Measurements of strain and strain rate by ultrasound

If total strain at end diastole is different to zero, the heart would either diminish or increase in size. This is obviously nonsense. (Even with minimal changes this would lead to the heart either disappearing or growing to the size of the whole body in a matter of hours. The same is true of displacement. If the end diastolic displacement is different from zero, the heart would walk away from the patient in a short time.)

And even if total strain is zero at end systole, each region also have to end with zero strain and displacement at end diastole. Else, this would be equivalent to a shape change that would turn the heart inside out in a short time. Thus, end diastolic strain has to be zero, and this condition can be used to compensate drift.

Drift can thus be compensated in post processing, from the necessary condition that strain at end diastole (end cycle) has to be zero.

Either the value can be reset at the end of each cycle. This will not compensate for drift during the heart cycle, and may be seen by a distinct step in the strain curve at end diastole. A smoother correction is to apply a linear correction during each heart cycle, by calculating the slope  of the baseline from the "step" at the end of the cycle and subtracting this slope from the baseline values. This correction is based on the assumption that the drift is linear during each heart cycle, which is an approximation, but not completely true, as seen in the example above where drift is probably more sinusoid shaped.

Resetting at the end of each heart cycle gives more ugly curves, but does only correct what is known to be false. Linear resetting will result in correction also during the heart cycle, but this is presumptuous. This principle is illustrated below.

Strain without drift compensation. It is evident in the image to the left that the strain curve  drifts from cycle to cycle. The drift may be both downwards and upwards, in this case downwards.	Drift compensation by resetting the curve to zero at the beginning of each heart cycle. This is evident by the vertical line at end diastole. Comparing to the image left, peak systolic value at cycle 1 can be seen to have the same value, as no drift is compensated during the heart cycle.The resetting prevents the drift to affect later heart cycles, so cycle 2 and 3 have similar peak systolic strain as cycle 1, far lower and stable than without compensation.	Linear drift compensation is applied linearly during the whole period. This results in a further correction, as values during each heart cycle are adjusted as well. In cycle 1, the peak systolic strain is lower (in absolute value) than without or with linear compensation. In addition, cycle2 and 3 have lower peak systolic values than with resetting at end cycle, although this may not be the real case.

Thus, linear drift compensation affects peak systolic strain unpredictably, and not necessarily in the correct direction.

Method for drift compensation should always be reported in clinical studies.

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

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 transmural 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.

Limitations of tissue Doppler

As can be seen from the equations given above, the strain rate is derived as a difference of two velocities. But this means that the signal (strain rate) has a noise that is the sum of the noise of the two velocities, while the signal itself is the difference between the same velocities. Thus, Strain rate has a far less favorable signal-to-noise ratio that velocities, as ca be seen from the figure below.

Velocity plot at one time during the heart cycle, taken from a 4-chamber view of a normal patient. The plot shows the distribution from the basis of the septum (left) through the apex to the basis of the lateral wall (right). It can be seen that there is a clear velocity gradient along the wall, but also that the velocities are fairly different from point to point (noise), resulting in even more noise in the derived strain rate.	Velocity curves from a normal patient. It is evident that there is some noise in the curves, but the curves can be interpreted very well.	Strain rate curves from the same dataset, showing how the data derived from the velocities multiplies the noise in the velocity data, due to the spatial derivation process.  In this image, no smoothing is applied.

The Subtraction algorithm will give substantial increase in random noise. The reason for this is the spatial derivation (11): There is a certain randomness of velocity measurement, the limit of precision of measurement. This is independent of the value measured, so lower velocities has lower signal (velocity) to noise (variability) than higher values. Strain rate, being the difference of two velocities (SR = (V₁ - V₂) / L) has a random variability that is the sum of the variability of the two velocities measured, or twice that of velocity.  The signal, however, is the difference between the same two velocities, resulting in a much lower signal to noise ratio, which is evident in the plots above.  there is considerable variation in velocity measurements. By calculating the mean velocity gradient along the strain length by linear regression, the noise is substantially reduced, compared to the simple subtraction algorithm (SR = (V₁ - V₂) / L) and regression is the present method of choice. However, random noise remains a problem, as seen in recent studies.

Random noise in tissue Doppler derived strain rate can be reduced by:

• Increased offset distance (strain length).
  
• Spatial averaging. Both points will reduce spatial resolution along the ultrasound beam (depth), and increase the susceptibility for non random noise as f.i reverberations and also for drop outs.
  
• Temporal averaging (curve smoothing). Reduces temporal resolution (effective frame rate), and may lead to undersampling.
  
• Integration to strain. Changes the physiological information, but the importance of this for clinical diagnosis is uncertain. However, the temporal resolution is reduced.
  
• Averaging of more than one heart cycle (cine compound). But this also will give some interpolation between frames, and reduce the effective frame rate. In addition, there will be the possibility of introducing non random noise into the compound cycle. It is argued that averaging peak values may be better.
  
