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What does strain and strain rate actually measure?

The relation between function imaging and physiology - contractility, load, work and phases of the heart cycle.


Asbjørn Støylen, Professor, Dr. med.

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

Any imaging modality, including strain and strain rate only shows muscle shortening, and thus only tells half the truth about cardiac contractility and work.
Function is contractile force, and shortening is force versus load. Work is the amount of shortening times load.

The page is part of the website on Strain rate imaging
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This section has been completely rewritten, taking into account a lot more of the early fundamental physiological research which still holds true, and which is important in understanding strain and strain rate imaging.  The basic relations to the phases of the heart cycle have been moved from the sections on global and regional systolic and diastolic function, while the clinical relations remains in the respective sections. This to present a more fully integrated physiology concept in this section,and an easier access to the clinical parts in the other sections.

It is important to realise that imaging, always shows the result of myocardial shortening. This is true of any imaging measure, whether it is fractional shortening, EF, longitudinal shortening, strain or strain rate. It is also true, irrespective of imaging method, MR, CT, MUGA or ultrasound. Myocardial contraction, on the other hand, generates force (tension). In an isolated myocyte or unloaded muscle preparation, this force generates shortening. Unloaded states, however, hardly exist in the intact heart. The opposite situation, the isometric contraction, generates force, but with no shortening. This actually exists during isovolumic contraction. In between, contraction generates force, but doesn't shorten until the force exceeds the resistance to shortening (load). Also, active contraction happens only during pre ejection, where there is no deformation (in fact about 80% of the systolic work is done during that phase), and first part of ejection, ejection and systolic deformation (chamber shortening, length and volume reduction etc), continues well into myocyte relaxation due to the inertia of the blood as discussed below.

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

However, as segment interaction is part of segmental load, it is in fact the load dependency (as well as the motion independency) of strain rate imaging is able to image regional inequalities in tension, which will result in inequalities in shortening. Here, however, timing is also of importance.

This section:


References for all sections

Contraction is neither exclusively tension nor shortening

Any muscle, including heart muscle, can contract isometrically; meaning that it contracts by developing force without shortening, or contract isotonically; meaning that it shortens without increasing tension. Thus any discussion that equals contraction with one or the other is off the track, at least halfway. On the molecular basis, this is evident.

Binding of myosin heads to actin, and subsequent rotation by release of energy, results in the actin and myosin filament sliding along each other. In the unloaded myocyte, this translates into a shortening of the sarcomeres, and thus of the whole cell.

Image of beating isolated myocyte. Image courtesy of Ph.D. Tomas Stølen, cardiac exercise research group (CERG), Dept. of Circulation and Medical Imaging, Norwegian University of Science and technology.

However, if the ends of the myocyte are fixated, the sliding of the actin and myosin filaments do not result in sarcomere shortening, but in the stretching of elastic elements withinin the sarcomere (titin). This generates tension in the sarcomere instead of shortening. Thus the contractile force can be used for shortening, tension development, or both:

This is discussed more below.

Imaging measures shortening, not contraction, nor contractility.

It is evident that any kind of cardiac imaging is based on visualisation of either

The first temporal derivatives of these parameters are

The spatial derivative of flow is

Pressure increase of 100 MMHg in 100 ml blood (LVEDV) = 13.3 J. Ejection of 50 ml blood (at an EF of 50%) at a velocity of 1 m/s at constant pressure, is about 0.025J. Thus, in terms of work, most of it is generation of pressure, and thus isometric rather than isotonic. 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. Load independent imaging modalities doesn't exist. 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.

Thus, deformation analysis, whether it is factional shortening, EF, longitudinal shortening, or deformation, all measure myocardial deformation in one way or other, and thus only a fraction of the work done by the heart.

Contraction equals shortening equals tension equals contractility only in the isolated myocyte

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

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

Excitation-tension diagram. After Cordeiro (234). The Action potential triggers the influx of calcium, which triggers further release of Ca2+from sarcoplasmatic reticulum. Calcium binds to troponin, and allows activated (by ATP) myosin heads to bind to troponin sites on actin (cross bridge forming) and release energy, causing the filaments to slide along each other, as long as there is a high calcium concentration in the cytoplasm.  As the cell membrane repolarised, this triggers the removal of calcium from the cytoplasm, mainly by the SERCA pumping it into the sarcoplasmatic reticulum again.  Thus, the forming of new cross bridges is inhibited, and relaxation starts. The pumping of calcium is energy dependent, and is the energy requiring part of the relaxation cycle. In energy depletion (f.i. ischemia), there will be less shortening in systole, but also slower relaxation.
Image of beating isolated myocyte. The myocyte is treated with an agent that fluoresces in the presence of free calcium in the cytosol. We see that the cell lightens and shortens simultaneously; stimulation causes an increase in free calcium (released mainly from the sarcoplasmatic reticulum), causing the cell to become lighter. The free calcium is the trigger for the binding of ATP, and the formation of activated ("cocked") cross bridges between actin and myosin, and the subsequent release, which leads to tthe buildup of tension in the cell. In the unloaded isolated myocyte, (as in previous studies in isolated papillary muscle), this will correspond almost directly with the shortening, as virtually no energy is used to overcome load. However, a small part of the energy needs to be stored for diastolic lengthening, even in isolated myocytes, as discussed in the section on dioastolic function. Image courtesy of Ph.D. Tomas Stølen, cardiac exercise research group (CERG), Dept. of Circulation and Medical Imaging, Norwegian University of Science and technology.

(The opposite process is the removal of calcium from the cytoplasm, and the uncoupling of the cross bridges, releasing tension. The removal of calcium is energy demanding, thus relaxation as well as contraction is energy dependent. However, there is no mechanism in the molecular contractile apparatus that leads to elongation of the cell. Thus, the elongation of the cell is dependent on energy stored in the cell's elastic apparatus from systole, which is released as contractile tension decreases. With energy depletion, the tension releases more slowly. 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 cell itself.)

Basically, an isolated myocyte is under no load (at least externally). In that case, the force developed leads to shortening. In this case, contraction equals force. And the relaxation corresponds to elongation. In any loaded state, however, there is a combination of isometric and isotonic work, so part of the force do not lead to shortening as discussed later.

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

All shortening in the ventricle is not active contraction

However, the opposite is also true.

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

  1. In the normal heart, there is active contraction (building up of force) only during pre ejection and first part of ejection.
    1. During isovolumic contraction, there is pressure buildup without volume changes, and hence, no deformation.
    2. Ejection results in volume decrease, and thus there is deformation (ventricle shortening and wall thickening). During first part of ejection, this deformation is active contraction
    3. Peak tension is reached at the time of peak ventricular pressure.
  2. After peak pressure, there is still tension, although decreasing, during the last part of ejection the ejection is partly driven by inertia. 
    1. As there is still volume decrease, there will still be volume decrease, and hence, wall thickening and shortening. This continuing decrease, however, is passive, and the muscle is in fact relaxing at the same time.
Thus, deformation is not even contraction in the cellular sense. The consequences for the physiology of diastole is discussed in more detail under diastolic function

To understand the relation of deformation imaging to contractility, it is necessary to understand the basic physiology of contractility.

Relation to load and contractility

What is contractility?

Looking at various definitions, all taken from medical dictionaries:

”a capacity for shortening in response to suitable stimulus.”
”capacity for becoming shorter in response to a suitable stimulus.”
        - Total confusion of shortening and contraction
”the inotropic state of the myocardium”
        - As inotropy is defined as change in contractility, this dfinition is absolutely circular: "contractility is contractility", which is correct, but useless
”the ability of muscle tissue to contract when its thick (myosin) and thin (actin) filaments slide past each other.”
”The ability or property of a substance, especially of muscle, of shortening, or developing increased tension.”
        - The last two are better, but has no quantitative connotations, it is simply the ability to.... (ability is non qyantitative, capacity is quantitative) , and no consideration of load
"a measure of cardiac pump performance, the degree to which muscle fibers can shorten when activated by a stimulus independent of preload and afterload"
        - Close, but no cigar, load independence, but still confusion of shortening and contraction

It could be argued that contractility don't need a definition, being hard to describe, but instantly recognizable when spotted, which is  the elephant test: I can't define an elephant, but I know it when I see it, or the equivalent duck test: When I see a bird that walks like a duck and swims like a duck and quacks like a duck, I call that bird a duck (James Whitcomb Reilly). However, this is insufficient:

This is not a duck, it's a penguin!

Contractility is defined as:

”The inherent capacity of the myocardium to contract independently of changes in the preload or afterload”(397)

Thus, the contractility is load independent, and reflects the inotropic state of the myocardium. The interaction between load and inotropy (i.e. contractility) is complex, but elucidated in fundamental experiments.

To understand the fundamental concepts of contraction, it is useful first to consider contractile force. The purest version of this is the isometric experiments, which has often been performed on isolated papillary muscle. With a muscle preparation, in a tensiometer, the development of force can be studied in its purest form. There are three measures that are of interest:
An isometric twitch can be described in a tension - time diagram as shown below:

Isometric twitch i.e. contraction without shortening, showing the tension. Peak tension, rate of force development and time to peak tension are all measures of contractile function.
Isometric twitches, showing the effect of inotropy (in this case noradrenaline), showing an increase in both peak tension, RFD and a shortening of time to peak tension.

Inotropy (increased contractility) increases both peak tension, peak RFD and shortens time to peak tension in isotonic twitches (208).

However, the contractile force also varies with the length of the muscle before contraction, stretch increases the developed force, both by passive elasticity and active contractile force:

Stretching the muscle before stimulation, increases tension. The increase in passive tension will be present at rest, before twitch, and is equal in baseline and inotropic state. During twitch, there is an increase in total tension with increasing pre twitch length. The increase in contractile tension is then the diference between the passive and the total curve. This effect is additional to the effect of inotropy.
Isometric twitces with increasing pre-twitch length. In can be seen that as opposed to inotropy, time to peak tension do not increase, even though peak tension does, and, as a consequence of this the rate of force development (as the rise to higher peak during the same time gives higher rate).
This is the Frank - Starling effect, increased contractile force with increased length of the muscle. It was observed long before this, that the stroke volume increased in response to acute increases in end diastolic pressure, and hence end diastolic volume (399).

Frank Starling's law of the heart:

Dilatation is caused when increased venous return or decreased ejection increases end-diastolic volume. This form of dilatation, within physiological limits, increases the heart’s ability to do work.
The stroke volume of the heart increases in response to an increase in the the end diastolic volume, when all other factors remain constant.

It has been theorized from consideration of sarcomere length, where there exist an optimal sarcomere length, with optimal overlap between actin and myosin, ensuring that all myosin heads can connect with troponin sites on the actin (398). In addition, there seems to be an interaction with calcium, making the myofilaments more calcium sensitive.

This means that there is a preload sensitive range, and a preload insensitive range above a certain length (404).

The fact that tension develops without shortening, shows that the cell has to have both contractile and elastic elements in series for this to take place. In order to develop tension, the contractile element has to shorten, as given by the molecular basis for contraction, and thus another part of the cell has to stretch. This role seems to be taken by the protein anchoring myosin to the Z-plates; titin (274, 275). Thus as the contractile element shortens, the elastic element of the sarcomere stretches as a spring. But this also means that the force that is generated is stored as elastic force. It also means that passive pre stretch may lead to some storage of elastic energy even before start of contraction, which will add to the contractile force being generated, but as this is intrinsic, it does not affect the contractility concept as defined.

However, the effect of decreasing tension may be somewhat uncertain, by the finding of increasing stiffness with increasing length, so the descending part of the Frank-Starling curve is unproven for the heart, at least without myocardial failure.

Hypothetical length tension diagram, based on the sarcomere hypothesis, that by increased fibre length initially will increase the overlap between the myosin head regions and the troponin regions on actin, optimising the number of cross bridges that can be formed, and thus the peak tension obtainable. In this model there is an optimal length, then the available number of cross bridges, and thus the peak tension decline again. This seems to be in accordance with (208), as far as active tension is concerned.
The Frank- Starlings law. Acute increases in end diastolic filling, will increase the stroke volume along the curve shown. This effect was observed with both increased venous pressure, but also with decreased stroke volume in previous beat, resulting in an increased EDV. Within physiological limits there is an increase, but with increasing dilatation, there will be less response. However, at least in normal hearts, there is little evidence for a descending limb of the curves.


The preload is defined as the load present before contraction starts (397). This is illustrated below left.

How is this in the complete ventricle?

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

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

The preload is determined both by:

Illustration of the preload. If a weight is attatched to the unloaded muscle, this muscle will be stretched, increasing the peak force the muscle can develope. But the preload is also part of the force the tension has to overcome in the contraction.
In an intact ventricle, the preload is also a function of size. In addition to the size being a measure of the pre stretch of the muscle, the intraventricular pressure acts on a larger surface, and thus the force that has to be generated must be proportional to the 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  × pi × r2).
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.


Afterload is the systolic load on the LV after it has started to contract (397). Afterload is force added to the preload as resistance to the muscle shortening. Total load is preload + afterload. This is the force the muscle must overcome ( e. the tension the muscle must develop) in order to shorten, also termed wall stress. This can be expressed as wall stress, the force acting on the wall. As shown above, middle, this is proportional to both the intracavitary pressure, and radius. Wall stress, however is the tension per cross sectional thickness of the wall, i.e. if the same load is applied to different wall thicknesses, the thickest wall has lowest wall stress per mm thickness as illustrated by the illustration top left.

This is summed up in Laplaces law: Wall stress () is proportional to pressure (P) x radius (r), and inversely proportional to the wall thickness (h):

In an afterloaded contraction, the muscle must first build up force corresponding to the total load, before it can start shortening. When the force equals the load, further contraction is translated into shortening without tension increase (isotonic contraction). Thus, neither peak force nor time to peak force are relevant measures of contractility.

The difference between pre- and afterload is illustrated here. After preload is added, a support is placed, preventing further stretch of the muscle when another weight is added. This second weight is the afterload. When the muscle contracts, it has to develop a tension that is equal to the total load, before it can shorten. If the peak force is higher than the total load, the muscle will then shorten without generating more tension, in an isotonic contraction.
Isotonic isometric twitches tension diagrams above, length diagrams below, after (208). From the diagrams, it is evident that shortening only starts after tension have reached load, and then, the tension is constant while the muscle shortens. Thus the first part of an unloaded contraction is also shortening, while the first part of a loaded contraction is isometric, becoming isotonic after tension equals load. Peak rate of force generation (RFD), occurs during the isometric phase (except in the unloaded phase, where there is no tension development). Peak rate on the other hand occurs during the first part of the shortening, after tension = load, and is thus later than peak RFD. The figure also shows that shortening decreases as load increases, as more of the total work is taken up in tension development. This affects both peak maximal shortening and peak rate of shortening.

  1. The load is related to the intraventricular pressure. This is the pressure the muscle has to overcome in order to shorten. The higher the volume, the more tension the muscle has to develop in order to shorten.
    1. Afterload may be taken as the systolic pressure.
  2. The load is also related to the chamber volume. The bigger the volume, the larger the surface area the force has to act on, for any given pressure. Thus, the greater the area, the greater the force that must be developed to overcome any given pressure any given pressure. (In fact this follows from the definition, as pressure is force per area unit).
  3. Finally, the force is related to the wall thickness. Wall stress, is the tension per cross sectional area unit. Thus is varies inversely with the thickness of the muscle.

Relation between tension and shortening

Applied to the model above with preload and afterload, the initial contraction will generate increased tension, without shortening untill the tension equals the total load. However, both total shortening and rate of shortening decreases with increased load (208):

This means that both increased load and reduced ability to develop tension(reduced contractility) will affect shortening.

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

Thus, imaging alone cannot measure contractility directly, without some knowledge of load.
As shortening of muscle is analogous to shortening of the ventricle, it is interesting that there is close similarity between the length curves of isolated muscle and longitudinal strain curves of the intact ventricle:

Shortening curves related to afterload, modified from the figure above.  The shortening in percent, is equivalent to the longitudinal strain of the muscle.
Strain curves from a normal subject. The strain curve is fairly similar to the shortening curves to the left.

