derivation
Displacement
Spatial derivation

Spatial integration

Spatial derivation


Spatial integration
Strain rate
Temporal integration



Temporal derivation
Strain

There are two different ways of determining strain and strain rate: Lagrangian and Eulerian.

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; .

This is described in details in the mathematics section, but the point is that the two formulas will result in slightly different values. The common use is that strain is given as Lagrangian strain, as this was first used by Mirsky and Parmley in describing myocardial strain (12). Strain rate was first measured by tissue Doppler, which gives the Eulerian strain rate. Thus, in integrating strain ate to strain, the value has to be converted in order to derive Lagrangian strain. 


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. Thus the momentum 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 strain

The term strain was first used in relation to the heart by Mirsky and Parmley (12) to describe to describe myocardial deformation. 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).






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.


Geometry of myocardial 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!!!).



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.

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

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.



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.




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. Wall thickening as 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 is the same as fractional shortening!







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. 

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:

Circumferential strain in the same ellipsoid geometrical model, showing circumferential strain as 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

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 is  area strain. 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 length.

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.

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 afain 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.


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.

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.

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 line width (being dependent again on frequency and focus depth), and line density (being dependent on frame rate and sector width). In addition, there has to be adequate alignment of the ultrasound beam, as angle deviation will reduce the number of lines within the wall in the far field. This is true for speckle tracking as well as tissue Doppler.

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.


A: Beam width. Speckles (true speckles: black) are smeared out across the whole beam width ( Apparent speckles dark grey, top). This means that with this beam width the speckles from to different layers cannot be differentiated, and layer specific motion cannot be tracked.
B: Line density. Only the lines in the ultrasound beams (black) are detected, and can be tracked, beams between lines are not detected or tracked.and differential mtion of the two speckles cannot be tracked. The spaces between lines cannot be seen doe to image lateral smoothing.
C:  Divergence of lines in the depth due to the sector image will both increase beam width and decrease line density in the far field. this may result in the line density and width being adequate (in this example for two layer tracking) in the near field, but inadequate in the far field, situation there being analoguous to A.
D:  Focussing. The beams being focussed at a certain depth mau mean that line density may be inadequate at the focus depth. Thus speckles in some layers may be missed. Optimal setting will give the best line density at the focus depth, but increased frame rate or sector width reduce libne denisty also at focus, as there is a given number of lines for a given frame rate and depth. In any case, in the far field, the beams will be broader, and the beam width will be more like A and C.
E: Focussing may even result in beams overlapping in the far field. A speckle in the overlap zone may be smeared out across two beams.

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.




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.

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 wall motion or deformation, cavity deformation or flow. And flow is the first derivative of volume, i.e. the flow in or out of the ventricle is the rate with which the volume changes. 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.

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 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.

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) .




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. This is illustrated above. From this, it is evident that the time before the muscle starts to shorten, and hence, the total shortening, will depend on the load. 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.



Shortening velocity and total shortening decreases with increasing load (after 208). Thus an increasing afterload load will result in less shortening, as well as less initial rate of shortening in an isotonic preparation like the one above. 

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

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.

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.



How can motion and deformation be displayed?

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. Motion parameters can be related to the dimension of the ventricle to derive strain as shown below.



Longitudinal M-mode through the mitral ring, displaying the displacement of the mitral ring. The total systolic displacement (MAE; mitral annulus excursion) can be measured.  If  the MAE 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 strain during systole is thus MAE /LD.
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 (Which is different from the Eulerian strain rate that is customarily used in ultrasound.) This is discussed below.


The annular The term mitral annular descent or mitral annular excursion (MAE) (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 measurements is unclear.

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

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.


The same diagram as above, but with the traces displayed.
Tissue velocity







Temporal integration



Temporal derivation
Displacement

Velocity curve. Velocities toward the probe are defined as positive, velocities away are negative.  The main motion patterns can be seen as positive velocities during systole (the S phase), while the early filling phase (e) due to ventricular relaxation and the late phase due to atrial systole (a) can be seen as the two main negative velocity spikes.

Displacement curve from the same point. Here motion is shown toward the probe during systole, while there is motion away from the probe in diastole, ending at the same point. Mark the similarity to the longitudinal M-mode shown above, actually, it's the same parameter, although obtained differently.  There is motion away from the curve in the two diastolic phases.
Spatial derivation

Spatial integration

Spatial derivation

Spatial integration
Strain rate








Temporal i
ntegration



Temporal derivation
Strain

Strain rate curve. Due to the definition given above, shortening is negative, and there is shortening during systole (negative wave). The curve has a different shape than the velocity curve. In diastole, there is elongation in diastole, but the pattern is much more complex than in the velocity curve, as will be discussed below.

Strain curve. Due to the Lagrangian definition given above, shortening is negative, so during the heart cycle, the strain can be seen to be negative during the heart cycle, the L0 being the end diastolic length. However, there is shortening in systole and elongation in diastole, although the pattern in diastole can be seen to be more complex than in the displacement curve.


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.

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 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. As only the end systole is of interest, there is no need for looping the image. In addition, the width of each coloured band 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.

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, when shown on a curved M-mode or a 3D surface:

The same curved M-mode showing displacement during the heart cycle. 3D displacement display in end systole.- This is explained below

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.
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, in strain rate, it is suited to detect the presence of reverberations as shown here. 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.

However, In order to display data for the whole ventricle. one need to display an array of CAMM recordings:

Array of curved M-modes from 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. This is similar to  the image abve left.

Thus for a display of the whole ventricle in one image, the Bull's eye plot may more useful.

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:

Bull's eye plot of segmental end systolic strain

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, it is possible to do an interpolation of values between the recorded planes, thus displaying :

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.


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.



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. 




The area distorsion in bull's eye is evident comparing these 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.
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.) 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).

Relations between systolic motion and deformation measurements

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 ratein 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 patient's diagnosis was not clear. The cause might be reduced contraction of the right ventricle, despite the normal TAPSE. as part of the TAPSE might be due to the rocking as well. 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.


There is an apparent well functioning right ventricle, but as the rocking motion of the heart adds motion to the lateral tricuspid annulus, so the TAPSE (3 cm) may be misleading.

In this case, the motion (velocity imaging) is mis informing, giving the appearance of dyssynchronous function of the left ventricle, while deformation shows this to be untrue. Thus, asynchrony is in some cases better characterised by deformation.




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. 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 segment is infarcted, and is akinetic and being pulled along by the active apical segment. The whole inferior wall seems stiff.

     


    Displacement curves shows all segments to move similarly, thus there is little differential motion, and at least below the apical point , little deformation.
    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).

    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, om 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.
  3. 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.


    (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).

Tehtering, however, being physiological phenomena, must not be confused by the effects of spatial smoothing in tissue Doppler or 2D strain. This is artefacts, being due to shortcomings (or actually,; attempts to overcome shortcomings)of the methods themselves and ultrasound in general.

The difference in shape between strain rate and velocity curves

It is obvious that strain rate and velocity curves are different. Apart from being inverted, which is due to the subtraction algorithm, the systolic strain rate curves are much more rounded, with a later peak, while velocity curves show a sharper and earlier peak. If strain rate is equal to normalised velocity, why is the shape different as illustrated below?



Left velocity curves. It can be seen that the two velocity curves have an early maximum, showing that the myocardial acceleration occurs early, and is an early event. Peak systolic velocity is seen at about 100 ms into the heart cycle, starting with ORS.  After this, there is a period of nearly constant velocity difference, before the velocity difference decreases again. Right, the strain rate curve from the segment between the two ROIs in the left picture. It can be seen that peak strain rate is a  later event, about 200 ms after start of QRS.  The strain rate increases after peak velocity, during the period of near constant velocity difference. This is due to the fact that the velocity difference is normalised for the instantaneous distance that is decreasing during systole, i.e.  Eulerian strain rate

This is due to the difference between Lagrangian and Eulerian strain rate, As we use Lagrangian strain, this is displacement normalised for end diastolic length. This is the original definition, and the one used to describe myocardial deformation by Mirsky and Parmley (12), and thus has set the standard. However, it has become customary to use Eulerian strain rate , which is a normalization for instantaneous length. The reason for this is that this is equal to the velocity gradient that was the original method used to calculate strain rate (4, 14) and is what is used.directly on the scanner.

This means that the distance between the points of velocity measurement decreases during the whole systole. Thus, after the peak velocity, while the phase where velocities are relatively constant, strain rate will continue to increase as the strain length decreases. Thus, peak strain rate is a later event than peak velocity, which means that it may be more load dependent than peak systolic velocity. This can be shown in simulations:


Velocity curves from two points with a set distance.
Strain rate curves based on the velocity curves to the left. The yellow represents Lagrangian strain rate, which is simply the velocity difference divided by the initial distance. The curve shows the same shape as the velocity curves. The green curve is the Eulerian strain rate, where the next point on the curve is the velocity difference divided by the distance which decreases by time interval × the velocity difference (the decrease in the distance given by the velocity difference).

This is explained in detail here. In addition, the Eulerian strain is slightly higher in value than Lagrangian strain as discussed here, as the systolic deformation is normalised to a decreasing in stead of a constant length. This, however, means that peak Eulerian strain is the highest contraction velocity (not rate, as contraction rate should be measured in terms of tension). Peak velocity (or Lagrangian strain) is probably closest to the time of maximum dP/dt, while peak Eulerian strain rate may be closest to the time of peak pressure.

The time of peak strain rate has not proven useful, however, as the method is so noisy that timing is more influenced by noise spikes than the true time point of maximum strain rate.

Lagrangian strain ( ) and Eulerian strain ( ) can be interchanged by fairly simple conversion formulas: and . 

The convention is that the strain is given as Lagrangian strain. Integration of Eulerian strain rate yields Eulerian strain, but this is converted directly to Lagrangian strain by the formula above, so the curves and values seen on the workstation are Lagrangian values. Conversion between strain is thus useful, and used all the time, even manually. The main point of interest is end systolic strain or peak systolic strain which will be simultaneous by both measurements. (Of course, to obtain a full Lagrangian strain curve from Eulerian strain, the correction has to be applied in each frame, which is a little more computationally expensive, and thus needs to be automated in the analysis program. However, peak Lagrangian strain rate will be at the time of the biggest velocity difference, while peak Eulerian strain rate will be later. Thus, peak strain rate is not simultaneous by the two variables, and peak strain rate with one method will not convert into peak strain rate of the other. Thus conversion of strain rates is practically useless for peak values. However, the conversion has to be applied to each frame if Lagrangian strain is obtained by speckle tracking, and then derived to achieve strain rate. This is also done automatically in the analysis programs.


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. The V-plot is also 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 (left) and deformation (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), 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 ereverse 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.

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.

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.

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 pre ejection period





The geyser Strokkur at Haukadalir, Iceland at immidiate 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. To the left, the steam can be seen within that bulge, 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 an eruption (ejection).




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). 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, which should logically mean that the initial pre ejection spike should start before mitral valve closure, as can be demonstrated below:

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.




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 base, and thus be a part of the closing mechanism, however, the displacement of the ring towards the apex is far less than the motion of the leaflets towards the base.
Pressure volume loop with a small pre ejection or protosystolic volume reduction before IVC (P). 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. During the IVC, there should be no shortening. This is solely a function of 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, it may be 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 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).

This is in acordance with known facts in physiology and experimental studies. However, it can still be 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. 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).




AS peak dP/dt is before aortic opening (241), a decline in the RFD before aortic opening is evident.


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.



Thus, the closest correlate to contractility would be peak dP/dt. However, as this is isovolumic, this is not measurable by deformation. Deformation measures changes during ejection, where there is volume decrease.

Ejection


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


As has been discussed above, only the first part of ejection is active contraction, the rest is actually relaxation. 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 velociotes, with an early peak, and the slower decline. The peak velocity is the the maximal rate of of shortening, slightly after the AVO.

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.




Global systolic function


From what have been discussed above, analoguous to muscle function, the systolic function can be described in various ways.

Peak rate of force development

As force is related to pressure, peak rate of force development is at the time of peak rate of pressure increase peak DP/Dt. This is during the IVC, and cannot be measured by imaging (deformation). However, the force continues to increase during the first part of ejection, as aortic/ventricular pressure increases during the first part of ejection, though at a decreasing rate of force development.