• reduce data to parametric images. In this modality, the information is reduced to qualitative information (shortening and lengthening) or semi quantitative information (f.i. colour WMS).
  

Spatial smoothing

The effect of Strain length can clearly be seen. Usual default offset at present is 12 mm.	ROI size. With offset 4 mm, the effect of averaging more samples is evident.  Usual default is 12 x 6 mm at SL 12 mm.	Illustration of how both strain length and ROI size reduces spatial resolution. each strain length is represented by a point in the middle of the length. In principle the radial (depth) resolution should be ROI length + Strain length, but as shown the effect of the points outside the ROI decreases with the distance from the ROI with the regression method.

Ideally, the strain length plus ROI should be as great as possible, giving the highest possible velocity difference to ensure the best signal-to-noise ratio. As there may be little added information by entering into sub segmental resolution, the resolution may be as low as the length of one segment. This will give the segmental strain rate and strain, although measured along one ultrasound beam. However, this also increases the risk of including areas of reverberations or drop outs. This is indeed true of all methods for spatial averaging.

Temporal smoothing

Temporal smoothing at SL=4 mm, ROI size 6x6 mm. Left no smoothing, right Gaussian smoothing at 40 ms. Default at present is Gaussian 40 mm at SL 12 mm and ROI 12 x 6 mm. #Examples of recordings with the default settings can be seen above at different places.	Effect of temporal integration. Left unsmoothed strain rate, right strain from the same dataset. As the noise is random, the summation will eliminate the random variations, resulting in smooth curves.

A detailed treatment of temporal filtering can be found in (75, 77).

In the original post processing application  no smoothing was applied. That meant that the original studies were done by visually correcting for noise. Later temporal smoothing, and in the latest software (from about 2002), the Gaussian temporal smoothing is implemented. In addition, the strain rate algorithm has moved from a simple subtraction algorithm back to the original (14) regression method, resulting in a more robust strain rate estimate.

The experience from the HUNT study (153), seem to show that strain rate by tissue Doppler is a more noisy method for strain rate than the others, including segmental strain, giving higher peak strain rate (probably due to noise peaks) and wider standard deviations (variability) as shown in the comparison study. Strain did not differ, showing that the integration to strain is efficient in eliminating random noise.

Averaging more than one heart cycle (Cine compound):

Random noise will not repeat from heart cycle to heart cycle, and thus averaging more than one consecutive heart cycle, will eliminate random noise. As can be seen from the recent comparison of methods in the HUNT study (153), peak systolic strain rate by tissue Doppler is much more sensitive to noise than other methods. This can be seen from the fact that the average (absolute) peak values are much higher then other methods, while the standard deviations are correspondingly wider. Thus the peak values incorporate noise. Systolic strain, on the other hand, are quite similar, showing that the increased peak values disappears as noise is integrated sto strain as discussed above and that the higher peak values are incorporating noise peaks.

On the other hand, averaging heart cycles has several disadvantages:

1. The frames will not be at exactly the same time point in the cycle, and thus corresponding franes will be from slightly different points in the cycle, and thus averaged. This effect is in fact similar to temporal averaging, and results in a similar reduction  in effective frame reate, and may lead to undersampling.
   
2. As there is significant beat to beat variation in cycle length, later events in the heart cycle will occur at different intervals from the R-wave. Systole and diastole varies differently with respect to RR-interval, especially at HR < 100 (29), it will especially affect the time around end systole / early diastole.This may lead to bizarre results as seen below.
   
3. Cine compounding by automated methods will always sample three consecutive cycles, and if one beat is of low qualituy due to motion or respiratory artefacts, or even as an extrasystole, the compound curves will include the artefact.
   

Native recording, showing four cycles. (Healthy child, HR around 90). It is evident that there is variation in heart rate, as it can be seen by the increasing fusion of E and A waves.	Cine compound x 2, i.e. each cycle shown in a compound of two cycles.  Systolic peak velocities does not change much, but e' wave velocities are almost halved, due to the averaging of E waves that are at different relative positions in the cycle.	Cine compound x 3, i.e. each cycle shown in a compound of three cycles.  There is not much change from cine-compound x 2, and still e' waves are very different from the native loops.
Velocity curves from the septum.  There is substatial noise as well as fusion of E and A due to beat 2 being an extrasystole at the end of cycle 2 (arrow).	Resulting in a high noise spike in the strain rate signal,	which again leads to a substantial artefact in the strain curve.
When this artefact is shown in a non-compounded image, it is limited to one cycle, and it it fairly evident that this cyscle should be discarded.	Cine compound x 2, extends the effect to two cycles	and cine-compound 3 extends the effect to three cycles, and in this image, it is not evident which cycles are representative.