The relation of strain and strain rate to load and inotropy are analogous to shortening and shortening velocity in muscle experiments (208):

Shortening velocity and total shortening,  Relation to preload and total load. Both shortening and velocity can be seen to decrease with increasing afterload (total load), but increase with preload.
Shortening velocity and total shortening,  Relation to total preload and inotropy. Both can be seen to increase with inotropy,  but decrease with load.

Thus, both shortening (strain) and peak rate of shortening (peak strain rate) is load dependent, and not independent measures of contractility, and looking at imaging, it is difficult to discern between reduced contractility and reduced load as shown below.

This means, of course, that both strain and strain rate are load dependent, although different parameters may relate differently to load.

The relations between shortening (strain), pre- and afterload and contractility can thus be summed up as in the figure below:

Myocardial shortening vs pre- and afterload and contractility. Force development increases with preload, and is load dependent as shown in both panels. Shortening is the resultant of force vs. afterload, the higher the afterload, the less the shortening, for a given contractility. Contractility is the load independent part of force development. The higher the contractility, the more the shortening for a given afterload. To explain the full picture, pressure-volume loops are useful.

As explained in the section on basal myocardial strain, taking the strain and strain rate of a whole wall, is equivalent to the basal velocities and displacement of the same wall, as the apex i almost stationary.
Thus seeking analogous shortening measures, there are several candidates for assessment of contractile function:
these two are near equivalent,
these two are also near equivalent.

Septal strain and strain rate (right) from (nearly) the whole septum,  and basal septal velocity and displacement (left). As the apex is (nearly) stationary, the basal velocity and displacement is a motion inscribing the whole of the shortening of the wall, the deformation curves from of the whole wall is very near the inverted motion curves from the base as described elsewhere. The strain rate and strain curves were obtained with an ROI length of 40 mm, and a strain length of 20 mm, both the highest possible with this software, and thus should cover a total length of 6 cm as described here. The negative deformation curves is from the original Lagrangian definition where shortening is baseline length + resulting length, becoming negative when there is shortening.  Motion measures are absolute, deformation measures are relative. The curves shown are from one wall only, for a global LV measure, the mean of at least two walls has to be used.

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 shown conclusively that both LV systolic annular velocity and displacement decrease, concurrent with mitral flow indices of filling pressure and LVEDV (160). (This study also showed load dependency of diastolic velocities). Already the first experimental works did show load dependency of strain (8, 163). This has been repeated in newer experiments (164, 216).

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.

Peak velocity and strain rate are early systolic measures, and thus might be more closely related to contractility, during active contraction, while displacement and strain are end systolic measures related to the total stroke volume. This was confirmed by an experimental study by Weidemann et al (78, 79), with pacing, beta blocker and dobutamine, showed strain rate to be most closely related to dP/dt, i.e. contractility, while strain (and thus by inference displacement) is more closely related to stroke volume and EF. It did not, however do pressure/volume loops. The finding, however, has been confirmed in arecent experimental studies in mice (254) and healthy normal human subjects (223). The study by Greenberg et al (80), did do pressure volume loops, and seemed to show that s strain rate was better related to end systolic pressure volume relation during different inotropic states (esmolol, baseline and dobutamine) than systolic velocities, but did not compare with end systolic measures.


The general definition of work is the force × the distance this force acts over. In this experimental setup: Work is total load (= force = tension) × shortening (W = F × s), as the isotonic contraction occurs at a constant load,  where tension = load.  In an isometric - istotonic twitch, this is only the dynamic work done in shortening. The static work done during isometric contraction is not counted in, as this builds up potential energy, which is then released during isotonic relaxation.

Thus, in work, load and shortening are inversely related, but work is still load dependent bu the following argument: If either force or shortening = 0, work = 0, for the dynamic work. If both are > 0, the work > 0 so the load dependency shows an inverted U - shape, that has been experimentally verified (208) as shown below.


The general definition of power is Work per time unit: P = W / t = F × s / t + F × v, i.e. force times velocity. As power is simply work per time, it is bound to follow the same inverted U shape as work, as experimentally verified (208) and shown below.

Effect of load on work and power. With increasing total load the muscle increases the work and power, despite decreased shortening, but only up to a peak. After that, increased load will decrease work and power by decreasing shortening. Increased preload increases shortening at all afterloads, and will increase both work and power.
Effect of inotropy on work and power. Inotropy will increase work at any given total load, by increasing shortening. It will also increase power, by increasing velocity of shortening.


Looking at strain and strain rate, these are measures in the intact heart. Thus, transferability from isolated muscle experiments is somewhat limited.

Diagram showing the similarity between the length curves in isotonic twitches and strain curve, demonstrating their equivalence. Thus, shortening being load dependent, strain has to be too. The rates of peak shortening (strain rate) are more closely related to contractility, although still load dependent.

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.Therefore, it is necessary to look at the heart cycle, and analogous measures in the intact heart, as well as looking at the phases of the heart cycle, which make contraction - relaxation in the intact heart differ from the isolated muscle.

In the complete ventricle, there is also a separation between the filling pressure (being the mean atrial pressure, which partly determines preload - together with end diastolic volume through the Laplace mechanism), and the ejection pressure, being the systolic aortic pressure, which is the main determinant of afterload (together with volume - again by the Laplace equation a,d wall thickness). So in the complete ventricle, there is pressure volume relations, which are the equivalents of tension length relations described above. Also, the complete heart cycle is more than the contraction relaxation cycle as described above.

The close relation between strain and stroke volume, as well as the relations of stroke volume to pre- and afterload, means that strain and strain rate re load dependent in the intact ventricle as well.

The picture shows a detailed LV volume curve from a healthy person by MUGA scintigraphy, the left a normal longitudinal strain curve. The similarity shows:

Load dependency of strain and strain rate

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

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

The heart cycle and pressure - volume relation

The length - tension relation in isolated muscle is equivalent to the pressure - volume relation in the intact heart. To go into the concept of cardiac work and contractility, the whole heart cycle has to be considered.

Simplified pressure volume diagram (Wigger's diagram) of a whole heart cycle. The diagram shows the atrial, ventricular and aortic pressure curves, the ventricular volume curve and the ECG on a time axis. Mitral valve opening (MVO) and closing (MVC) occurs about the crossover between atrial and ventricular curves, aortic closure (AVC) and opening (AVO) occurs near the ventricular and aortic valve closure, while aortic valve closure occurs at the aortic dicrotic notch pressure curves having crossed much earlier during ejection. Isovolumic contraction (IVC) is between MVC and AVO, there being no volume change, this is a true isometric contraction.  Isovolumic relaxation is between AVC and MVO, this is the isometric phase of relaxation. The three peaks of the atrial pressure curve, are a (atrial contraction), c (closure wave) and v (ventricular contraction).

Below is shown the analogous isotonic - isometric twitches. As seen there is initial preload increase during atrial contraction, increasing passive tension as well as the subsequent tension and ate of force development. Then there is isometric contraction, during IVC. In the isolated muscle, there is isotonic contraction (shortening). In the working ventricle, there is less increase in tension (
Systolic load can be considered more or less equal to central pressure during ejection for acute changes), but pressure continues to increase during first part of ejection due to aortic elastance, and then drop during last part of the ejection due to aortic run off. Thus, in the intact heart, the contraction is far from isotonic. The corresponding  shortening curve as it would have been in an isolated muscle is shown in dark blue, pre stretch during atrial systole, peak shortening early in the isotonic contraction with lengthening still during isotonic contraction, returning to baseline length at the start of isometric relaxation. The true curve as it is in a working ventricle is, of course, parallel to the ventricular volume curve and shows continuous shortening during the whole ejection (isotonic analogy) and only partial return to baseline length even after completed relaxation.

The Wigger's diagram is fairly common in this form, but is incomplete, as rapid filling is shown as a passive event, and as valve openings and closures are shown at pressure crossover.

Pressure volume diagram of a heart where pressure is plotted against volume, a pressure-Volume loop (PV-loop). The top version shows the cardiac phases, with the same simplifications as the Wigger's diagram to the left; rapid filling is shown as a passive event, and as valve openings and closures are shown at pressure crossover. Time runs around the loop in a counterclockwise direction. The width of the loop is equal to the stroke volume. The top of the diagram shows the pressure curve during ejection.

The red, dotted line touching the loop is the end systolic pressure - volume relation. The slope of the tangent is  P / V, which is the common definition of elastance. In filling, the elastance is usually taken to mean how much (counter-) pressure a given volume generates, but end systolic LV elastance is a function of emptying. Thus this must be taken to mean how much volume reduction a given pressure has generated. The blue dotted line, the left ventricular end diastolic pressure relation, is the passive tension that the diastolic filling generates, i.e. at atrial filling.

The bottom diagram shows the LV work, which is the area within the PV-loop (cyan).

During isovolumic
contraction pressure rises, with no change of volume. During ejection, volume is ejected, reducing ventricular volume from end diastolic volume to end systolic volume. During isovolumic relaxation, the relaxation reduces pressure from LVESP to LVDP, and during diastolic filling the volume increases from LVESP to LVEDP.   The area within the loop is P × SV.
The equivalent area with mean pressures is shown as the dotted rectangle, to give an intuitive visualisation of the P × V. The Ees
is shown to increase with positive inotropy (red dotted line) and decrease with negative inotropy or failure (blue dotted line). The potential energy delivered to the remaining (end systolic) volume, which is not converted into ejection work, is the yellow shaded area.

The most striking difference is the fact that while the isolated muscle starts elongation at the start of relaxation, in the intact heart muscle continues to shorten while relaxation starts and tension declines as explained above.  This is also shown in the Wigger's diagram above.

Basically, pressure-volume loops are useful concepts for visualising and explaining the relations between stroke volume, pressure and contractility, and to address physiology in animal experiments:

The pressure-volume loop on the right is derived from the pressure and volume curves on the left. It is basically a tool to assess and explain the relations between contractility, load and output.

But a spin off of this is the myocardial work, which is the area of the PV-loop.

Converting the SBP to mean SBP, and DBP to mean LVDBP, converts the PV loop to a rectangle (blue dotted line), shoing that the area is BP × SV.

Myocardial work

As we have seen, work is load × shortening. In the intact heart, this is equal to the area of the pressure volume loop, as shown above.

Pressure-Volume relation, normalised to show mean ejection and diastolic pressures. The generic expression for work is W=P*V, and in this case this is easy to see that this is SV * (mean systolic pressure - mean LV diastolic pressure).

Systolic load is more or less equal to central pressure during ejection. This is a simplified model, excluding the volume and wall thickness part of the Laplace equation, and not taking into account the LV diastolic pressure, which may be important if elevated. But it is valid for acute load changes, being proportional to pressure changes.  But the ejection phase occurs with a non-constant pressure as seen above, so the contraction during ejection is not isotonic.

Ejection work (left ventricular stroke work - dynamic work)

Left ventricular stroke work is the dynamic work done in ejecting the stroke volume at a given pressure (mean BP during ejection). This is equal to the potential energy that is converted to kinetic energy. Hence, LVSW = mean SBP × SV. This is the dynamic work during ejection. For an average SV of 50 ml, at 100 mmHg, this will be ca. 6.5J. (100 mmHg = 13 KPa, 13000 N/m2 × 0,5 dl = 6.5Nm). The kinetic energy of this stroke volume is only 1/2mv2,  if ejected at an average velocity of 0.5 m/s, this will be about 0.125 J, i.e. about 2% of the total energy, with the rest remaining as potential energy in the aorta and the blood column, and is used in interaction with the vascular bed, as pressure drops along the vasculature.

Thus, the LVSW is mainly used for pressure increase, not much for moving the blood out into the aorta, first building the pressure, and then maintaining this pressure through aortic elasticity. The LVSW is equal to the area within the PV-loop. This has been confirmed experimentally (358) and clinically (359) by demonstrating a close relationship between PV-loop area and myocardial oxygen consumption.

Basically, LVSW increases if SV increases, thus, it is preload dependent. It also increases if SBP increases, but as SV is inversely related to afterload, the relation is not as evident. Overcoming increased afterload demands more energy, but this might be compensated with lower demand by reduced SV, but as more energy is demended by the ressure work than the ejection work, this is less probable.

Increased preload will increase SV, and thus GMW. But as seen to the right, of course increased SV will lead to increased SBP, which reduces the SV somewhat (increased afterload), blunting the preload response, while increasing GMSW.

Increased afterload (SBP) decreases SV, while increasing GMW. As we see to the right, reduced SV will increase EDV (preload), increasing SV somewhat, blunting the afterload response.

Again, there is an inverse relation between SV and SBP, but as in the isolated muscle, if either SV or SBP = 0,  LVSW has to be zero, and in any in-between states, both SV and SBP > 0, means that LVSW > 0. Thus, the theoretical relation has to be U-shaped. However, the the theoretical situations of either load being higher than maximal power, resulting in zero SV, or SBP being zero, are both outside the physiological, and even pathophysiological range. Experiments, however, have shown LVSW to be both pre- and afterload dependent within the physiological (401) range, but SW increases with afterload contrary to SV (and strain):

Curves from isolated heart experiments (401), showing that LV stroke work is both pre- and afterload dependent, within physiological pressure ranges, but while SV decreases with afterload, SW actually increases with afterload.

In practice, this means that myocardial work can be estimated by SV * SBP, which does not take LVDBP into account, and simplifies the ejection pressure, but the systematic error may be assumed to be constant in acute changes, and thus changes in LVMW may be assumed to be more valid.

But is it useful? While contractility is load independent, contraction measures will decline with increasing load, while MW will increase due to the increased demand. Though it increases with contractility, it is not load independent. While SV increases with preload and decreases with afterload, GMW increases with preload and INCREASES with afterload. Thus, decreased function will give a lower MW, unless there is increased BP, where  it might pull the other way.
It is thus not a measure of contractility, and not load independent.

It iw what the name says, myocardial work, which is a measure of myocardial expenditure. And this means that increased demend will be met with increased myocardial performance, as long as there is myocardial reserve. But as it is a complete different measure, the clincal meaning of this needs to be established.

A new measure of global myocardial work, based on estimated Global strain - pressure Loops, has aroused interest lately. I suspect that it is the same as for regional vs global strain, while regional strain is noise sensitive, research turned to global strain, which is more robust, but which, however, probably do not add anything to MAPSE (417).

Regional pressure strain loops are similar to global PV-loops, and shows regional oxygen consumption in animal experiments (476).

As described here,  regional myocardial work do not add information to regional strain, and will be just as noise sensitive, so thus interest is again turning into global myocardial work.

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 correspond 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.  It is evident that the longitudinal shortening describes most of the volume changes. Again the shortening might seem to be contraction, and the (early) elongation relaxation.

As those curves are very similar, so would pressure volume vs pressure strain be similar:

Left: Conventional pressure volume relation, the volume curve taken from a MUGA scan. The area in the PV loop is the myocardial work, and the loop is defined by the DBP-SBP-difference giving the height of the loop, while the SV is the width of the loop at the time of AVC. Right pressure-strain relation. Since the strain and volume curves are similar, so must pressure-strain and PV-loops be. The height of the loop would be the same, derived from the DBP-SBP-differenc, but the width of the loop is defined by the end systolic strain at the AVC. As myocardial work would be expected to be lower, the loop has to be narrower if they are drawn to cale, representing only about 75% of global myocardial work. 

The pressure-strain curve is equivalent to the work derived from the tension length relation. But as the whole ventricle is a volume, the two measures are not the same, longitudinal strain only accounts for between 60 and 80% of stroke volume, and the area of the pressure strain loop would be correspondingly lower, except that speckle tracking strain will over estimate longitudinal strain.

The relation, however, would reflect acute changes just as well, but a non-nvasive method is in addition based on an estimated blood pressure curve, derived from a normalised curve, adjusted in time by valve closure and opening points, and in height by cuff pressure, as described under regional work.
  • It does not take LV diastolic pressure into account, but must assume this to be normal, and
  • It does not take pressure augmentation by reflected waves into account.
In this case, as opposed to regional work, this may introduce a systematic error, as both relaxation and compliance may increase diastolic pressures, and reduce the PV-loop area. This makes the method even more similar to the SV×SBP, and it remains to be seen if the method actually contributes anything new.

But is it useful clinically?

