Strain rate imaging.

An object undergoing strain. In this case there is a 25% elongation from the original length (L₀), thus, according to the Lagrangian formula there is positive strain of 25% or 0.25. This strain can, however happen at different rates, as shown in fig. 4b.

Strain in three dimensions. The cylinder shows strain, which can be described as Lagrangian strain from L₀ to L. However, the figure also shows simultaneous thickening or expansion in the two transverse directions. If the cylinder is incompressible, the sum of the longitudinal and the two transverse strains will be zero.  All three-dimensional objects show strain in three dimensions. In the heart, the usual directions are longitudinal, transmural and circumferential as shown to the left. In systole, there is longitudinal shortening, transmural thickening and circumferential shortening. (This is an orthogonal coordinate system, but the directions of the axes are tangential to the myocardium, and thus changes from point to point.) As the heart muscle is generally considered incompressible, transmural thickening has to be balanced by longitudinal plus circumferential shortening.

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

The basic direction in three dimensions are given by the coordinate system given. In a Cartesian coordinate system, the directions are x, y, z, somewhat randomly chosen. In relation to the heart, the directions are longitudinal, transmural and circumferential. In relation to the ultrasound beams, the directions are axial (along the beam), lateral (across the beam in the imaging plane) and elevation (out of the imaging plane), the coordinate systems are described here. Thus the terms "radial" should be avoided, as it can mean both axial in  relation to the ultrasound beam and transmural in relation to the heart, "lateral" can mean both transverse and transmural (although those may be the same in the apical views.)

Incompressibility.

If  the object is incompressible, the volume (not mass!) remains constant during deformation.This is the true definition of incompressibility. Thus, compression in one dimension has to be balanced by expansion in others as shown in fig. 8, i.e. strain in the three dimensions in a coordinate system cancel out, in way described in more detail here. This means that strain in three dimensions are interrelated, so strain in one direction is representative of regional deformation in more than one direction, as has been shown for heart muscle where wall thickening and wall shortening gives the same information about regional function (7).

Motion vs. deformation - velocity and displacement vs. strain and strain rate.

As the apical parts of the ventricle pulls on the basal, the displacement and velocity increases from apex to base, as shown in figs 6, 7 and 9. This means that some of the motion in the base is an effect of the apical contraction - tethering. In fact, completely passive segments can show motion due to tethering, but without deformation, as illustrated in fig3a. (4, 6, 7). This means that the velocity (and displacement) are position dependent, if not normalised while strain rate (and strain) are much more position independent, if the velocity gradient is evenly distributed.

The difference between motion and deformation as well as strain rate and velocity in the heart, is shown below.

Velocity, displacement, strain rate and strain from three different points, apex, midwall and base, in the septum of a normal person. Left, velocity curves. By temporal integration one obtains displacement. By spatial derivation of velocity, one obtains strain rate, and by temporal integration of strain rate one obtains strain. These curves all represent the same data set. It is evident that motion (velocity and deformation) increases from apex to base, showing a gradient, while deformation (strain rate and strain) is more constant, in fact a direct measure of the motion gradient. 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 , as shown previously and illustrated below (16).

Basically, longitudinal strain and strain rate are methods to measure regional deformation, the basic algorithm subtracts the motion due to contraction of neighbouring segments (tethering effects). In principle, velocity and displacement measures the effect of contraction of the whole ventricle apical to the point of measurement. Thus, annular plane displacement and velocity measures the global function of the left ventricle (13). This has been demonstrated in several studies, both for systolic annular displacement (30 - 36) and velocity (37 - 40).

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

In principle, one might measure annular motion in one point, and get information about the function of a sector of the myocardium. However, this is theoretically difficult, as different motion of various points of the mitral ring would mean that the ring would tilt, however, the ring is not an isolated structure, but an integral part of the annular plane, and tilting of the mitral part would mean deformation of the whole annular plane. In addition, global ventricular function by annular descent or velocity measured in four points of the mitral ring reduces variability by 25%. Limiting measurements to one point, will increase random variability, and drown out systematic variation ion regional dysfunction. Finally regional dyskinesia is seldom limited to one sector, and may be compensated by hyperkinesia in other areas. We demonstrated in a clinical study (40) that while annular measurements of motion or velocity could not demonstrate regional differences, segmental analysis of peak strain rate could. But taking average peak strain rate of a sector corresponding to a point on the mitral annulus, this "sector" index again failed to demonstrate regional differences.