Basically, If one is concerned about peak values, averaging peak values from three cycles will be more robust that automatically creating a cine compound cycle, and especially if cycles that deviate are eliminated. Thus, one is not restricted to three consecutive cycles. Cine compound may seem an attractive way of averaging three cycles, and then being able to reduce the number of measurements to one set in a cycle that is the average of three, but then the following caution should be observed:

1. It should only be applied to systole. Also, velocity measurements are fairly smooth already, while strain rate is noisy and is the case where one profits most. Thus peak systolic strain rate maight be the one case where it it feasible and favorable. Strain curves are fairly smooth already, and cine compound will not add anything.
   
2. It should only be applied where there are three consecutive cycles of good quality, but as can be seen above, the noise is not very evident in the velocity curves, and if cine compound is applied before conversion to strain /strain rate, the artefacts may be less evident.
   

Amount and method for temporal averaging should always be reported in clinical studies.

Drop outs

Where there are drop outs, no data can be obtained, and the resulting velocities will be zero:

Drop out in the anterior wall. In this area there are no B-mode data, indicating that there are no velocity data either (although this may not always be the case).	Schematic figure corresponding to the loop to the left. In this case there are no data in the drop out, resulting in zero velocity, i.e.  v1 = 0.	As is evident from the traces, the velocity in the drop out area (cyan curve) is zero. Below the drop out, the velocity curve is normal.

Stationary reverberations

In stationary reverberations, the mechanism is similar to the effect of drop outs. The various artifacts may arise from the effect of measuring zero velocities in some areas:

Stationary reverberations shown in B-mode, the mechanism is explained in the ultrasound section. Stationary echoes are called clutter.	The effect being that in the area of the reverberation, there are zero velocities (V2), while the velocities above (V1) and below (V3) are normal.	The result is that the reverberation shows up as a stationary area of inverted colour, showing sharply in the strain rate image. However, this is not the only effect.

The problem of reverberations are even greater in tissue Doppler, as this is done in fundamental, and not harmonic mode. Suppression of reverberations by harmonic imaging is not feasible due to the low frequency giving a low Nykvist limit, resulting in aliasing in tissue Doppler. Although strain rate would unwrap most of the aliasing, this would mean that separate recordings would have to be made for velocity (fundamental) and deformation (harmonic) imaging, instead of deformation being post processed from velocity recordings.

Insonation angle deviation

The main limitation of tissue Doppler due to the angle dependency is the inability to analyse anything other than longitudinal strain in all segments of the ventricle. Tissue Doppler may give transmural strain in the anterior and inferior segments (crosswise), and circumferential strain in the lateral and medial segments (tangentially), but full segmental analysis is not possible. Thus, if the other strain directions should prove to give added information, this means that at least combined methods would be preferable. However, this is still not definitely proven.

Insonation angle deviation means that the ultrasound beam deviates from the direction of the wall at the point of measurement. This is due to different mechanisms:
The wall is curved, while the ultrasound beams are straight and deviates with depths in a fan,  as shown in the figures below.
The probe may be placed off centre, although this may not be apparent in the imaging plane, only in the orthogonal plane (76). Off centre placement of the probe, however, may both increase angular error (76) in the segments with best alignment, or decrease it due to curvature compensation (42).

The angle dependency is mainly a problem in tissue Doppler, but reduced lateral resolution in B-mode in order to achieve a high frame rate (or indeed, 3D images), may increase angle dependency in speckle tracking by reducing the ability to track in the lateral direction.

It is well known that velocity measurement is dependent on the angle between the ultrasound beam and the velocity direction (vector) – insonation angle, and that the measured velocity v_m is reduced in proportion to the cosine of the angle a between the velocity vector and the ultrasound beam as discussed in the ultrasound and mathematics sections.

For strain rate and strain measurement by velocity gradient, the angle dependency is somewhat more complex. In the longitudinal direction, the longitudinal velocity gradient is reduced by the cosine of the insonation angle, as for velocities. But in an incompressible object, there is simultaneous strain in the transverse direction, in order to keep the volume constant, and the two strain components are opposite and will detract from each other (1, 2, 7). This results in further reduction in the measured strain and strain rate (7).  This is illustrated below.

The true velocity vector is shown as the straight arrow, the ultrasound beam as the dotted line. The vector measured along the ultrasound beam is reduced by the cosine of the angle between the true vector and the ultrasound beam.

An object undergoing longitudinal shortening (negative strain). The ultrasound beam (dotted line crosses the longitudinal direction at an angle. In addition to the apparent reduction of the shortening by the angle, there is simultaneous thickening in the transverse direction (positive strain), which further detracts from the n numerical value of the shortening. It's important to realise that this double angle problem is limited to the velocity gradient method. Tissue Doppler is still angle dependent, but segmental strain by tissue Doppler has only the basic limitation common to all Doppler measurement. And using it in combination with transverse speckle tracking, eliminates this angle dependency also, to the same degree as in speckle tracking (meaning that speckle tracking is not altogether angle independent).