In an observational study (477), GMW correlated with both SBP and GLS, but a correlation between a compound measure and its components is hardly surprising. It also correlated with SV, EF, MAPSE, and diastolic measures, also unsurprising. Myocardial work increases if cardiac output increases. But this seems to be in a normotensive population, although the correlation with SBP was even stronger in multivatiate analysis..

In HFrEF, lower GMW predicted a poor prognosis, slightly better than GLS alone (478). In this study, however, despite (lower) BP being significant in univariate analysis, it was taken out of the multivariate analysis. So then........

But more hilarious: In a study of hypertension and diabetes (479), GMW increased from normal to HT pts. (hardly surprising), and even more in pts. with HTR + diabetes, despite lower numerical GLS. So now, it seems that a high GMW is suddenly bad for you.

This means that it is a measure of myocardial work = energy expenditure. It might be useful for acute changes, but again it seems to point both ways.

Myocardial power

Myocardial power = Work / time. This means that it can be calculated as LVSW / ejection time, which is mean SBP × SV / ejection time, or approximated by SBP × SV / ejection time. As with myocardial work this has to be load dependent as illustrated above.

Another approximation will be MAP × SV / RR-interval, as the SV is the same in aorta as in the LVOT, but smeared out over the full heart cycle, where the work done in systole to dilate the aorta is recovered in diastole for the diastolic aorta flow. And this again, can be translated to MAP × CO, which is the same value, although this has been named cardiac power output.

The same limitations, however applies to myocardial power.

Pressure work (potential energy - static (isovolumic) work)

However, as the ventricle contracts, the pressure increases in the whole end diastolic volume, not in the stroke volume only. This means that the total work done during contraction, also imparts potential energy to the end systolic volume. During isovolumic relaxation, this energy is released, but to which extent this is recovered, decides whether this is part of the net total stroke work.

Left ventricular end systolic elastance, relation to load and inotropy

LV end systolic elastance is defined as Ees = P / V, which is the slope of the line through the end systolic pressure-volume point in the PV loop as shown above. The relation of the PV loop to load and contractility, is illustrated below:

Effect of preload. Increased preload (increased LVEDV), will, through the Frank-Starling balance increase stroke volume. This increased stroke volume will be ejected at the same pressure, thus returning to the same point on the ESPVR line. Myocardial work, bing BP×SV, will increase.
Effect of afterload. Increased afterload (increased SBP), will reduce the stroke volume, This can be easily seen here, as the end systolic point moves up the ESPVR line, shortening the width of the loop, i.e reduced SV. The effect on work is more uncertain, as SV decreases while BP increases.
Effect of inotropy. Inotropy shifts the ESPVR line to the left, thus increasing the force and thus LV emptying, increasing stroke volume through reduced LVESV.

In reality, an increased SV will cause increase in SBP, causing an increased afterload on the same beat, thus reducing the effect on SV somewhat, through interaction between pre- and afterload.
In reality, an acute increase in afterload, will reduce emptying (increased LVEDV), so on the next beat, the preload is increased, partly offsetting the effect of afterload on SV.
In reality, decreased LVESV, without increased venous return, will in the next beat result in reduced LVEDV, thus offsetting the effect of inotropy somewhat by reduced preload.

Thus, as seen, above the ventricular elastance is a measure of contractility, as it seems to be load independent (400), and it has achieved a "gold standard" status for measurement of contractility. In reality, this index is not easily obtainable in the clinic, even in continuous invasive monitoring, as volume measurements are not available in routine monitoring. But in animal experiments, using conductance catheters, where multiple pre- and afterload manipulations can be done, and where the ESPVR can be obtained by linear regression, it serves as a reference method, to test other contractility indices.

However, the LV elastance may not be a perfect gold standard anyway.
- Firstly, using end ejection for end systole, means that measurements are done at a point in time where the myocardium is in relaxation (but not relaxed) phase.
- Secondly, as we see below, the true end systolic volume is not easily defined due to the protodiastolic volume decrease as discussed below.

Peak systolic pressure volume relation might be closer to the real thing, but is not easily discernible.

Several studies have found that the ESPVR is not a straight line, curvilinear depending on contractility (411, 412), and afterload (413, 414).

Finally, however, of course these volume considerations are only related to acute changes. In inter individual differences in healthy individuals, as well as in LV dilation, the EDV is not a measure of preload, and the PV-loops can only be interpreted in relation to the individual. PCWP, on the other hand, is a measure of preload, that is relatively standardised and thus a more universal measure of preload when applied across individuals, although it does not take the Laplace effect into consideration.

Thus, LV elastance seems to be an imperfect measure of contractility as well, although it is fairly well able to separate different contractile states.

Preload recruitable stroke work

Glower (414) introduced the concept of preload recruitable stroke work as an alternative measure of contractility. Basically, this is the slope of LVSW versus LVEDV in pressure-volume loops: LVSW / LVEDV
It is very similar to LVSW/EDV, but must be obtained by PV loop experiemnts as the slope do not cross LVEDV = 0. (And thus, of course, as for elastance, it only relates to intra individual changes in volume, not absolute LVEDV). Theoretically, this is interesting. As SW is curved (convex) with preload, EDV is curved the other way (concave), this giving a more straight line relationship for the composite value. Due to greater ease in obtaining EDV (by ventriculography) during a routine cardiac catheterisation, it was suggested to be easier to obtain than LV elastance (415). However, as LV ventriculography is now rarely part of a routine cath, as well as caval obstruction for varying preload, this is just as cumbersome in the routine clinic today.

Interaction with the body

Finally, of course, the body regulates both the cardiac performance and load in relation to the needs of the body:
  1. The contractile state as well as heart rate is a function of the total autonomic balance of the body
  2. The afterload is regulated both by the autonomic balance as well as the other blood pressure regulatory mechanisms affecting the peripheral resistance
  3. The preload is a function of both blood volume (which again is regulated both by the kidneys (and fluid regulatory hormones) and the tissue capillary filtration/resorbtion
  4. And the venous tone is the main regulator of venous return as well as balancing the fluid volume
  5. The early indices are HR dependent, with increased HTR, S' and SR increases without increase in LVSW
  6. The total systolic performance on the other hand may change less with HR as reduced cardiac power or increased afterload may be offset by longer ejection time.

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

Relation to heart rate

This means that heart rate is in itself a determinant for especially shortening rate, and more indirectly, shortening, and secondly to stroke work and cardiac output.

  • Firstly, there is an increase in myocardial tension with increasing heart rate, due to the Bowditch effect or force-frequency relationship. Basically, this will increase strain rate. With unchanged ejection time, it will also increase strain, and stroke volume.
  • In the intact heart, however, the effect will depend on the effect on venous return, and the method for reducing .
    • If there is no change in venous return, stroke volume will actually drop. This effect will reduce strain, but as ejection time falls as well, strain rate will not drop as much (lower volume during shorter time may in fact maintain ejection - and thus - strain rate). But with lower SV, EDV will also drop, and thus preload, reducing both strain and strain rate. The effect will then theoretically be greatest for strain. This was shown by Weidemann (78), with atrial pacing with increasing HR, but with no change in CO, (meaning SV dropped inversely), There was a decrease in EDV, a tdecrease in strain, but no change in SR.
    • If venous return increases, the preload will remain unchanged or increase, in the last case stroke volume will increase by the Frank-Starling effect, and both strain and strain rate will increase. But in this case, the increase is often achieved by chronotropic medicaments that also have inotropic effects. Weidemann (78) did show that with dobutamine, which in low dose has positive inotropic effect, increasing stroke volume and venous return, but in increasing doses avbove this has a more pure chronotropic effect, increasing HR and increasing CO, thus increrasing venous return, but without increasing SV further. With dobutamine, a steady, dose dependent effect on HR, very close to that with pacing, but also a steady increase in CO was achieved. In this case there was a similar decrease in EDV, but with a parallel decrease in ES, and thus maintained SV (but increasing EF). Strain did show an initial increase with low dose (inotropic), but a subsequent decrease with high dose (pure chronotropy, while strain rate showed a linear increase (maintained SV, shortened ejection time), due to both inotropy and Force-frequency relationship.

Afterload: ventriculo-arterial coupling

The afterload is largely related to systolic aortic pressure (with the modifications give by the law of Laplace). However, looking at changes in afterload, they are mainly related to changes in pressure. This is dependent on various factors in the abscence of significant LVOT or aortic valve obstruction:

  1. 1: Peripheral resistance. The peripheral resistance determines the run off through the whole of the heart cycle, i.e. both systole and diastole. The resistance is usually given by the simplified concept of the Ohm's formula:   P = Q x R, where P is the the mean arterial pressure, Q the cardiac output and R then defined by R = MAP / Q. However, this is the mean pressure during the heart cycle, while the afterload is related specifically to the pressure during ejection, which depends not only on the mean pressure, but the balance between systolic and diastolic pressure. Basically, the resistance is the arteriolar function.As diastole is longer than the systole during rest, the main effect is on the diastolic arterial pressure, especially as the aortic compliance may compensate for the peripheral resistance during systole.
  2. The elasticity (compliance) of the arterial (especially the aortic) wall. During ejection, the volume ejected into the aorta distends it. The distensibility of the aorta is called the compliance, and this is defined as: C = V / P, which means how much the volume will increase for a given increase in pressure. As can be seen, the compliance is the inverse value of the elastance, but in this case the aortic elastance, and in this case the elastance means the ability to generate recoil (force or pressure) from a given expansion (volume). This means that the systolic distension of the aorta will lead to diastolic recoil, in other words the aorta acts as a diastolic pump, maintaining flow during diastole. i.e. some of the ejection energy is taken up in the aortic wall (and delivered again to the blood during diastole, providing the energy driving the blood out into the arteries during diastole and maintaining central diastolic pressure, being higher that the diastolic ventricular pressure). The more distensible the aortic wall, the less the pressure in the aorta will rise, and the lower the CAP. The stiffer the aorta, the less it will be distended (the less the compliance) for a given pressure increase, or conversely the more the pressure has to be increased in order to inject a certain volume (stroke volume) into the aorta. Thus, increased arterial stiffness will increase the systolic pressure, and hence, the afterload.  Arterial stiffness increases with disease and age, and thus the systolic pressure will increase, increasing the afterload.

The total of the arterial effect can be described by the arterial elastance: Ea = P / V and ventriculo arterial coupling (405):

PV-loop illustrating arterial elastance. The arterial elastance is a measure of how much pressure the stroke volume generates in the arterial bed, and is simply EA = ESP/SV.
LV end systolic elastance is approximately EES = ESP/ESV, so EA / EES = (ESP/SV)/(ESP/ESV) = ESV/SV = (EDV - SV)/SV = EDV/SV - 1 = 1/EF - 1. Thus the concept of VA coupling simply eliminates the pressure, and ends up with a load dependent measure of LV performance as a result of this load!

Thus, the concept of VA coupling is simply a circular argument, that ends up with the fact that load dependent measures are load dependent.

Thus, we end up with the result that there are no non invasive ventricular performance measures that are load independent, although peak systolic measures are somewhat less than end systolic, and gives a closer relation to contractility. These occur early in systole, and may be less load dependent, as maximum afterload is reached later in systole. They all occur during the first part of systole, and thus are more closely related to contractility, and especially to contractility changes, as shown in studies (78, 79, 80, 223). But even so, early systolic measures during ejection are also load dependent. End systolic global measures , on the other hand, are stroke volume, ejection fraction, end systolic strain and mitral annular displacement. However, this can be achieved at a lower force, if done over longer  time, so they are farther from contractility (78, 79), being closer related to the stroke volume and EF, i.e. to the total left ventricular volume change, i e systolic performance and work.

Wit increasing arterial stiffness, the systolic pressure will increase through reduced aortic compliance, thus increasing afterload (406). This will be seen as increased peripheral systolic pressure. However, this do not necessarily equal the central blood pressure, which is the real afterload the ventricle works with.

With increasing arterial stiffness, theee is increased pulse wave propagation velocity (406). But, the forward traveling pulse waves are reflected back from the periphery. This forwards and backwards travel takes a fraction of the heart cycle.The pulse wave leads to an increase in pressure and arterial diameter. This will propagate as a wave along the arterial wall, faster the stiffer the wall is. (Not to be confused with flow velocity, which is far slower). As the stiffness of the arterial wall increases with age and disease (as well as with pressure itself), the pulse wave propagation will increase too. But as the pulse wave travels along the arterial bed, at various levels the waves will be reflected back from the periphery, and thus there are two waves traveling back and forth during each heart cycle.

Pulse wave propagation. The pulse wave travels as a wave of expansion along the arteries in each pulse beat (red), and is reflected from the periphery (blue). When the two peaks do not coincide, there is no augmentation of the peak pressure (top). If the two peaks coincide in diastole (middle), there is still no augmentation of the systolic pressure, as only the diastolic pressure is augmented. If the two waves coincide in systole (bottom), there is systolic summation, augmenting the peak systolic pressure, and thus increase the afterload. With low pulse wave propagation velocity, this augmentation will be seen in the periphery, with increasing pulse wave propagation velocity it will be seen more and more centrally. If the augmented pressure is central, peak central systolic pressure will be higher than the one measured peripherally, and the afterload higher. The augmentation pressure can be identified by the anactrotic notch on pulse tractings. The augmentation index is the augmentation pressure / pulse pressure.

Thus, the faster the pulse wave propagation the faster it returns toward the central aorta, and the earlier it will meet the next wave. Thus, with increasing pulse wave propagation velocity, the more it will augment the peak systolic central aortic pressure (253). This means that the central systolic pressure may be higher than the peripheral as measured by the manometer cuff or radial catheter. Thus, the arterial stiffness and resistance are factors contributing to the afterload, but the compexity of the issue, 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. Assumptioons about the true afterload can be made from measurement of pulse wave propagation velocity (carotid to femoral delay / length, or by differences in augmentation index (carotid vs femoral by measuring the anacrotic notch on pulse tracings).

 but will need invasive measurement or complex modeling.

Relation to the phases of the heart cycle

The main intervals of the heart cycle is defined by the valve closures and openings. That means start and end of flow, but with the right positioning of the sample volume /beam, it can also capture the valve clicks.

With the right positioning if the sample volume, all left sided valve closures and openings can be registered simultanepously. Valve closures can be seen as clicks, and valve openings can be seen by the start of flow.

Valve opening and closures then will define the main intervals of the heart cycle, IVC, LVET, DFP and IVR.

Pulsed wave Doppler with sample volume positioned between the aortic and mitral ostia. Both start and stop of the flows, as well as the valve closure clicks are seen, dividing the heart cycle into the four main phases, ejection, diastolic filling, and between them the isovolumic contraction and relaxation phases..

Doppler flow is the reference method for the timing of valve motions. However, there is much going on in the intervals, which is revealed by tissue Doppler. Much of the earlier work, unfortunately, was marred by unproven assumptions, which later have been shown to be erroneous. The relation between the main intervals in the tissue Doppler curve is shown below.

As seen, a lot of phases can be seen in the motion and deformation curves. To understand their relation to the phases of the heart cycle, it is necessary to go into the heart cycle in a little more detail. Already Wiggers (402) was clear that the phase pattern was more complex than the original six phases depicted above.

But, again, there are manu things happening during each of the main intervals, as will be seen

The pre ejection period

The pre ejection period (PEP) is defined as the period from the start of the first deflection of the QRS, to the start of ejection, as defined by the aortic valve opening, or the onset of flow in the LVOT (235). Onset of ECG happens before active contraction, and also before the MVC, meaning that the IVC is only the last part of PEP, as shown below.

Pre ejection and ejection visualised by Doppler flow in the LVOT with simultaneous ECG.

Even PEP is sub divided into periods.

Electro mechanical delay (EMD)

To start with, there is electrical conduction of the signal from the AV-node through the His' bundle and the anterior and posterior left hemi-bundles.

Early experimental and invasive studies seemed to show that there is initial endocardial activation almost simultaneously in mid septum and mid lateral wall, after 10 - 15 ms after onset of ECG (350, 351), but this will be partly concomitant with EMD at the cellular level.

