Det medisinske fakultet

Strain rate imaging.

Cardiac deformation imaging by ultrasound / echocardiography

Tissue Doppler and Speckle tracking

by Asbjørn Støylen, 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. Revised edition 2011. An error has been corrected 050312; see what's new.

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, regionla 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 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 chapters on clinical evidence and the how-to chapter 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.


Link to website index.
Link to what's new.


Icebergs

Welcome

The internet is free, so feel free to use the examples found on this website in demonstrations and lectures. However, ordinary ethics dictates that credit should be given to the author. Remember also that your audience may have visited this website too, or I might even have been at the same congress. For publishing, I and the Norwegian University of Science and Technology retain the copyright to all material published here.

About the website:


The previous paragraphs "Is deformation imaging useful?" on how to do, interpret and about clinical evicence as well as "Measurements of strain and strain rate by ultrasound" has been moved to separate sections in order to allow quicker uploading as the website grows. I apologise for links being corrupted in the process, and will work on bringing them up to date.

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.

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

Website updated: October 2011.     This section updated: October 2011.


Recent updates:

March 3rd 2012: There was an error in the wall specific values for e' given below. This has now been corrected.

November 15th: The discussion on differences between contraction and deformation has been evolving for some time, now it has been collected in a separate paragraph at the beginning of this section. It seems too easy to assume that the ejection (which equals volume reduction or systolic deformation) = Myocyte contraction. And likewise that Early filling = myocyte relaxation. This is definitely not true! And the discussion attempts to relate to myocyte function at the cellular level, in order to emphasize that systolic deformation (whther by ultrasound, MR, MUGA tissue Doppler or Doppler flow (not only strain and strain rate), all relates to deformation, which is not equivalent to contraction. And certainly not contractility. Firstly because much of the myocyte work does not generate deformation at all, but only tension (relating to pressure), secondly because relaxation starts in mid ejection and in fact, a part of the systolic deformation happens during myocyte relaxation. However, regional deformation, i.e. strain and strain rate are images of relative contractility, as discussed below.

October 28th: Added a short paragraph on area strain, as this parameter now is starting to be published. As this is measured as endocardial strain, the geometry tells us that this is simply * fractional cross-sectional shortening * longitudinal shortening, the utility of this needs to be assessed more.

October 11th: Just a small extension of the paragrpah on atrial strain, incorporating the relation to LA size, thanks to Mads Ersbøll for pointing it out. Atrial strain during ventricular systole is mainly annular systolic displacement, divided by a measure of atrial size, and thus simply a composite of LV function and atrial size.

Sept 1st 2011: I have no new updates so far, but having attended the Eur. Heart Congress, I still find the mis apprehension that circumferential strain reflects the function of circumferential fibres being perpetuated in talks. This is definitely not the case, as shown below circumferential strain is mainly a function of wall thickening.. On the other hand, there is no such thing as "radial function". Radial function relates either to wall thickening (being a function of longitudinal shortening and to a small degree circumferential shortening) as shown below, or to fractional shortening of the cavity diameter. And if the distinction of these two is fuzzy, the results may be strange.





Website index:

List of tables of normal values




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.


This section:

 

Other sections:

Measurements of strain and strain rate by ultrasound
This paragraph has been moved to a sepatate section in order for the main page to upload quicker. The section deals with the fundamentals of the different methods for measuriong strain and strain rate by ultrasound, and their limitations. It is a continuation of the basic ultrasound section, which only deals with deformation imaging in a cursory way. However, the understanding of the basic principles of ultrasound will add to the understanding of the methods as described in detail in the measurements section. The links in the "measurements" section have been repaired.


Is deformation imaging useful?
The previous paragraph on "how to" and clinical evicence in the main section has been moved to a separate section in order to avoid too slow uploading as the website grows. It 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. 


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. 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 b read separately even if deformation imaging is not interesting.


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



Basic concepts in  strain and strain rate.


Motion and deformation:

Motion. Floating iceberg in hurricane.
 Deformation. Calving glacier.





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 of 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 and running evenly, 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.  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. AS the engine starts, there is stretching between that and the first carriage (blue). 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. 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, as shown below in myocardial images.


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), thus, according to the Lagrangian formula there is positive strain of 25% or 0.25. This 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.

The three main deformation components are : 
Strain in three dimensions. All three-dimensional objects can be deformed in three dimensions (along all three axes).  This elaborated in the mathematics section. The figure also shows incompressibility, it's stretched along the x axis, and compressed along the y and z axes.
Strain in three dimensions. 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.

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 a separate chapter. For present and clinical purposes, the present method is one dimensional. 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").


Incompressibility.

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.

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 deformation. But 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 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.

(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 diastole, 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.)