Peak rate of shortening

will be the most rapid shortening rate. As described above, the peak rate of shortening is close to the point where tension overcomes total load i.e.) the point of AVO. However, the peak rate of shortening (which is the same as the peak rate of ejection), will be delayed due to the acceleration of both blood and muscle. (As the blood reaches a velocity 10x the velocity of the tissue, it seems that this is the main mass that must be accelerated. But, as can be seen this point of maximum velocity is lightly after AVO.






Peak velocity of annular systolic motion should thus be a fraction of the peak flow velocity, by the ratio of LVOT area / LV outer area.

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 also be more closely related to peak force. But as it still is related to rate of shortening, it does not include the rate of pressure rise during IVC. It is a function of the force needed to accelerate the blood volume, mainly, and inversely related to the stroke volume. Also, the temporal derivation of acceleration from velocity will result in a less favourable signal-to-noise ratio than the velocities.




Thus both peak acceleration and velocity are early indices of systolic LV performance, and earlier than the peak pressure. Thus, they should be less afterload dependent, and may to a greater degree reflect changes in contractile state, however, determined partly by preload.

Peak systolic force

Is a measure of the peak tension developed, and should be closely related to peak systolic pressure, as this is the force that has to be overcome (taking into account that this also depends on LV volume). This point is later than peak rate of shortening, but may actually be closer to peak (Eulerian) strain rate.

Maximal shortening

which in the isoloated myocyte is the same time as peak tension, but in the intact heart is at end ejection, which is far into the relaxation phase of the myocytes. End systole is the time of measurement of FS, EF, MAE and global strain.



Peak systolic versus end systolic measures of ventricular function.

Peak systolic measures are the measures of peak ventricular performance, and can be measured as peak ejection velocity in the LVOT, peak annular systolic velocity, and global ventricular strain rate. These occur early in systole, and may be less load dependent, as maximum afterload is reached later in systole. Peak velocity is related to acceleration, which is a direct measure of force, and thus to contractility. 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.

Also: Increased contractility will not to the same degree lead tio increased stroke volume, if there is no concomitant increase in venour return. Thus stroke volume wil be maintained, but at a lower end diastolic volume. This means end systolic measures will be less affected by contractility increase as discussed above.

Early global systolic measures are Peak ejection flow velocity measured in LVOT, Peak systolic mitral annular velocity and mean peak systolic strain rate. 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.



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, annular displacement and global strain, in addition to EF. Whether this influences the sensitivity of the measures, is not clear so far.

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.

Peak strain rate, has a slightly later peak maximum, the reason for that is discussed above, and in more details in the mathemathics section.




Left velocity curves. It can be seen that the two velocity curves have an early maximum, showing that the myocardial acceleration occurs early, and is an early event. Peak systolic velocity is seen at about 100 ms into the heart cycle, starting with ORS.  After this, there is a period of nearly constant velocity difference, before the velocity difference decreases again. Right, the strain rate curve from the segment between the two ROIs in the left picture. It can be seen that peak strain rate is a  later event, about 200 ms after start of QRS.  The strain rate increases after peak velocity, during the period of near constant velocity difference. This is due to the fact that the velocity difference is normalised for the instantaneous distance that is decreasing during systole, i.e.  Eulerian strain rate

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.


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.

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 MAE, 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 corelation 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.

However, in other cases the 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 unchaged. 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 unchanged, the ventricle is reduced in size, meaning the the cavity volume 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.



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.


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


Longitudinal M-mode through the mitral ring, displaying the displacement of the mitral ring. The total systolic displacement (MAE; mitral annulus excursion) can be measured.  If  the MAE 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 strain during systole is thus MAE /LD.


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

The annular The term mitral annular descent or mitral annular excursion (MAE) (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 measurements is unclear.

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

In addition, the MAE 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 MAE correlates better with BNP in heart failure, that the fractional shortening (204).

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

There has been some arguments for measuring MAE 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. 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 MAE, 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 MAE x cross sectional area = SV still holds. However, this means that some of the variations in MAE 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), where the varation in heart size is great, the advantage in adults, where variation in heart size is less (and less that the diffenence 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).


Peak annular systolic velocity


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 (Which is different from the Eulerian strain rate that is customarily used in ultrasound. This is discussed below.

Peak annular velocity occurs early in systole, and may be less load dependent, as maximum afterload is reached later in systole. Peak velocity is related to acceleration, which is a direct measure of force, and thus to contractility. However, peak velocity is not load independent, as increased load will result in a delayed and blunted development of force and velocity, as opposed to the pressure/volume relation. In addition, as most pressure work is done before ejection, the pressure work will not be measured.

Peak systolic velocity (S') has been validated as a measure of systolic function (37, 38, 39, 40).



The correlation with EF is weaker than for MAE, which is not unsurprising, EF and MAE 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.


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.

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 should measurements be done?

As the velocities are 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).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.


Global strain and strain rate

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), 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 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.

Normalised displacement and velocity.



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

Normalised MAE. The normalised MAE for this ventricle with an end diastolic length of 9.2 cm and an MAE 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:




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

Thus, it is emerging evidence that normalisation of MAE, 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.

The normalised velocity may also be taken as a global strain rate.



Dividing the mitral annular displacement by L0 gives the Lagrangian strain. Dividing the MAE by end systolic length gives the Eulerian strain.
Dividing the peak annular systolic velocity by L0, gives the peak systolic Lagrangian strain rate, not the velocity gradient which equals the Eulerian strain rate. Dividing the peak velocity by the end systolic length, however, do not give the Eulerian strain (this is obtained by divideing the velocity difference in each frame by the instantaneous length in the same frame).


This however, will be the Lagrangian strain rate
, not the Eulerian, with the differences described above. Peak annular velocity  normalised for  end diastolic  LV length, will yield peak Lagrangian strain rate.  Peak annular velocity  divided by  the length at the time of  peak velocity, but this will be Eulerian strain at the time of peak velocity, not peak Eulerian strain rate, and thus be less meaningful. There has been no documentation of this so far.

Normalisation of velocities is thus less established, and systolic velocities are related to diastolic velocities.



Normal systolic 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 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 does the early diastolic.


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.


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. 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 id 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 ha 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.


Locating the AVC by this assumption, the method of tracing an M-mode across the anterior mitral leaflet has been published. Hoever, still with AVC as te onset of the early diastolic negative spike.

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 obervational study (16) of high frame rate, we saw that this took place in mid septum before the valve click of aortic closure:


Colour 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, 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.
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. The aortic cusps then are closed due to the action of 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 aortic valve 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.



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.

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: "The apical cap can only be appreciated on some contrast studies. A 16 segment model can be used, without the apical cap, as described in an ASE 1989 document."

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. the amount of myocardium in the apeical 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).

Do annular measures 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.It might be conceivable that tilting of the mitral ring in response to different actions of the different walls in regional dysfunction might lead to tilting of the ring. Again, this seemed to be something "everybody knew", because it seemed so obvious.  Indeed that hypothesis has been maintained for a long time, and still is, by some.

This hypothesis is illustrated below:
Hypothesis



 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).

There are fundamental anatomical and physiological reasons for this.

Firstly: The AV plane is not only the mitral ring. 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.

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

Segment interaction

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. This again, is due to the point that the global deformation happens within a framework of a virtual "eggshell", and the AV plane. 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.


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.



 (This load dependency is also the basis for  the post systolic shortening. )

Both acute ischemia (46, 99), as well as 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. This, however, may give different deformation patterns, depending of the amount and location of the contractility loss. Again, it is to be emphasized that the deformation does not measure contractility directly, nor is deformation dependent on muscle action alone.


Deformation patterns in apical loss of contractility. A: normal pattern as in the diagram above.  B: partial loss of contractility, as shown by the shorter black arrow pulling on the midwall segment. In this case several things may happen: If the residual contractility is just about to balance the force from the two other segments, no deformation occurs, thus the segment will be akinetic, but not due to a total loss of force. Thus, akinesia does not necessarily mean total loss of function. If the contractility is a little better, there will be shortening, i. e hypokinesia. If the contractility is a little too small, there will be stretching, i.e. dyskinesia as in C. In the case of akinesia shown here, there will be a little motion of the middle of the midwall segment, due to the shortening of the apical part, but not much, and the basal segment will have substantially reduced motion as well, despite both segments having normal shortening.  C: Total loss of contractility. (Of course, in this case normal function of the midwall is improbable, this is just an illustration of the mechanics.  In this case, as the apex is anchored, there will be stretching of the apical segment.  The midwall segment may then have no motion, as the stretching of the apex and the shortening of the basal segment may cancel out, as depicted here. Or there may be net motion in the apical direction, as the stretching may require more force than moving the (more freely moving) basal segment.  Also, especially in infarction, the picture may be complicated by fibrosis. Heavy fibrosis in scarring may render the segment totally un-stretchable, thus mimicking situation B. Apical infarct. In LAD infarcts, the whole of the apex is usually affected, the infarct sits as a "cap" over the apex, although the extension towards the base may vary in the various walls. Thus, the reasoning in the illustration to the left holds for the whole ventricle.


In apical infarcts, some of the mechanics is thus determined by the fact that the apex is anchored (by the recoil force) and does not move. In basal inferior or inferolateral infarcts, the infarcted segments are situated close to the more freely moving ring.  Thus, even with loss of contractility, there will be less load, so the base can shorten, and even with total loss of contractility, the segment will move. so the tendency to stretching is less, and even in functionless infarcts there may be no or nearly no stretching. However, this is not the only point.  In LAD infarcts, the infarcted segments are situated in the apex, as shown above left, meaning that all walls are affected, although the extension towards the base may vary, so the wall are not affected to the same degree. In Infarcts of the RCA or distal Cx, as well as isolated obtuse or diagonal infarcts, the infarct does not extend around the whole circumference, and the effect is more regional as shown below.





Inferior infarct. A: Normal function. (The arrows indicating normal shortening are smaller, to give room for the hyperkinesia in the infarct situation in B.) B: Total loss of force in the basal segment. Even with total loss of force, the segment can be pulled along, due to the tethering effect, and the fact that the mitral ring, as opposed to the apex, is movable. A perfect example of this can be seen here. Thus the probability of any great degree of stretching is less probable.  A small amount of stretching my be present, depending on the interaction with the other segments pulling on the mitral ring.  There is thus no force from the basal segment acting on the rest of the wall, and thus the load on the two other segments are reduced, leading to increased shortening, which may be interpreted as "compensatory hyperkinesia".  However, this follows as a function of reduced load, not hyper function.  AS the mitral ring moves around the whole of the circumference, the shortening normally distributed to three segments, in the infarcted wall is only distributed to two.
Inferior infarct. There is slight stretching, but the main point is the fact that the infarct only affects the base and midwall of the inferior wall, and the base of the septum. Thus only the basal part of 1/3 of the circumference is affected.
Thus, it may seem that in apical infarcts, there is more resistance to the normal segments, as the infarcted segments are stretched, and thus, there is a slightly higher load, while the basal infarcts, sitting at a moving ring, will offer less resistance to the normal segments, allowing them to shorten more.

In studies of the course of infarcts (92, 188), it has been seen 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 hyperkiesia will regress as illustrated below.



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).


What "everybody knew" was wrong. There is no regional reduction of mitral motion in regional dysfunction.

Only global reduction of mitral motion, and segmental hypokiesia with resiprocal hyperkinesia.


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. 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 development, as shown below. 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.


In relaxation, this means that while protodiastolic elongation is mid ventricular, it will result in elongation also in the base, early relaxation has different timing of deformation in different levels, but still results in an over all motion of elongation. Segements may contract differentially, but this is not reflected in regional differences of motion. Finally, global strain is simply global ring motion normalised for LV size.


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 disecussed 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. 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.


However, if there is akinesia of one of the layers, both outer and inner layer akinesia will result in less circumferential strain in the inner layer. as illustrated below.


Akinesia of the outer layer, normal thickening of the inner layer.  This will result in no thickening or circumferential shortening of the outer layer, less inward displacement of the inner layer, resulting in less thickening (due to more space) and less midwall circumferential strain due to both less thickening and less inward shift.

Thus, reduced circumferential strain in the endocardial layer will be present even if the dysfunction is in the outer layer. Of course, this instance is nearly hypothetical, at least in ischemia, if there is differential myocardial function, the reduction will always be most severe in the endocardial layer. It  serves onbly to demonstrate that reduced endocardial circumferential strain is not necessarily due to reduced function of the endocardial layer, but rather a function of geometry. AS the ischemia usually will affect the innermost layer, this is illustrated below:


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.