Mapping of earliest endocardial electrical potential in normal subjects. Numbers show time after earliest ECG deflection in QRS, and the earliest endocardial activation can be seen in mid septum and laterally
- corresponding to the two parts of the left bundle, as indicated here.

Thus, electrical activation occurs earliest in mid septum and inferolateral base through the left anterior and posterior bundles, delay 5 - 15 ms.

Then, there is electromechanical delay at the cellular level, the action potential generating Calcium influx, again generating release of more calcium form the SR, resulting in onset of cell shortening as shown here. This process takes about 30 - 40 ms (234), and leads to onset of local shortening.
Active contraction could be expected to start in the mid septum and mid lateral wall after about 50 ms; i.e. before the end of ECG.

Simultaneously, there is propagation of the action potential over the whole ventricle, this is the propagation that is seen as the QRS potential, and the time it takes is the duration of the QRS (about 80 - 110 ms, although the last part may be activation of the right ventricle).

Proto systole

The next question is when the start of electrical activation starts in relation to the MVC. The initial active shortening is very visible both in longitudinal M-mode and tissue Doppler, as a small, short event of  apical motion, terminating abruptly:

A short duration event of apical displacement as seen by M-mode
 - and tissue Doppler

The question is, whether this occurs before or after MVC. I early TDI publications, it was simply assumed to be the isovolumic contraction, although this is a contradiction in terms, as there is no volume reduction during IVC. It seemed that everybody "knew" that the first spike was isovolumic contraction, as seen in a number of publications (330, 366, 367, 368, 369, 465).Some studies used peak R as a proxy for MVC (466), which is an unfounded assumption, and other have used used the LA/LV pressure crossover (467). Both would place the pre ejection spike after MVC, i.e. in IVC. While the latters is physiologically reasonable, it has been shown that pressure increase starts before mitral valve closure, showing that active contraction is present before MVC, and even, LA/LV pressure crossover occurs ca 40 ms before MVC (236, 403). This is equally intuitive, thinking about it, the initial contraction being the force for increased LV pressure that closes the mitral valve.

As LV pressure at this point is low, some shortening would be expected too. By M-mode of the Mitral ring, a small, initial displacement, or a short velocity spike on tissue Doppler.

Pre ejection spikes evident bt tissue Doppler, both septally and laterally.
By colour tissue Doppler they can be seen to be simultaneous
And they correspond to a very small pre ejection displacement of the annulus, which stops abruptly, presumably at MVC.

Newer experiments with high fidelity conductance catheters (173), shows a small volume decrease at end diastole, calculated to about 4.7% of the largest end diastolic volume (173). Thus, it isn't isovolumic, but before MVC.

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

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

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

This is zoomed in the recordings below, showing MVC at the end of the pre ejection motion:

The pre ejection spike thus occurs BEFORE MVC, as seen here (valve openings and closures from Doppler flow - different cycles).
MVC is concomitant with the stop of apical motion.

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

Logically, the MVC should be at the abrupt stop of the pre ejection displacement, i.e. where the velocity trace crosses the zero line after the spike:

Blown up image of the pre ejection period, displacement to the left, velocity to the right. The logical time for the MVC is when the apical displacement stops abruptly. This is equivalent with the velocity spike retuning to zero, as can be seen with the relation to ECG. As we see, there is a slight initial velocity, and then a break point in the velocity curve, concomitant with the onset of shortening as seen by the displacement curve, corrsponding to the second spike as seen below.

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

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

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

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

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

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

The spike is present in atrial fibrillation (173), and is thus not any kind of "recoil" after atrial systole, as has been suggested. The recoil is seen when there is P-wave without LV tension, as in AV-block.

What we see, is that after the a' wave, there may be some rebound oscillations visible in long PQ time or dropped beats, which normally would be dampened by the stiffening of the ventricular myocardium by the onset of contraction. This is evident even in spectral Doppler, as seen here in a patient with a very long PQ time, causing EA fusion, and showing positive velocities before the protosystolic velocity spike:

PW Doppler of mitral flow and tissue Doppler from a patient with a PQ time > 400 ms. This pushes the A wave forward to the preceding heartbeat, causing EA fusion as explained here, but increases the interval between atrial and ventricular systole. After the a' wave in tissure Doppler there is a clear positive spike, that can be seen before the normal protodiastolic spike, and may represent a rebound from atrial contraction. With HIS pacing on, the PQ-time is normalised, and both EA fusion and the rebound wave are abolished, the latter may be dampening with the onset of ventricular myocardial contraction (stiffening). Images courtesy of Prof. Dr. med. H. Kühl, Chefarzt, Klinik für Kardiologie und Internistische Intensivmedizin, Klinikum Harlaching, München.

The second spike is isovolumic, and present only in the septum, with a corresponding negatiove deflection in the lateral wall, thus representing a rocking motion, not a volume change.

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

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

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

This means that there is

In the initial situation, with open mitral valve, the left ventricle is close to unloaded, and active contraction should lead to shortening rather than pressure increase. This would mean that the PEP motion would give a very small volume decrease, before the mitral valve closes, but without any regurgitation, as the valve moves within the stationary blood volume. But is still means active ventricular contraction, and, at the stop of the blood, this will mean closure of the mitral valve as the cusps stay in the stationary blood stream.
This, again would give a small volume reduction in the pressure - volume loop, by exclusion of part of the blood volume, even without regurgitation. This has been shown experimentally (173), the volume reduction before MVC was 4.7%. This is illustrated below. This also means that the isovolumic contraction phase, defined as the period from MVC to aortic opening, starts later and is shorter than PEP (235), and also than the duration from onset of contraction to start ejection

The pre ejection velocity spike is thus due to active contraction, as has been verified experimentally in simultaneous pressure - tissue doppler recordings (173). That, rather elegant study, demonstrated again the early fiondings, pre ejection spike was before mitral valve closure. But taking the experiment a little further, they demonstrated that by stenting the mitral valve, the velocity of early onset of contraction continued smoothly into the ejection velocities, thus demonstrating that the stop of the apical motion (and thus onset of IVC) was actually due to mitral valve closure. Thus, the pre ejection spike is simply onset of contraction, resulting in shortening, which is interrupted by the MVC that then results in shortening being interrupted, and continuing contraction being isometric without shortening.

Schematic representation of the findings in (173), showing that as onset of contraction results in shortening, this is interrupted by MVC (onset of IVC), when mitral valve is stented (red curve), this results in a smooth non-interrupted transition to ejection velocities.

Thus it's the MVC that is actually terminationg the pre ejection longitudinal motion /volume reduction.

At the end of late filling (atrial systole), there is again equal pressures in atrium and ventricle, and no flow. The start of contraction will then lead to closure of the mitral valve, as they move in a stationary  blood column, they will be pushed toward the base and toward the middle. The motion of the leaflets is mainly lateral, i.e. towards the middle, and thus may be greater than the longitudinal displacement of the annulus.This motion of the nitral ring would tend to displace the mitral eaflets towars the middle, and thus be a part of the closing mechanism. The mitral leaflets move towards the middle, and thus the displacement of the ring towards the apex is far less than the motion of the leaflets towards the base. Volume reduction due to pre ejection shortening. This volume reduction is also evident from  displacement and strain traces.This volume reduction is not due to flow, but the fact that the mitral annulus excludes part of the blood volume by , sliding along a stationar column of blood that then is "atrialised", illustrated by the light red cyllinder in the image above.

Even if one study found a fair correspondence between isovolumic periods using colour tissue Doppler and Doppler flow (369). Others, using the same assumptions that the spikes represented the isovolumic periods did not find good correspondence between tissue Doppler and Doppler (370), mainly due to discrepancies in isovolumic periods. This is consistent with mesurements being right, but premises being wrong.

In conclusion:

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

The problem with a lot of publications is that as they do not separate proto systole from IVC, there is a lot written about deformation during IVC, that really relates to the pre MVC dynamics.

However, in addition, there is a vortex formation from the late inflow (A-wave), the enters the LVOT delayed from the inflow, which may be an additional mechanism for MVC. THis can be seen both by vortex imaging, colour M-mode, and even by pwDoppler:

Vortex image during pre ejection. The A wave is seen as the orange flow column, inflow is ended, but the column propagates toward the apex. in addition, there is flow towrds the LVOT, behind the anterior mitral valve, turning towards the mitral commisure. Colour M-mode. Left, in the mid ventricle, showing the inflow during the A-wave (orange), with propagations towards the apex. Right, the M-mode from tyhe LVOT, showing flow towards the base (blue) during the same period, both in pre ejection and IVC. pw Doppler, capturing both inflow and outflow. Both the E and the A waves can be seen to give a reverted flow towards the LVOT, with a delay due to the vortex flow. The flow after the A.wave is the J-wave.

Colour flow M-mode of atrial and ventricular flow. During the pre ejection period, before the valve click of mitral valve closure (MVC), a small flow away from the apex can be seen across the mitral valve.

The first pre ejection spike spike is thus pre MVC. This means that it represents the initial shortening velocity, before any appreciable afterload. This means it is seems to be as close as we come to the unloaded shortening velocity as seen in the isolated muscle experiments (208), although still preload dependent. Hypothetically, peak pre ejection velocity or strain rate is thus a candidate for contractility measurement.

Diagram showing the similarity between the length curves in isotonic twitches and strain curve, demonstrating their equivalence. Thus, shortening being load dependent, strain has to be too. The rates of peak shortening (strain rate) are more closely related to contractility, although still load dependent.

However, this doesn't hold when looking at the usual findings. If the pre ejection spike in basal velocity or global strain rate should be the peak unloaded shortening velocity, it means that the peak should be higher (in absolute values), than the peak systolic (during ejection ejection) velocity or strain rate. This both because the initial shortening velocity is higher, and becaouse the shortening velocity during ejection is afterloaded.

This, however, is not the case in almost all normal recordings, irrespective of measurement (velocity or strain rate) or method (spectral Doppler, colour Doppler or speckle tracking):

Pre ejection spike can be seen to be lower than peak ejection

-by spectral tissue Doppler
by colour tissue Doppler
and by speckle tracking.
In both velocities and strain rate:

By tissue Doppler, although this might seem closer to the reality of bing higher (absolute) than peak systolic SRI,
THis is also the method giving the highest variability due to noise.
Also in speckle tracking pre ejection peak is less than peak systolic SR, although in ST, there is substantial undersampling and smoothing.

Thus, the proto systolic velocity or strain rate spike is not in accordance with the physiological expectations, and peak protosystolic velocity is not a close measure of maximum unloaded shortening velocity / rate.

The reasons for this may be that as an event of very short duration;
The main point is that the peak protosystolic velocity is not a contractility measure. Peak acceleration is neither a contractility measure, being measured from start to peak velocity of the spike.

Isovolumic contraction

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

The true isovolumic contraction time (IVC)  is defined from MVC to the start of ejection. Thus, in this phase there is no volume change, and, hence, no deformation. This phase it on the other hand, the period of most rapid pressure rise, peak dP/dt, which occurs during IVC, close to the AVC (241). This represents the most rapid rate of force development (RFD).

Muscle twitches, showing that the most rapid rise of tension occurs during isometric contraction
Peak rate of pressure rise, which is the closes correlate to the rate of force/tension development. This occurs during IVC
dP/dt can be meastured by the velocity increase, if there is a small MR, too small for generating a pressureincrease in the atrium. It is customary measured between 1 and 3 m/s, which is equivalent to a pressure increase of 32 mmHg, and the dP/dt becomes a function of the time interval between then, and is used as proxy for peak dP/dt (463)

and may also be one correlate of contractility. As it occurs before AVO, it is not afterload dependent, and is a useful invasive index of contractility. However, as seen fom the length force relation above, this maximal force measure is not preload independent(395, 409, 410, 416).

The duration of the IVC may be a measure of contractility, as increased (mean) rate of pressure rise will reduce the IVC. This, of course, is still preload dependent, as is dP/dt. However, the time to AVC, will be a function of both the rate of pressure increase, as well as the pressure at the time of AVO, and thus will also be afterload dependent.

Mahler et al concluded that no single measure can always be used for defining an acute contractility change in the intact circulation (416).

Normalising for EDV, has been suggested as a normalisation for preload (410). However, again, this holds only in acute changes. LVEDV is still highly variable between subjects, both by body size and LV hypertrophy and dilation. Thus it would again have to be derived as a slope during manipulation of filling, or actual measurements of changes in dP/dt and LVEDV simultaneously.

The IVC duration is shortened by  the rate of force development, which again is a function of preload and contractility.  However, it is also shortened by increased HR, by the force-frequency relationship. The time to AVC depends on the SBP, I.e. after load, so IVC is both preload, afterload and HR dependent.

The ejection period

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

By valves it it defined as the period from AVO to AVC, and thus the phase of flow, volume reduction and deformation. Ejection results in volume decrease, and thus there is deformation (ventricle shortening and wall thickening).

Contraction is not isometric as in muscle twitches, as ejection of a volume into the aorta will distend the aorta, and the pressure increase depends on the aortic compliance C= V/P, which is part of the afterload. The peak pressure is during the middle of ejection. In the isolated cell, elongation starts at start of tension release (- decrease). In the intact heart, tension decrease starts at the start of pressure decrease, this means before mid ejection. But as blood is still being ejected, the ventricle will continue to eject, and thus reduce its volume, and we measure systolic deformation in the meaning volume reduction/wall shortening all the way to end ejection. This is due to the blood being accelerated to ejection velocity, meaning that the inertia will cause it to flow for a time even as pressure drops.This means that myocytes are still shortening as well, despite tension release as volume decreases due to continuing ejection. Also, any imaging modality will show continuing systolic deformation (i e longitudinal and circumferential shortening, volume decrease and wall thickening), despite myocyte relaxation, all the way to end ejection. (224, 225)

Flow, is the rate of ejection of volume, in l/min. But this rate of volume ejection must be equal to the volume change, i.e. the rate of volume decrease.

Comparing a tension length diagram of an isotonic/isometric twitch, and a pressure/volume (Wiggers)diagram. I've added the division of pre ejection into protosystole and IVC as discused above. The ejection period is not isotonic, as pressure increases and then decreases, and the myocardial tension must follow a similar course. Thus the tension increase is only during the first part of ejection, and then tension decline so last part of ejection is relaxation.
With conventional pressure/flow recordings, the peak pressure / tension is around mid ejection, but looking at flow, peak flow through aortic ostium is much earlier. Peak flow must mean peak rate of volume decrease, and occurs early during ejection.

Peak flow can be seen to be very much earlier than peak pressure / tension (464).

Flow velocity (m/s) is a nice proxy for flow (l/min), as long as the ostial area is constant, and peak flow velocity is likewise an early event during ejection. Annular velocity is the peak rate of shortening, which again is a proxy for the rate of volume decrease. Peak annular velocity is likewise an early event during ejection, and peak flow and peak shortening velocity are closely related.

Flow velocity of LVOT. This is closely related to flow, showing an early peak during the ejection time.
Tissue Doppler of the mitral annulus from the same subject, showing early peak annular velocity (a measure of peak longitudinal shortening rate), a proxy of volume reduction rate.
Colour tissue velocity from the same subject, with transferred valve openings and closures, showing how early the meak annular velocity is in the ejection time.

So why is the peak flow /volume reduction rate/flow velocity/tissue velocity  so much earlier than the peak pressure / tension? Afterload:

As flow is afterload dependent, the increase in afterload reduces flow compared to the continued tension increase.
Both strain and strain rate are afterload dependent, as described above.
And as annular velocity is a reflexion of wall strain rate, as discussed below, this means the same is true for the annular velocity.

But this means that the peak velocities are afterload dependent, not only by the reduced contraction rate, but because the dynamic increase in afterload actually terminates the peak velocities earlier. Thus peak velocity is determined not only by the shortening rate, but by the termination of the peak, which also is afterload dependent. This is depemndent on the stiffness of the aorta. And finally the stiffness of the aorta also determines the pressure augmentation by reflected waves, as discussed below, adding to the afterload.