Excitation-tension diagram. The Action potential triggers the release of Ca2+from sarcoplasmatic reticulum. Calcium binds to troponin, and allows activated myosin to bind to actin (cross bridge forming) and release stored energy, causing the filaments to slide along weach 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 occurs. The pumping of calcium is energy dependent, and is the energy requiring part of the relaxation cycle. However, in energy depletion, there will be less shortening in systole, and thus also slower recoil.







The contraction relaxation can be visualised either in stimulating isolated myocytes in a nutrition solution, or by measureing 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).  

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.)

In the intact heart, however, there is external load as well, and deformation (shortening - elongation) is the relation between tension and load. This means:

The heart cycle can basically be described in terms of volume changes:

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.






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.
Top,  Ventricular volume curve, with the different phases demarcated. 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. The isovolumic phases are exaggerated. The Wiggers cycle. The myocardial tension is evident from the pressure changes. The ejection phase is during aortic opening, and the early filling phase is during the first (E) phase of mitral 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. The relaxation continues into the isovolumic relaxation phase, and then (probably) into the early filling.

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).
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.

It is important to realise that  imaging measures only deformation, while contraction is generation of tension, and contractility is the ability to develop tension. 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. However, a considerable part of the energy from myocyte contraction is not used 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. 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. And only a part of this is converted to verlocity (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.

Basically, imaging only shows part of the contraction of the myocytes.

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. Only a small part of this work is seen as ejection velocity (or rate of volume decline, as most of the orsk is required to build the pressure up to equaslling the aortic pressure. (This doesn't mean that the energy is lost, it is stored in the elasticity of the aorta, and as the aorta recoils in diastole, the energy is recovered.) The aorta then functions as a diastolic pump into the periphery, using the energy imparted to the ventricle from systole.

Thus, only the pumping action of the heart, i.e. the ejection work can be described by imaging of the heart itself.

Secondly, there is inequality between the contraction phase and the ejection 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. The last part of ejection, which is still imaged as flow or volume relaxation, happens during myocyte relaxation. The flow is simply due to the inertia of the blood pool already having been accelerated. Thus, imaging shows continuing shortening/volume reduction/ejection, diring late ejection, despite the initial myocyte relaxation. This is due to the inertia of the blood already being accelerated and flowing out of the ventricle. But this is the main shortcoming of cardiac functional imaging, that the deformation does not reflect the myocyte contractile state. And this is true whether we talk about MUGA, MR, B-mode or M-mode echo, tissue Doppler or deformation imaging and even Doppler flow. This is a fundamental concept of call cardiac imaging.

Ejection phase is not contraction phase. This is a fundamental concept of call cardiac imaging.

However, the ejection work, is reflected in the total flow or volume change, even if timing is not.

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.


Load dependency of (systolic) strain rate and strain.

It has been assumed that the deformation and velocity parameters are load independent, but this is not the case, they are clearly load dependent, although 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.

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 than the force the muscle must overcome at the start of contraction, i.e. the force acting on the muscle at the start of contraction.
Afterload is the force that is generated by the heart muscle during ejection, i.e. the contraction force.
This is illustrated below left.

Force and tension are interchangeable concepts relating to the state of the muscle, i.e. the force developed by the muscle. Load, is thus the work force developed by this tension. In a heart chamber, the load is related to the pressure in the chamber. Preload thus to  end  diastolic pressure, afterload to peak systolic pressure, and the terms are often used interchangeably. However, load is also related to the surface area, as 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). Thus, the load is the result of both surface area and pressure as shown below middle. (However, changes in pressure in a ventricle with little changes in dimensions, are more closely related to changes in load, and the pressure changes may be taken as expressions of load changes).

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.






The concepts of pre and afterload are easily defined and studied in isolated muscle preparations:.Preload is thus the weight standing at the table. It may stretch the muscle or the muscle may be completely at rest. The main point is that the muscle, in order to contract, must lift the weight off the table before it can start to shorten, this is the preload. Through a hole in the table the preload weight is connected to a second weight, standing at the floor, and connected with a spring coil. As the muscle starts to shorten, having overcome the preload, the tension in the spring will increase as the muscle shortens and the spring elongates, adding to the load. As the tension in the spring equals the second weight, this will be lifted off the floor, and the rest of the muscle contraction is isotonic. The second weight is the afterload, and the total  force developed by the muscle is equal to the total load. In this case, the first weight is equivalent to the preload - related to end diastolic pressure (and volume), the contraction during the elongation of the spring equivalent to the isovolumic contraction (IVC), and the second weight the afterload - related to the systolic aortic pressure (modified by the ventricular volume).  The isovolumic contraction may be considered mainly isometric, the ejection mainly isotonic work, as there is no volume change during IVC. (This is a shortcoming of this model, as the IVC simulated by the stretching of the spring is not isometric). Of course, in a ventricle, the situation is even more complex, as there are different fibre directions that are responsible for different proportions of the pressure and ejection work.
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.