Thus except in the case where there is stiffness of the ischemic layer, there will still be some mid and endocardial layer thickening and circumferential shortening, even if there is no function. The same is true about circumferential strain in general:

There will be reduced circumferential strain due to reduced wall shortening, even if the circumferential tenison is unaffected. This reduced circumferential and transmural strain is NOT restricted to the affected layer, and the affected layer may show some strain that is not due to layer function.

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:

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.



Post systolic shortening

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). A small amount of post systolic shortening may be present in up to 1/3 of normal segments (47), but not more than ca 3%. Pathological strain is concomitant with reduced systolic strain, and higher post systolic strain (in magnitude), as well as later peak PSS. Post systolic shortening and post systolic thickening are to some degree equivalent, due to the incompressibility as discussed above.

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. However, PSS can be seen in segment that have systolic shortening as well, as shown below. 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 below.

Thus, PSS can be present where there is systolic shortening as well, and here the mechanism has to be different from the recoil. It has been proposed that storing of elastic forces due to the interaction with normal segments during systole maybe a mechanism, but it is difficult to see how this can be the case, as elasticity is a function of stretch. In ischemia, the development of force is reduced, due to a lower energy state. Both the rate of shortening as well as the total shortening (i.e. strain rate and strain) is reduced. Thus the increased relative load in ischemic / infarcted segments is important, in that it delays the force development, and the ischemic segments will shorten less due to the decrease in contractility relative to the regional load.

But in the energy depletion (as in acute ischemia), the availability of ATP for the removal of calcium from the cytoplasm is also reduced, thus leading to a continuation of tension. Thus, ischemic segments maintians tesion longer than the other segments of the ventricle. This means that when the normal segments relax, the ischemic segments maintain the tension, and thus will shorten due to the decrease in regional load form the normal segments.

When healthy myocardium relaxes, the delayed relaxation of the pathologic segments will cause them to shorten, as a function of the reduced force in normal segments. Thus, the post systolic shortening is a function of the interaction between segments. In this phase, there is pressure decay as well, decreasing global load, further reducing the load on the affected segments. Thus, post systolic shortening is mainly the reduced, but prolonged contraction of a segment due to ischemia and / or relative load increase in the early diastolic interaction with normally relaxing segments.


Diagram of post systolic shortening in an apical segment. In systole, there is reduced contractility (force) in the apical segment, causing reduced shortening compared to the other segments. In early diastole, there is no force from the normal segments, as they now are elongating during relaxation. (Elongating being the result of elastic recoil from the systolic compression as discussed above). The prolonged contraction (force development) in the affected segment, is allowed to continue shortening as it is not counteracted, causing further shortening during early diastole.

That segment interaction is a prerequisite for PSS, can be seen in the example below, where there is total ischemia, and hence, no normal segments and (almost) no PSS in the ischemic segments.


In ischemia, the cytoplasmic calcium transient is also reduced, leading to more prolongation of the contraction, thus there may be more PSS in ischemia than in old infarcts where the mechanism is mainly relative load. This seems to be the case as the presence of PSS decreases in the three months following the infarcts (92). 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.

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).


Looking at Strain rate,  it is evident that any systolic stretch with early diastolic recoil will show up as post systolic shortening. However, with strain, it is useful to separate between systolic shortening followed by post systolic shortening. This is better shown in the curves with strain, but also in the colour M-mode of strain rate, which in addition gives the extent of PSS.


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.
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). There is little indication of active contraction at all (except possibly a little overshoot, but that may be elastic). However, the stretchability and recoil indicates that the tissue has not lost it's elasticity. 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.  In fact, these curve is very similar to the curves in the original work of Tennant and Wiggers from 1935 (46).

The presence of post systolic shortening in the earliest phase of acute ischemia, was demonstrated already by Tennant and Wiggers in their experimental work in 1935 (46), although in the paper they chose not to discuss the phenomenon, concentrating on the initial stretching and decrease in amplitude of shortening, and the full dyskinetic pattern showing up after a minute or so. It is rumored that they considered this an artifact, but the phenomenon is clearly visible in the published traces. Post systolic thickening in ischemia was shown in a case by Jamal et al in 1999 (185), and demonstrated during angioplasty by Kukulski et al (100). Decreasing systolic and increasing post systolic shortening with increasing ischemia is demonstrated below. (In fact, there is a striking similarity with the traces by Tennant and Wiggers in their original paper. It was shown to be present in both is chemic and scarred myocardium (47), in about 75 to 80% of segments.



Development of apical ischemia during stress echo.; showing normal contraction at baseline, increased during low dose (10 µg/kg/min, may be a biphasic contraction at 20 µg/kg/min, not very evident in this animation, but may be better visualised by stopping and scrolling the loop in the clinical situation.



Colour SRI M-modes from septum of the same examination, showing clearly at 20 µg/kg/min the development of a prolonged shortening period in the apex,  but still systolic shortening as well. During peak stress, there is virtually no systolic shortening, only post systolic.
Strain curves at 20 µg/kg/min (top) and peak stress (bottom), showing systolic hypokinesia at low dose with PSS and akinesia in septum / dyskinesia laterally with PSS. Thus, PPSS are seen also with hypokineqsia, and is not only a recoil after stretch.



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). Two examples of systolic dyskinesia with post systolic shortening in myiocardial infarction are shown below.





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). 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 the infarcted wall.
In the systolic images, the areas of dyskinesia are especially evident, but as in the stress example above, areas around may be  hypokinetic (not as evident in the parametric images), but in the diastolic images the PSS is seen to be  fairly extensive, proving that this is not purely  recoil.


According to the description above, if all segments are pathological, the PSS should be less obvious or even absent due to the lack of interaction with normal segments as demonstrated below.
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 synchrony.

Strain rate  curves (left) and strain (right) 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.

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.In pathological myocardium this has also been demonstrated in hypertrophic cardiomyopathy, where the prolonged contraction persists into diastole, even causing ejection from the hypertrophied apex (87).






Recording from a patient with apical hypertrophic cardiomyopathy.  During systole there is virtual obliteration of the apical cavity.  Ejection can be seen in blue, and there is a delayed, separate ejection from the apex due to delayed relaxation. There is an ordinary mitral inflow (red), but no filling of the apex in the early phase (E-wave), while the late phase (A-wave) can be seen to fill the apex.  Left,  a combined image in HPRF and  colour M-mode.  The PRF is adjusted to place two samples at the mitral annulus and in the mid ventricle just at the outlet of the apex. The mitral filling  is shown by the green arrows,  and the late filling of the apex is marked by the blue arrow.  In addition, there is a dynamic mid ventricular gradient shown by the red arrow, with aliasing in the ejection signal in colour Doppler. The delayed ejection from the apex is marked by the yellow arrow (the case is described in (87).  
Strain rate from the same patient, showing PSS in the apical part of the septum, and nearly the whole of the lateral wall. (images were made in a very early software, but yellow is still shortening, blue lengthening.)

Also in hypertension is PSS a frequent finding (187).

Asynchrony:


Conduction delay:

Conduction delays may lead to asynchronous contraction of the left ventricle.


Dilated cardiomyopathy with left bundle branch block. It is evident early contraction of the septum with short duration, due to  the lack of load provided by the rest off the ventricle  and then there is delayed contraction of the lateral wall.


This is evident in the M-mode, where there is an early, short lasting dip of the septum, about 300 ms earlier than the peak of the inferolateral wall. The phenomenon has been described as "septal beaking" and is a sign of left bundle branch block (251).





Looking at velocities, there seems to be an earlier peak velocity in the septum than the lateral wall, this may indicate asynchrony.



Looking at the deformation parameters, there is septal shortening (initial negative spike in the yellow curve) of brief duration, and then lateral shortening (larger negative spike in the cyan curve) of much longer duration. In this case the mechanics is much more evident by strain than by strain rate when looking at the traces, showing a brief shortening of the septun, and then prolonged stetch (yellow curve), and delayed and prolonged shortening in the lateral wall (cyan).


However, looking at the strain rate colour M-mode the same is evident, even despite the heavy reverberations in the lateral wall.

This finding was described first in 1974 (251), described that the septal activation vcame already after about 40 ms, corresponding to the electromechanical delay. This is during the pre ejection period, where there normally is no shortening.However, due to the absence of activation in the rest of the ventricle, the seotum will be free to shorten without pressure increase, thus giving an early and rapid contraction in what would normally be the IVC. The rest of the ventricle contracts delayed, when the contraction of the septum is finished, and the work is done without assistance from the septum.

In this case, the asynchrony is evident from velocities, but the mechanism is more evident looking at deformation.

Post systolic shortening


Presence of PSS may give asynchrony between walls, where almost all of the wall may be out of phase, even if there are gradients of ischemia as shown below.


Stress echocardiography with development of ischemia in the inferolateral wall. At peak stress, the whole of the wall can be seen to move paradoxically, moving inwards (and towards the apex) after end of septal contraction.  Again, in a clinical situation, the interpretation can be facilitated by stopping and scrolling.

The velocity (motion) confirms the visual impression, the whole inferolateral wall moves downwards in systole, and upwards after end systole (Yellow and green curves), while the septum shows normal apically directed velocities giving a total asynchrony between the two walls. This asynchrony is also evident by the curved M-mode, starting a the inferior base, going through the apex and ending at the septal base.This might be due to both apical and basal ischemia.



The strain curves below, separates the effects of the segments, showing systolic dyskinesia (lengthening)  with some net post systolic shortening in addition to the recoil in the base (yellow curve), and systolic hypokinesia in the apical segment (green curve) with post systolic shortening, compared to a fairly normal strain curve in the septum. Thus, deformation imaging showing most severe ischemic reaction in the basal part, giving highest probability of a Cx ischemia, which was confirmed angiographically.

In this case, the tissue velocities are sufficient to detect the presence of ischemia, but the deformation imaging shows the location and extent of the ischemia, while velocities shows asynchrony of the whole inferolateral wall. Thus, the basolateral ischemia might have been mis interpreted for lateral asynchronia.




The presence of regional systolic dysfunction in combination with post systolic shortening, may cause asynchronous motion of a whole wall, as shown above. This means that the presence of asynchrony in motion imaging is not specific. A further example, also from stress echo; i.e. ischemia, is shown below.



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, om 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 streching 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 both these cases, it is evident that asynchrony between walls, as seeen by motion imaging is not real asynchrony, but an effect of tethering to a smaller asynchronous (ischemic) area. Thus, simply showing asynchrony by motion imaging is insufficient in the diagnosis of conduction abnomalitiy induced asynchrony.

Also,


In this peak stress image, the tissue Doppler confirms the presence of initial asynchrony: The whole of the inferolateral wall seem to show dyskinesia (Yellow and cyan curve), with early motion (after IVC) away from apex. It seems to be most pronounced in the apical part.The septal base moves normally, toward apex (red curve). By placing the sample volume in the aortic ostium, the high velocities of the aortic closure is identified, giving the timing of end systole. This timing can then be transferred to the deformation images below.
Stress echo. In this case, the image is suspect of a delayed inward motion of the base of the wall at start systole at medium and peak dose.



Strain rate (left) and strain (right) showing that there is a slight reversal of shortening in the early diastole, but only in the base (cyan) .  The delay, however, is shown to be entirely within systole. The clinical meaning of this is uncertain, but it was not due to ischemia, as the coronary angiography was completely ("super"-) normal.
In this case, the deformation imaging helps in the timing confirms the delay,but shows it to be less pronounced, and not indicative of ischemia, and it also helps in showing the the extent, compared to tissue velocity. (The patient had completely normal coronaruy angiography).

Translation effects

However, translation effects with motion of the whole ventricle, may also result in apparent asynchrony as shownin the exemple above (main images repeated below for repetition):


The whole heart can be seen to be rocking. This might indicate asynchrony, or dyskinesia of the septum.
However, looking at the short axis view, the wall thickening (transmural strain) can be seen to be synchronous.






Tissue Doppler left shows delayed onset and peak velocity of motion of the lateral wall, but this is due to the rocking motion of the whole heart. Strain rate shows symmetric timing of onset and peak shortening.  This difference between motion and deformation imaging was evident already in B-mode, when knowing what to look for.

In this case, the motion (velocity imaging) is mis informing, giving the appearance of dyssynchronous function of the left ventricle, while deformation shows this to be untrue.