Angle deviation is most usual in the apex and base:

Angle deviation is biggest in the parts that are most perpendicular to the ultrasound beams, as shown here, in the apex and the base of the sigmoid septum.	The sigmoid septum illustrated here, showing systolic  positive  strain (blue - apparent lengthening) due to the angle being crosswise to the wall, in reality measuring thickening	Another patient with no sigmoid septum shows no artifact in the base of the septum. In addition, as the ventricle is not dilated, the area with apparent lengthening (blue) is fairly small.	Strain rate curves from the same patient showing it top be perfectly feasible to measure strain in the basal part of the apical segment (red ROI and curve), the area with inverted values (being in reality thickening) is fairly small (yellow ROI and curve).

This is described in a more detailed mathematical analysis in the mathematics section.

Which segment that is most in alignment with the ultrasound beam, may vary with LV shape and depth, as shown here.

  Lateral resolution

Another problem, being related to the insonation angle, but with mechanism similar to the drop out and reverberation issues, is arising from the low lateral resolution of tissue Doppler. This is due to low line density which is applied in order to achieve a high frame rate, as discussed in the ultrasound section. If the frame rate is around 150 FPS, there is usually less than 20 lines in a sector. This is even more enhanced by using the MLA technique where a broad transmit beam  is used, and the signal is received along more, narrower receive beams. The simultaneity of the parallel receive beams results in signals partially being received by the neighboring beam. In addition, as tissue Doppler is acquired in the fundamental mode as discussed above, side lobes are more prominent, contributing to reduced lateral resolution.

Relation between frame rate and lateral resolution in tissue Doppler.  The numbers are receive lines, this means that in 4MLA, the number of transmit beams are one fourth. In reality, the lines have the same width, the data are interpolated between the lines.  (Image courtesy of E Sagberg.)	Example of how this affects velocity measurements, In this image, taken at 150 FPS, the four sample volumes placed side by side in the base of the lateral wall, generates exactly the same velocity curve, showing that the data are the same.

Initially the default frame rate was 150 FPS in tissue Doppler, but now the default is intermediate (about 100). The low lateral resolution may have effects similar to the effects of drop outs and reverberations, as one of the velocities of the strain length may be from cavity or pericardium as illustrated below.

Two wide ultrasound beams are shown in grey, with the middle marked in red. The velocities that are recorded within the beam are transposed to the middle line.  Strain rate is analysed along the middle line. In the apex the angle makes the beam miss v1, and may instead use pericardial velocity (red circle) in strain rate analysis, thus v1 - v2 will be equal to -v2, too high value.  In the midwall, missing v2 and using pericardial velocity instead, v1 - v2 will  be equal to v1, a velocity curve, inverted and too high numerical values.  Here, this is shown in the midwall, but the base is even more prone to this artifact. In the base is shown another artifact, the beam misses v1, and uses velocities from the cavity instead, which are zero, being removed by the low pass filter. v1 - v2 will then again be equal to -v2, accentuated numerical values, being an inverted velocity curve.	Normal myocardial strain rate curves (orange, cyan and green ROI and curve), show a fairly even distribution of strain rate. In the lateral wall  a sample volume too far into the cavity (cyan ROI and curve) will give high numerical strain rate values, for the reason shown in a, basal. A curve too near the pericardium (red ROI and curve) shows reduced values, due to a partial effect of the pericardial influence on v2, as illustrated to the left; midwall. Averaging makes this effect partial, pericardial velocity only detracting from the numerical strain rate values.	Pericardial artifact  as illustrated to the left in the midwall. Top, systole, bottom, diastole. Here, near the base is seen high, inverted strain rate values.

The effect may explain why some authors have found higher strain rate values in the base than in the rest of the ventricle in normals, which is an absolute artifact. It may also explain why some authors have found differential strain rate values across the wall, which is fairly improbable as discussed above.

Integrational drift in tissue Doppler:

In tissue Doppler, the package acquisition of colour Doppler, results in drift from one package to the next, as shown below.

This effect is not only due to the mathemathical integration of displacement from velocity, it is actually also a property of tracking by tissue Doppler, as the position of a kernel is calculated from the position and velocity in the previous frame. (this is in reality the same thing). A frame rate of 1 KHz would to some degree eliminate this. Then each velocity could be calculated by single acquisition i.e. from one frame to the next, without the gaps due to FR being much lower than PRF. This has been shown to be technically feasible (215).

Segmental strain and strain rate.

Segmental strain and strain rate is taken to mean the deformation measured over a complete segment, giving the average value for the segment.

Tracking of segmental borders. The strain is the relative change in segment length, and the strain rate the strain change per time.