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. However, the load independence of diastolic velocities is also only partial (160).
Thus, strain rate and strain is 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. 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.


Shortening velocity and total shortening decreases with increasing load. This relation holds for both pre- and afterload for any given initial length.  (after 208) Shortening velocity is about the same as strain rate, and total shortening is about the same as strain (for longitudinal fibres and deformations) , so those relations should hold for strain rate and strain as well.

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).

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.


Thus, both the peak rate of shortening, the extent of shortening as well as the time to maximal shortening will be affected by load. In 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.

Publications attempting to show early myocardial dysfunction in low grade aortic stenosis, are thus mistanken in the premise that deformation indices are load independent.

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. 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 a study in healthy normal human subjects (223)


The study by Greenberg et al (80), did show that 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.


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. 


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 .

Thus, relaxation happens during the last part of ejection, isovolumic relaxation and early filling, and is thus part of both systole and diastole, as systole and diastole are commonly defined.




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. The elasticity (compliance) of the arterial (especially the aortic) wall. During ejection, the volume ejected into the aorta distends it, 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. Arterial stiffness increases with disease and age, and thus the systolic pressure will increase, the diastolic pressure decrease. But even so, the stiffness of the wall is also directly increased when the pressure increases, adding to the effect.
  2. The peripheral resistance, is to a lesser degree responsible, the resistance mainly located to the arterioles determines the run off from the arterial to the capillary bed. But the higher the resistance, the higher the pressure. 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.
  3. The stiffness of the arterial wall. Although the stiffness is already influencing the arterial compliance, it has another effect, the effect on the propagation of reflected pressure waves. The pressure wave from the ventricle travels much faster than the blood, along the arterial bed. The pulse pressure propagation velocity is also a function of the stiffness of the arterial wall. This pulse pressure is reflected from the periphery, and thus there are two waves traveling back and forth during each heart cycle. Where the pressure peaks coincide, there will be augmentation, where one peak an one through coincides, there will be neutralisation. 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.

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.

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.


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, the M-mode method will measure along the straight line, while segmental strain will measure along a straight line in each segment, thus being somewhat in between, as shown by this figure.



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:
 

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:
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. As the ventricle shortens, the wall has to thicken in order to maintain the wall volume, as the myocardium is incompressible, the total wall thickening must be a function of wall shortening, as the wall volume has to remain constant if it is incompressible. Wall thickening reflects the thickening of the individual muscle fibers inn all directions as they contracts. As the outer contour changes little during systole, this means that as the ventricle shortens, the wall has to thicken inwards. Thus, longitudinal shortening determines wall thickening. Thus, assuming an invariant outer contour, the wall thickening is determined by the longitudianl shortening, as shown below. As wall thickening is given in percent of diastolic wall thickness, wall thickening is determined by wall thickness and wall shortening.


However, circumferential strain needs defining. The circumferential strain has no meaning except as a shortening of a defined circumference. And this is dependent on which circumference, as circumferential shortening icreases from the epicardium (being close to zero, to the endocardium (being maximal), as shown below right. As long as the wall is seen as a whole, the reduction in circumference depends on where it is measured. Endocardial circumferential shortening is greater than midwall circumferential shortening, which is greater than epicardial circumferential shortening  (which is fairly close to zero - see below). The common definition is midwall shortening, and is the measure most used in publications as well as the value given out by the 2D strain application. (In that application, it is a necessity due to the method used. Other systems may have the possibility of tracking endocardially.). Thus:
Of course, this has only to do with the wall thickening, as the circumference is dependent on the diameter only;  the circumferential shortening is a function of internal diameter shortening, as the circumference, C is given by C = 2(D/2) = D, and the systolic circumferential shortening is CS = Cd - Cs = (Dd - Ds). Thus: endocardial circumferential shortening is simply * fractional shortening (which is (LVIDd - LVIDs)/LVIDd), while midwall circumferential shortening is midwall fractional shortening.  This means that the circumferential shortening is just the inward shift of the circumferential line (irrespectively of wether the endocardial or midwall line is used) due to the wall thickening,  is simply a function only of cavity diameter, wall thickness  and wall thickening.

This also means that for global systolic function, circumferential strain is in reality a cavity measurement, not a wall measurement.
Relation of long axis shortening and wall thickening.  As the heart muscle is generally considered incompressible, transmural thickening has to be balanced by longitudinal plus circumferential shortening. 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.
 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. The circumferential shortening is simply a function of the reduction in radius, which again is mainly a function of wall thickening (although a small reduction in outer contour will contribute slightly).



Thus, as can be seen, the circumferential strain is a parameter that is not as anatomy independent as the longitudinal. (And the wall thickening is indeed the function of longitudinal shortening.)