Pulse wave propagation. The pulse wave travels as a wave of expansion along the arteries in each pulse beat (red), and is reflected from the periphery (blue). When the two peaks do not coincide, there is no augmentation of the peak pressure (top). If the two peaks coincide in diastole (middle), there is still no augmentation of the systolic pressure, as only the diastolic pressure is augmented. If the two waves coincide in systole (bottom), there is systolic summation, augmenting the peak systolic pressure, and thus increase the afterload. With low pulse wave propagation velocity, this augmentation will be seen in the periphery, with increasing pulse wave propagation velocity it will be seen more and more centrally. If the augmented pressure is central, peak central systolic pressure will be higher than the one measured peripherally, and the afterload higher.

Already Wiggers (402) was clear, based on previous works and reasoning from pressure curves, that the ejection was most rapid during the first part, with very reduced ejection rate during the last part of ejection.

Today, this, of course, is very evident, both from the LVOT flow curve, and from the rate of volume reduction (tissue velocity / strain rate): 

Thus, Wiggers suggested dividing the ejection phase into two, the maximum ejection phase and the reduced ejection phase. As seen from the velocity curves, there is a deceleration of ejection rate from an early peak, due to the pressure increase from to aortic elastance, even while tension still increase. Then the peak pressure marks the peak tension, and after that, there is actually relaxation (tension decline) at the cellular level, although still shortening due to the inertial flow, as discussed above. As the ventricles contract in systole, some of the energy is stored as elastic forces in:

The apex beat

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

As described elsewhere, and shown above, volume changes can be seen to be equivalent with length changes, and as seen by the curves, the two can be seen to be interchangeable.

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

The last end of the ejection period has continuing, although decreasing, flow, which means volume reduction, and continuing shortening despite myocyte relaxation. SV, EF, MAPSE and absolute strain continues to increase, while velocity and absolute strain rate decreases. This is illustrated below.

Measures of global long axis function

Peak velocity and peak strain rate.

As explained here, the basal displacement and velocity is equivalent to the summing of the regional strain rates along the wall, it follows that the basal displacement is the spatial integration of the strain, and the basal velocity is the integration along the wall of strain rate as explained here.

But then it follows that strain is the basal displacement, and strain rate the basal velocity, normalised for wall length:

As we see, apical velocity is close to zero. When strain rate (SR) is taken from tissue velocities, the definition is SR=  (v(x)-v(x+Δx)) ⁄ Δx where v(x) and v(x+Δx) are velocities in two different points, and Δx is the distance between the two points. If the two points are at the apex and the mitral ring, the apical velocity v(x)  ≈ 0, apex being stationary, and v(x+Δx) is annular velocity. Δx then equals wall length (WL), and peakSR = (0-S') ⁄ WL=  (-S') ⁄ WL.

Thus, peak velocity and peak strain rate are equivalent, early measures of global function, and strain rate do not add information. Both are early measures of the rate of emptying/peak flow, at the peak is actually determined by the ternination by the rise in afterload. Of course, since the denominator for normalisation varies with the different methods, values obtained by different methods are not equal, but show the same relation and variability (417, 462). Normalising basal peak systolic velocity S', do actually increase body size dependency, so global strain rate (which in fact are equivalent to the normalised S'), are more body size dependent than S' ( 462), as explained here.

Peak systolic measures are the measures of peak ventricular performance, and are basically

But this, of course, also means that the strain rate of the whole wall, equals the negative value of the basal velocity of the wall, as the apex is close to stationary:

If the two points are at the apex and the mitral ring, the apical velocity , apex being stationary, and  is annular velocity.  then equals wall length (WL),
thus and peak 
. It's also evident that the basal velocity curve and the strain rate curve approaches each other's shape when strain rate is sampled from most of the wall length.

Thus, peak strain rate is peak annular velocity normalised for wall length.

This, of course, means that peak strain  rate for the whole wall, must have the same shape as the basal velocity curve, as shown above and below:

When strain rate is sampled from most of the wall length, the shape is close to the basal velocity curve.

These occur early in systole, and thus are more closely related to contractility, and especially to contractility changes, as shown in studies (78, 79, 80, 223) and discussed here.

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

Thus, for a whole wall, peak annular velocity and peak strain rate should be the same. However, looking at velocity curves they seem to have a much earlier maximum that the strain rate from some areas, as shown below:

In this example from another person, the velocity curve has a much steeper initial slope, an earlier, and also more defined peak (A) and a steeper declinethan the strain rate curve (B) from the same sample volume. Thus, peak myocardial velocity in the area is not simultaneous with peak strain rate (rate of shortening). Looking at the two velocity curves from the ends of the strain rate sample volume, it is evident that the velocities peaks at A, while the maximum offset between the curves is at B.

Left: Real velocity curves from two points at a distance of 1.2 cm, right, strain rate calculated from the velocity traces as the velocity gradient SR= (v(x) - v(x+x))/x.

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

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

However, as shown above, looking at the whole wall, the basal velocity has to be close to the inverted velocity curve. Thus, the translational velocities has to correspond to deformation in another part, as the apex do not move:

Looking at the basal half of the septum, there is an early peak in both basal and midwall velocity curves (yellow and cyan), while the apical curve (red) is flat. Looking at the strain rate curves, the basal half shows a rounded curve (green) with later peak, while the apical half shows an early peaking strain rate curve (orange), closely resembling an inverted velocity curve. This, of course corresponds to the velocity differences shown by the corresponding areas between them, the  basal and midwall curves have parallel early peaks, and thus there is no strain rate peak between them, the midwall curve shows a peak, the apical is flat, and thus there is a corresponding early strain rate curve.

This means there is initial translational velocities in the basis, corresponding to early deformation in the apex. The mechanism for this may be the recoil from ejection, creating (most of) the motion towards the chest wall, the apex beat (ictus cordis).

The deformation of the whole wall, however, must have an early peak, although this may vary:

During early ejection, there is acceleration of blood out of the ventricle. The flow rate, if the LVOT diameter is constant, is reflected in the peak flow velocity. But the flow rate also is the rate of volume decrease, which is reflected in the annular velocity. Thus, the peak is related to the early cut off of peak flow rate, due to the increase in afterload.

As shown here, peak rate of vloume decrease is reflected in both strain and strain rate in this case, as septal and lateral peak velocities and strain rates are simultaneous.

This, however, is not exact.

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

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

This, of course means that no peak will correspomd exactly to the peak volume decrease, as there must be some additional translational velocities being added in one wall, and subtrated in the corresponding wall, reflecting a slight rocking motion. This may, for instance be due to ejection at a slight angle to the LV long axis. The true peak is in the mean curve, i.e. not the mean peaks value, as the peaks are not simultaneous:

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

Looking at the corresponding peak strain rates, they should subtract the velocities due to translation:

Early lateral peak velocity, late septal; early septal peak strain rate, later lateral, mean peak strain rate later than mean peak velocity Early lateral and later septal peak velocity, earlier lateral than septal peak strain rate, mean peak strain rate later than mean peak velocity. Early peak velocity on both sides. Still slightly later peak strain rate in lateral wall, and thus mean peak.
- but even this is not absolutely perfect, as seen above, and also when comparing with peak flow as seen below.

As the ejection continues, the ejection of blood volume causes the ventricle to diminish, LV volume, LV length and diameter decreases, stroke volume, EF, annular displacement and absolute strain increases, and strain rate remains negative during the rest of EP. Pressure, however, still rises in the aorta, the aorta being stretched by the ejected volume which is higher than the run off (has to be as there is continuous run off in diastole as well). Thus, the increasing aortic pressure decelerates the blood, and the energy for the pressure rise is thus taken from the kinetic energy of the blood, which decreases correspondingly, as seen from Doppler. And as the rate of flow decreases, the rate of volume change must decrease as well, even if the peak ventricular and aortic pressure continues to rise. Thus, peak myocyte tension occurs at peak pressure, later than peak annular velocity, peak strain rate and peak flow velocity.

    1. During first part of ejection, this deformation is active contraction
    2. Peak tension is reached at the time of peak ventricular pressure.
    3. After peak pressure, there is still tension, although decreasing, during the last part of ejection the ejection is partly driven by inertia and possibly elasitc recoil. 
    4. As there is still flow, there will still be volume decrease, and hence, wall thickening and shortening. This continuing decrease, however, is more passive, and the muscle is in fact relaxing at the same time.

Peak systolic versus end systolic measures of ventricular function.

Peak systolic measures are the measures of peak ventricular performance, and are basically
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

The last end of the ejection period has continuing, although decreasing, flow, which means volume reduction, and continuing shortening despite myocyte relaxation. Thus, SV, EF, MAPSE and absolute strain continues to increase till end ejection, despite declining tension. Velocity and strain rate decreases. This is illustrated below.

During last part of ejection, pressure decreases (at least when reflected waves are not taken into account, and so does flow. Thus, despite afterload decrease, there is simultaneous tension decrease and flow decrease.
Peak systolic annular velocity (S'), which is early systolic,  compared to peak annular displacement (MAPSE), which is end systolic. S' is actually the peak rate of annular displacement, and is thus closer to contractility, while MAPSE is end systolic and thus closer to ejection fraction.  Peak strain rate, being early systolic,  compared to peak strain, which is mainly end systolic, and closer even, to ejection fraction.

Basically these measures are also afterload dependent.

As flow is afterload dependent, the continuing afterload reduces flow during tension release. Both strain and strain rate are afterload dependent, as described above. And as annular displacement is a reflexion of wall strain rate, as discussed below, this means the same is true for the MAPSE.

The same as for velocity vs. strain rate, of course, must then hold for displacement vs strain.
Likewise, strain = (d(x)-d(x+Δx)) ⁄ Δx where d(x) and d(x+Δx) are displacements in two different points, and Δx is the distance between the two points. If the two points are at the apex and the mitral ring, the apical displacement d(x)  ≈ 0, apex being stationary, and d(x+Δx) is annular displacement = MAPSE. Δx then equals wall length (WL), and Strain  = (0-MAPSE) ⁄ WL=  -MAPSE ⁄ WL.

The relations can be seen here:

Relations between global strain and MAPSE (417) are studied in the HUNT study. Of course, since the denominator for normalisation varies with the different methods, values obtained by different methods are not equal, but show the same relation and variability (417, 462).

Looking at walls, it seems that the cavity volume reduction (i.e.) the stroke volume, depends on both shortening and wall thickening as well as outer diameter reduction. But the wall thickening is simply a function of outer diameter reduction, and shortening.
If the myocardium is incompressible, the myocardial volume has to be the same in both systole and diastole. Thus, as the total (outer) volume is the sum of myocardial and cavity volume, the systolic reduction of cavity volume has to equal the reduction in total volume, and thus the stroke volume is only determined by the longitudinal and outer diameter shortening. If the myocardium is partly compressible, the myocardial compression will detract from the stroke volume.

In modern MR studies (420, 430) the longitudinal shortening contributed about 60% to stroke volume, outer contour reduction the rest, even when the AV-plane motion was depressed (431). A newer ultrasound studyy found the longitudinal shortening to contribute as much as 83% of the stroke volume (158). The correlation between MAPSE 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 of about 3% should be present to explain the rest of the stroke volume , although it may be more in real situations.

The close relation between longitudinal shortening and stroke volume seems evident, when looking at the volume and strain curves below.

Interestingly, normalising basal peak systolic velocity S', or MAPSE for length, do actually increase body size dependency, and likewise global strain and global strain rate (which in fact are equivalent to the normalised measures), were more body size dependent than S' and MAPSE (417, 462), as explained here.

Why is this? Annular displacement and strain is closely related to stroke volume. The annular displacement contributes 60 to 80%  to the total stroke volume. Ventricular diameter increases with body size, as does the length Thus, even with the same MAPSE, a larger ventricle will have a larger stroke volume. So MAPSE is less body size dependent.

As the main determinant of stroke volume is MAPSE (158, 420, 430) the relation between MAPSE, stroke volume and body size is geometric. With increasing body size the heart size increases both in length and diameter, while the ratio between them stays constant (386). With increasing diameter, the same MAPSE will result in increased stroke volume, as MAPSE is responsible for about 75% of SV, thus annular motion (S' and MAPSE) do not have to increase as much with body size to increase SV. Thus LVlength increases more with SV than annular motion, inducing a negative relation between global strain / strain rate and body size, as illustrated below.

Relation between stroke volume and mitral annular plane systolic excursion (MAPSE) in ventricles of different size. It has been shown that while heart size increases with body size, the ratio between length (LVEDL) and external diameter (LVEDD) does not. As the stroke volume is mainly determined by the systolic shortening (MAPSE), a larger ventricle has a larger radius, and thus, a larger stroke volume (increasing proportional to the square of the radius) even without any differences in MAPSE, as shown by the very low correlations between MAPSE and BSA. Thus, in the ventricle to the right, for the same MAPSE, the SV is far higher. As length increases proportional to the diameter, GLS being MAPSE/ LVEDL, GLS actually decreases with increasing heart size. This is a systematic error that occurs due to the one-dimensional normalization. As there is a strong correlation between S′ and MAPSE, this is also the case for S′ vs GLSR, even if those measures are more closely related to contractility than stroke volume

The use of global functional measures in clinical context as well as normal ranges are discussed in the section on global systolic function.

As we can see, peak shortening can be measured as either peak systolic annular displacement (MAPSE) and peak systolic strain, and peak shortening rate as peak systolic basal velocity, the S' or peak systolic strain rate, SR. The peak shortening velocity is equal to the slope of the shortening curve, at the point where the curve has the most rapid change, i.e. where the curve goes from convex to concave, and the slope crosses the curve. All four measures are in clinical use with ultrasound.

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

The global measures should be either mean of the lateral and septal walls, or the anterior, inferior, lateral and septal walls. 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.

Left ventricular ejection time (LVET)

LVET is related to SV. Thus, just as IVC, it increase with preload and contractility. But on the contrary, LVET decreases with afterload (decreases SV). And finally, it decreases with HR. Thus, for LVET to be useful, HR correction must be applied (LVETc).

But is LVETc useful? It may be useful in assessing low flow - low gradient AS. A patient with low EF will have a low LVETc, if it is near normal, it means the gradient is real, if substantially reduced, it’s the LV function that is the cause of low SV. This is actually utilising the afterload dependency. Though I’ve never seen any studies, I’d think that the same would be the case if LVEDV and SV are low (in that case LDDDE doesn’t work), but a low SV and normal LVETc would be suspicious. Could be case for a nice study, although the gold standard for AS might be troublesome.

But how to correct for HR? We all know Bazett's formula QTc = QT/ SQR(RR) is on observations observations on mechanical systole, nearly lost in history, and applied to electrical systole by Bazett in 1920. This is a non linear correction of QT time vs RR-interval. Normal values, however, only gives an upper cut off against arrhythmia risk.

Weissler (468) did a linear regression, LVETC = LVET+1.7*HR with normal mean (SD) 413 (10) in men, and LVET+1.6*HR with normal 418 (11) in women. This was based on carotid pressure tracings, corrected with phono, at rest. This gives both upper and lower normal values, which are more interesting hemodynamically. As the relation between HR and RR-interval in fact is non linear (but hyperbolic, not quadratic), it seems that both corrections may be fairly accurate. In an exercise study (29), we found Bazett’s formula to be a bit better, but as the relation of LVET to HR seems to be fairly linear, it seems useful:

As we see, the relation between RR interval and HR is hyperbolic, while LVET seems more straght lined- LVER vs RR inerval, is mobviously non linear.

Even if Bazett's formula is related to RR interval, it performed better against HRT over the whole range, Weissler's formula showed a significant increase with Increasing HR, while Bazett did not.

This, however, may be a difference between high and low HR.

Thus, the imaging measures are all measures during ejection, and all have weaknesses, as they become afterload dependent at the time of AVO.

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

Again, the exact timing of AVC, and by this, the end of LVET, is precisely defined by the valve click in Doppler:

It becomes less evident in tissue Doppler, and there is just as much confusion and errors there as for the pre ejection spike.

Proto diastole

It has been assumed that the first negative spike in tissue velocities after ejection was due to isovolumic relaxation, basing it on the erroneous assumption that there is elongation during IVR. (47, 366, 369, 370, 465, 466, 467). This negative event can also be seen in colour M-modes of tissue Doppler, both in the mitral ring and the mitral leaflet. However, already Wiggers showed that the event relating to the closure of the aortic valve was a relaxation preceding the IVR, and he termed it proto diastole (402).