Strain rate imaging is not the only method for regional analysis. Segmental velocities is another (25), the advantage is that the measurements are "cleaner", not being so processed, the disadvantage is that the values are level dependent. There are indications that segmental strain rate is the more sensitive method (41).

On the other hand, peak systolic strain rate and strain is an index of regional systolic function, but mean peak systolic strain rate measured in all segments of the left ventricle and averaged, is another global index (6, 7, 40). This index ought to be equivalent to annular plane velocity and displacement. In myocardial disease, however, where there is heterogeneous reduction in function,  segmental analysis may theoretically have higher sensitivity for small changes.

What does Strain and strain rate actually measure?

It is important to realise that  strain and strain rate measure only deformation. This is true also of 2D and M-mode measurements, fractional shortening, longitudinal shortening, myocardial velocities 2D volumes and EF are all related to myocardial motion. None are measurements of contractility, which involves myocardial tension (stress). Contractility is the stress / strain relation. One example, myocyte contraction is finished during the first half of ejection period, the rest of the emptying is inertial effects, but still, so long as volume is ejected, LV volume, LV length and diameter decreases, stroke volume, EF and absolute strain increases, and strain rate remains negative during the rest of EP while the myocytes relax. However, while systolic strain is more closely related to stroke volume, peak systolic strain rate, being an early systolic event, is more closely related to contractility (78).

Flow is pressure driven and the flow velocity measurements are the real indices of pressure differences.

The definition was extended by Uematsu et al (15) to include the transmural velocity gradient across the parts of the wall where the scan line is not perpendicular to the wall, by the cosine correction of the velocities. The velocity gradient measured in this way, was transmural (radial). As transmural strain rate is the rate of change in wall thickness, the strain rate is the

Pulsed Doppler recordings of longitudinal velocities from a normal left ventricle. Increasing velocities (i.e. velocity gradient) from the apex to the base is evident, as will be expected .

Distribution of strain rate / Strain

If systolic displacement and velocity decreases evenly from base to apex, the systolic deformation (strain) and velocity gradient (strain rate) is evenly distributed throughout the myocardium. Some of the earliest studies seem to indicate this (10, 19), although later studies seem to find differences (74). However, with the high possibility of  systematic errors (see problems and pitfalls), this question must be considered unresolved, some of the findings of inequalities are obviously artefacts (46, 47). Theoretical volume considerations may indicate a relatively even distribution, while considerations of fibre architecture may not.

This is a different algorithm from the velocity gradient, but it can be proved (here) that the two formulas result in the same ratio. The distance  is called the offset distance or strain length.

This is explained in more detail here. The velocity gradient and SR are equal to the Eulerian strain rate, which normalises the velocity difference to the instantaneous length, while it is customary to use the Lagrangian strain, which normalises the change of length to the initial length,which is explained in more detail here.

The difference in shape between strain rate and velocity curves

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

Above left velocity curves. It can be seen that the two velocity curves have an early maximum, showing that the myocardial acceleration occurs early, and is an early event. Above right, the strain rate curve from the segment between the two ROI's in the left picture. It can be seen that peak strain rate is a much later event. This is due to the fact that the velocity difference is normalised for the instantaneous distance (although indirectly, see below), i.e.  Eulerian strain rate.  This can be demonstrated by the simulation in the lower row. Left: two systolic velocity curves with velocities somewhat arbitrarily chosen, but within normal range, and with a fairly normal shape.  The values on the cyan curve is two thirds of the red one, and both have peak velocity at 0.05 sec.  Left: strain rate curves calculated from the velocity curves on the right side.  Assuming an initial distance between the points of the two velocity curves of 2.5 cm, again a realistic distance for the velocity difference.  Lagrangian strain (yellow) is derived by dividing the velocity difference at each time point by the initial distance.  This results in a simple inversion of the velocity difference, in a different scale, and with minimum value (maximum absolute) at 0.05 sec. Eulerian strain (green curve) is obtained by dividing with a strain length that decreases by the time interval times the velocity difference. In this case the differences between the curves is evident, and the minimum value (maximum absolute) is reached at 0.25 seconds.