Circumferential strain (midwall circumferential shortening as a function of cavity diameter, wall thickness and wall thickening (transmural strain). In all cases a systolic outer contour diameter reduction of 5% is assumed.
Circumferential strain as a function of diastolic LV cavity diameter (LVIDD), given a constant wall thickness of 10 mm and systolic wall thickening (transmural strain) of 40%.  As cavity diameter increases,  with consatnt wall thickening, the diameter increase, and hence, the circumferential decrease becomes a smaller percentage of the increasing initial (end diastolic) circumference. Hence, circumferential strain decreases. The same would be the case with fractional shortening.
Circumferential strain as a function of wall thickness, given a constant LVIDD of 40 mm and wall thickening of 40%. As wall thickness increases, the absolute wall thickening increases, and the end systolic diameter decreases, leading to a decreased midwall circumference, hence, increased circumferential s strain. Circumferential strain as a function of wall thickening (transmural strain), given a constant LVIDD of 40 mm and end diastolic wall thickness of 10 mm. As wall thickening increases, end systolic diameter decreases, leading to a decreased end systolic midwall circumference, hence, increased circumferential s strain.


Area strain


Hypothetically, with the advent of 3D echocardiography, it would also be possible to measure the area strain. The systolic reduction of the area would be a product of both longitudinal and circumferential shortening, and this would increase the magnitude  of the change, and thus possibly the sensitivity.


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, the area reduction being the product of longitudinal and circumferential
shortening. Thus, the magnitude of the area change would be greater than the circumferential or longitudinal shortening alone.

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. In the 2D strain application, the circumferential strain is measured in the midwall, which is consistent with the use of the parameter previously. However, in recent publications, the area strain has been defined as endocardial area strain. But as described above, the endocardial circumferential shortening is simply * fractional cross-sectional shortening. Thus, endocardial area strain will simply be equal to * fractional cross-sectional shortening * longitudinal shortening.

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. Howeever, it could still be computed to  certain degree, as endocardial circumferential shortening can be computed from the fractional shortening through the hypokinetic area.


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. 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. In dealing with the principal strains, the wall is treated as isotropic, which it is not. For circumferential and transmural strains, 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 imagine what that would have done to the rest of the fibrous plane), 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 strain components are totally interrelated, and cannot be decomposed into different layer functions. This is discussed in more detail in the mathematics section.
Thus the three principal strains are totally interrelated and does not convey separate information. 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 below,  this 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.


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.

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.


The eggshell model


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). 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.

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). He also elaborated on the description of the working mode of the heart into the so called "eggshell hypothesis", based on model experiments:

1: The heart strives to do its pumping with a fairly constant total volume and outer contour in an environment conferring a substantial moment inertia.

The basic point of this was that the heart by this mode behaved in systole like it worked in a rigid shell, by systolic shortening of the ventricles sucking blood from the large veins into the atria, while the longitudinal expansion of the ventricles in diastole in fact "gripped" the blood in the basal part of the atria. His model is based on the filling pressure, and does not take into account the ventricular suction.


2: The interventricular septum regulates ventricular stroke volumes to maintain a proper balance between systemic and pulmonary circulation.

The main point of this is that the radial motion of the septum in diastole is determined by the differences in filling pressure of the left and right ventricles. If the filling pressures are reasonably similar, as in the normal situation, the septum has little radial displacement, and event the left side of the heart can be described by the eggshell model. Lundbäck's main point was that the radial motion induced by unequal filling pressures in the two sides, would increase the filling volume on the side with the highest pressure, reducing the filling volume at the other and thus balance the stroke volumes at the two sides. This model does not take into account the geometrical effect of interventricular interaction, as the model stresses the longitudinal pumping effects. 
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 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).




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.

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.


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.


Thus, the pumping action of the heart, i.e. the ejection work 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.




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 integration



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.

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. 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.
The same curved M-mode showing displacement during the heart cycle.

The curved M-mode is superb in showing the time-phase relations, and inequalities 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.

Three dimensional display and bull's eye plot

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.
 3D strain rate display in systole and diastole. 3D displacement display in end systole

The disadvantage of the stationary 3D display is that it will only show one side of the ventricle at one time, and for each picture only one point in time. As the reconstructed dataset is really 4-dimensional, 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.  (Image courtesy of E. Sagberg.)


Another way is to display the ventricle in a bull's eye plot showing the whole ventricle (although in a distorted view, and at one point in time only). Bull’s eye projection is a 2 - dimensional map of the entire surface of the left ventricle, but only at one instance in time. It is analogous to displaying the curved surface of the earth on a flat map, resulting in distortion of the surface. 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.
 Bull's eye projections of a normal ventricle. Top velocities corresponding to the 3D images above, in systole and diastole, middle strain rate similarly and the bottom image shows how parametric image can be combined with numerical information. This image shows an end systolic strain map,  with segmental end systolic strain values superposed on the image.