The peak negative dP/dt, is the transition point from convex to concave point . This transition should be no earlier than AVC. It has been seen to be close to the AVC (244), and has been suggested as a marker of aortic valve closure in pressure tracings, so some studies used this, but it seems that this also places the AVC reference a bit early. That study, however, used correlation between end of aortic flow and pressure traces, with no attempt to calculate bias or significance of bias.

In an early study of high framerate (16) we noticed the initial midwall elongation in the septum by strain rate, bfore the AVC. Thus, the negative spike in velocities corresponds to a protodiastolic elongation seen by strain rate.

Colour strain rate M-mode from the septum of a normal subject. It is evident that there is an elongation in mid septum, resulting in initial negative velocities in mid and basal septum before closure of the aortic valve. Notice also how the initial elongation of the mid septum occurs before the closure of the aortic valve, i.e. the initial negative velocities in the basal and mid septum are protodiastolic. Colur TVI and SRI derived from the same recording, showing that the midwall septal elongation and the basal downward velocities are corresponding. The difference in locartion is a tethering effect.

The basal downward motion of the mitral ring is also demonstrable in both M-mode, Colour TVI M-mode and spectral Doppler:

Left, M-mode of the mitral ring, showing a downward motion of short duration, marked by the white dashed rectangle. Middle: This becomes far more evident in colour TDI M-mode. The downward motion is evident in spectral Doppler as negative velocities.

Due to the proximity to the peak dP/dt, this spike was assumed to be occurring before AVC, and the downward motion as isovolumic relaxation.

The same event was seen in the motion of the mitral ring, where mitral motion could also be seen, and AVC was erroneously taken to be at the end of the event (369).

Colour TDI of the mitral valve, showing the same negative event as the mitral ring. The phono shows the AVC as the end of this event, not at the start as previoulsly maintained (369)

The location of the AVC in relation to tissue Doppler can  be easily demonstrated by the method of transferring the opening and closing events from Doppler recordings to the worksheet of analysis software, to be used in other quantitative analysis:

Recordings from LVOT (top left) and mitral annulus (bottom left ) with closing and opening of aortic and mitral valves marked and measured. The analysis software has then transferred the mean values for events to the tissue Doppler analysis , and the basal post ejection spike can be consistently seen before AVC.

This is zoomed in the recordings below, showing AVC at the end of the protodiastolic tissue Doppler spike:

The post ejection spike thus occurs BEFORE AVC, as seen here (valve openings and closures from Doppler flow - different cycles).
AVC is concomitant with the stop of basal motion.

However, this is slightly less accurate as events are transferred from separate recordings (different cycles) and thus are vulnerable to heart rate variability., as the ejection time is related to the total cycle length (RR - interval) (29), but not completely linear.

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

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

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, it was proved conclusively that the post ejection spike was protodiastolic:

Thus, the elongation spike corresonds to a small protodiastolic volume expansion before AVC. A little later, this was proven experimentally
(173). It demonstrated also, by simultaneous volume, pressure and tissue Doppler tracings that the post ejection spike was before AVC. But taking the experiment a little further, they demonstrated that by stenting the aortic valve, that the stop of the motion was actually due to aortic valve closure. That, rather elegant study, demonstrated again the early fiondings, the velocity of early onset of relaxation continued smoothly into the early filling velocities, thus demonstrating that the mitral valve closure (and thus onset of IVC) Thus, the post ejection spike is simply onset of elongation, rwhich is interrupted by the AVC, and continuing relaxation being isometric without elongation until MVO.

Schematic representation of the findings in (173), showing that as onset of elongation is interrupted by AVC (onset of IVR), when aortic valve is stented (yellow curve), this results in a smooth non-interrupted transition to early filling velocities.

The study showed a small volume increase at end systole, before AVC, on the order of about 1.4%(173). Again, this must result in a motion of the aortic root after end of flow, and thus volume expansion by the motion of the aortic orifice at a period of no flow.

The lengthening seems to be more pronounced in the septum, possibly because the open aortic valve offers less resistance to motion than the closed mitral valve to motion against the blood in the atrium.

Post ejection spike seems to be most pronounced in the septum, both seen with ring velocity or wall strain rate.

Curved M-mode showing the protodiastolic deformation before AVC, predominantly in the septum (valve motions transferred from Doppler.

Thus the motion of the aortic valves in the stationary blood, will tend to close them.

Proposed mechanism for the aortic closure. During ejection the ventricle can be seen to shorten, and there is ejection (arrow), keeping the cusps open. Ejection is  decreasing towards the end of the ejection period, as shown by the decreasing length of the arrow. At end ejection, there is no flow, and the relaxation that started during ejection as a reduction in tension, leads to a slight elongation (blue arrows). The aortic cusps then are closed due to the valve motion in the now stationary blood column, similar to what happens if a scoop is put into the water (opening forward) from a boat that is moving forward. In this case, the motion of the cusps are mainly lateral, i.e. towards the middle, and thus may be greater than the longitudinal displacement of the annulus Volume increase due to proto diastolic lengthening. This volume increase is also evident from  displacement and strain traces. This volume increase is not due to flow, but the fact that the aortic annulus includes part of the blood volume by , sliding along a stationary column of blood that then is "ventricularised", illustrated by the light red cylinder in the image above.

The assymmetry is not taken into account in this illustration.

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

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

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

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


Isovolumic relaxation period (IVR)

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

Thus, the IVR, being defined by the valve clics as the gold standard:

But in tissue Doppler is is different than expected, because the AVC is later than expected.

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

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

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

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

When is mitral valve opening?

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

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

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

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

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

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

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

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

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

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

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

Deformation during IVR

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

Curved M-mode showing the protodiastolic deformation before AVC, as well as he isovolumic period (valve motions transferred from Doppler. During IVR, there is no net volume change, so dimension changes in one part of the ventricle has to balance against opposite changes in other parts. Here, elongation in the apex (blue) is balanced by shortening in the base. However, this may create a pressure gradient(and volume redistribution) that will shift the blood towards the apex during IVR.

The same can be seen in strain rate curves, elongation in the apex (white), shortening in the base (orange)

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

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

The apically directed intraventricular flow during IVR, must mean that the apex has to deform during this phaset. The flow has to be taken as an indication of a base-to-apex pressure gradient, and hence, that relaxation starts in the apex. As described above, true relaxation starts earlier, during ejection, but the gradient is an indication that early deformation starts in the apex. There has to be a space for the blood volume to flow into. Thus, the earliest deformation starts during isovolumic relaxatio0n in the apex. This has been confirmed by MR (247).

Summary iollustration, showing again, the apically directed flow during IVR.

What about strain rate and strain curves?

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

Strain rate tracings in this subject show positive strain rate (lengthening) during IVR in the septal apical and lateral apical and midwall segments, concomitant with negative strain rate (shortening) in the basal segments. 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.

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

Diastolic function

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

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

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

In the intact heart, however, there may be external structures storing elastic energy as well:
Thus diastolic deformation may be seen as the interaction between the tension release. which again is dependent on the rate of calcium removal, and the elastic recoil.

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

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

In the free cell, elongation starts at start of tension release (- decrease).
In the intact heart, tension decrease starts at the start of pressure decrease, this means before mid ejection.

But as blood is stille being ejected, the ventricle will still reduce its volume, and we measure systolic deformation in the meaning volume reduction/wall shortening. This is due to the blood being accelerated to ejection velocity, meaning that the inertia will cause it to flow for a time even as pressure drops.This means that myocytes are still shortening as well,despite tension release;still shortening as volume decreases due to continuing ejection, as mentioned above. Also, any imaging modality will show continuing systolic deformation (i e longitudinal and circulferential shortening, volume decrease and wall thickening), despite myocyte relaxation.

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

However, these are different physiological events:
Thus, it is also evident that "diastolic dysfunction" may be a very complex entity, where both the rate of calcium removal by SERCA, and any fibrotic process of the myocardium or large vessels that increases collagen and reduces elastin may contribute.

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

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

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

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

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

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

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

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 which was described already by Wiggers (402) and confirmed repeatedly (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. (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).

The main point is that when there is pressure drop (negative P) concomitant with volume expansion (positive V), this means that there is negative compliance C = V / P, which means suction, as argued already by Katz (407)

Suction driven filling (vis a fronte; a force acting from the front), versus pressure driven (vis a tergo; a force acting from behind) filling of a chamber (B).  In this simplified model, the level of fluid (and, hence, pressure) in chamber A is assumed to be constant during filling. 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 fronte, energy is applied to creating a pressure drop in chamber B, in vis a tergo, the force application (energy) is applied to the fluid in chamber A.
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.  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 (red); showing volume increase of the LV (chamber B) with simultaneous pressure drop (negative dP/dV),  the driving force being left ventricular recoil, while late filling is vis a tergo (blue) 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.

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).

The concept of erarly filling by suction in the normal ventricle now is considered firmly established (397)

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.

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.

Load dependency of diastolic tissue velocity (e')

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

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

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

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

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

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

Looking at the full descrioption of the events during the heart cycle, especially the proto diastolic and systolic events, a full heart cycle describing this can be theoretised: 

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

During isovolumic relaxation there is no filling, as both valves are closed, and hence, no downward motion, although there is a slight initial velocity in the septum, that is visible without discernible shortening in the dsplacement trace. When relaxation (tension decrease) has progressed to the point where atrial and ventricular pressures equalise, the mitral valve opens, and the two filling phases follow. At the end of late filling (atrial systole), there is again equal pressures in atrium and ventricle, and no flow. The start of contraction will then lead to closure of the mitral valve, as they move in a stationary  blood column, they will be pushed toward the base and toward the middle. Motion again will stop when the valve is closed, and the isovolumic contraction follows untill aortic valve opens and ejection starts.

These volume changes are seen in the tissue Doppler velocity, displacement strain rate strain diagram to the right.

Ventricular compliance

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

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

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

Reduced compliance should thus be mainly restricted to end diastole.

With a rapid pressure rise in the LV with atrial contraction, the atrial inflow will be abbreviated. The pulmonary veins, however, are not thus restricted, and backward flow into those will continue for the full atroial systole. The difference in timing between mitral and PV A-flow can thus indicate if LVEDP is increased.

Comparison of pulmonary venous flow and mitral flow A waves, indicates increased end diastolic pressure.

The heart cycle visualized by motion and deformation measures , all from tissue Doppler of the same cine loop. Valve openings and closures are taken from Doppler flow registrations, and transferred by the software to the actual heart cycle

Thus all systolic work has been provided by the contraction of the myocytes until peak pressure. The rest of the ejection phase is only a shift between flow and pressures, translating pressure work into flow / shortening.

The Wigger's diagram and volume pressure loop revisited.

This also will mean that the Wiggers cycle and PV-loops may be shown more detailed:

Revised Wigger's cycle showing the valve closures as phono traces, with pressure crossover and a small volume expansion before MVC, dividing the pre ejection interval into three; EMD, proto diastole and IVC, also the small volume reduction in proto diastole before AVC, and also the pressure drop during early (rapid) filling concomitant with rapid volume increase.
Revised PV-loop, based on the full cycle as it is. The small volume reduction in proto systole and the small volume increase in proto diastole before valve closures is shown as the red shaded areas. The two notches before valve closures is in accordance with experimental findings (173). In addition, the diastolic part of the PV-loop is shown with the first part having pressure drop and concomitant volume increase, in accordance with the established physiology of early filling.

The heart cycle in motion and deformation imaging

And the whole heart cycle can also be visualised by the motion and deformation measures in a combined diagram as seen below:

The heart cycle visualized by motion and deformation measures , all from tissue Doppler of the same cine loop. Valve openings and closures are taken from Doppler flow registrations, and transferred by the software to the actual heart cycle

Diastolic strain rate

Looking at the diastolic veklocity pattern, it is evident that the motion, both in the E' and the a' show a start at the base, the peaks are also earlier at the base, but the ends of the velocity waves are almost simultaneous. The Strain rate pattern shows again earler start and peak at the base, but the end is also earlier:

While both start and peak systolic velocities are near simultaneous, both the e' and a' velocity waves show a progressive delay of both start and peak from base to apex, while the ends are simultaneous,
Strain rate, on the other hand, show delay of both start, peak and end of the two diastolic waves.

This is also very evident in colour M-mode, and the delay in onset may even be seen in an ordinary M-mode along :

Delayed onset of velocity and strain rate during early and late filling, seen by both velocity and strain rate, but with a different pattern, as a triangle in velocity plot, showing the simultaneous end of the velocity wave, but as a tilted band in the strain rate. Onset, however follows the same propagation front.
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.

Why is that? During filling the volume of the ventricle increases, which means the wall elongates. As the apex is fixed (against the chest wall and pericardium, motion has to go in the basal direction (away from the apex. But this means it has to start at the base. Compare with a row of standing cars, if the row shall start to move, motion has to start with the foremost.

But this will look differently in a velocity plot and a strain rate plot, as seen in the colour M-modes above, and in the cars below:

Colouring the cars acquiring velocity in blue, we see the start of the wave in front, adding one car at a time till all have the same velocity, and thus are blue. Colouring only the cars with DIFFERENT velocity, we show the interval where distance increases, i.e. where the row deforms. It shows the difference between deformation and motion, and illustrates that the diastolic deformation is a discrete event, propagating in a wave.

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

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

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

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

This is analoguous to:

Diastolic strain rate propagation. 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. Diastolic strain rate propagation velocity is the slope of the elongation wave.

Relation between diastolic strain rate propagation of the E-wave and 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.

Strain rate propagation is thus a global measure that relates to the peak e' in tissue Doppler.
Thus, there is a geometric relation between strain rate propagation and e', which is both theoretically and empirically (19) probable.

What does strain rate propagation mean?

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

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 due to incompressibility), and shows how local early diastolic strain is delayed in the apex compared to the base.

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

And if global diastolic function is to be measured by strain rate imaging, the propagation velocity is the true the global measure- An average of peak strain rates, not being simultaneous, is a more difficult concept, although it corresponds to an average local rate of deformation. However, another agerage diastolic strain rate is by measuring along the whole wall simultaneously:

As we see, apical velocity is close to zero.
When strain rate (SR) is taken from tissue velocities, the definition is SR=  (v(x)-v(x+Δx)) ⁄ Δx where v(x) and v(x+Δx) are velocities in two different points, and Δx is the distance between the two points. If the two points are at the apex and the mitral ring, the apical velocity v(x)  ≈ 0, apex being stationary, and v(x+Δx) is annular velocity. Δx then equals wall length (WL), and peakSR = (0-S') ⁄ WL=  (-S') ⁄ WL.

But as apical velocity is close to zero, this means that peak diastolic strain rate is equivalent to peak e', and it is hifhly dubious that this adds clinical information, why should it?

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

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

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

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

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

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

The double peak of Una peaks (Cape Renard, Lemaire Channel, Antarctica) may be a reminder of the double peaks of diastolic strain rate.

Diastolic strain rate. The strain rate 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).

Proposed explanation of the return wave of the two filling phases, which may be 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. Diastolic strain rate. Diastolic events 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.

It is uncertain whether this is a reflected wave from the apex, or a continuous wave passing around the apex:

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.

Thus, the complex series of events in the heart cycle can be visualised by strain rate:

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

Strain rate propagation vs flow velocity propagation

It might be tempting to compare this strain rate propagation to flow propagation, which, in some studies have been shown to be a measure diastolic function (83, 84).

However, flow propagation as seen by colour M-mode, is not the inflow of blood, as related to the volume expansion, but the propagation of the velocity vectors. Also, the flow propagation is a more complex phenomenon, consisting of both a propagation of velocity vectors, not volume propagation, and a vortex formation, that also propagates more slowly towards the apex (421).

Colour flow, showing how inflowboth during early and late filling shows vortices (blue colour to the sides of the main inflow.
Still picture from the loop to the left at the time of early filling, showing the negative velocities (blue) to the sides of the positive main inflow (red).

Also, while strain rate propagation is a sharply delineated phenomenon, flow propagation may be measured in various ways:

Colour M-mode from a normal ventricle. In this image, early filling (E) can be seen as a fairly steep wave from base to apex. The propagation velocity is the slope of the column, but as seen, values varies depending on how it is measured, as the front of the column (black to colour), the front of the aliasing velocity or the main vector of the aliased velocity (which both will depend on the PRF). The black-to-colour, however may be difficult to discern from the intraventricula flow during IVR.