This is due to the difference between Lagrangian and Eulerian strain rate, which is explained here. As we use Lagrangian strain, this is displacement normalised for end diastolic length. However, it has become customary to use Eulerian strain, which is a normalization for instantaneous length. This means that as velocities increase, the length decreases,  (or, in reality, the absolute velocity difference increases relatively), thus blunting the absolute increase in the velocity difference (i.e. the decrease in the negative difference) in the first incremental phase, while the phase where velocities are relatively constant, strain rate will continue to increase as the strain length decreases. Thus, peak strain rate is a later event than peak velocity, which means that it may be more load dependent than peak systolic velocity. In addition to giving a higher and later value for peak strain, it will have consequences in resulting in a higher peak strain value as shown below.

Strain rate by linear regression

Instead of measuring just the velocities at the ends of the offset distance;  or  respectively, the velocity gradient / strain rate can be calculated as the slope of the regression line of all velocities along the offset distance as described originally (14). With perfect data, the values will be identical, both formulas defining the slope. With imperfect data, this method will tend to make the method less sensitive to errors in velocity measurements, as the value is an average of more measurements.

Fig. 16a. In short axis view,  the septum and inferior wall can be imagined in cross section. Here displacement and velocity can be measured across the wall, meaning that deformation imaging with tissue Doppler can be done in only those two areas in real time.

Fig. 16b.  Wall thickening . The relatively constant outer contour and inward moving endocardium, shows clearly a displacement gradient (strain) and hence, a velocity gradient across the wall.

In the transmural direction, strain and strain rate can be measured where the ultrasound beam crosses the wall at an angle. This means in the septum and inferior wall, just as the M-mode. As the outer contour of the left ventricle is relatively stationary, while the endocardium moves inwardly, there is a gradient of displacement and velocity across the wall.

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

The velocity gradient can be measured by the strain rate imaging method, which is quicker than tracing the endo- and epicardial borders. Measuring the transmural systolic strain by integrating strain rate, however, is a roundabout way of arriving at the relative wall thickening, which can be measured with equal temporal resolution and much higher reliability with M-mode. In addition, anatomical M-mode can imagine wall thickening in other directions as well, although with only 2D grey scale frame rate.

 

Segmental strain and strain rate.

Segmental strain and strain rate is takjen to mean the deformatioon measured over a complete segment, giving the average value for the segment, as shown in figs. 19 and 20. Also the application 2D strain does in practice give segmental values, althoug in some versions local values can be extracted. Segmental strain has several advantages: As measuremnts are fairly noisy, the average of a whole segment will tend to be more robust. The segments are the basic unit for evaluating regional wall mnotion score (WMS) in the recommendations of the ASE/EAE (146), and so far the clinical usefullness of a higher resolution has not been demonstrated.

Tissue Doppler measures the velocity gradient along the ulotrasound beam. Increasing the strain length will reduce noise, but the strain length will follow the direction of the ultrasound beam, and this will give problems where the alignment is not perfect, as discussed in the pitfalls chpter, under the discussion on lateral resolution. However, the size and shape of the ROI, averaging gradients from more than one beam may be made to follow the segment contour fairly well.

Instead of calculating strain rate along one ultrasound beam as shown in figs 10 a and b, it has been proposed (44) to calculate strain rate from the velocity differences at the segmental interfaces and segment length along the wall. (Any points will do actually), as shown in fig. 10c. This will make the method less angle sensitive, as well as more similar to the other methods as the measurements are related to kernels at the segmental borders. However, this may be a more noisy solution, compared to averaging measuremkents over a whole segment.

Strain rate by speckle tracking in grey scale images.