Relations between systolic motion and deformation measurements

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.

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.

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). 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.


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. 
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.

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.



     

    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.

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.

Systolic events







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, which is explained in detail here. 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. 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.



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.
 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.

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. 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.


However, as one knows that there is relaxation during the last period of ejection, it is 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. In addition, using high frame rate imaging of the septum together with a high fidelity phonocardiograph, we could se this elongation before the AVC in an observational study (16).
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 mitral ring. (The same can be seen in 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.
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.

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. Thus, 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.

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.  If AVC should be placed by strain rate traces, it can only be located from the M-mode or the midwall race, 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. In strain curves, however, AVC can again be seen as a "notch" (as in displacement), most evident in the midwall (cyan) trace.

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.
  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 is not "strain during IVR", and it 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. 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.)

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.

Diastolic events



When is mitral valve opening?

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 traces, instead of being transferred from other cycles.

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. However, this will correspond to a shift from positive to negative velocity in the velocity traces ans a red to blue shift in the colour traces, as seen below.

Mitral opening possibly corresponding to the start of elongation after the MVC. This means again a shift from positive to negative velocity.
 Mitral valve opening identified by the shift from positive to negative velocity. It is the second zero crossing after the protodiastolic dip. Event marker may placed by velocity, and then carried over to the displacement traces, as the zero crossing point may be easier to identify than the transition in the curvature in the displacement trace.  However, as seen from the M-mode, the transition from positive to negative (red to blue) is not evident at all levels.

But the exact time point is not as well defined, and it may correspond to another event, such as the point of maximum negative acceleration. So far, the positive to negative shift in velocities is an approximation.


What about the mitral valve itself?

As the mitral valve is visible in all apical views, it should be possible to identify the mitral valve opening directly. However, as the base of the heart moves slightly towards the apex after AVC, the mitral valve motion follows the mitral ring. 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 pitfalls 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.

The aliasing velocities of the ring are even later, 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.



Motion of the mitral ring, mitral leaflet and mitral tip.  Bottom; zoomed to the time period of interest. The mitral ring (yellow curve) can be seen to "bounce" after AVC.  The middle part of the  mitral  leaflet (green curve) can be seen to be partially following the mitral ring, and motion towards the apex starts before MVO.  The mitral tip does not follow the "bounce" of the ring (probably due to the inertia of the blood in the cavity, and in fact there is a slight billowing of the valve in the middle, evident by the continuing motion away from the apex). The motion towards the apex starts simultaneously with the motion of the ring away from the apex.  However, here, the "notch" marking AVC is also absent, but the change from negative to positive velocity should be evident.  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.
Velocity traces of the same points as seen to the left. The mitral tip can be seen 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.





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.

From the images above, it seems that the mitral tips billow away from the apex during the IVR (as expected), and the starts to move towards the apex at MVO. Thus registrations from the mitral tip might be feasible, but this should be done with high frame rate. However, high framerate leads to less lateral resolution, thus mixing the lateral parts and the tips. Narrow sector in the middle of the mitral tips might be used, but if the time point then needs to be transferred to another full sector cycle, the MVO time could just as easily be taken from pwDoppler of mitral flow. Thus no reference for the ground truth can be established within one and the same heart cycle with any reliability.


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.




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.


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.





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.



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. The protodiastolic phase cannot be seen in the traces from the base, only in the mid wall in the M-mode. Also 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.







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:



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. 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.


Thus: The AV-plane motion is determined by the systolic function of the ventricles. 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, and thus the "reservoir function", but says nothing of the atrium itself.


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.


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, an independent contribution of LA strain to the echo evaluation may be doubtful.

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 morte than EF. Thus, in comparing the efficacy of different parameters, the longitudianl shortening should be used as systolic measure, and included in multi variate analyses in order to determine whether atrial strain during ventricular systole actually gives independent information.

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.


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.

Thus: the atrial long axis function by deformation, basically reflects the AV plane motion. The added value of using of atrial strain and strain rate instead of annular displacement during atrial contraction is uncertain. However a theoretical advantage is that it corrects for atrial dilation, and thus mau be more sensitive, but this needs to be estabolished in clinical studies.





Global systolic function

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.

What does Strain and strain rate actually measure?


It is important to realise that  strain and strain rate measure only deformation. Deformation is definitely NOT contractility. In fact, any imaging technique, by any parameter measures deformation which is the visible contraction, not contractility. This is due to more than one point:
  1. The greatest apart of the work is the pressure buildup, during the isovolumic contraction, i.e. the pressure work, which is mainly isometric. This cannot be measured by imaging (including deformation imaging) at all.
  2. Deformation of the ventricle during ejection, i.e. the contraction is load independent, the work being a function of both deformation and prerssure.
  3. Basically, contractility is described in terms of the volume-pressure relation, meaning that the increase in contraction due to the Frank-Starling mechanism is excluded
So any imaging measurement will measure load dependent contraction, unless some correction is done to obtain a measure of load. (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.)