All measures have been used in studies (83, 84, 85, 422)

In a normal study (20) of 12 subjects, the mean values were as follows: Black-to-colour: 55.5 cm/s (17.7), Front of aliased contour 54.8 (5.5), 72.1 (40.6), showing the front of the aliased contour to be the most robust, with least variability, but, dependent on the PRF setting. The strain rate propagation in the same group was 66.6 cm/s.

Proposed filling model of the left ventricle. The length of the arrows represents the inflow velocity. As the first volume of blood (red) enters the ventricle, it turns out to fill the wider space of the ventricle, creating a vortex, while the next blood volume (blue) passes through to the middle ventricle, and then expand to fill the expanding cavity at that level. The third volume of blood will then pass through, and expand in the apical part. Thus, the velocity propagation and strain rate propagation will match, but both being slower that the inflow velocity. Propagation of the blood volume.

In dilated ventricles with heart failure (which will necessarily have diastolic dysfunction) (83, 84), all inflowing blood may turn into vortices and thus have a slower propagation due to ventricular geometry as shown in model experiments (88).

Inflow during early filling in a normal subject. The E wave can be seen as a fairly steep wave from base to apex (I), followed by a more "smeared out" wave arriving later in the apex, representing the vortex following the initial flow velocity propagation.
Inflow in a dilated ventricle ventricle of a patient with heart failure. Flow propagation is reduced, not due to the  reduced propagation of velocities in the early phase, but because most of the flow propagation is vortex propagation.

In the study mentioned above,  strain rate and flow propagation (20) was compared between then normal subjects and a group of 13 patients with compensated hypertension, but with slight concentric hypertophy and reduced diastolic function, without increased filling pressure. In this group, the strain rate propagation, as well as all diastolic functional measures was reduced, while the flow propagation was increased. The patients were older (mean 46 vs 64), so the effects on diastolic function was partly hypertensive, partly age dependent.

IVSd (mm)
LVIDd (mm)
EF (%)
E (cm/s)
Dec-t (ms)
IVR (ms)
e' (cm/s)
Strain rate prop (cm/s)
flow velocity prop (cm/s)
29.6 69.9
<0.005 NS
<0.005 <0.005 <0.05
<0.005 <0.005 <0.005

Thus, we see that flow propagation velocity actually increases in the group, despite the finding that all other diastolic parameters including strain rate propagation was reduced. Thus, it seems not to be a measure of diastolic function in this study, possibly because LV geometry is a confounder. Nor were there a close connection between the two propagation measures, in the whole group there were negative correlation between the two, R= - 0.57, but not between flow velocity propagation and e'. Strain rate propagation correlated with e' .

Inflow during early filling in a normal subject. Inflow in a patient from the study, showing much more rapid flow propagation, as well as reduced vortex propagation.

It seems that flow propagation though preload insensitive, (85) related to left ventricular geometry. And finally, there was a strong correlation between the ratio of E / strain rate propagation velocity and flow propagation velocity, R=0.67, i.e. with a higher ratio (low strain rate propagation and high flow velocity), this will drive a high flow propagation velocity.

Proposed filling model in a narrower ventricle with delayed relaxation.  With slower strain rate propagation, the ventricle will remain narrower for a longer time. In this time, there will be less volume to absorb the inflow, thus more of the initial inflow will proceed into the narrower part of the ventricle, with the flow propagation like the inflow velocity. However, the model proposes that with a more profound decrease i E, the match between flow propagation and strain rate propagation may be restored, while increased filling pressure would aggravate the mismatch.

A corollary would be that with a more pronounced reduction of flow velocity (ie. a low E), the flow propagation would decrease towards the strain rate propagation, but this would have to be confimed in further studies.

Atrial function

As for all chambers, atrial function can be described in terms of pressure, flow and volume changes, that all interact. The atrium, however, is influenced by the ventricles in various ways.
The atrial pressure curve have been extensively studied invasively and experimentally (451, 452, 453).

The left atrial pressure is low, but the curveform is still influenced by both atrial and bi ventricular function.

Atrial pressure curve (red), has an a-wave, related to atrial contraction, sometimes a c-wave related to onset of ventricular contraction, and a v-wave related to end ejection. Minumum pressures are at mid ejection (x-descent) and during early filling (y-descemt).

Atrial contraction results in a pressure rise, the a-wave. This can be seen form the time delays in this experiment (453) to propagate backwards to the lung veins, and forwards into the leftventricle, thus confirming thia as an event originating in the atrium. During atrial relaxation, the pressure drops from the peak. Onset of ventricular contraction occurs before mitral valve closure (236, 403, 268). Thus there is a pressure rise while the MV is open, so this may be accompanied by a slight atrial pressure rise (c-wave) in some instances, depending on the differences in pressures between atrium and ventricles. In the case of the c-wave, the pressure rises earliest in the ventricle, followed by the atrial and then pulmonary venous c-wave, confirming a ventricular origin. The increase in atrial pressure stops when mitral valve closes, separationg ventricular and atrial pressures.
With or without the c-wave, there is a net pressure drop from peak a to a nadir during the ejection period (x-descent), followed by a pressure increase, still during ventricular ejection (v-wave). This seems from this experiment to start in the right ventricle, being a pulse wave that propagates from the RV through the pulmonary veins to the left atrium. It has also, however, been suggested as being due to the atrial contraction wave reflected from the pulmonary vascular bed (455).

Flow velocity (m/s) is related to pressure, or actually to pressure differences.
Flow is the volume rate (l/min). If the vessel or orifice diameter is constant, the changes in flow velocity and flow are tightly related.

Pulmonary venous flow has three phases:

Pulmonary venous flow can be seen to have three main phases: A; retrograde flow from the atrium backwards into the pulmonary vein, S; Forward flow from pulmonary vein to atrium during ventricular systole and D: forward flow during early ventricular filling.
Sometimes the S-wave can be seen to be split into two peaks, the S1 and S2 waves.

The A wave is due to the atrial contraction. As the mitral valve is open, just as the pulmonary veins are without valves, this contraction will result in increased atrial pressure, and flow from the atria, both into the ventricle and backwards into the pulmonary veins:

Pulmonary venous flow, with retrograde flow into the pulmonary vein during atrial contraction.
Mitral flow from the same subject with antegrade flow into the ventricle during atrial contraction.

Pressure gradients from PV to LA from the figure above, compared to  a standard flow velocity curve. The pressure gradient is negative (magenta) during the a wave, driving flow backwards (A), and positive during the rest of the cycle (violet), driving flow forward. Looking only at the arial curvem, however, this very closely mirrors the pulmonary flow velocity profile. Looking at the atrial pressure alone, it can be seen that pulmonary venous flow is almost perfectly mirroring the atrial pressure curve alone. Pressure peaks correspond to velocity nadirs, pressure troughs to velocity peaks, pressure decrease to acceleration and pressure increase to deceleration.

If the ventricle is compliant, pressure in the LV will rise in parallel with the atrial pressure as seen above, and flow will stop at the same time at the end of atrial relaxation. If the ventricle is less compliant, however, pressure will increase in the ventricle terminating antegrade flow, while the pulmonary veins, being more compliant, will have less pressure rise, and the A-wave persists longer:

Pulmonary venous flow showing termination of the A wave at start of QRS in the ECG.
Mitral flow showing premature termination of the A wave before start of QRS in the ECG.

The S-wave have been shown to correspond to the pressure drop during ejection (x), while the D-wave corresponds to the pressure drop during early ventricular filling (y) (453, 454). It is reasonable to assume that the flow deceleration at the end of the S1 wave corresponds to the c wave, pressure increase before the MVC. This is delayed in the pulmonary vein, compared to the atrium, as it propagates from the ventricle (453), through the atrium and into the pulm. veins as shown above.

The S wave (S1) has been suggested to be (at least partly) due to suction from atrial relaxation. However, relaxation starts at peak pressure (as in the ventricle), in this case peak a-wave. thus the first event of atrial relaxation is the decline of pressure and velocity of the PV A-wave. In the ventricle there is suction from elastic recoil of the ventricle at the last part of early ventricular filling. However, in the atria, the initial ventricular contraction, leading to the c-wave and to MVC, precedes the S1 wave, so ventricular contraction would seem to be the dominant force here.


is also the rate of volume expansion. Looking at the heart, the atrial volume expansion can be seen directly:

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 here), 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 wasted. 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.

Near invariant outer contour shown in this image. As ventricles shorten in systole, the same AV plane motion expands the atria, sucking blood into the atria from the veins. This means that the work in compressing the ventricles is used for atrial filling. At the same time, not reducing outer contour much, ensures that work is not wasted in moving surrounding tissue in each heartbeat.

This means that the systolic atrial filling is to a large degree dependent on ventricular function. Looking at the atrial pressure curves, we see that pressure drops from peak a-wave to the nadir (x) during first part of ejection.

Thus: During x-descent, we have volume increase (positive dV) and pressure decrease (negative dP). This means that there is negative compliance C = dV / dP. Negative compliance is equivalent with suction, so the whole of the x-descent represents suction, generated by the AV-plane descent. This was also shown by wave intensity analysis (455). Wave intensity is the product of the change in velocity X the change in pressure, dv × dP. Wave intensity is also negative during the x-descent, but has been interpreted that suction was only present during S1, although compliance considerations is different.

The M-mode of the AV plane shows the atrial expansion:

M-modes through the mitral ring (septasl - left and lateral - right), showing that there is shortening of the ventricles and concomitant expansion of the atria throughout systole

Thus, we see than there is atrial expansion during the whole systole. However, looking at the pressure gradients in relation to flow:

Atrial pressure increases during last part of ejection. Looking at the atrial pressure curve alone, this corresponds to the deceleration of flow velocity after peak S (S2), but there is still volume expansion. In the wave intensity study by Smiseth (454), wave intensity was positive, indication positive pressure as the driving force. This would mean that the last part of systolic filling was due to push from the right ventricle.

Looking at the AV-plane motion, there is still atrial expansion, but at a declining rate. This is even more evident from the tissue Doppler curve, with an early peak, close to the peak flow:

Comparing PV flow with LVOT flow and tissue Doppler. Reducing clutter filter, the tissue signals can be see as described here. Here compared with the septal TVI curves (aligned by ECG - cyan lines). In LVOT, there is a near perfect match in timing of the TVI signal from clutter, and the TVI signal from the adjacent mitral ring. It also coincides fairly closely to peak flow velocity, indicating peak active contraction. Thus the tissue Doppler clearly shows the declining rate of annular motion and atrial expansion.

As discussed above, the second half of the ejection phase is actually myocardial relaxation, ventricular tension devolution starts at peak pressure. Flow out of the ventricle continues through inertia, and flow means ventricular volume decrease and shortening, but this is a more passive phase, and so will atrial expansion be, as this is due to left ventricular shortening (AV-plane motion.  However, the left ventricular shortening, expanding the atria is still present, but the continuing flow may simply be inertial as in the LVOT.

With pressure increase and simultaneous volume increase, in this phase dV/dP has to be positive, indicating the end of suction. The pressure increase is seen as deceleration of PV flow velocity, but the amount of "push" will depend on the ratio of dV and dP. It would still be conceivable that the driving force for AV-plane motion might be the ventricular emptying, but not to the extent of generating suction.

The diastolic D-wave is characterised by increasing flow velocity. In this phase, the ventricle relaxes, MV opens, and there is generated a suction into the left ventricle from the left atrium. This is the phase where the ventricle ant atrium are contiguous, (conduit phase), However, as seen above, the combined volume of the LV and LA do not change much. The atrium decreases in size, so there is a shift of the volume from atrium to ventricle, in addition to the diastolic flow. But in addition, the suction cvauses flow from the atrium into the ventricle, (E-wave) to be followed by replacement flow from the PV into the atrium (D-wave). The two waves can be seen to be contiguous:

During LV relaxation (early filling), there is contiguous flow into the atrium and ventricle, driven by ventricular suction.

As this represents flow, there has to be a volume increase of the whole LV-LA cavity, and this means that the D-wave is a function of suction.

Strain and strain rate in the atria

Atrial strain during ventricular systole

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.

Atrial strain. It is very evident that the atrial expansion during ventricular systole is simply a function of LV shortening, i.e.  the same AV-plane motion that describes the ejection.
The same shown schematically in colour. Shortening is yellow, stretch is cyan, and here the reciprocal nature of the strain in atria and ventricles is shown. In diastasis, there is no deformation, both are green.

Comparing the motion curves from the mitral ring and the AV-plane motion, it can be seen that the curves are very similar:

Top: Atrial strain curves. Below: mitral ring motion curves by tissue Doppler (left, and M-mode: right. The curves are similar, as they simply reflect the same motion.

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

The AV-plane motion is determined by the systolic function of the ventricles. It has been proposed that atrial strain is a measure of atrial "reservoir function". This means that the AV plane motion does mean different things when looked at from opposite sides, which is obviously rubbish. Looking at the systolic AV-plane motion from the ventricle, it is LV shortening, and from the atrial side it is "reservoir function", even if it is the same thing, i.e. the MAPSE. However, longitudinal strain is normalised for length. Thus: Longitudinal ventricular strain is MAPSE / LV length, while atrial strain is MAPSE / LA length, giving different values as shown below.

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

  However, this atrial expansion by the ventricular shortening, actually drives inflow to the atria:

Colur flow image showing both ejection from the ventricle, as well as systolic inflow to the atrium is concomitant with the systolic AV plane motion that shortens the LV and lengthens the LA. During IVR, there is intraventriccular flow towards the apex. During LV relaxation (early filling), there is contiguous flow into the atrium and ventricle, driven by ventricular suction.

This is even reflected in the venous flow curve:

Pulmonary venous flow from the sme person. The systolic component is due to expanmsion of the atrium, i.e. a function of the MAPSE, i.e. LV systolic function. The diastolic flow is the substitution of the blood flowing from the atria into the ventricles, and thus a function of the early diastolic suction of the ventricles, i.e. ventricular diastolic function. Thus the venous S/D ratio is a composite of systolic and diastolic function. The systolic component, however, will be influenced by ventriculoatrial regugitation.

Atrial "reservoir function", is thus due to the ventricular shortening, the numerator is simply the MAPSE. Using strain, this is normalised (denominator) by atrial length.

This means that atrial strain during ventricular function is a composite measure of LV shortening and LA size.

AS both are prognostic parameters, LA size being an 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). LV shortening is a sensitive prognostic parameter as well, (36, 190, 191, 192, 193), far more than EF.

Being a composite parameter, it may be more sentitive than single parameters, but not independent. Thus, atrial strain during ventricular systole does not add new information, as shown clinically (245 280).

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 the 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.

What do Strain and strain rate actually measure?

Strain and strain rate measure motion independent shortening

Strain and strain rate subtracts the effect of overall (translational) motion of the whole heart, as well as the motion due to tethering from other segments, as discussed in the basic concepts section.

Splashing humpback whale in Wilhelmina Bay, Antarctica.

Strain and strain rate do NOT measure load independent shortening

This is discussed in detail above.

It cannot be emphasized enough that  strain and strain rate measure only deformation. As we have seen from this section, strain and strain rate are as load dependent as other measures of longitudinal function.

Also we have seen that for global function, global longitudinal strain is closely related to annular displacement (MAPSE), and to stroke volume while peak systolic strain rate is closely related to peak annular systolic velocity, the S' and to contractility.

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

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

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.

Strain and strain rate measure relative regional contractility

It is when we measure regional function, the advantages of deformation indices appear.

Once we move from measuring global to regional shortening, shortening is much more closely related to function. This is due to especially two factors:

  1. Deformation measurement is restricted to the segment where it is measured, subtraction the motion due to the neighboring segments. Motion is global function, only deformation can be regional.
  2. But it is still influenced by the contractile action of the neighboring segments. This contraction of the neighboring segments is actually part of the load acting on the segment. In fact, the pulling action of the other segments are part of the load of each segment. This means firstly, that pressure alone do not describe the load on a segment well enough, and secondly that in segmental imaging, we actually have infomation about part of the load (the shortening of the other segments). Thus deformation imaging can be used to infer load/tension, in the form of inequalities in force development, as shown below. 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.