The basic principle of speckle tracking is based on the interference of the reflected ultrasound giving rise to an irregular - random - speckled pattern. The random distribution of the speckles ensures that each region of the myocardium has an unique pattern, a fingerprint (fig. 18a).  The speckles follow the motion of the myocardium so when the myocardium moves from one frame to the next, the position of this fingerprint will shift slightly, remaining fairly constant (fig 18b). Thus, if a region (kernel) is defined in one frame, a search algorithm will be able to recognise the lie sized and -shaped area with the most similar speckle pattern in the next frame, within a defined search area (fig. 18c), and hence, to find the new position of the kernel (26). This has been shown to be feasible in flow (94) and strain rate imaging (95).

The basics of speckle formation and speckle tracking is given in more details here.

Fig 18 a. Typical speckle pattern in the myocardium. The two enlarged areas show completely different speckle patterns, which is due to the randomness of the interference. This creates an unique pattern for any selected region that can identify this region and hence, the displacement of the region in the next  frame.	b. When the speckle pattern is followed by an M-mode in the wall, the alternating bright and dark points are seen as alternating bright and dark lines. The lines remaining to a large degree unbroken, shows the pattern to be relatively stable, the speckles moving along with the true myocardial motion, and thus myocardial motion can be tracked by the speckles.	Fig c. Speckle tracking. Defining a kernel in the myocardium will define a speckle pattern within (red). Within a defined search area ( blue), the new position of the kernel in the next frame (green) can be recognised by finding the same speckle pattern in a new position. The movement of the kernel  (thick blue arrow) can then be measured.

The application also uses automatic segmentation, reducing the variability compared to manual placement of the ROI.

 The advantage of this method is that it tracks in two dimensions, along the direction of the wall, not along the ultrasound beam, and thus is angle independent. This means true longitudinal strain. The disadvantage is that if the algorithm does not track one kernel correctly, the strain values will be wrong for the segments on both sides of the kernel. This is evident in areas of drop outs or reverberations as shown here. This can be overcome by increasing the number of kernels, or manually avoiding placing a kernel in an area of drop out or reverberation.


It is important to be aware that strain measured by speckle tracking  is Lagrangian strain directly. Derivation yields Lagrangian strain rate, while tissue Doppler yields Eulerian strain rate. Commercially, it has been customary to display the Eulerian or natural strain rate (velocity gradient) derived directly from tissue velocity data, but to apply a correction when integrating to strain rate and display Lagrangian strain. For Strain rate from speckle tracking, a reverse correction has to be applied, either calculating velocity from displacement and then strain rate from velocity, or calculate strain rate from strain and then apply a conversion. If not, the values are not comparable. Even so, the values are not absolutely identical, speckle tracking measuring along the wall, tissue Doppler along the ultrasound beam, and that may affect the relation to previously published normal values. The method described above, is robust, due to the large kernel size.

This method is also relatively angle independent, giving true longitudinal strain. In addition, it gives very much improved lateral resolution, using the line density of grey scale rather than tissue Doppler imaging. Finally, the lateral resolution is better, as the grey scale images has much higher number of scan lines (typically 64) as compared to tissue Doppler (typically 16).

However, as the lateral resolution is far less than tha axial, the two directions are not equal. This means that tracking in the longitudinal direction is better than tha lateral, so the method is angle depentden to some degree. And increasing the frame rate (for instance to compensate for high heart rate) reduces the lateral resolution even more, reducing the angle independency of the speckle tracking method even further. The clinical value of the angle independency remains to be demonstrated.

The method is dependent on frame rate. Too low frame rate will result in too great changes from frame to frame, resulting in poor tracking. This may also limit the use in high heart rates, as the motion and thus frame to frame change increases relative to the frame rate. On the other hand, too high frame rate is obtained by reducing lateral resolution, and thus resulting in poorer tracking at least in the transverse direction. At present, the optimal frame rate for speckle tracking seems to be 50-70 FPS. Thus, speckle tracking has limitations in sampling rate. Shorter events like the isovolumic phases may disappear all together, and peak values may be reduced due to under sampling, especially isovolumic and diastolic velocities and strain rate. This is most important for measuring peak values in diastole and isovolumic phases, not so much in systolic strain rate, and systolic strain has least frame rate sensitivity of all.

2D Strain by speckle tracking.