Segmental strain in six segment in four chamber view.  Schematically , the motion of the segmental borders is shown by the arrows, decreasing from base to apex. The segmental strain is the difference between the motion of the two ends of a segment. The curves are from a real example. The blue strain curves show segmental values, while the green curves are the average of the wall for comparison.Image courtesy of H Dahlen.

Segmental strain has several advantages:

1. As measurements are fairly noisy, the average of a whole segment will tend to be more robust. This will give a high signal-to-noise ratio as discussed above. The segmental strain is equivalent to a strain length equal to the segment length, i.e. about 3 cm. The segments are the basic unit for evaluating regional wall motion score (WMS) in the recommendations of the ASE/EAE (146), and so far the clinical usefulness of a higher resolution has not been demonstrated.
   
2. Tissue Doppler measures the velocity gradient along the ultrasound beam, not along the segment. 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 chapter, under the discussion on insonation angle and  lateral resolution. Tracking the end of each segment, ensures a better measurement of the segmental longitudinal shortening.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.
3. As long as segmental length is followed by tracking the ends of the segment, the value will be little affected by smaller artefact's within the segment as illustrated below.
   

Limitations of segmental strain

The disadvantages may be that

1. The method will be measuring only two points along the line and thus
1. be less robust than the full segmental average (provided the data in the segment are good).
   
2. be extremely sensitive to artifacts at the points of tracking as seen below.
   
2. The low resolution in the radial (longitudinal) direction. Sub segmental values cannot be extracted (although they could be interpolated).
3. If the tracking at one segmental border is poor, it will affect two segments on both sides of the border as discussed below. 

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 illustrated schematically below.

Effect of a reverberation on the border between the apical lateral and the midwall lateral segment. A kernel  in this area will not track, as illustrated by the arrow.  The next border between the basal and midwall segment moves normally, leading to an exaggerated shortening of the midwall segment, while the basal segment shortens normally. (The segmental strain in the apex is the difference between the apical motion (zero) and  the apparent motion ( near zero) in the reverberation, the midwall strain is the difference between the apparent motion ( near zero) in the reverberation and the (normal) motion of the border below.) This is evident by the curves (compare to the average curve: The apical curve shows little strain, the midwall curve shows far more than the wall average, and the basal shows average strain).  Compare with the image above. Image courtesy of H Dahlen.

The kernel is in a reverberation in the lateral wall, and will not track. In this example the reverberation is in the border between the basal and midwall segment. the shortening of the basal segment is exaggerated, and the shortening of the midwall segment is reduced.

Thus, one kernel tracking poorly will then lead to two segments being discarded, giving a high discard percentage. This was seen in the HUNT study with automated analysis, we consider this an advantage of the study, leading to little contamination of the data by artifacts, thus ensuring the data to be "clean". However, it is a disadvantage of the method, leading to a lower feasibility. However, in clinical studies, the feasibility was around 80%, and in addition showin added diagnostic value to B-mode (128). But basically a high discard rate ensures higher quality of the studies.

Segmental strain by tissue Doppler

Instead of calculating strain rate along one ultrasound beam, 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 below. This ensures that tracking is done at the real segmental borders, and makes the method less dependent on the alignment of the ultrasound beam and the myocardial wall. The method is still angle dependent, but this is the ordinary angle dependency of Doppler, not the angle dependency of strain and strain rate. The method has not been implemented in clinical use.

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, just as in the whales.  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. 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.

Typical speckle patterns in the myocardium, demonstrating the differences between different areas (kernels).  The difference in the pattern is the basis for speckle tracking.	Speckle tracking. the speckle pattern from the first frame (red) has moved to a new position (green) in the next, and can be recognised by a search within the search area.

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. The fundamental advantages as well as limitations of segmental strain remains.
In addition, the combined method has additional advantages:

1. As longitudinal strain is the main issue so far, the advantage specifically of the combined method is that longitudinal tracking is done with the high frame rate of tissue Doppler. This may give an additional benefit, at least in strain rate.
2. Doing only transverse search by speckle tracking 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.
   
3. The transverse tracking by speckle tracking eliminates the problems of both insonation angle and low lateral resolution of tissue Doppler alone. Thus, the method is just as angle independent as speckle tracking, as opposed to the segmental strain by tissue Doppler alone.
4. If the tracking of tissue (lateral tracking) is poor, the measurements will be similar to the segmental strain by tissue Doppler, meaning that it will be somewhet angle dependent, but still less than the velocity grasdient method.
   
5. Finally, it utilises the full dataset inherent in the combined image.
   

The combined method can be used in different ways to analyse strain rate imaging (127):

1. Segmental strain by speckle tracking alone
2. Segmental strain by Combined tissue Doppler and speckle tracking
3. Strain rate by longitudinal velocity gradient, by placing an ROI and strain length in mid segment (in end diastole)
1. Letting the ROI remain stationary or
2. Letting the ROI follow the segment being tracked by the combined method

3b is similar to ordinary strain rate by tissue Doppler, 3a is improved, as the present applications only offer the manual tracking as a possibility, while the combined method gives the strain rate. The tracking has been shown to be advantageous in the apical segments, in a comparative study.