Diastolic events

Isovolumic relaxation period (IVR)

The isovolumic relaxation period is defined at the time from aortic valve closure to mitral valve opening, i.e. the period when there is no ejection or inflow to the ventricle. Thus, there can be no overall volume change. It is easy to show in Doppler flow tracings, if the tracings include both aortic valve click and start of mitral flow:


Isovolumic relaxation period (IVR), is the period from aortic valve closure (AVC) to mitral valve opening (MVO). In a Doppler flow recording with the sample volume between the aortiv and mitral valves, this is easily seen by the valve click of AVR to the start of mitral inflow.



The opening of the valves is a passive event, where the valves follow the blood flow, with the same motion and velocity. Thus the valve opening is the start of flow through the valve. As with AVC, due to heart rate variability, it would be advantageous if the mitral valve opening (MVO) could be identified in the tissue Doppler recordings, instead of being transferred from other cycles. This problem actually is trivial, but for pedagogical reasons it may be wothwhile to look closer into the mechanics of mitral annulus and leaflet motion.


When is mitral valve opening?

The trivial part of the problem is that the start of anterior mitral motion can be identified by placing a sample volume at the tip of the mitral valve, and identifying the point of earliest anterior moment:

Mitral valve opening. The point of initial high velocities in a sample volume placed close to the tip of the mitral leaflets at end systole will identify this.

As the mitral valve is visible in all standard planes, this is feasible for all tissue Doppler measurements. It should be possible to identify the mitral valve opening directly. The real opening point is the point where the mitral leaflet moves toward the apex, but independently of the apical motion ot the mitral ring. However, as the parts of base of the heart moves slightly towards the apex after AVC, the mitral valve motion follows the mitral ring and may have apical motion as well, and the leaflet may have partly motion from the ring, and partly from the tip:





Motion of the mitral ring, mitral leaflet and mitral tip.  Bottom; zoomed to the time period of interest. The septal mitral ring (yellow curve) can be seen to "bounce" after AVC, meaning that it has apical motion during IVR.  This motion is of course imparted also to the mitral leaflet, and means that the start of apical motion do not mark the MVO.

Velocity traces of the same points as seen to the left. The start of apical motion of the mitral ring (yellow curve) corresponds to a shft from negative to positive velocities after the protodiastolic negative velocity spike (i.e. the crossing of the zero line.
A sample volume at the middle of the mitral leaflet (green curve), will have the same motion as the ring, although with some delay. However, we see that apical motion starts around the middle of  IVR, before MVO.
This corresponds to positive velocities in the last half of IVR (green curve).
The sample volume at the mitral tip (red curve) shows no apical motion during IVR, rater motion in the opposite direction, but an abrupt start of apical motion at the end of AVR, at the same time as the mitral ring shifts to motion toward the base. Thus, this is an independent leafet motion, and marks the MVO, and it can be seen that during IVR, there is ballooning away from the apex of the mitral leaflets.
Both mitral valve traces can be seen to deflect sharply downwards at a later time point (white markers) , this is due to aliasing of the tissue velocity when the velocities reaches the Nykvist limit.
 
The mitral tip (red curve) can be seen to have negative velocities (moving away from the apex) during IVR, and to cross from negative to positive velocities at the same time as the mitral ring crosses from positive to negative.

The points of aliasing can be seen at the abrupt downward stroke in the traces from the mitral leaflets (White markers), which is earlier at the tip than in the middle of the leaflet. Only in the mitral ring can AVC be seen with certainty.

The aliasing velocities of the mitral vale are later than MVO, as this marks the time when the leaflet movement (moving with the same velocity as the flow, as discussed here) reaches the aliasing velocity of the tissue Doppler, being dependent on the PRF and depth. This is also earliest at the mitral leaflet tips, as they have the most rapid motion, but still later than MVO.





M-modes from the mitral ring (left), middle mitral leaflet (in terms of distance from ring to tip - middle image) and mitral tip (right image), corresponding to the traces above.  The traces show only systole and early diastole, as above. As in the traces there is shift from negative (blue) to positive (red) at AVC and from positive to negative at the event taken to be closest to MVO.  In the middle mitral leaflet, however, this is less well defined, only in the lowest part can these event being identified. At the mitral tips, the transition marking AVC is absent, (as above), while the second transition from blue to red is visible in a short part of the M-mode.


Thus when the mitral valve opens, flow starts and the ventricle expands (elongates) corresponding to the downward shift in displacement of the mitral ring. However, the mitral valve opens, meaning motion of the leaflets into the ventricle, continuing the motion towards the apex. Thus the leaflets do not have the shift from positive to negative velocities.  Some authors have described this  anyway, but  this is due to the fact that the lateral resolution in tissue Doppler is very low due to the low line density, in order to achieve a high frame rate, meaning that an M-mode line placed across the mitral leaflet close to the ring actually will be ring velocities as discussed in the measurements section. In addition, the base of the mitral leaflets will tend to follow the ring motion more than the tips. Also, the opening of the mitral valve is gradual, starting at the tips, and moving outwards towards the ring.

Looking at mitral ring traces, the logical candidate would be the moment the mitral ring starts to move away from the apex, after the "bounce" following the AVC. This would hypothetically be the time point where the ventricle starts the volume increase, seen as elongation by the mitral ring. But as this is not an abrupt mechanical event, but rater a gradual transition (an upwards convex curve in the displacement traces), this is not as easily delineated. Also , it is not necessarily present in all parts of the mitral ring (theoretically, it shouldn't, of course!).



Looking at the mitral ring, which would reflect the overall volume changes, there is concomitant negative velocities (basal motion during the protodiastolic event in both parts of the mitral ring. But after AVC, we se negative velocities continuing in the lateral part, while there is a positive motion (bounce) in the septal part. This is consistent with no volume change, but a tilting of the left ventricle during the IVR. Mitral opening thus possibly corresponding to the start of basal motion as seen by the septal curve. Only after MVO do the septal part start basal motion concomitant with the lateral part. And only then will there be overall elongation (volume increase). This do correspond to s shioft in the septal velocity curve from posisitve to negative. It is the second zero crossing after the protodiastolic dip.




Thus, it will correspond to a shift from positive to negative velocity in the velocity traces from the septum (but not from the lateral wall), and a red to blue shift in the colour traces, as seen below.

However, as seen from the M-mode, the transition from positive to negative (red to blue) is not evident at all levels.

Fundamentally, however, the identification of MVO in an apical tissue Doppler recording is truly trivial, using the mitral leaflet itself (which can be seen in all apical views), as long as care is taken to place the sample volume at the tip of the leaflet.

What about strain rate and strain curves?

As shown above and discussed in detail below, the strain rate curves show a very complex pattern, and is unsuited for locating events in this part of the heart cycle. Also the strain curves shows different patterns in different levels of the myocardium. Thus, the deflection points can be seen to be located differently in the different levels of the wall. In addition, the presence of post systolic shortening, especially in pathology, but also in normal ventricles, will result in the shortening will last longer in the  strain rate then the  upward movement in the  displacement. Mitral valve opening should thus be identified in velocity images and transferred to deformation images from the same loop.




Zoomed images of velocity (left) and displacement (right), showing that there is a peak apical mitral ring displacement at  the event taken to correspond to MVO. This is equivalent with the second zero crossing of the velocity trace after protodiastolic dip.
Peak negative strain occurs later in base and midwall. AVC can be seen best by strain curves in the midwall segment. No definite deflection can be seen to correspond to the event assumed to be MVO transferred from the Velocity/displacement traces.

During the IVR, there is a rapid pressure drop. The pressure curve is sigmoid, with a transition from convex curve during last part of ejection, to a concave curve at the start of mitral inflow. The time constant of the pressure drop , the tau, is taken as a measure of diastolic function, meaning relaxation velocity. AS the maximal relaxation is during the IVR, this would be the logical time for measurement of diastolic function, but as there is no overall volume change or flow, and little deformation, this may be les than optimal from an imaging point of view.

The peak negative dP/dt, is the transistion point. This transition should be no earlier than AVC. It has been seen to be close to the AVC (244), and has been suggested as a marker of aortic valve closure in pressure tracings.This however, was the case in open chest experiments, which may differ in the closed chest physiology.


Deformation during IVR

As discussed above, there is an elongation and volume expansion at end ejection, due to continued relaxation after the flow has stopped, but this occurs before aortic valve closure, and is thus protodiastolic. It may be the mechanism for aortic valve closure itself.


During the true IVR, from AVC to mitral valve opening (MVO), there can be no overall volume change. However, intraventricular flow in normal subjects during the IVR has been described early (246).




Colour M-mode in normal subject. The mitral valve is included, and to the left the colur is removed from the same two cycles in the same recording, to locate the point of mitral valve opening better.
IVRT: Zooming in on the images, at end ejection can se the valve click as a vertical bar (Just as in pulsed Doppler recordings as seen above) thus, the IVR is very easily defined, and apically directed flow (red) above the mitral valve, i.e. intraventricular can be seen during the IVR.

The apically directed intraventricular flow during IVR, must mean that the apex has to deform during this phaset. The flow has to be taken as an indication of a base-to-apex pressure gradient, and hence, that relaxation starts in the apex. As described above, true relaxation starts earlier, during ejection, but the gradient is an indication that early deformation starts in the apex. There has to be a space for the blood volume to flow into. Thus, the earliest deformation starts during isovolumic relaxatin in the apex. This has been confirmed by MR (247)

Thus, there has to be regional deformation during IVR, but no overall change in volume. This would mean that there should be expansion in the apex, but without overall volume increase, this shoud correspond to a decrease in volume in the base.





Strain rate tracings in this subject show positive strain rate (lengthening) during IVR in the septal apical and lateral apical and midwall segments, concomitant with negative strain rate (shortening) in the basal segments. (In the apical area, there are near field reverberations, which have to be excluded. These, however are evident by the abrupt shift in direction between high strain rates. )

Further examples of this isovolumic deformation in the apex can be seen here, here, here, here and here, and the net result would be a shape change without net increase in volume, as indicated by the annular tracings:




This is also evident in strain curves:


In this recording there is shortening in the septum in the IVR , coresponding to apical displacement of the septal annulus (cyan), showing up as post systolic shortening, but elongation from the AVC in the lateral wall (yellow).

However, the consistency of the patterns needs to be evaluated in larger studies. The main points, however, are:
  1. During IVR thre is early deformation of the apex, as seen by MR and intraventricular apically directed flow
  2. There is no net increase in LV volume, thus there has to be change in over all shape of the LV

Diastolic function

Diastolic function of the left ventricle needs to be defined. In practice, it has been taken to mean the relaxation of the myocardium. However, this is not very precise. Myocyte contraction is followed by lengthening, in isolated myocytes, restoring the original shape as shown below:

Isolated beating myocyte. In systole the cell can be seen to increase free calcium and simultanously shorten, as explained above. Thus in the cellular diiastole, the cell can be seen to elongate, and simultaneously free calcium disappears from the cytoplasm. Basically this is an interaction between various processes. The removal of free calcium is an energy (ATP) demanding, active transport of calcium into the sarcoplasmatic reticulum by SERCA. This releases tension, as the actin myosin cross bridges are released. However, this alone will not cause elongation of the cell. Thus, the elongation has to be release of the elastic energy from systole. in an isolated myocyte, this elastic energy has to be stored in the cell itself, probably in the cytoskeleton.  We see that the calcium increase/shortening is a quick process, while the calcium decrease/lengthening is a much slower processImage courtesy of Ph.D. Tomas Stølen, cardiac exercise research group (CERG), Dept. of Circulation and Medical Imaging, Norwegian University of Science and technology.


The rate of relaxation is governed by the rate of removal of calcium from the cytoplasm, this removal unbinds the cross bridges between actin and myosin and releases tension. But this is an active, energy consuming process, due to the  active calcium transport into the sarcoplasmatic reticulum. The lengthening itself has no active mechanical component in the contractile apparatus itself, and must be due to elasticity, i.e. stored elastic energy from systole. Whether this is due to titin that acts as a two-way sping, or other elements in the cytoskeleton in addition, remains to be seen. In practice, an elastic element in parallel to the contractile element might be expected.


In the intact heart, however, there may be external structures storing elastic energy as well:
    • the interstitium - being compressed
    • the atria - being stretched
    • the large vessels - being stretched by the apical motion of the AV-plane
Thus diastolic deformation may be seen as the interaction between the tension release. which again is dependent on the rate of calcium removal, and the elastic recoil.

And as the elastic recoil is partially dependent on systolic shortening, this means that diastolic function is afterload dependent as well. (Preload dependency come only when the relaxation rate is so low that the filling shifts from a vis a fronte to a vis a tergo mechanism.