With a greater number of kernels, distributed both along and across the wall, each can be tracked individually, and displacement and velocity can be measured in two dimensions, both longitudinally and transversally for each (73). From this, differential motion - i.e. deformation - can in principle be measured, both in the longitudinal and transverse direction. The smaller the kernel, the less certain will the tracking be, but this can be compensated by selection of kernels on the basis of a stable pattern from one frame to next.  One method of insuring stable tracking is to discard kernels that are not present in a sufficient number of frames. In the same way, kernels that does not move can be discarded, reducing the influence of reverberations.However, the dependence on recognising stable kernels from one frame to next, makes the method even more frame rate sensitive.

Averaging a large number of kernels may make tracking more robust, although this reduces the number of useful speckles in each kernel. This can be done in various ways and combinations. With more than one layer of kernels across the wall, the longitudinal measurements can be averaged from all layers, giving a transmural average. Longitudinal averaging can be done along one segment, giving the segmental average. This can also be done in a more sophisticated way, by spatial interpolation along the wall. This will result in a gradual effect of spatial smoothing, although the extent of the smoothing is less easily discerned. It will reduce the effect of artefacts such as drop outs and reverberations. But it may also mask abrupt changes in deformation pattern, e.g. at infarct borders. In addition, this kind of interpolation will reduce temporal resolution as well, in the case of regional timing differences.

The 2D strain method uses stable speckles, and measures the displacement

On top of this, smoothing in post processing may be applied in the same way as for tissue Doppler based methods.

Fig. 21 a. 2-dimensional strain by speckle tracking.  Each red point represents a kernel for speckle tracking. Velocity and displacement decreases from base to apex, and the differential motion along the segment gives longitudinal strain and strain rate. As the true direction of the motion is tracked in this instance, the transverse component can also be tracked, and the differential motion from epi- to endocardium can also be tracked., giving transmural strain and strain rate.

b. 2D strain in practice. The midwall line is used for the longitudinal strain, being an average of all points in the wall. The ROI follows the wall, the limits can be seen diverging in systole, converging i n diastole, giving the transmural strain and strain rate at the same time. The colours show longitudinal strain rate, green is shortening and red is lengthening.

c.  In order to make the speckle tracking more robust, values are averaged over a whole segment.

This method can the calculate segmental longitudinal velocity and displacement:

Fig. 22.  Longitudinal displacement and velocity, derived from speckle tracking. Each curve represents the average of a segment. The curves are very smooth, due to a specific smoothing by curve fitting from segment to segment as well as temporal averaging.

We did an initial evaluation of an earlier version of this application in February 2004, comparing the longitudinal motion and deformation measurements by this application with those obtained by tissue Doppler, in separate images. The study consisted of 20 patients with a wide range of function.

Fig. 23. Strain rate and strain, comparison of 2D strain and Tissue Doppler. There is a considerable spread between methods, but most probable due to variability of both methods. There 2D strain gives lower values than DTI, and this tendency increases with increasing strain rate/strain. The term "CEB" meaning "computerized eye balling" was an early term to describe the application.

When measurements was sorted in quartiles, Concordance was only between 27 and 34%. Feasibility was the same with 2D strain and TVI. Further investigation was not undertaken at that time, as the application was modified in later versions.

Other authors have found a much better correspondence between TDI and 2D strain (73), with correlations of 0.94 and 0.96 for strain rate and strain, respectively. However, as seen by the curves in the figure below, both data sets are analysed by the 2Dstrain software, and thus subject to the same high degree of smoothing, so the results do not reflect independent analysis.


Another study by Cho et al (148) finds only correlations of longitudinal strain by 2DS and TVI with MR tagging of 0.51 and 0.40, respectively. This may reflect the real precision of both methods (and of MR tagging as well?) but then the correlation between the methods cannot be higher.


Transverse displacement an velocity can also be derived, but as this will be the segmental average, this value has little meaning, the velocity and displacement increased from outer to inner contour (c fr. fig. 16b). It is the displacement and velocity gradient that is of interest, i.e. transverse strain and strain rate. However, this can also be calculated by this method:

	Longitudinal	Transverse
Strain rate
Strain

Fig 23. Longitudinal and transverse strain derived from speckle tracking.  It can be seen that in this case the differential tracking in the transverse direction is poor in the basal segments, thus underestimating transverse thickening in this healthy subject.