So, it is in fact the load sensitivity of strain and strain rate that makes them useful in regional function assessment.
Thus, strain rate images shows gradients of relative contractility in the ventricle, even if one does not measure absolute contractility.

And that is the main point in regional diagnosis.

Segment interaction

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

To appreciate the imaging of regional dysfunction, it is important to appreciate how segments deform if they have different contractility (strength) when they pull on each other.
Brown skua, Deception Island, (South Shetland Isles)
, Antarctica.

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

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

1: Segments interact within the framework of the AVplane.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


S' (cm/s pwTDI) S' (cm/s cTDI) Segmental SRs (s-1)
Patients: 41
Controls: 55*

Mean intra subject variation (max - min)



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

MAE(mm) S' (cm/s pwTDI) S' (cm/s cTDI) Segmental SRs (s-1) Mean SRs (s-1) per wall

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

This has recently been confirmed in a newer MR study (436).

Motion is global function, only deformation can be regional.

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

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

Strain rate (A, B) and strain (D, E), of an inferior infarct at day 1 (A, D) and Day 7 after successful acute PCI (B, E). There is akinesia in the basal segment (yellow curve) and hyperkinesia in the apex (cyan curve). The hyperkiesia can be explained by the load reduction due to the lack of force from the infarcted segment. 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. After 92

Another patient shows the same segmental interaction, and with no effect on the regional mitral ring motion:

Day 1:

Patient with a small apical infarct at admission, showing reduced strain rate of - 0.25
s-1, and strain of  -2% in the apical segment (yellow), with slightly high strain ate and strain (-1.3s-1 and -25%, repectively) in the basal segments (cyan). Mitral ring motion is 16 mm, both by tissue tracking (integrated velocity, and by annular M-mode.

Day 7:

Same patient after sucessful PCI of the LAD. There is moderate recovery of contractility in the apical segment (to peak strain rate - 0.5
s-1 and peak strain - 7%). There is decrease in basal strain to 20%. Peak strain rate do not seem to have decreased, but as strain rate is instantaneous, we see that strain rate in the base at the time of peak strain rate in the apex has decreased to - 1s-1. The reciprocal changes in strain in the two segments results in no change in the regional annulus motion which still is 16 mm by both methods.

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

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

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

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

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

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

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

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

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

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

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

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

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

Example from a real stress echo, as described in full below. The cyan curve is apicolateral segment, which is maximally ischemic, and shows conformance to the model above. The red curve is basal septal, which conforms bst to the non/ischemic segment, while the yellow curve is apicoseptal, and ischemic, although to a lesser degree. The white vertical line shows the AVC.

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

5. And finally, if all segments have reduced function, the shortening pattern will be more normal

Without any normal segments to interact with, there will in fact be less delay and no PSS, as shown by the following example where there is total ischemia, and hence, no normal segments and (almost) no PSS in the ischemic segments. Thus, the segmental pattern will be more normal, all segments have reduced contractility and delayed relaxation.

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

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

Regional circumferential and transmural strain

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

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

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

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


Changes in timing of different segments may occur without concurrent reduction in contractility. In especially left bundle branch block, there is different inset of contraction in different segments or walls, leading to some segments (or walls) contracting while others are  passive, both at the start and end of the contraction-relaxation cycle, and where both intraventricular pressure and elasticity contributes to specific patterns of shortening that are quite different from the normal patterns. In this case, it is differences in timing, that leads to different segments or walls having different tension.

Left bundle branch block

left bundle branch block may have  very different mechanical effects. This is due to the very large variability in how much, and which parts of the left bundle that are affected, and to what degree.

Basically, left bundle branch block means a reduced conduction velocity in the left bundle, below that of the right bundle, causing the septum activation direction to shift from left-right to right-left, but also meaning that parts of the left ventricle are activated later than the right, and later than normal, causing a widening of the QRS. The mechanical effects of the LBBB may be quite various, however:

Thus, the mechanical manifestations are various:

The bundle branch block may cause

Mechanics of asynchrony in left bundle branch block

The pattern of deformation in left bundle branch block is also due to interaction between walls, as they interact differently when the activation sequence interact.

The most evident pattern, originally called "septal beaking"(as it was origially described in M-mode), was described early (251). Later, it has been termed "septal flash" (252).

The "septal beaking" in M-mode , a short inward motion starting at the peak of QRS, and peaking at the same time as the onset of inward motion of the inferolateral wall. The contraction of the lateral wall is the force terminating the septal flash, so the time from onset of septal flash to onset of inferolateral wall thickening is the true mechanical delay between the walls. The same phenomenon is seen in B-mode of the same patient as "septal flash", which consists of a short inward and then outward motion of the septum, the outward motion start about simultaneously with inward motion of the lateral wall. The   "septal flash" is evident in both parasternal long axis and short axis. Images from patient with normal systolic function.

The isolated contraction of the septum probably will not generate pressure increase, but rather stretching of the lateral wall as seen by strain rate and apical rocking. During septal tension, the start of lateral wall contraction will generate pressure increase, which can be seen by the transverse outward motion after the inward peak.

Howeve, as post systolic shortening is in ischemia is just a part of the ischemic pattern, the septal flash is just a part of a complex interaction between the walls and the intracavitary pressure:septal flash, shortening during ejection, late systolic stretch and post systolic shortening.

The complex motion pattern in the septum must be explained by the interaction between the walls:

To understand the mechanisms of the asynchrony, the normal pumping physiology has to be considered. Normal electrical activation starts nearly simultaneously in mid septum and mid lateral wall (350, 351). The whole of the left ventricle is then activated within 80 - 100 (120) ms (the duration of a normal QRS). Electromechanical delay at the cellular level is 20 - 30 ms (234, 268).

 The normal mechanical sequence is illustrated above:
After mechanical activation, there is an intial shortening seen in the velocity traces as a positive spike of short duration - the pre ejection spike. This initial contraction gives a small pressure rise which closes the mitral valve (236) about 30 ms after initial contraction (268).

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

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

Delayed intraventricular conduction, on the other hand, will lead to delayed activation of the lateral wall.

Thus, the septum will contract for a time alone, with no balancing tension in the lateral wall, meaning that the septal contraction is free to stretch the initially passive lateral wall as seen by the rocking apex. This again means that the initial contraction of the septum actually results in shortening and thickening of the septum, and simultanelos stretch of the lateral wall, with no pressure increase (A).  Thus, there is septal deformation (shortening) earlier than in the normal ventricle.

At the time of initial lateral wall contraction, there will be tension of both walls, leading to pressure increase. Continuing tension in both walls will increase pressure (IVC). The increase in pressure will start to push the septum back (as seen on M-mode, but is not so evident in longitudinal shortening), thus the peak of the septal beak is the start of the lateral contraction (B).

Then there will be shortening of both walls, but with uneven tension, as the septum will start tension decrease while lateral wall tension is increasing. There has to be some remaining tension in the septum, or else, with a totally passive septum, lateral contraction would simply stretch the septum, resulting in only rocking with no real ejection work . However, ejection will lead to volume decrease, and thus shortening of the left ventricle, even with very little remainng tension, another example that tension do not always equal shortening. Once ejection is under way, there will be shortening of the septum even if it is largely passive (C).

When the septum relaxes, there is still tension in the lateral wall. This will lead to stretching of the septum (D), and actually an increase in shortening of the lateral wall, as shortening now is unopposed.

And finally, there will be relaxation of the lateral wall, when this is passive, there will be elastic tension in the septum, and it will recoil in a post systolic shortening  (E), which is another mechanism entirely from that seen in ischemia.

Septal activation alone. leading to septal shortening and thickening, with concomitant lateral stretch - the septal flash. No pressure increase.
Lateral wall activation, ending the septal flash which peaks) with remaining septal tension (or else there would be only rocking, no pumping). In this case there is pressure buildup, MVC, IVC and probably start ejection.
During most of the ejection there will be shortening, but part of this may be partly passive due to volume decrease, especially in the septum.
In the last end of the ejection there will be little or no remaining tension in the septum, which then will stretch, due to the remaining tension in the lateral wall (which have been activated later). Thus, there will be stretch of the septum and shortening of the lateral wall. As the septim now causes little load, the lateral shrtening will increase.
Finally, there is no tension in the lateral wall, which relaxes. In this phase there will be elastic tension in the septum due to the previous stretch, which will shorten in post systolic shortening, while the lateral wall stretches (due to both septal shortening, and also in the course of normal early filling).

All of this can be demonstrated by strain:

And by strain rate colour M-mode:

Using the same cycle as for normal ventricles above, the mechanical effects of dyssynchrony is evident in the same case as shown above.

Mechanical dyssynchrony seen by tissue velocities and strain rate and strain, all from the same heart cycle. The phases during systole are shown with the letters corresponding to the diagrams above. Valve closures and openings are marked on Doppler flow recordings, and transferred to the present loop. The apical rocking during phase A is evident from the apical velocity tracings. The action of the two walls can be inferred from the ring motion, and the interaction as one wall or the other is active while the other is passive, explains the complex pattern seen in the tissue Doppler above. This raises the question, which is the septal e' wave? The late systolic septal stretch, is the septal relaxation, but firstly, is mainly introduced by lateral contraction, and secondly, do not occur during filling. In fact, the relaxation of the lateral wall is seen to be absorbed by the septal PSS, before MVO, which is delayed. Thus the active LV seuction is abolished. The post systolic shortening, is closest to the early filling, but is actually an impediment to the filling itself. The strain rate from the same patient shows this more directly, illustrating the simultaneous stretching of one wall and shortening of the other.

Regional myocardial work

As we see, the PV loop represent the myocardial work, where myocardial tension is mostly related to pressure, while myocardial shortening is related to volume.

Going back to isolated muscle preparations, it was shown early that the tension-length loop was very similar to the pressure volume loop, seen in intact hearts, and also correlated very closely with oxygen consumption (360). Measuring segmental myocardial length in open heart animal experiments, it was also shown that as the shortening decreased in myocardial ischemia, the segmental end systolic pressure-length relation and the length-pressure loop decreased (361), and also that the segment length loop correlated with estimated segmental work (362). As segment length changes are equivalent with strain, the segmental strain-stress loop, even without strain imaging thus cold be shown to be equivalent with segmental myocrdial oxygen consumption in an elaborate experimental setup (363) in whole ventricles as well, and myocardial blood flow and oxygen consumption was much lower in early than late activated segments during asynchronous pacing..
Glower (414) showed that there was a very close parallel between the findings from pressure volume loops and pressure strain loops from segmental strain. Thus again, demonstrating a close relation between strain and stroke volume. This means, that the pressure-strain loops in a symmetric ventricle, may be a measure of regional myocardial work (472).

With strain imaging, regional strain pressure loops can be estimated, as described in (470).
  1. Using a standard LV pressure curve from the scanner software, based on previous experiments.
  2. Normalising the length of the heart cycle (temporal normalisation) by valve closure and openings
  3. Normalisation for SBP by non invasive cuff BP.

Construction of regional strain pressure loops. A standardised pressure curve, is calibrated in time by valve opening and closures, and in height by arm cuff BP. With regional strain curves, regional strain-pressure loops can be constructed, and the illustrations to the left shows how the loop is different in a normal segment and an ischemic segment. But the height of the PV loop is equal to the pressure, and the width is equal to the regional systolic strain. And as the different segment loops are derived from the same pressure curve, they have the same height, the only difference in the loops are actually the strain, and the different width of the loops equals the peak systolic strain.

It does not take diastole into consideration, as the normalised curve is based on normal diastolic pressures, so neither relaxation or compliance differences will be taken into account. As argued by the inventors, this does not matter when regions are compared, as the error will be the same for all regions (470). It's a pity they didn't take the argument one step further, actually the pressure curve itself, doesn't matter as it is the same for all regions. Thus, the differences will only be due to differences in the regional strain curves.

As the difference between segments are only the strain, while the pressure curve is the same, only the strain carries the information of the difference in regional function. Thus, this is actually the Emperor's new clothes. And the method will be just as sensitive to noise, as regional strain, of course.

However, as discussed above, in regional dyssynergy, there is work done by segments when they shorten, by stretching other segments during part of the heart cycle, without concomitant change in pressure. This is the result of the segment interaction being part of the segmental load. But this means that there is an assymmetric relation between segments.

In ischemia, it is easy to show that there may be reduced or even negative work in segments being stretched, for. instance by strain-pressure loops , which can be demonstrated pathological (364). However, in the healthy segments, the pressure-volume loops will be normal, although the work will be increased as shown by the increased shortening, as demonstrated above. But to see this, is dependent on robust cut off values. Thus, the "wasted work" by healthy segments may not be particularly evident.

In LBBB, the concept of wasted work is interesting, as this may be a part of the detrimental effect of LBBB on global LV function where the LV is weakened initially, and which is potentially recruitable by CRT (290). However, it is unclear what adding a global systolic pressure measure will add, compared to just looking at net strain in opposing walls (294):

Top left: strain pressure loops in a patient with LBBB. It's the same patient as above. Top right, the pressure curve. Bottom, strain traces.  The strain-pressure loops are generated by plotting the strain ratces against the pressure curve, but as the pressure curve is the same for both walls, the differences between the loops are only due to the differences between the strain curves.

Strain and strain rate DO NOT measure size independent shortening

It was a reasonable hypothesis that strain (and strain rate) was shortening normalised for heart size, and thus was size independent measures of LV shortening. However, it has always been known that global longitudinal strain was gender dependent (153). However, as body size, and presumably heart size is gender dependent as well, gender differences is just an effect of body size, while linear regression showed that only body size was an independent variable in the HUNT study (417). What was more interesting was that non-normalised MAPSE was not gender dependent.

Comparing global strain, normalised global strain (MAPSE / LV length) and global longitudinal strain, a weak correlation of MAPSE with BSA was noted, while normalised MAPSE and GLS was stronger, but negatively correlated with BSA (417).

Findings are summarised in the following picture:

As shown by the boxplot, no significant gender differences in MAPSE, but in normalised MAPSE and GLS (women highest). All three measures are age dependent. Lower panels shows weak positive correlation between MAPSE and BSA, stronger negative correlations between BSA and normalised MAPSE and GLS. Gender differences only due to differences in BSA, no independent contribution.

Why is GLS/ normalised MAPSE more BSA dependent than MAPSE?

This relation to body size is due to the fact that normalisation for length, corrects only for one dimension of the heart size. However, we have found that the ratio between LV length and LV diameter is the same for all body sizes (386), although it varies with length. The Global strain (MAPSE/L) is related to stroke volume, which is a function of MAPSE x LV external surface. Thus, a longer ventricle also has a larger cross sectional surface. This means that the cross sectional area increases by the square of the diameter, and so does the stroke veolume, even without any increase in MAPSE. On the other hand, as LV length and diameter are proportional, With unchanged MAPSE, the Normalised MAPSE and Global strain decreases proportional to the increase in length. Thus, normalising for length only, induces a systematic error, exaggeration of the heart size (or body size) effect:

Simplified and exaggerated example of the inverse relation between heart size and normalised MAPSE: We have previously found that the ratio between LV external diameter and length is constant across the spectrum of body sizes. In this example the LV2 (left) is twice the LV1 (right). This then means that as the length L2 is twice tle L1, the external diameter D2 has to be twice the D1. With an incompressible myocardium, the myocardial volume inside the outer contour has to be constant through the heart cycle. Then the SV is cross sectional external area x MAPSE as shown by the green volumes, thus the SV increases by the square of the LV diameter, without any increase in MAPSE. Given equal MAPSE, the area and SV in the largest ventricle thus has to be 4 times that of the smallest ventricle. Given the same MAPSE, thisthe  is normalised to a shorter length in the smallest ventricle, (I.e. the shortest length L1 in ventricle 1, and the longest length L2 in ventricle 2), and thus , on the other hand decreases by the inverse of the increase in length. Then the strain of the larges ventricle is half that of the smallest, for the same MAPSE, hence, the inverse relation between heart size (and body size) and global strain. The gender difference is solely a function of difference in body size.

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