These are released by the decrease in myocyte tension, and contributes to the restoring of the ventricular diastolic shape, the restoring forces (173), and may explain some of the correlation between systolic and early diastolic velocity observed in the HUNT study (165).
But even so, the shortening-elongation cycle (the physiological systole-diastole) seen in the isolated cell do not correspond to the ejection-filling cycle (the cardiological systole-diastole)of the intact heart at all. This is due to another component, the wall-fluid interaction (especially fluid inertia in ejection):

In the free 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.

The Wiggers cycle: Heart cycle in terms of pressure changes
                                             
Heart cycle in terms of volume changes ( =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.

But as blood is stille being ejected, the ventricle will still reduce its volume, and we measure systolic deformation in the meaning volume reduction/wall shortening. 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.

The cardiological diastole starts with Aortic Valve closure, and comprises the isovolumic relaxation period (IVR) and the filling period.

However, these are different physiological events:
  • IVR is the continuing myocyte relaxation, causing pressure drop, but no volume changes. Thus virtually no deformation (although small shape changes). The duration of IVR, however can be measured by imaging, and is among other things a measure of relaxation rate as discussed below. In this case, there is no deformation, and hence, the rate of presure drop is the real measure of diastolic relaxation rate.
  • The early filling period is contuinuing myocardial relaxation, the volume increase due to elastic recoil generates the suction of early diastole, leading to early filling, early volume increase and deformation (lengthening/wall thinning) as shown by any imaging method (e.g. tissue Doppler.
  • The rest of diastole, the diastasis and late filling is a period where the ventricular myocardium is passive, and the volume changes /deformation is due to passive flow and last. atrial contraction. This also means that in the intact heart, the ventricular myocytes are dependent on atrial contraction to restore the original length.
  • By imaging, it seems that ejection is the event of long duration, while "early relaxation" is an event of very short duration, quite the opposite of the cellular processes.
Thus, it is also evident that "diastolic dysfunction" may be a very complex entity, where both the rate of calcium removal by SERCA, and any fibrotic process of the myocardium or large vessels that increases collagen and reduces elastin may contribute.

It has been shown that the decline in diastolic function by age may partly be a function of inactivity, resulting in a decline in SERCA, which can be rectified by endurance training, as SERCA can be increased by training. However, the main part of the reduction is not influenced by training, and may probably mainly be due to increased fibrosis by age (226). The main training induced compensation for age in order to maintain oxygen uptake seems to be increased LV volume.



Ventricular systole has generally been taken to mean isovolumic period and ejection period, ending with the AVC. By this definition, the diastole is IVR and diastolic filling period. However, myocardial relaxation ends with the end of the early filling period, ventricular myocardium being passive during the diastasis and late filling (which is due to atrial contraction, the ventricles being passively stretched). Ventricular diastolic function has thus been concentrated about the events in early diastole, with the late diastole as comparison (E/A ratio).

Diastole is traditionally divided into four phases as shown above; Isovolumic relaxation period, early filling period, diastasis, and atrial filling period. The last three comprise the diastolic filling period, and is schematically displayed below.


Diastolic filling. There are three distinct phases.  Early filling (E - wave), where there is inflow from the atrium to the left ventricle (red curve and arrows), the ventricle increases the volume, evident by the velocities of the annulus away from the apex (dark blue arrows. Diastasis, with little or no movement. There may or may not be some passive flow into  the left ventricle in this phase.  Atrial systole (A - wave), where there is atrial contraction,  pushing blood into the ventricle again (light red) and a new motion of the mitral ring away from the apex (light blue), due to pressure increase, or direct pull from atrial contraction, or both.  The resulting flow and tissue velocity curves are illustrated below.
Mitral flow curve. The conventional measures of diastolic function are shown: E: Peak flow velocity of early filling phase; a measure of rate of relaxation during this phase. Dec-t: Deceleration time of early flow; measured from peak E along the slope of velocity decline to the baseline.  IVRT: Isovolumic relaxation time; the time between end ejection and start of mitral flow. It's conventionally measured from the valve click at AVC to the start of mitral flow. A: peak flow velocity of atrial systole. The E/A ratio shows the relative contributions of the two phases to filling, and is a more sensitive index of reduced early filling.

Early filling is thus the filling during ventricular relaxation. It has traditionally been described as "passive filling", from the view that the late filling is a function of atrial systole, but modern physiology recognises the relaxation as an active energy demanding process, and also the process of releasing some of the elastic energy that was stored in systole. Whether filling pressure is a component, is discussed below. Arguments for this, is the finding that early diastolic velocities are load dependent (but this can be explained by other means), arguments against, is the finding that as the ventricle enlarges during this phase, the pressure drops. The main point is that ventricular myocardium is far from passive in this phase. Diastasis is a truly passive phase.

During atrial systole, there is filling and enlargement (elongation) of the ventricle, due to atrial systole. It has also been argued that the main effect of the atria is to pull on the mitral ring, restoring ventricular end diastolic volume and length, and less by increasing volume by the direct effect from the injected blood. However, this view does not take into account the action of the auricles, and  also, the fact that during A phase, the pressure increases during ventricular expansion, points to the pumping (load) as the most important mechanism, as also discussed below.

Traditionally, this means that diastolic function of the ventricular myocardium, is shown during isovolumic relaxation and early filling, and the invasive measure, tau, is the time constant of pressure decline of the ventricle during isovolumic relaxation.



Mitral flow

Traditionally evaluation of left ventricular diastolic function has been by mitral flow (82) as shown below. The late filling (A) is more about left ventricular compliance (126) in the passive phase.


A: Relation between mitral flow indices and pressure in the normal situation. Mitral flow (red curve) is dependent on the pressure gradients between the left ventricle and the atrium, which is created by left ventricular relaxation. The decline in pressure gradient during IVRT ( = relaxation constant tau) after AVC determines the length of the isovolumic relaxation time. The decline in the pressure difference between atrium and ventricle as the ventricular pressure increases, determines the deceleration time.  This again is dependent on the relaxation rate, as the active relaxation, creating a quick pressure drop in the ventricle, a high gradient and a short deceleration time.  Atrial pressure increases during atrial systole, forcing blood to flow again in the A wave.
B: Slower relaxation leads to a decrease in the tau, and thus a longer IVRT before the mitral valve opens; Increased IVRT. In addition, the slower relaxation leads to a less profound but longer drop in LV pressure, leading to a reduced E amplitude and a prolonged dec-t.  The lower filling volume leads to a higher atrial volume at the start of atrial contraction, and thus a higher atrial stroke volume (perhaps by the Frank-Starling mechanism), and a higher A- wave. The E/A ratio is reversed. (Light gray flow curve is from A, for comparison).
C: Decreased LV compliance due to fibrosis or dilation, leads to a higher increase in LV pressure from the injected volume from the atrium. This leads to an earlier equilibration of LV and LA pressure, and an abbreviated A-wave, which can be seen by comparing with the duration of the reverse A wave in the pulmonary veins. Decreased LV compliance shows up first in end diastole, as this is the phase where the ventricle is  at the highest volume.  (Light gray flow curve is from B, for comparison). D: Increased filling pressure (Left atrial pressure) due to filling problems, will decrease IVRT as shown here, as the pressure gradient between LA and LV is less. In addition, the gradient is higher in early filling, due to the higher LA pressure, with a subsequent higher E-wave. But then LV pressure increases faster in response to the filling from the LA, due to both the increased filling rate, slower relaxation and finally less compliant ventricle already during diastasis. The filling time and dec-t is shortened. Finally the A wave is blunted, due to the higher LV pressure at the start of LA systole, and the E/A ratio reverses back.  When the mitral flow looks normal due to delayed relaxation compensated by higher pressure it is called pseudonormalisation, when the E/A, ratio is higher than normal, and the IVRT and Dec-t is shorter than normal, it is called restrictive filling. Restrictive filling is usually a sign of  reduced compliance already in early diastole; i.e. severely reduced compliance leading to early pressure increase. (Light gray flow curve is from CB, for comparison).

This means that the rapidity of relaxation is a measure of pressure decline, and is reflected in the peak velocity during early filling. However, in order to normalise for total filling (stroke volume), the conventional measure has been the ratio of early versus late filling E/A. As early filling declines due to decreased relaxation, the A wave increases as contributor to the total filling. As shown above, the IVRT and Dec-t are other measures.

The load at the mitral valve opening, where the left ventricle starts lengthening as shown above, may be supposed to be a contributing factor to the e' (lengthening load). However, there is evidence for left ventricular negative pressure during early relaxation (180, 181), and ventricular suction is conceivable even without negative intraventricular pressure, it is the rate of pressure drop relative to the atrial pressure that generates the suction. But it still remains controversial (182). (Of course keeping the discussion out of the range of physics where the concept of suction really doesn't exist, it is the pressure that fills a void, not the void that sucks. But as suction is in everyday use, and a suction pump is one that uses the energy to generate negative pressure in the chamber too be filled, (vis a fronte), instead of using the energy to generate positive pressure in the chamber to be emptied as in a pressure pump (vis a tergo), the terms still makes sense).



Pressure driven (vis a tergo; a force acting from behind) filling of a chamber (B),  versus suction driven filling (vis a fronte; a force acting from the front).  In this simplified model, the level of fluid (and, hence, pressure) in chamber A is assumed to be constant during filling.
In pressure driven filling,  the force driving the piston is the pressure in chamber A (actually the pressure difference between chamber A and B.  The force, F (black arrow), is the pressure * area, and the pressure is a function of the height of the level of A over B, and the density of the fluid. Thus, the energy for the movement of the force is potential energy of the pressure difference. Flow (Q) is driven by the pressure gradient between A and B. In this case the pressure increases in chamber B up to the level of A. This transmits the force to the piston expanding the chamber B by the pressure.
In suction driven filling,  there is a force, F, applied to the piston, expanding chamber B. This creates a pressure drop in the chamber, and a pressure gradient between A and B.  Thus, the energy is applied to the creation of a pressure drop in chamber B. Flow (Q) is gain driven by the pressure gradient between A and B. 
In both cases the flow is driven by the pressure gradient between A and B (i.e. there is a potential energy in A versus B that drives the flow, shown by the blue arrows), but in vis a tergo, the force application (energy) is applied to the fluid in chamber A , in vis a fronte, energy is applied to creating a pressure drop in chamber B.

Looking at LV diastolic function, seeing that flow velocity is the rate of volume change, and thus volume increase, it seems that early filling is vis a fronte; showing volume increase with pressure drop (negative dP/dV),  the driving force being left ventricular recoil, while late filling is vis a tergo showing volume increase with pressure increase (positive dP/dV), the driving force being atrial contraction.

From the model above, it would seem that as long as there is pressure drop in the ventricle simultaneous with volume expansion, the filling in early diastole is equivalent to a suction pump. (The converse must also be the case, during atrial systole, the most important mechanism is load, and not the atrial pull on the mitral ring, as pressure in this phase increases concomitant with ventricular expansion as discussed above. If atrial pull was the most important mechanism, it would expand the ventricle leading to a pressure drop as in the early filling).

Relaxation is shown to be energy dependent, but this is due to the uncoupling of cross bridges and removal of calcium from the cytoplasm, not lenthening per se. The molecular biology of the myocytes give no mechanism for lengthening. However, there is an empirical fact that isolated myocytes, being totally unloaded, still lengthens after contraction. Thus, the only mechanism in this case is the storage of elastic forces in the cytoskeleton itself, meaning that lenthening is a function of shotening. In the intact heart, there are additional structures for storing of elastic energy from the contraction, both the interstitium (being compressed, as well as the large vessels (being stretced by the descent of the AV plane) may store elastic energy. But the rate of lenthening is modulated by the rate of calcium removal from the cytoplasm, thus there is an independent contribution to relaxation rate by diastolic mechanisms.

As ventricular shortening (S', MAE) is load dependent as well, the recoil is related to diastolic function, as shown by the correlation between e' and S'being between 50 and 60% (165, 201). This also explains the arterioventricular coupling, having impact also on diastolic function.

Ventricular compliance

Due to the old concept of LV filling as a passive, pressure driven process, filling has been described as a function of ventricular compliance. This is repeated in numerous representations of pressure-volume loops, and may partly be a result of open chest experiments, where the elastic recoil generating suction may be altered. However: Compliance is defined as volume change per pressure change: V/P. AS pressure generally drops during early filling, this would mean negative compliance.