Contractility is the ability to develop force independent on load, and is closely related to the stress-strain relationship. I.e. the shortening in relation to the load. (Thus, for any given force, the deformation is load dependent, but as force may change with both heart rate (force-frequency effect) and volume (actually initial load; the Frank-Starling effect), the interaction may be quite complex. Contractility may be defined as end systolic (actually end ejection) pressure volume relation, (even though this changes with inotropy, this is slightly dubious as the myocytes actually are in a relaxing mode at that time). An other measure is the peak dP/dt. This occurs during the isovolumic contraction period, when there is no deformation. Thus this is a simple measure of force development, but it's still dependent on preload, which is a function of volume (diameter) and end diastolic pressure.

But, again, this the part of work related to pressure buildup, the pressure work. 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. This may be considered as the mainly isometric part of LV work, as there is little deformation. The strain and strain rate are both indices of ejection work. In this phase, there is significant reduction of volume, but far less change in pressure. So this may be considered a more isotonic component of the work. And it is only this part that is measured by the systolic deformation indices. As described above, there may be differences in the different fibres in the contribution to the two parts of the work.

Thus, to lump everything together and calling it contractility, may be meaningless, there may be a correlation, but the concept of contractility, outside of isolated muscle experiments, is more theoretical. Strain and strain rate measures deformation, and deformation has to be interpreted in terms of load, to infer contractility.

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). 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).

Thus, as deformation is a result of tension, or rather tension versus load, strain does not measure function directly. 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. Thus, strain rate images shows gradients of relative contractility, even if one does not measure absolute contractility.


And that is the main point in regional diagnosis.











Cavity measurements of systolic function

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. Thus it will remain in use for an foreseeable future. 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.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:

1: A person with an EDV of 125 ml, a stroke volume of 70 ml has an EF of 56%, which is fairly normal values for a grown man.
2: A dilated ventricle to 250 ml, with maintained stroke volume of 70 ml, gives an EF of 28%, which is reduced. This is in accordance with reduced systolic function.
3: Concentric hypertrophy reduced the cavity volume. A little old lady of 80 years with concentric hypertrophy may have a cavity of 75 ml, a stroke volume of 40 ml and an EF of 53%. Thus EF is normal, but in terms of stroke volume, the systolic function is not!

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 fractionla 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.

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


Thus, fractional shortening and wall thickening may be considered inversely reklated. But they are not interchangeable as measures of "radial function" as the same erroneous results will be obtained by the fractional shortening as of EF, as shown by the example below.

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. 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 ejection fraction" (HFNEF).

But as EF as a measure of systolic function in the case of small, hypertrophic ventricles is meaningless, the whole concept is still dubious. The EF is introduced to characterise the reduced myocardial function in dilation, by normalising an unchanged stroke volume for the increasingly dilated ventricle. But this does not work the other way, if the EDV does not increase or even decreases, the ratio has no logical physiological meaning.


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. 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.


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%.  In the case of concentric hypertrophy, 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!

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.

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.

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.



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.




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.

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 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 (13, 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

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.

As described above, the annular displacement divided by the length of the ventricle is a measure of global strain. Similarly, the annular velocity divided by the ventricular length is a measure of global strain rate. In fact, both displacement and velocity can be normalised for (divided by) the distance from the apex to the point of measurement as shown below.  



Normalised velocity/ displacement.  The velocity and displacement in each point along the wall from apex to base is the resultant (sum) of the contraction of all the segments apical to the measuring point. Thus dividing the velocity or displacement at a certain point along the wall by the distance of the point from the apex, will normalise the velocity and displacement for the distance, resulting in values that are similar to strain rate and strain.

Mainly, this approach will be a compensation for the velocity / motion differences between apex and base, making the evaluation of these measures position independent (54). For displacement, being maximal at end systole, this will be similar to the strain of  the whole myocardial segment between the apex and the measurement point. 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.

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

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.

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.

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.

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.

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

Segment interaction

The segment-segment interaction is necessary to understand the effects of regional function measured by deformation imaging.


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 iis secondary to deformation, but deformation is secondary to force and load.

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 froce from neighbouring segements, is the basis for both the changes in systolic deformation and the post systolic shortening. 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 other segments that is caused by the contraction from that segment, is reduced.  But that means that  deformation by neighbouring segments may increase, due to reduced load, 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. Thus, regional loss of contractility may be inferred from the reduced regional deformation.

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.
 The AV plane. Not only is 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 arteru (PA),  the aorta (Ao), the MItral (MV) and the tricuspid valves. Thus even the possibility of tilting of themitral ring as each wall functions differently, is severely restricted.
Thus, it may seem that in apical infarcts, there is more resustance 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.