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. It is also the method used for the HUNT study (153), for automated analysis. In this study methods 2, 3a and 3b was compared as well, and compared to 2D strain, comparisons shown below, showing little differences between mean values and normal variations.

The limitations of the combined method is the same as for echo in general issues related to image quality, and the general limitations of segmental strain.


It has been considered a problem that the combined method is not commercially available, at present it is a research tool at the Norwegian University of Science and technology. It has been criticized by some, that the results are not useful, as they are not transferable. I consider this criticism only partially valid.

1. Firstly, this is a research tool so far for doing research into and comparing speckle tracking and tissue Doppler. And the speckle tracking is "pure" speckle tracking, not advanced applications utilising a lot of computing to achieve results. The application makes it possible to compare tissue Doppler, speckle tracking and the combination directly (151), and as shown below.
   
2. The HUNT substudy showed little bias between methods.
   

So far, the two data sets could be combined in different ways, not limited to the application described above. Further research should be undertaken to assess this.

It seems rather absurd in the long run, that having access to high quality grey scale tissue data as well as high frame rate tissue Doppler data in the same loop, the quality of measurements will improve by discarding one of the data sets.

2D Strain (AFI) by speckle tracking.

The application known as 2D strain or AFI (automated functional imaging) by GE Vingmed, is generally seen as a speckle tracking method, which actually is  the basic  method. Tracking is done by the same method, (sum of absolute differences). However, the method also has implemented:

User friendly interface (if strain rate imaging by tissue Doppler had had the same interface from the start, it would probably have gained more acceptance). Some may call it seductively user friendly.
A high degree of smoothing, making the results very robust (but may have disadvantages)
Method specific processing that imposes specific limitations.

With a greater number of kernels, distributed both along and across the wall, each kernel 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.

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 kepi- to endocardium can also be tracked., giving transmural strain and strain rate.

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.

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

However, this is one of the main limitations of the data in the bottom: The smaller the kernels, the greater the uncertainty of position, and the more noise. Thus, a liberal amount of smoothing has to be done. 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. Thus, the tracking of a region of the ROI, is not speckle tracking alone, but also extrapolation of the AV-plane motion i.e. virtual tracking. This is discussed below.


The method starts with generating a velocity field across the sector (velocity being the displacement between one frame and the next, / 1/FR), more or less as in tissue Doppler, but the velocity vectors being angle independent. Thus the displacement ad strain rate and strain can be derived in the same way.

Longitudinal velocity	Longitudinal displacement
Longitudinal strain rate	Longitudinal strain

Thus, it is evident that both tissue Doppler and 2D strain will give four modalities from one dataset:

2D strain derived displacement, velocity, strain rate and strain. Note the smoothed curves.	Tissue Doppler derived velocity, displacement, strain rate and strain. Note that these are unsmoothed curves.

Quality evaluation of tracking in 2D strain

The first step in processing will be the quality control of the tracking, as described above. The application has built in automated assessment of the quality of tracking, with methods similar to the ones above. Thus the application will suggest acceptance or rejection of the segments in the view. However, the segmental quality assessment is compared to the average, there are no absolute criteria, so tracking should still be evaluated visually, and segments that do not rack, should be excluded manually.

Visualisation of the tracking. Observe how the bullets in the midline follows the myocardial motion. However, due to the smoothing function of the application, this may be virtual tracking, being extrapolated from AV-plane motion, thus the true tracking of the local tissue may be difficult to assess.	Loop from another patient. Tracking seems fair, visually.	Automated quality assessment accepting the tracking results from all segments. The assessment is presented as a suggestion, and manual acceptance is required, i.e. the accept button has to be pushed in order to process.

In this case, the application suggested to accept all segments, which would result in the values as shown.  The poor tracking in the apical lateral segment does not reflect in the values, due to the spatial spline smoothing in the application.	The same loop as left, but manually override of the automated quality assessment, excluding two segments before pushing the accept button, lateral basal as it exaggerated the tracking by tracking side lobes, and the apical lateral, as the tracking was poor due to near field reverberations.

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 o0f 20 patients with a wide range of function.

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 especially of tissue Doppler. 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.



This is illustrated below:

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.
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.

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.

Limitations of 2D strain

The main limitations of 2D strain are the general ones, as well as the ones specific to speckle tracking.
In addition, 2D strain has method specific limitations related to:

• Curvature dependency, due to the technicalities of the specific applications, which may give too high values in the apex.
• Smoothing, relying heavily on AV-plane motion,
• which may give strain values even where there are none, and may reduce sensitivity for reduced regional function
• Makes the tracking more difficult to assess visually
  

Reverberations and drop outs are illustrated above. Those examples are all taken from 2D strain, but shows the general principle.