Pressure volume loop. The dotted line represents the concept of early filling as a passive process. Compliance is the volume increase relative to the pressure. It is evident that the compliance decreases at the volume increases, but this means that the definition of LV compliance is mainly relevant in end diastole, not a description of the left ventricular diastolic function per se.

Basically, left ventricular compliance is a measure of LV distensibility whan filling is pressure driven, i. e. during atrial systole. Reduced compliance will be earliest detectable in that phase, by increased prassure or reduced flow in atrial systole as seen above. In restrictive filling, compliance is reduced during the whole systole, but still most in end diastole.

Reduced compliance should thus be mainly restricted to end diastole.



Normal values for diastolic mitral flow indices from the HUNT study (conventional diastolic values)

For completeness I will add the normal values for the mitral flow indices from the HUNT study. The values were published in (165) in supplementary online tables.


Mitral E
(cm/s)
Mitral A
(cm/s)
E/A
(ratio)
DT
(ms)
IVRT
(ms)
Females
Feasibility N (%) 657 (99%) 657 (99%) 657 (99%) 657 (99%) 653 (98%)
<40 years, N=208, mean (SD) 80 (16) 48 (15) 1.85 (0.76) 212 (55) 85 (16)
40-60 years, N=336, mean (SD) 74 (15) 59 (15) 1.32 (0.40) 220 (66) 95 (20)
>60 years, N=119, mean (SD) 69 (16) 75 (18) 0.96 (0.32) 244 (79) 105 (23)
All, N=663, mean (SD) 75 (16) 58 (18) 1.42 (0.62) 218 (66) 93 (21)
Males
Feasibility N (%)
599 (99%)
599 (99%)
599 (99%)
599 (99%)
597 (99%)
<40 years, N=126, mean (SD)
75 (15)
44 (14)
1.86 (0.64)
217 (65)
91 (17)
40-60 years, N=327, mean (SD)
64 (15)
52 (14)
1.30 (0.42)
232 (81)
100 (21)
>60 years, N=150, mean (SD)
61 (14)
65 (18)
0.99 (0.34)
269 (97)
118 (29)
All, N=603, mean (SD)
66 (15)
54 (17)
1.34 (0.54)
238 (85)
103 (24)

As is evident, the early diastolic indices decline with ageas does the systolic, A increases.

Diastolic function by tissue Doppler

Thus, it is evident that mitral flow gives information about LV relaxation, but the secondary changes in pressure tends to complicate the picture. With a low E/A ratio and long dec-t, it is obvious that the filling pressure is NOT increased, and no further information is necessary. Pseudonormalisation will camouflage delayed relaxation, and the restrictive pattern can be seen also in the young, due to a very quick relaxation (although seen in the old, it should be seen as pathological).




Diastolic function seen by tissue Doppler and M-mode of the mitral ring. To the left a normal subject showing normal e' velocity and normal e'/a' ratio, to the right a patient with hypertension, showing reduced e' velocity as well as e'/a'. The delayed relaxation is evident also in the M-modes, but may be more difficult to measure, if the deflection between the diastasis and the late diastolic displacement is less sharp.

Fundamentally, the physiology discussed her will not be representative for situations where there may be marked asynchrony of the e' waves, such as bundle branch block or pacing.


A: Patient < 30 with normal diastolic function. E/A > 1, Short Dec.T and IVRT, high e'. In this patient it is normal for age, but might have been severe heart failure with restrictive filling, even given the patient's age.  Compare with patient F. In this case the tissue Doppler helps to discern.
B: Patient about 50 years with near normal diastolic function. for age. E/A = 1, somewhat longer Dec-T and IVRT.
C: Slightly impaired relaxation. Patient at about 70, with slightly delayed relaxation due to a history of hypertension. Prolonged IVRT, dec-T, reduced E and E/A ratio < 1.  Also reduced e'. D: Severely impaired relaxation. Patient with heart failure (and normal EF and LV EDV), but with normal filling pressure due to diuretic and ACE inhibitor treatment. Severely reuced relaxation with prolonged IVRT, dec-t, decreased E and E/A ratio <<1. Very low e'.
E: Pseudonormalisation. Patient age 69 with history of hypertension. Mitral flow (top left) shows normal values for E, A and Dec. time, and the IVRT (top right) is also normal. Tissue Doppler (bottom) shows impaired relaxation, (E/e' about 15), indicating that the atrial pressure is elevated. This is demasked by doing a mitral flow acquisition during Valsalva manouver (decreasing venous return and hence, atrial pressure) below: F: Patient with restrictive pattern (actually same patient as in C, but before treatment, and then with increased LVEDV  and low EF), due to high filling pressure. Short IVRT, dec-t, high E and E/A ratio. e' still low showing that there is delayed relaxation, despite the high E and E/A. Compare with A, little difference, but taking the patient's age into consideration, it is actually evident that this is restrictive filling, even without tissue Doppler showing a low e'.



Valsalva manouver in patient E above, demasking pseudonormalisation and showing the typical pattern of impaired relaxation.


As shown above, the global diastolic function is more robustly assessed by tissue Doppler of the mitral ring, being the resultant of the local relaxation events, than of regional diastolic strain rate (except possibly for diastolic strain rate propagation shown below). The early diastolic annular velocity (e') has been shown to be related to tau, and to be less preload dependent than mitral flow (69, 70, 71). This means that the tissue velocity can be used to separate impaired relaxation with increased filling pressure from normal situations, in impaired relaxation the e' remains low despite increased atrial pressure. Thus diastolic function of the LV (relaxation) can be more directly measured by the e' than E, and the closest correlate to relaxation rate.

Normal values for tissue Doppler annular left and right ventricular diastolic velocities from the HUNT study


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

e' (pwTDI)
a' (pwTDI)
e'(pwTDI)
a' (pwTDI)
Females




< 40 years
14.6 ( 2.3)
8.8 (1.9)
14.7 (2.9)
12.4 (3.5)
40 - 60 years
11.3 (2.4)
10.0 (1.9)
13.1 (2.9)
15.0 (3.5)
> 60 years
8.2 (3.2)
10.6 (1.9)
11.0 (2.3) 16.1 (3.1)
All
11.8 (3.2)
9.7 (2.0)
13.3 (3.0)
14.4 (3.7)
Males




< 40 years
14.1 (2.7)
9.1 (1.7)
14.5 (2.9)
12.3 (3.5)
40 - 60 years
10.7 (2.3)
10.4 (1.6)
12.5 (3.2)
14.3 (3.7)
> 60 years
8.2 (1.9)
11.1 (1.6)
11.0 (3.0)
15.8 (4.2)
All
10.8 (3.0)
10.3 (1.7)
12.5 (3.3)
14.2 (3.9)
Annular velocities by sex and age. Values are mean (SD).  pwTDI: Pulsed Tissue Doppler recorded at the top of the spectrum with minimum gain.  Values of e' decline with age, a' increase. 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.



E is pressure driven, but e' is not to the same degree, the relaxation actually being the cause of the pressure drop. However, this load independency is not absolute, as discussed below.

This means that the ratio of E/e' can be used for assessment of left atrial pressure (71, 72, 177). If both E and e' increases, the ratio remains unchanged, and the increase in flow is due to higher relaxation rate. (For instance in exercise in normals (29).)  However, if E increases without e' increasing simultaneously , the increase in flow  must be driven by increased filling pressure  instead of by relaxation (as for instance in exercise in patients with impaired relaxation reserve (160), and the increase in the E/e' ratio is related to the increase in filling (atrial) pressure. However, if E remains unchanged and e' decreases, it is not physiologically meaningful to take the increased ratio as a measure of increased filling pressure. In fact, in transition from supine to sitting the E/e' increases while filling pressure decreases (160). Thus the E/e' relates only to filling pressure when E increases.

An E/e' < 8 is considered normal, while E/e' > 15 is considered a sign of elevated LA pressure.


Normal values for left ventricular E/e' from the HUNT study.

The E/e' ratio was age dependent, as has been shown previously in a smaller study (166):


< 40
40 - 60
> 60
All
N
327
651
263
1241
Mean
5,6 (1,3)
6,5 (1,7)
8,2 (2,6)
6,6 (2,1)
Values are mean (SD), and is the average of four walls.  The E/e' can be seen to increase with age.

The age dependency of E/e' is evident. This is actually one of the reasons for the "grey zone" between 8 and 15, as normal range for the age group < 40 is below 8.2 (mean + 2SD), between 40 and 60 it would be < 9.9 and above 60 years it would be below 13.4.

In a smaller sample of 100, cTDI was compared to pwTDI, and the values by cTDI were 2.2 lower than pwTDI. The ratio in the septum was 2.5 lower than in the lateral wall, but very similar to the mean of four walls. It is evident that by a normal range of mean ± 2SD, the normal range in the youngest group is 3.0 - 8.2 and in the oldest group 3.0  - 13.4. This explains previous findings of the ambiguity of the interval from 8 - 15 concerning relation to filling pressure. It should be age adjusted.

Where should measurements of e' be done?
The differences between walls are even greater in early diastolic than in systolic velocities. Thus, the e' and hence, the E/e' is highly site dependent. This has been shown several times, in the largest normal material being the HUNT study (165). In the HUNT study the e' did show the following normal values for pulsed Doppler per wall

05.March 2012:Thanks to observant reading by Charlotte Bjørk Ingul it was discovered that the values given in the table blow were S' values, not e'. Now the correct values (which are in accordance with the normal values given in the table above) are given below:


Mean
Septal
Anterior
Lateral
Inferior
e' (SD) cm/s
11.3 (3.2)
9.9 (2.9)
11.6 (3.7)
12.5 (3.5)
11.2 (3.5)
The general principles of the site specific variability, however, still applies, and the E/e' valøues below were correct from the start.

This means, of course, that the E/e' also varies with the site of e' measurement:
E/e' from pwTDI according to age and site of e' measurement

Mean of four points
Mean septum-lateral
Septal Anterior Lateral Inferior
All
6,6 (2,1)
6,6 (2,1)
7,5 (2,4)
6,6 (2,4)
6,1 (2,2) 6,8 (2,3)
<40 years 5,6 (1,3)
5,6 (1,3)
6,5 (1,7)
5,4 (1,6)
5,1 (1,3)
5,7 (1,6)
40-59 years 6,5 (1,7)
6,5 (1,8)
7,4 (2,0)
6,5 (2,0)
6,0 (1,8)
6,7 (2,0)
>60 years 8,2 (2,6)
8,2 (2,7)
9,0 (3,1)
8,5 (3,0)
7,6 (3,0)
8,4 (2,9)

 It is evident that there is considerable site dependency of the E/e' as well. It is also evident that there is little difference between mean of four points versus two points, when only mean and SD are considered. However, the Standard deviation is a large population study reflects biological rather that measurement variability. The study of Thorstensen et al (154)did show an improvement in reproducibility of about 15% of e' measurement using the mean of septal and lateral, compared to either of them alone, and a further 30% (p<0.001) using four-point compared to two point averages.



Also, all systolic measurements of MAE and systolic peak velocity have been established from the start as being the mean of four points, although two points seem to work equally well in terms of mean, if not in terms of reproducibility. Thus, in the interest of robustness and to harmonise systolic and diastolic measures, the logical thing would be to chose four point average for e' as well. But logic has not got anything to do with it.

Rodriguez (69) in one of the first observational studies used the lateral point. In the early invasive validation studies; Nagueh (71, 196, 200) and Sundereswaran (197)  used the lateral wall alone, Sohn the septal point (70, 198, 199)   while Ommen (177) studied both the septum and the lateral point, as well as the mean. He found the best correlation between E/e' and filling pressure using the septum alone.  Present recommendations, however, favors mean of septal and lateral (195). It is argued by some that the invasive validation work has been done with one-site measurements, but at least, the HUNT provides normal data for all sites.

Load dependency of diastolic tissue velocity (e')

However, the e' is not entirely load independent. As normal subjects are sat upright on a bicycle (not using their leg muscles, and thus reducing venous return), the filling pressure drops, and so does e' (29, 160). The drop in filling pressure is evident by decreased mitral flow E, decreased LVEDV and increased HR (160). This has also been shown as e' changes after dialysis (178) and in applying lower body negative pressure (179).

This has beeen taken as indications of the early diastolic motion of the mitral ring (and hence e') being partially a function of atrial pressure (lengthening load).