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).


Even so, the basal infarcts, sitting on a moving ring, will counteract the tendency to stretching as well, the other basals egments will move the ring.

But to complicate things, it must be emphasized that the mitral ring is stiff, each segment does not move independently. It's easy, looking at one wall at a time to see only one mitral segment at a time. It has been maintained by some (32), that the motion of the mitral ring is semi- regional, identifying the wall, although not the segment affected, but this is not the case. 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. But as shown above there is no isolated mitral ring, the ring is simply part of the much bigger fibrous AV plane, and thus the possibility of the ring tilting is restricted.

Thus it can not be inferred that only the segment close to the infarct can identify the affected wall. In a study of 19 infarct patients versus 19 control subjects, in 2003 (40), we did show that. There 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, segmental reduced function will not cause the ring to lag in part of the circumference, so much as 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).


 EF (%)
 WMSI
 MAE (mm)
 S' (cm/s pwTDI)
 S' (cm/s cTDI)
Controls:
 55
 1
 16
 9.9
 7.6
Inferior infarcts:
 45
 1.4
 13
 8.0
 5.0
 Anterior infarcts:
 38
 1.7
 11
 7.5
 4.7
All differences between controls vs patients were significant, and also inferior vs anterior except for S' (by both TDI methods).

What was more important was that the variability of measurements around the ring was the same in controls and patients, and there were no differences between segments close and remote to the infarct in the patients. (Not only no significant differences, there were no differences at all). Thus the concept of the segmental motion of the ring being a semi regional measure is wrong.

The most interesting finding was that while the infarct segments did show significantly lower strain rate compared to remote segments, despite the higher variability of strain rate measures. However, when the strain rate of the three segments in the affected wall was averaged, the differences disappeared, confirming the finding from the mitral ring measurements that the total wall shortening is not a regional measure.

Thus, 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).

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.



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. 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, as well as in loss of function, both the rate of shortening as well as the total shortening (i.e. strain rate and strain) is reduced (208, 209)as shown above. But in isotonic twitches in isolated muscle, this reflects the force development. Thus the increased relative load in ischemic / infarcted segments is important, in that it delays the force development. This means that the affected segment is still shortening when neighbouring segments relax, resulting in reduced load on the affected segment, which then can contract while the other segments relax. 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.
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). 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).


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 fiorst 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 (Left, bottom, shows delayed and prolonged shortening, but more or less in all segments. This is equivalent with the balanced ischemia of scintigraphy.

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.



Asynchrony:

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 this case, 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 area. Thus, simply showing asynchrony by motion imaging is insufficient in the diagnosis of condiuction abnomalitiy induced asynchrony.
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.
 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 can be more reliably done from basal recordings as shown above, but these were early days. Actually the AVC timing here is a little off, it should be closer to 0.27 or 0.28). This timing is then transferred to the deformation images to the left.


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 dely,but shows it to be less pronounced, abnd not indicative of ischemia, and it also helps in showing the the extent, compared to tissue velocity.

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).

The new concept of "mechanical dispersion", meaning unequal duration of the shortening phase, seems to be due to variable amount of PSS within the ventricle.



Regional circumferential strain

The regional circumferential strain may be affected in different ways, depending on the degree of transmurality, as sub endocardial infarcts to little degree affects the midwall circumferential fibres, with little or no effect on circumferential force. Transmural infarcts affects those, leading to regional loss of circumferential force. However, as circumferential strain is defined as midwall circumferential shortening, even sub endocardial infarcts will result in loss of circumferential strain due to loss of substance. As subendocardial infarcts leads to loss of subendocardial fibres, there will be a reduced wall thickness and also less wall thickening in the infarcted area in absolute terms. However, thickening in relative terms (percent of end diastolic wall thickness. i.e. strain) may be less affected (i.e. less absolute thickening in a thinner wall may give the same strain).

However, as the wall is thinner, the midwall circumference is greater, but shortens less (in absolute terms) due to reduced wall thickening. Thus, there will be less circumferential shortening of a longer circumference, i.e. the circumferential strain will be reduced, even without affection of circumferential fibres as shown below. Howeever, this will not lead to changed function by segment interaction, as the circumferential force is not affected.


  .