Whether this adds clinical information, remains to be seen, as longitudinal and transverse strain are interrelated.


As speckle tracking is angle independent, it may be applied to the short axis as well:

Fig. 24a.  2D strain applied to short axis image. Again this can be seen to track in two dimensions, the thickness following the wall thickening, and the mid line in the ROI Showing midwall circumferential shortening.	b. Transmural strain. In this image the application only measures between 10 and 15% transmural strain, while the true values in a normal person as this may be as high as 40 - 50%.	c. Midwall circumferential shortening.  In this image about 15%, which may be closer to the actual values.

The transmural strain measurement needs to be validated, while the physiological meaning of midwall circumferential shortening may be discussed in terms of the circumferential strain tensor.  However, subject to validation, midwall circumferential shortening may be established as a separate measurement with its own reference values. Whether this adds information remains to be shown, as the different strain components are interrelated.

The application will also give transmural velocity and displacement as an average of the whole segment. These values have no physiological meaning, as there is a transmural gradient of both displacement and velocity as described before. However, in a clinical setting, the measurements may separate normal from reduced wall function, and thus have a meaning in a clinical setting. It is rather doubtful, however, if this adds anything to transmural strain and strain rate, and the use of these values is physiologically unsound.

The lines looking smoother, is a function of the averaging function used in the algorithm, the application will do the same to tissue Doppler data.
Fig. 25. Strain rate curves from speckle tracking and tissue Doppler from the same cine - loop.  The same smoothing is applied to both, showing that smoothing of the curves is not the result of the robustness of the algorithm, but of specific temporal and spatial smoothing applied by the application. The curves differ somewhat (but not too much), as strain rate is calculated with different angle and lateral resolution.

Smoothing in 2D strain

There is a liberal amount of temporal smoothing. In addition there is built in a spline or polynomial smoothing along the whole region of interest (ROI). The AV plane is the heaviest feature that is tracked, and contributes the most to the motion. Then there is a curve fitting along the mid ROI curve, resulting in a smoother transition from segment to segment, distributing the deformation along the ROI. This diminishes the effect of poor tracking of single kernels, but may result in diminishing the differences between normal an hypokinetic segments, and reduced sensitivity for hypokinesia as seen below.



In the case of asynchrony, this may be reduced as well by the same function. Thus the diagnostic accuracy of this application is so far not very well documented. For global strain, however, this is of no importance, and the idea of measuring shortening normalised for LV length appears to be sound (150).

The same limitations apply to this application as to speckle tracking in general, concerning frame rate, heart rate and under sampling. The amount of smoothing may increase the undersampling even more.

Both methods have been compared for longitudinal strain, and compared to tissue Doppler (126). Both seem to agree fairly well. In addition variability is lower by both methods than by tissue Doppler. However, as both methods use automatic segmentation, this may be the main cause for better repeatability, not speckle tracking vs. tissue Doppler per se. Feasibility of both methods is reported to be between 70 and 80% of segments.

Segmental strain by combined use of tissue Doppler and Speckle tracking.

Modern ultrasound equipment has the capability of acquiring second harmonic grey scale images with an acceptable frame rate of 40 - 50 FPS and good lateral resolution, simultaneously with tissue Doppler data. This opens the possibility of tracking along the ultrasound beam by tissue Doppler,  while tracking transverse to the ultrasound beam by speckle tracking (124) in the grey scale data.


This simplifies the search algorithm, limiting the search area to a sector extending in the radial direction and thus reducing the time for the speckle search.  In addition, if the method is used to compute longitudinal velocities or strain rate, the longitudinal tracking is done with the high sampling frequency of tissue Doppler.  Finally, it utilises the full dataset inherent in the combined image. In fact, it seems rather absurd that having access to high quality grey scale tissue data as well as high frame rate tissue Doppler data in the same image, the quality of measurements will improve by discarding one of the data sets.

Thus it seems probable that in the future, some combined approach will be the state of the art. The combined method can be used in different ways to analyse strain rate imaging (127).

1. Segmental strain and strain rate can be calculated directly from segment length, in the same way as by speckle tracking alone as described above.
   