  But if there is suction during early filling, there can be no simultaneous lengthening load. Even if the pressure at MVO is positive, continuing relaxation (and recoil) can generate suction. But then the motion cannot be due to lengthening load at the same time! And in fact, as the volume expands and there is inflow, at the same time as the pressure drops, it's inconceivable that the motion of the mitral ring is driven by pressure at the same time. In fact, the negative dP/dV was the original definition of left ventricular suction by Katz in 1930 (183). Thus it seems that the mechanism of diastolic function is elastic recoil, modulated by the rate of calcium removal from the cytoplasm. It's as simple as that: There cannot be suction and pressure driven expansion at the same time, it is not possible to spit and suck simultaneously.


However, even without lengthening load, the e' may be load dependent as shown in studies (29, 160, 178, 179). The IVR is clearly load dependent (126) as explained above. As the motion of the mitral ring starts at MVO, the beginning of the e' wave is dependent on the IVR. In the case of unchanged relaxation rate, later MVO means that the e' wave starts at a lower rate, and does not reach as high peak, as illustrated below.




Proposed mechanism of load dependency of e' in the presence of unchanged relaxation rate.  The LV pressure curve can be taken as a measure of relaxation (and restoring forces). The lengthening starts the time of MVO as discussed above. The MVO is at the time of the crossover of LA and LV pressures, and thus, given constant LV pressure decline, on the LA pressure as shown (LA pressure 1-3). The acceleration of the mitral ring downwards starts with the relaxation rate at the time of MVO as represented by the tangents to the LV pressure curve at the times of the MVO (MVO1-3). The peak downward velocity is reached dependent on the acceleration, but with declining relaxation rate. The time to reach peak e' is determined by the relaxation rate at MVO,  the peak e' by the relaxation rate at the time of e' represented by the tangents at the time of peak e' (e'1-3).  Thus peak e' is dependent on the relaxation rate at the time it is reached, and the time is dependent on the time of MVO.

AS the relaxation rate declines, and atrial pressure increases, however, there will surely be a cross over point where the load takes over as the main lengthening mechanism. In this case the diagram above will no longer be valid, and the e' relates to filling pressure more than relaxation and elasticity. In this case the e' relates to lenghthening load.


Splashing humpback whale in Wilhelmina Bay, Antarctica.

Load dependency of E/e'

As the e' is load dependent, even the E/e' may be be. At low pressures, the e' actually changes more than the E, thus increasing as LA pressure decreases, as has been shown consistently by the supine to sitting transition (29, 160). This may be due to the mechanism of load dependency being different, and e' may be more load dependent at low loads, which could be explained by the diagram above.



E and A fusion

In hemodynamic thinking, it is customary to start the heart cycle with ejection, and the to proceed to diastolic filling, hence S - E - A. This is the way tissue Doppler is presented as well. However, each hart cycle start with a sinus node activation, followed by an atrial activation and atrial systole, and this is the customary way of describing the ECG, hence P - QRS - T. But this corresponds to the sequence of A - S - E, which may be a help in describing the relation of E and A in relation to heart rate as illustrated below.


Four heart cycles illustration the relation between E and A with heart rate and PQ time.  (NB: the numbers on the image below are not related to the numbers on the image above.) Cycle 1 shows normal PQ time and heart rate, resulting in a normal diastasis period between E and A.  Cycle 2 shows higher heart rate. As heart rate is increased,  it means that next P and hence A, comes earlier after the previous cycle. Thus, this explains why it is the diastasis that is shortened with increasing heart rate. Cycle 3, shows the same RR-interval as 1, i.e. same heart rate, but with longer PQ time.  Heart rate regulation modulates the RR (or, actually PP) interval, but in this case the PQ interval is prolonged in relation to the RR interval. This has the same effect as reduced RR interval; the PQ as fraction of RR decreases, and the diastasis is abolished.



Recordings from a patient with 1st degree AV block, PQ time of 272 ms at a HR of 73.  There is partial EA fusion at rest, showing up in mitral flow (left), pw and colour tissue Doppler (middle and it also changes the annulus motion pattern, as the diastole moves more or less continuously.

Thus, as heart rate increases, it is the diastasis that is shortened first, however, after the diastasis interval is zero, the next step is fusion of the E and A waves as shown below (NB: the numbers on the image below are not related to the numbers on the image above.):



E/A fusion with increasing heart rate (or PQ time). (NB: the numbers on this image are not related to the numbers on the image above.) 1: No fusion and discernible diastasis. 2: Shortening of RR-interval first abolishes the diastasis. 3: Further shortening of the RR-interval leads to partial fusion of the E and A wave and e' and a', respectively. the peak E and e' is still separate, but the A and a' are atrial velocities added to the remaining velocities of the early phase, as shown by the arrows in the upper diagram. In the velocity curves, this is seen as the A/a' wave "climbs" up (down) the descending limb of the E wave. 4: At higher heart rate, the E and A are completely fused, and the separate effect of ventricular relaxation ant atrial contraction can no longer be discerned.

Although there is adaptive shortening of both QT interval and PR interval, this does not compensate for the shortened RR interval, with fusion the diastolic period shortens more with decreasing RR interval (29) and below.



Left ventricular diastolic filling period (DFP) and ejection period (LVET) in relation to heart rate during exercise.  Below HR 110, the RR interval and DFP shortens in parallel, showing the the diastasis is shortened first, while ejection time shortens much less. Above 110, there is parallel shortening of LVET and DFP, both contributing to the shortening of RR interval. The study also showed that the LVET and RR interval was only linear below HR 100 (29).
E and A with increasing heart rate during an exercise test in one patient. At HR 65,there is separate E, a and diastasis, both in mitral flow and in tissue Doppler as evident by the fact that tissue velocity is 0 between e' and a'. At HR 88 there is partial fusion, neither E nor e' reaches 0 before the start of A and a', respectively, and the A and a' are higher in absolute values due to this.  At HR 94 there is more fusion, but the peak of the E and e' are still discernible, and can be measured, as a measure of ventricular diastolic function. The E/A and e'/a' ratios, however, are useless, as the A and a' are summation velocities. The A and a' are increased further. At HR 121, the E/A and e'/a', respectively, are nearly completely fused. The peak E and e' can no longer be discerned. The peak diastolic velocity is far higher (in absolute values) that the E or e' and cannot be compared.




With partial fusion, peak E and e'
, and thus the effect of ventricular relaxation can still be seen and measured. However, peak A and a' are now a sum of the velocities due to atrial systole and the remaining velocities due to ventricular relaxation. This means:
  1.  The A and a' are higher than when separate, and no longer a measure of atrial function, and thus:
  2. The E/A ratio is no longer a measure of the relative contribution of the two mechanisms, and is nearly useless.
With total fusion, the E and e' velocities, and thus ventricular diastolic function cannot be measured separately. The diastolic function measured by the fused wave, is the sum of ventricular relaxation and atrial contraction velocities, and can still be taken as a measure of atrioventricular  diastolic function. But this means:
  1. Ventricular diastolic function cannot be measured separately.
  2. In an exercise or inotropic test , when  heart rate becomes high enough, the fused wave cannot be compared with the E wave at lower heart rates.
This  point is important in three situations:

  1. Children have higher heart rates, and partial fusion is common at rest, and even total fusion in neonates.
  2. First degree AV-block may give fusion at normal resting heart rates.
  3. In exercise testing, the increasing heart  rate leads to total fusion, usually at HR around 100. This means that for diastolic dysfunction, exercise tests are not as useful at HR > 100. In dysfunction due to ischemia at higher heart rates, however, ischemic stunning may persist for some time, while heart rate falls, and may still be useful.

Some invasive studies, however, seem to indicate that using the ratio between the fused EA wave and the fused e'a' wave, the filling pressure can still be estimated (198), as well as in atrial fibrillation where the a wave is absent, and the E and e' waves are higher (199).

Limitations of the E/e' ratio

As the investigantions have continued, there has been shown severe limitations of the E/e' in estimating atrial pressure.

E/A fusion:
The most evident is explained above, where there is total E/A (and e'/a') fusion, the combined e'/a' wave do no longer measure the relaxation alone, but the combination of ventricular relaxation and atrial systole. Also the E/A wave do relate to atrial pressure, but no longer the mean  pressure but the peak pressure during atrial systole, which may differ.

Position dependency:
AS we have shown earlier, the E/e' increases in the sitting position, while filling pressure drops. Thus the studies are mainly valid for supine acquisitions.

High filling pressures:
If the filling pressures are high, the filling pressure (lengthening load) may take over as the main mechanism for the early motion of the mitral ring, as discussed above. This is in accordance with
Mullens (272), who found no clear relation between filling pressures and E/e' in a heart failure population (except that most had high E/e', of course).

Constriction:
In constrictive pericarditis, the filling pressures are generally elevated, but longitudinal diastolic function (e') intact (273), giving a lower E/e' for any given filling pressure.



Diastolic strain rate

Looking at the velocity and displacement traces, even with the addition of the protodiastolic motion event, the diastole looks fairly straightforward, after AVC, the three fundamental phases known from Doppler flow can be seen: Early filling phase (E), seen as the first negative phase (e') after AVC, diastasis with little or no motion, and the atrial systole (A) seen as the second negative velocity spike (a'). The atrial displacement of the ring may be described as the atrium pulling the ring away from the apex, and in addition the added volume pushed into the ventricle by atrial (esp. auricular) contraction pushing the atrioventricular plane. The relative contribution of the two mechanisms is uncertain.


Taken from the mitral ring, diastolic ventricular displacement and velocity show the left ventricular diastolic global function.

Velocity and displacement in the base of the septum, showing systolic motion toward the apex, protodiastolic motion away, and the the two basis diastolic phases, early (e') and late (a') motion way from the apex, separated by diastasis.
In strain and strain rate, the pattern can be seen to be much more complex in these tracings from the base alone. There are at least four positive spikes (elongation) during diastole, this is reflected by much more "steps" towards zero in the strain curves. As strain rate is fairly susceptible to noise, this might have been interpreted as noise (as is the small negative spikes between) , but integrating to strain eliminates the random noise, and shows what is real. 





However, using strain and strain rate, the diastole can be seen to be far more complex, showing a sequence of events that are different, and with different timing in the different segments. Thus  is seen due to the better spatial resolution, as deformation imaging eliminates the effects of the tethering of the base to the more apical parts. In addition, these events interact, to result in the simpler pattern seen in motion traces, and the main finding is that there are more than one peak in each of the two phases of E and A, and also, the peaks are not simulatneous in all parts of the ventricle.


The double peak of Una's tits (yes, that is the actual, official name of this mountain) may be a reminder of the double peaks of diastolic strain rate.



The M-mode reveals that some of the diastolic phases has the characteristics of elongation waves between base and apex.  The differences between base, midwall and apex can be seen clearly in the traces diagram to the left, showing that not only are there more elongation phases, but they don't even coincide in the different levels of the heart.


After the protodiastolic elongation, there is a diastolic elongation that is most evident in the apex. This occurs before the opening of the mitral valve. The opening of the mitral valve signals the main elongation (and wall thinning) that starts at the base (19).


Tissue M-mode from the septum, showing the dip of the AVC event, and the time delay from base to apex of the initiation of downward motioning the filling phase.

The relation of this propagation to diastolic function is discussed below.

But as this wave has propagated to the apex, it can be seen to return to the base. And the elongation during atrial systole can be seen to behave similarly with a wave toward the apex, and back to the base, but with a higher propagation velocity that the early relaxation, which makes sense considering that during early filling the ventricular myocardium is in a relaxing, and in the atrial systole, the ventricular myocardium is relaxed.


Events of the heart cycle seen by strain rate. Both the curved M-mode and the traces shows the separation into:
  1. Midwall protodiastolic lengthening
  2. Apical isovolumic lengthening
  3. Early filling propagating from base to apex and back
  4. Late filling propagating from base to apex and back.

Proposed explanation of the return wave of the two filling phases, in reality being a crossing over from the opposite wall. The protodiastolic lengthening is less evident in the lateral wall, but this is due to a drop out in the wall.



The finding of a complex pattern in diastole, shows that no single parameter can be used as a criterion for diastolic function. Regional early strain rate might be taken as an indication of regional diastolic function, but only if care is taken to identify the elongation spike, and avoid the return wave. And as the traces above show, there are differences in both the amplitude and timing of early diastolic strain rate, the implication being that there is no meaningful way of averaging the values into a more global function measure. The e', being the resultant velocity of the mitral plane, however, is a truly global measure, being the summation of all local measurements and taking the time differences into account, as well as being less pressure dependent, is a more robust measure of diastolic function as discussed below.