Diagram of a sub endocardial infarct, not affecting circumferential fibres. The infarcted area is depicted as an area with loss of endocardial longitudinal fibres. As shown this leads to a thinner wall in the infarcted area, and the midwall line is shifted outwards. As the wall thickens in systole, the thickening is less in the infarcted area, and this effect is even greater than the loss of fibres, as the effect of the fibre rearrangement would have been most pronounced in the endocardial layer due to the geometry. However, the effect on transmural strain is unpredictable, as there is less thickening of a thinner wall, the transmural strain, being relative, may be preserved.  The midwall circumference, however, is increased, while the circumferential shortening (absolute) is decreased due to less thickening as shown above. This means less shortening of a longer circumference.  Thus, even without loss of circumferential fibres, there has to be reduced circumferential strain in the infarcted area. However, analysing program using an ROI, will give the shortening of the midwall line of the ROI as circumferential shortening. Thus, the ROI width, not the wall thickness is determining factor, and this effect may be lost, if the ROI is not very well fitted to the endocardium. This is indicated with the dotted lines representing an assumed equal width ROI around the circumference.  The effect on the width of the ROI in 2D strain is illustrated below.




In infarcts affecting the circumferential fibres; i.e. infarcts with a higher degree of transmurality, the geometry may be somewhat different. In this case the circumferential force is reduced or absent in the infarct, resulting an an imbalance of forces equivalent to what is seen in the longitudinal direction. This means that there may be a systolic stretching of the infarcted wall in the circumferential direction, and also an increased circumferential shortening of the intact part of the wall. This is shown below.


Exaggerated diagram of an infarct affecting circumferential fibres.  In this case, the force (black arrows) from the circumferential fibres will pull and extend the affected area in systole (boundary marked by green arrows), the infarct being without balancing forces.  The intraventricular pressure will still serve to keep the wall distended (blue arrow), preventing the infarcted area to be pulled straight across the gap. Thus, the wall structures in the infarct may even diverge from each other, which is hypothetically detectable in speckle tracking. Transmural strain may also be more affected, as there will be no wall thickening due to crowding and inward motion of longitudinal fibres (even if there are some left).

Some authors have found a higher sensitivity for transmurality by circumferential strain (221). However, this may also be a function of reduced sensitivity for subendocardial infarcts, due to the ROI issue as discussed above. The effect of ROI width is illustrated below.

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 the entire truth. Myocyte contraction is followed by lengthening, in isolated myocytes, restoring the original shape. This is an active, energy consuming process, due to the uncoupling of the actin myosin as well as active calcium transport into the sarcoplasmatic reticulum. But the lengthening itself has no active mechanical component in the filaments, and must be due to the elasticity in the cytoskeleton. But the lengthening of isolated myocytes is in an unloaded situation, where lengthening starts at the start of relaxation.

Basically, the myocytes starts relaxing before the middle of the ejection, creating pressure decline, but are still shortening as volume decreases due to continuing ejection, as mentioned above. Thus myocyte lengthening starts much later in the intact ventricle. And the lengthening is due to more mechanisms than myocyte lengthening alone.
  • As the ventricles contract in systole, some of the energy is stored as elastic forces in:
    • the myocardium itself - being compressed
    • the interstitium - both being compressed
    • the atria - being stretched
    • the large vessels - being stretched by the apical motion of the AV-plane
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).

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.
 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. 
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.

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.



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.



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: 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: Patient with heart failure (and normal EF and LV EDV), but with normal filling pressure due to diuretic and ACE inhibitor treatment. Severely prolonged IVRT, dec-t, decreased E and E/A ratio <<1. Very low e'. Patient age 75 with apparent normal mitral flow curve (top left), similar to the curve of the much younger patient in B. However, the mitral ring velocity shows delayed relaxation, indicating that this finding is pseudonormal (delayed relaxation masked by slightly elevated filling pressure). This is shown by recording during the Valsalva maneuver, (top right), where the mitral flow curve changes from beat to beat, showing decreasing E and E/A, and increasing Dec-T. The third beat shows a delayed relaxation curve.
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'.

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.

This means that the ratio of E/e' can be used for assessment of left atrial pressure (71, 72, 177). E is pressure driven, but e' is not, the relaxation actually being the cause of the pressure drop. 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).


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.

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.
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.

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.

 If there is suction during early filling, there can be no 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.


Splashing humpback whale.

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.

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).

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 forwards. 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




Animations above displayed as a sequence of instances, analogous with M-mode recordings.  Left: A, middle: B and Right: C. The slowing of the propagation velocity from A to B by reduced velocity, and from B to C by increased time  between start of cars is evident.





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,.
 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.



We did show early that the strain rate propagation velocity (the slope of the elongation wave) was reduced in reduced diastolic function (19). This is a global measure that relates to the peak e' in tissue Doppler, and is a global measure of diastolic function.




Strain rate propagation velocity is the slope of the elongation wave.
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.


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). 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.





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 to the right.

And if global diastolic function is to be measured by strain rate imaging, it is the propagation velocity that is the global measure, not an average of local strain rates (not being simultaneous). However, the finding contributes to a better understanding of the physiology.

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.


Measurements of strain and strain rate by ultrasound


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Editor: Asbjørn Støylen Contact address: asbjorn.stoylen@ntnu.no, Updated: 2011

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