Det medisinske fakultet


How to display cardiac motion and deformation

by 
Asbjørn Støylen, Professor, Dr. med.
Department of Circulation and Medical Imaging,
Faculty of Medicine,
NTNU Norwegian University of Science and Technology


Contact address: asbjorn.stoylen@ntnu.no

The page is part of the website Strain rate imaging

This section updated:      February 2017


This section:

The main aim of this section is to explain how the different displays (curves, colur M-mode and 3D displays) are generated, what they mean and how they relate.  As functional imaging is display, the different methods for display are given here, in order to being able to interpret the different displays.All methods can give the information as numerical traces, parametric (colour) images (in 2D or Colour M-mode). 3-/4D reconstruction has some limitations using segmental strain, however. Basically, however, irrespectively of method, the fundamental indices of motion (velocity and displacement) and of deformation (strain rate and strain) are the same. Also, the display of the indices can be used irrespectively of the method for acquiring them. However, some of the methods set limits for how the display can be made, and this is explained here.


References



Basic displays

Again, it's important to realise that strain by itself is  myocardial deformation. This means that all normal strains (longitudinal shortening, wall thickening and even circumferential strain are visible in B-mode images, and even available for direct measurement in ordinary B-mode.

B-mode

Longitudinal shortening of the left ventricle. The absolute shortening is the MAPSE, while the relative shortening is the normalised MAPSE = MAPSE / L0. Wall thickening and circumferential shortening. Both are measurable from the short axis loops.
Even wall motion is a semi quantitative measure of transmural strain, as discussed here.

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

M-mode

For direct measurements, however, M-mode is more feasible.

Lookng at an M-mode of the ventriculoar base (the mitral annulus), the systolic motion of the base can be displayed as a motion curve, and the peak systolic displacement of the base (the MAPSE - Mitral Annulus Plane Systolic Excursion) can be measured. Lomngitudinal strain is then MAPSE/L0 as shown above Cross sevtional M-mode. In ventricles without regional dysfunction, both transmural strain = wall thickening = (Ws - Wd)/Wd, and circumferential strain = ( xLVDs - xLVDd)/xLVDd = (LVDs - LVDd)/LVDd = -FS



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

Regional function

Global measures have proven useful, but the main point of strain rate imaging is regional function.

It is also evident, that as the apex is stationary, there is no displacement, and the whole of the ventricle is deformed, as there is differential motion:
AS we seen the systole results in a longitudinal shortening. This means that the basal parts of the heart has motion towards the apex, while the apex is stationary (almost). Thus, the whole ventricle shortens - deforms. The deformation is evident when looking at the M-mode in the septum, the tissue  lines (which in reality is M-mode of speckle lines) moves more, the more basal they are, and thus the convergent lines shows the differential motion (deformation).
This is speckle tracking without advanced software.


Tissue velocity

It's important to realise that both motion and deformation parameters can be derived in a variety of ways. M-mode and pulsed tissue Doppler records the motion (displacement and velocity, respectively) at one point at a time. Tissue Doppler gives the motion velocity of the tissue.
Pulsed tissue Doppler of the mitral ring.  These are the velocity traces of the longitudinal motion. The peak systolic velocity of the annular plane is a measure of (but not equal to) strain rate. As motion decreases from apex to base, velocities have to as well. Thus there are differential longitudinal velocities, decreasing from maximal at the base to zero (almost) at the apex. The differential velocity also described as the velocity gradient, is equivalent to the local rate of deformation; the strain rate.




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

Numerical traces



Displacement

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



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


Tissue velocity

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

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




Relations between systolic motion and deformation measurements

Strain rate equals the velocity gradient along the wall, and can be calculated from velocities:



Comparison between velocity and strain rate. left: Velocities from two points; v(x) and v(x+x), separated by the distance x. The strain rate curve is then the instantaneous difference between the two curves, divided by the distance:


This is the spatial derivtion of velocities, velocity difference per length unit.

Thus, there is a relation between motion and deformation parameters by derivation and integration as explained elsewhere: Below is a more graphical illustration of the same.


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

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



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

Strain rate assessed by offset between velocity curves


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



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

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






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


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

Here is apical: initial dyskinesia, reduced peak strain rate, but also post systolic shortening, midwall hypokinesia and basal normal strain rate.
Thus, no offset between velocity curves means zero strain rate (no deformation). Another example can be seen below.


Normal vs. large apical infarct, see the lack of distance between the two apical velocity curves (red and green).

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


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

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



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

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

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

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

Wall strain rate

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  .

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


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, 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 as argued above:


Left strain rate curve with ROI expanded as much as possible, to get a near full wall curve, showing how this closely resembles an inverted tissue Doppler curve (here  shown a spectral curve, for variation).