Diastolic strain rate: This picture is too busy to be really informative, it summarizes the information given above, and is mainly a way of showing that there is no meaningful way of averaging the diastolic peak values into a more global function measure, as the peak local diastolic strains are not simultaneous.



For global diastolic function, diastolic tissue velocity is still the most important measure, as this is the resultant global peak measure. This is not the average, but the resultant of all the local (non-simultaneous) diastolic strains AND the propagation along the wall.


On the other hand, the finding of the filling phase as a propagation wave from base to apex shows another measure of diastolic function, as well as a different relation between tissue velocities and strain rate as shown below:


Diastolic strain rate propagation

The finding of the filling phase as a propagation wave from base to apex shows another measure of diastolic function, as well as a different relation between tissue velocities and strain rate as shown below:



A. In this animation, the two autos where distance increases (the one starting up, and the next, standing still) are coloured cyan to visualise the segment with positive strain (lengthening). The time delay of initiation of motion from one element to the next, creates a wave of increasing distance between the elements that propagates backwards, while the autos move forward. This is analogous to the elongation waves from base to apex during the filling phase.  Below this is illustrated as an M-mode.



B: In this animation, the autos have reduced velocity after start, compared to the one in A.  This can be seen by the decreased distance between the moving cars. The propagation wave becomes slower as the cars drive slower. This is analogous to a reduced rate of local relaxation (lower early diastolic strain rate. M-mode below.




C: In this animation, the autos move with the same velocity as in B, once they have already started, but the time between the start of each auto have increased.  This also shows up as increased distance between the moving cars, but here the increased distance is due to delay in starting, not a decrease in velocity, compared to B. This is evident if looking at the distance the the cars have moved from one frame to the next. This also leads to a slower propagation of the elongation wave, and this effect is analogous with reduced propagation per se, even if the local relaxation rate is unchanged. M-mode below








Tilting the M-modes 90°, the motion is downwards and the elongation wave propagates upwards, as in a conventional M-mode of a myocardial wall that is shown to the left.  The relaxation rate can be seen by the slope of the red line.  The forward (downward motion of the first car is shown by the black line, being equivalent to the motion of the mitral ring,.

This is analoguous to:




M-mode from a myocardial wall, velocities at the top, and strain rate at the bottom.  During the two diastolic phases, there is blue colour showing downward motion, which can be seen by the tissue lines as well. The elongation can be seen to propagate from the base to the apex over time. Strain rate propagation velocity is the slope of the elongation wave.

What does strain rate propagation mean?

It is important to realise that this propagation of a deformation (elongation) wave does not mean that the relaxation propagates from base to apex. This is pertinent to the initial discussion, what do stain and strain rate actually measure. The diastolic function of the myocytes is a local event, depending on the rate of relaxation (tension decline) due to the rate of inactivation of myocardial cross bridges, which again is related to the rate of removal of calcium from the cytoplasm as discussed above. (In addition to elastic recoil, which is both inherent to each myocyte and to the heart in total). But the effects of relaxation may be taken to be more simultaneous than deformation. Thus it is deformation  thant starts in the base, not relaxation.

Thart deformation starts at the base may simply be the expression of the fact that there is more room for expansion where the mitral valve opens, analoguous with the wave shown in the cars above, the wave has to start with the first car, before the next car can move. Thus, strain rate propagation may simply be another measure of the global rate of relaxation.



And if global diastolic function is to be measured by strain rate imaging, the propagation velocity tis the true the global measure- An average of peak strain rates, not being simultaneous, is a more difficult concept, although it corresponds to an average local rate of deformation.

So far, there is conflicting reports if the propagation velocity is different in different walls (19, 175). The strain rate propagation velocity has been shown to be preload dependent (175).

However, we did show early that the strain rate propagation velocity (the slope of the elongation wave) was reduced in reduced diastolic function (19). This may mean that if the rate of relaxation is reduced, the propagation must necessarily also be reduced, as in the difference between animations A and B above, the propagation wave goes slower if there is slowed local deformation.




Strain rate propagation is thus a global measure that relates to the peak e' in tissue Doppler.



Relation between propagation of the E-wave ant the peak early diastolic  velocity of the annulus.  If the wave propagates slower, the resulting velocity wave of the annulus will be broader and lower, even with regional strain rate may be the same, but the strain rate propagation is dependent on both local diastolic strain and the properties of the wall. . In reduced diastolic function as shown here to the right, there is a lower peak diastolic annular velocity as well as a reduced early magnitude of motion of the mitral ring.


Thus, there is a geometric relation between strain rate propagation and e', which is both theoretically and empirically (19) probable.

Basically from the models above, most of the information in peak e' and strain rate propagation may be identical, and no added clinical value of strain rate propagation has been shown (so far, but not many studies have been done either). However, the finding contributes to a better understanding of the physiology, and the strain rate propagation is a direct measure of the rate of volume expansion of the ventricle, as shown below.



Elongation and simultaneous thinning of the wall can be seen to propagate from the base to the apex simultaneously with the motion of the mitral ring.  The local early diastolic strain rate is shown as the arrows indicating wall thinning (but thinning and elongation has to be simultaneous as explained above), and shows how local early diastolic strain is delayed in the apex compared to the base. This is illustrated below.



However, even if flow propagation velocity also is related to diastolic function, there was no relation of flow propagation velocity and strain rate propagation velocity, and indeed the flow propagation can be increased in hypertrophic ventricles with reduced diastolic function, even while strain rate propagation was decreased (20). In our comparative study, we found the patient group to have reduced strain rate propagation (30 cm/s vs controls 67 cm/s), but increased flow propagation (70 vs. 55 cm/s). In this study there was a negative correlation between the two.


Strain and strain rate in the atria

As the outer contour of the heart is relatively constant, the apex is stationary, and the atria is attached to the large veins, the atrioventricular plane has to be the piston of a reciprocating pump as discussed above), expanding the atria while the ventricle shortens and shortening the atria while the ventricle expands. This is energetically useful, 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.

Basically, the deformation of both chambers reflects the motion of the atrioventricular plane. In systole, the ventricle shortens while the atria expands. This is a function of ventricular contraction. In early diastole there is elongation of the ventricles and shortening of the atria, the active component of this is the ventricular relaxation. In late diastole, there is further elongation of the ventricles and shortening of the atria, but in this phase the active component is the atrial contraction. However, deformation of both chambers are reciprocating, both reflecting the atrioventricular function, and for  the elongation of the atria during ventricular systole is not an independent parameter, and is mainly due to the systolic function (shortening) of the left ventricle.

Deformation in the atria is reciprocally related to the deformation of the ventricles. as both  apex and the atrial roof are relatively immobile, the ventricle shortens  (yellow) while atria elongates (cyan) during systole, ventricle elongates (cyan) and atria shortens (yellow) during the diastolic phases. In diastasis, there is no deformation, both are green.




Curved M-mode going through both ventricular and atrial septum shows the reciprocal colours of the atria and ventricles. Strain in atrium (yellow) and ventricle (cyan) are seen as almost mirror images of each other. However, the absolute values in the atria are higher, as the atrioventricular plane motion is a greater percentage of the smaller atria as illustrated below. Strain rate curves are also basically mirror images of each other. As deformation is active in one chamber and passively transmitted to the other, the peak values may be higher in the active chamber, and there will be a time delay of events as waves propagate as shown in the ventricle during diastole.

Thus, deformation during ventricular systole, reflects ventricular contraction, early diastolic deformation reflects ventricular deformation and A wave reflects atrial contraction, irrespectively of which chamber the measurements are done, although values may vary. as shown below.



In this subject there is a ventricular systolic strain of 15%, while atrial strain during ventricular systole is 38%. However, taking the different lengths of the atrium and the ventricle, and calculating the absolute change in length, it can be seen to be the same within the limit of accuracy.  This is simply the MAE, reflecting both shortening of the ventricle and (longitudinal) expansion of the atrium.

Thus: The AV-plane motion is determined by the systolic function of the ventricles. It has been proposed that atrial strain is a measure of atrial "reservoir function". This rubbish means that the AV plane motion does mean different things when looked at from opposite sides, which is obviously rubbish. The atrial wall being thin, there is little resistance to AV-plane motion, and does not express distensibility of the atria. If one choses to measure strain in the atria instead of the ventricles, the ventricular strain being MAE/LV length, the atrial strain will be MAE/ atrial length. Thus the atrial strain will reflect the relative change in LA length, but this is due to ventriculoar contraction and says nothing of the atrium itself.


Atrial strain during ventricular systole

Reduced "reservoir function" (atrial strain during ventricular systole) in the atria in atrial dilation, is simply a function of the increased atrial length, given normal ventricular systolic function. And this will be relative, the absolute increase is the same, given the same MAE. In fact: the same MAE will result in the same absolute longitudinal expansion of the atria, and thus, much the same volume increase irrespectively whether the atria is long or short.

The relative expansion,  however has different contents.
  • Atrial strain is MAE divided by the atrial length. Thus, in reduced systolic function, the MAE is reduced, and so is atrial strain.
  • In atrial dilation, the atrial strain during ventricular systole will be reduced even with normal MAE, as atrial length is increased.
Thus atrial strain during ventricular systole is a composite of longitudinal ventricular function and atrial size. Left ventricular filling pressure (LA pressure), is elevated in reduced LV function, especially in heart failure. Thus, studies showing reduced left atrial strain with increased filling pressure may thus suffer from confounding with LV function.

Also, the left atrial size per se, is a sensitive index of chronic atrial pressure over time (195), and thus, even in normal LV function, the LA strain may correlate with LA pressure (and indeed may be a function of LA pressure), but the parameters are not independent. Thus, atrial strain during ventricular systole does not add new information, as recently confirmed clinically(245)

Being a composite parameter, it may be more sentitive than sigle parameters, but not independent. Long axis shortening is the most sensitive parameter of both function and prognosis (36, 190, 191, 192, 193), far more than EF.

Furthermore:
  • The longitudinal expansion of the atria corresponds to a greater volume dependent on the width (cross sectional area/diameter).  The atrial expansion times the cross sectional area, would thus reflect a part of the reservoir volume in the atria. However, the auricles would not be included, and the volume function would not be complete.
The wall length should probably be related to a curved strain length (as in 2D strain). However, because of its thin wall, strain rate imaging in the atria from the apical position is extra prone to artifacts due to low lateral resolution at the large depth, which may affect transverse tracking in the atria, and result in under estimation of the wall shortening anyway.

Thanks to Mads Ersbøll of Copenhagen, who pointed out the connection to LA pressures in studies, leading to the discussion in this paragraph being extended, incorporating the relation to atrial size.

His group has recently confirmed in a large prognostic study confirming that atrial strain during ventricular systole does not add independent prognostic information (245).

Atrial strain during early diastole
Early filling phase is likewise related to ventricular diastolic function, the mechanisms being elastic recoil modulated by the rate of calcium removal from the cytoplasm as discussed below. Thus, the amount of the systolic atrial strain being reversed in early diastole is also a property of the ventricle, divided by the atrial length.

Atrial strain during late diastole
Finally, the atrial contraction is a property of the atria.


It has been proposed that the main function of the atrial systole is to pull the mitral ring back to the end diastolic point, thus pulling the mitral ring over a volume of blood contributing to the end diastolic volume(13). However, this model disregards the finding by Doppler flow that there is an active flow component as well. And, as the pressure in the ventricles increase during the atrial systole, there is evidence for the vis a tergo mechanism being an important component also of the motion of the mitral ring, i.e. pressure being the driving force. Thus, the peak A is the volume flow due to the contraction of the atrium, but modified by the rate of pressure increase in the LV, being a function of the LV compliance. However, the AV-plane motion and  a', would be measures of atrial function. And, as this is pumping volume driven the total atrial action (including the pumping of the auricles) would be the driving force.

As e'/a' ratio decreases, the a increases, so this function is not independent on LV function, but comes closer than other measures. And is of little use where there is partial fusion of e and a. as the velocities then are combined partially of ventricular relaxation.

Atrial strain and strain rate are simply displacement and velocity normalised for atrial length as shown below.


The true atrial contractile function is the length change during atrial systole. Changing hte start of tracking to the start of the a-phase, shows atrial strain to be 13%. Peak strain rate can be measured independent of the starting point for tracking.





Basic principles of ultrasound and scanner technology.

Measurements of strain and strain rate by ultrasound


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Editor: Asbjørn Støylen Contact address: asbjorn.stoylen@ntnu.no   
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