Curvature dependency of 2D strain

The longitudinal values that are obtained by the 2D strain application are curvature dependent, as shown below:

Curvature dependency of strain measurement. If the ROI is curved, the midwall line will move inwards, and thus shorten, even if there is no shortening of the segment. This will result in an apparent shortening of the segment itself, adding to the real longitudinal shortening. This curvature effect is dependent on the curvature, the width and the widening of the ROI.

Curvature dependency of strain in 2D strain by speckle tracking. The two images are processed from the same loop, to the right, care was taken to straighten out the ROI before processing, while the left was using the default ROI. In both analyses the application accepted all segments. It can be seen that the apical strain values are far higher in the right than in the left image (27 and 21% vs 19 and 17%).  However, the curvature of the ROI even affects the global strain, as also discussed above in the basic section.

The width and thickness as well as curvature of the ROI is non standard, defined ad hoc. In addition, the ROI width is uniform from base to apex, while the myocardium is thinner in the apex, giving a discrepancy between ROI width and wall thickness. As the curvature effect is also a function of ROI width, this may add to the curvature effect. This effect may account for the observed base-to-apex gradient of strain values observed in some studies. The combined method (and indeed tracking of segment length by speckle tracing alone without TDI by the same application) is curvature independent as shown below.  It may be the reason why some authors find a base-to-apex gradient in the strain values obtained by this application, while we did not in the HUNT study.


The curvature dependency of 2D strain is a parallel to the angle dependency of tissue Doppler.

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, which is then distributed along the whole ROI by a curve fitting along the mid ROI curve, resulting in a smoother transition from segment to segment, distributing the deformation along the ROI. Thus, the 2D strain application does not reflect pure speckle tracking, but also a great amount of model fitting. The spline smoothing is weighted, being least in the basal segments, most in the apex, which may be a way to compensate for some of the curvature effects in the apex, but that means tat adjustments in the base will affect measured strains in the apex.




This is illustrated below.

Spatial smoothing in 2D speckle tracking strain. The smoothing, using longitudinal information from the AV-plane motion results in strain values even in areas where there is no speckles. This means that there is movewment of the points of the ROI, in areas without speckles. This is due to the information from the AV-plane motion being "splined" along the ROI, and the motion of the points is due to this, not to local tracking. Thus, there is  only "virtual tracking", and the true local tracking cannot be fully assessed .

Segmental values from this tracking. Left: medium (default) spatial smoothing, right: Minimum.  This was done in the latest software version (2011), where values and traces carry over to segmental values after adjustment of smoothing, but the effect is small, compared to the total amount of smoothing.

This example was obtained by manual override of the automated positioning of the ROI, as well as manual override of the automated quality check, which suggested rejection of all segments. However, the application did track, as can be seen above, left, and these images are to show the general principle.

Inferior infarct in two chamber view, being akinetic in the basal inferior wall, although with considerable passive motion due to tethering	2D strain (left) vs. tissue Doppler (right) in an inferior infarct, analysed from the same cine loop recording.  The akinesia in the base is missed due to smoothing. In this case, as there is dropout of the whole anterior wall, the smoothing may be harder in the remaining three segments.  Also, in basal infarcts, the effect on AV-plane motion is less (40) as shown above.

Inferior infarct. Hypokinesia of the basal segment. Not immediately evident.	Strain and strain rate. Basal hypokinesia and post systolic shortening (yellow). Also normal curves in the inferior apex as well as in the anterior wall (red and cyan).

Same infarct as above. Tracking shows poor tracking in the basal and midwall segments have poor thickening due to poor tracking. The anterior wall is less visible. The segments are not approved for analysis.	Longitudinal strain. The apical anteior segment shows reduced strain, but this is due to poor tracking. The basal segment does not show reduced systoloic strain. However, looking at the curve, the infarcted segment does show post systolic shortening, so the infarct is still indicated.

Lateral tracking in 2D strain

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 increases from epicardium to endocardium. 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

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. (Images with better resolution may be seen above).

This is one of the fundamental limitations of speckle tracking as discussed previously.

Transmural and circumferential strain.

As speckle tracking is partially angle independent, it may be applied to the short axis as well. The main concern about tracking in short axis views, however, is the long axis motion. This means that there is between 1 and 1.5 cm out of plane motion of the base, and about half that in the midwall. That means that the tissue present in end diastole is not the same as in end systole. This also means that the speckles that are tracked do not represent physical myocardial points. Thus, the meaning of transmural and circumferential strain becomes slightly dubious. However, this do not only pertain to 2D strain. As shown above, this is the same problem even in parasternal M-mode. (Which, despite this, has worked well for 50 years). However, this remains a caveat when new measures are added. In the question of rotation, especially torison, the spiral course of the longitudional fibres may even cause the displacement to cause the fibres to be traced as rotating around the cavity centre.