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

Tethering

Tethering giving rise to motion of passive segments, can be assessed by the lack of deformation (strain and strain rate being zero). However, purely passive motion will also show up as passive segments following the exact same valocity and motion curve as the active segments, without any distance between. This is illustrated below.


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



     

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

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


Apex to base differences


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

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


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

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

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

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



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

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





Parametric imaging

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

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

2D parametric images.


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



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

Curved anatomical M-mode.

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


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

This has the advantage of displaying the whole sequence in a still picture, giving a temporal resolution like the sampling frequency. Curved M-mode .
Curved M-mode showing velocities.  In this case, the curve is drawn from the apex to the base, showing one wall. The shifts between positive (red) and negative (blue) velocities are clearly demarcated.
Curved M-mode showing strain rate ( the curve is the same as in the image to the left, but the mode is shifted to display strain rate).  The pattern is different, due to the better spatial resolution when deformation is imaged, as discussed in details below.



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


Strain rate CAMM has better spatial resolution than segmental curves.

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







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


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



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




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






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

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

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

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

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



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

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




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




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






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

Bull's eye plot

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

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




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

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



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

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

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






Three dimensional display

However, drawing a curved M-mode, one part of the information is discarded, both in the CAMM and the bull's eye. The curved M-mode is a line that curves through the two dimensional plane, containing information about the spatial relations between the point on the line in the plane, or said in another way, the curvature of the line. Using that information, it is possible to make three dimansional surface:
The curved M-mode is a line (one dimensional) that curves through the two dimensional plane (left). The curvature gives information about the spatial relations between the pints on the line.
 Keeping the curvature information enables the mapping of the points of the line in two dimensions (middle).
 Using three standard planes, it is possible to reconstruct a grid with the true curvature of the surface, in this case a curved plane, that curves through three dimensions (left).

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



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

Four dimensional data sets

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

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

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

If the three planes are combined, like in the 3D reconstruction above, we arrive at a four dimensional dataset, where there are data on a curved surface, in reality a 3-dimensional figure, and a time sequence, the dataset is in fact four dimensional. As the reconstructed dataset is really 4-dimensional (22), three spatial dimensions and time as well (through one heart cycle), the image can be scrolled in time and space as shown below. But again, as in 2D, in order to see details, the scrolling has to be stopped for visual inspection.

Strain rate 4D mapping. The problem with the moving loop is the same as in 2D display. During ejection there is a short period with homogenous colour, when all the ventricle shortens simultaneously. But during diastole, there is a continuously shifting array of colours, as different parts of the ventricle elongates at different times.  the continuously shifting colours are not easy to interpret. In addition it won't show all of the surface simultaneously. Stopping the scrolling will allow closer inspection, but scrolling in space will show only one instance in time.  (In this case it's mid systole). (Image courtesy of E. Sagberg.) Strain rate 3D mapping in space. Stopping the frame in one point in systole shows a fairly even distribution of colour (yellow - shortening), meaning an image with normal systolic function and fairly free from artefacts. In order to see all of the surface, however, the 3D. image has to be rotated in space. . The image can also be scrolled in time, showing that it contains a full reconstructed 4D dataset and displaying the full time course of the data. Stopping the scrolling will allow closer inspection. 

The four dimensional dataset cannot be intelligibly displayed, but three dimensional information must be extracted at a time, either by looking at
  1. Looking at only one side of the 3D plot at a time, and only in one instance in time
  2. A bull's eye plot, which shows the whole surface, but only in one instance of time
  3. A set of curved M-modes showing the walls separated, and not as a spatial figure, but through the whole cycle
  4. Extracted curves from one point, but through the whole cycle.

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

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



Inferior infarct in strain rate 3D mapping in time.There is an area of akinesia in the inferior wall, although this is not easily distinguished in the loop.(Image courtesy of E. Sagberg.)  Inferior infarct in strain rate 3D mapping in space. Stopping the loop in systole reveals the area of akinesia and hypokinesia,(Image courtesy of E. Sagberg.) while the stopping in diastole shows the post systolic shortening in the same area.(Image courtesy of E. Sagberg.)




Strain rate 3D mapping of apical infarct. (Image courtesy of E. Sagberg.) Systolic frame showing apical akinesia to hypokinesia in the apex(Image courtesy of E. Sagberg.) Diastolic frame showing an area of post systolic shortening.(Image courtesy of E. Sagberg.)





3D reconstruction into bull's eye and 3D surface is not only for display, it enables another quantitative measurement:

Due to the correct area representation of the LV surface (22), combined with the representation of the strain rate values on that surface, the area with values below a cut off limit can be delineated, and the area can be measured as a percentage of the total LV area as dexcribed in detail in the measurements section.

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




Apical

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





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