2. Velocity, displacement, strain rate and strain can be calculated by tissue Doppler, placing an ROI in the middle of the segment, and letting the ROI follow the segment as it moves longitudinally and transversally by the combined tracking method, ensuring that the ROI stays in the same position relative to the myocardium, instead of in space as in the original application and in standard tissue Doppler, we have called it dynamic TVI.
3. The automated segmentation can be used to place the ROI in mid segment in the first frame, without tracking. This results in a stationary  ROI as in traditional tissue Doppler, but the reproducibility will improve compared to manual ROI placement.
   

Feasibility was reported to be between 75 and 80% of segments, compared to 92% with manual analysis. There may, however be reasons why the latter number may be too high.

This method  has already been shown clinically useful in stress echo (128), giving a sensitivity of peak systolic strain rate for ischemia of 84% and an AUC of 0.9, compared to coronary angiography, and with a feasibility at peak stress of 80% of segments.

Differences and limitations of different methods.

It is important to be aware of the limitations of each method. It should also be emphasized that different methods are not necessarily directly comparable, and may yield different normal values and cut offs. Some of these are discussed in more details in the chapter on problems and pitfalls. One of the fundamental differences stem from the different geometrical assumptions that are present as shown below:

Ejection fraction is still the most widely used measure of systolic left ventricular function today. This is mainly due to the vast amount of prognostic information from earlier studies, and the prognostic interventions that are geared to a cut off point in EF. Thus it will remain in use for an foreseeable future. In assessing EF, it should be emphasized, however, that EF is not a direct measure of myocardial function, as it measures the cavity, not the myocardial deformation. At best, it could be characterised as an indirect measure. Does this matter? Yes. If we look at a few examples:

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

The same erroneous results will be obtained by the fractional shortening of the left ventricular cavity by M-mode, as shown by the example below.

Thus, the EF or FS is a measure that actually only works with dilation of the ventricles, and becomes erroneous in the cases of reduced EDV. Because this has been poorly  recognised, it has lead to some fairly bisaqrre results. As systolic function has been measured by EF, and diastolic function with mitral flow parameters, the hypothesis of "isolated diastolic heart failure" has been proposed. At the outset, measuring systolic and diastolic function by different measures with different sensitivity, is methodological nonsense in any case.

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

But as EF as a measure of systolic function in the case of small, hypertrophic ventricles is meaningless, the whole concept is still utter nonsense.

In all cases of pathological hypertrophy, the long axis measurements of displacement and velocity (ref), as well as strain (ref), will be reduced, demonstrating a reduced systolic function. In fact there is a close link between diastolic and systolic function when the same measures (e.g. tissue Doppler) are used for both (ref).

	Normal		Hypertrophic
	Diastole	Systole	Diastole	Systole
Outer diameter (cm)	6.5	5.85	7	6.6
Wall thickness base (cm)	0.9	1.35	2	2.3
Wall thickening (%)		50		15
Midwall diameter (cm)	5.6	4.5	5	4
Midwall circumference (cm)	17.6	14.1	15.7	12.6
Circumferential strain (%)		20		20
Inner diameter (cm)	4.7	3.15	3	1.7
Fractional shortening (FS %)		33		43
Outer length (cm)	10	8.7	10	>10
Longitudinal strain (%)		-13%		>0
Total volume (ml)	221	155	256	230
Cavity volume (ml)	110	45	42	17
Wall volume (ml)	111	111	214	214
Stroke volume (ml)		65		25
EF (%)		59		60

Theoretical comparison of a normal versus a hypertrophioc ventricle, with the end diastolic length, diameter,  wall thickness and wall thickening chosen as shown above. Then Circumferential strain and fractional shortening can be calculated. The total volume and wall volume can likewise be calculated from an ellipsoid model. Assuming an unchanged wall volume (incompressibility), the length can be calculated, giving longitudinal strain and systolic total volume, and the cavity volume is given as the difference between systolic total volume and (unchaged) wall volume. Although the values are arbitrarily chosen, it goes to illustrate that in the case of hyopertrophy, there may be an increase in all cavity measurements, despite no increase in any strain values (absolute).