Parasternal long axis image. The longitudinal motion of the basis is evident.	End diastolic parasternal long axis image.  The yellow line crosses the ventricle near the middle.	End systolic parasternal long axis image from the same loop.  The yellow line crosses the ventricle much closer to the base transecting a different part of the myocardium.

The speckles may be the endocardial borders, or even the fibres that may run in spiral. Thus, in the base, the physiological meaning of the obtained values is questionable.


Accepting the validity of speckle tracking in short axis views, it then allows tracing of transmural and circumferential strain. Transmural strain is wall thickening, and the tracking in the transmural direction will be dependent on the resolution, which is better along the ultrasound beam than laterally. The physiological meaning of circumferential strain, shouold be midwall circumferential shortening, which actually is nothing more than * midwall fractional shortening as reasoned above. 

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.	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%. This is probaly due mainly to a too thick ROI (default), although poor lateral tracking combined with smoothing may contribute.	Circumferential strain from the same processing.   In this image about 15%, which is closer to normal. This, however, does not mean that the circumferential strain is more reliable, it means that the thickness error in the ROI is compensated by an underestimation of the cavity volume. It's equivalent to the fractional shortening increasing in hypertrophy, despite reduced wall thickening. (Actally circumferential strain = * midwall FS. )

Width of the ROI

Transmural strain all thickness and wall thickening. But in the 2D strain application, this means ROI width as shown below.

Normal ventricle in short axis view.	The loop can be used to generate an anatomical M-mode, the line is skewed to avoid the papillary muscles. On this M-mode the following values were measured: LVIDD: 53mm ,LVIDS: 36mm, giving a FS of 32%, IVDS 7 mm, IVSS 11mm, giving a wall thickening of 57%, LVPWD 8mm, LVPWS 11mm, giving a wall thickening of 38%, and a mean wall thickening of 48%.

Below are shown transmural strain by 2D strain with different ROI width. The images are all processed from the loop above, and endocardium traced in standard manner. In reprocessing, only ROI width was changed without changing the initial contour. All ROI's were accepted by the analysis software for all segments:

Transmural strain with narrow ROI setting. Tracking seems fair, except perhaps in the lateral wall.  This is due to drop out of the wall, not hypokinesia, as seen to the right, where tracking is far better.  However: Given poor tracking in the lateral wall, mean WT = 57%. This is due to the tracking in the septum, which is good, but where the wall thickening is absurd, 77 and 91!; normal  endocardial motion in absolute terms, gives a too high relative wall thickening in percent of the narrow ROI.	Transmural strain with default (medium) ROI setting. Tracking seems fair.  Mean WT = 58%.	Transmural strain with a wide ROI setting. Tracking seems fair.  Mean WT = 37%, because a normal endocardial motion in absolute terms will result in a low percentage of the too wide ROI.
The measured wall thickening is evidently as expected a function of diastolic ROI width, as expected. Compare also mean and the relevant segments with the values above

It is evident that the transmural strain is extremely sensitive to the ROI width. This is pertinent to long axis analysis also, as the curvature in the apical segments will lead to an increased susceptibility of the ROI width. This may be some of the reason why Becker et al (212) found transmural strain even in segments with total transmurality of scars, and not tethering as presumed.

Repeatability of 2D strain.

Basically, the 2D strain application, due to a high amount of smoothing, should have a high repeatability, as shown here. However, this will only be the case as long as the tracing is done in the same manner each time, in the same loops. This means a very standardised endocardial tracing, and a standardised ROI width. As shown above, the values are extrmely dependent on the ROI, both curvature and width of the ROI. Utilising the automated features of the application will ensure this, but will not necessarily ensure the correct shape and  width of the ROI, and hence, not necessarily the correct values either. In a study (208) where repeated measurements in the same loops was compared for different centres, the 95% limits of agreement were -11.4% to +11.8%, but with very little bias. Repeated recordings within one hour (presumably by the same observer), had limits of agreement of -9.6 to + 9.7%.


Both segmental strain and 2D strain have been compared for longitudinal strain, and compared to tissue Doppler (151, 153) as shown in this table. Both seem to agree fairly well. In addition variability of strain rate (but not strain) is lower by both methods than by tissue Doppler. However, both Segmental strain and 2D strain use automatic segmentation, this may be some of the reason for better repeatability, not speckle tracking vs. tissue Doppler per se. However, the higher variability of strain rate by velocity gradient, shows this method to have a somewhat higher noise componenet. Feasibility of both methods is reported to be between 70 and 80% of segments (lower in the HUNT study,but this is due to the aim of the study, to provide normal values as free as possible from artefacts.

Summary of 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, due to the different ways parameters are measured. One of the fundamental differences stem from the different geometrical assumptions that are present as shown below: