Basic limitations of strain rate and strain imaging
It must be emphasised that the present study is about the method of 3-dimensional reconstruction and display, while the basic method of strain rate imaging is not different from that published previously [6–12, 14]. Strain rate imaging in itself is based on post processing, and has a number of inherent limitations.
The most basic limitation is the one-dimensional nature of the data. While deformation is three-dimensional (longitudinal, transverse and circumferential), the present tissue Doppler derived method measures only longitudinal deformation. However, heart muscle is generally assumed incompressible, which means conservation of volume. Hence, strain in three dimensions must balance (the basic equation in volume conservation: εx + εy + εz = 0), so in systole longitudinal plus circumferential shortening equals transverse thickening, and vice versa in diastole. Previous studies have shown similar diagnostic information by longitudinal strain rate and transverse wall thickening (which is the same as transverse strain) by ordinary echocardiography . This means that the longitudinal strain rate may be representative of the compound regional deformation. The practical value for clinical work of adding more deformation directions remains to be demonstrated.
Data represents only a line along the wall, but to achieve a high frame rate, the tissue Doppler beams have to be wide, and the lateral resolution is low anyway. This means that differential strain across the wall cannot be measured, however, this is true for all tissue Doppler derived data sets.
The one-dimensional nature of the data also results in angle distortion, when the ultrasound beam deviates from the direction of the motion. While velocity measurements decrease by the cosine of the insonation angle, strain rate decreases more, adding the transverse strain rate with the opposite value [6, 18]. This means that in areas where the angle between the wall and the ultrasound beam is more than 45 degrees, the strain rate values and hence, the colour will reverse [11, 18]. This problem is apparent in the apex and the base . However, all clinical studies of strain rate have found it possible to measure strain rate and strain in the apical segments, by measuring in the basal parts where the walls are more parallel to the ultrasound beams [8, 9, 12, 14, 19, 20]. As can be seen from fig. 4, the area of distortion is quite small, and during the last part of the study, blanking was applied to this area to avoid displaying misleading information. This limitation is more theoretical than practical.
Strain rate/Strain imaging are prone to reverberation artefacts, due to the basic algorithm. If one of the two velocities is measured as zero, the strain rate value will be inverted in part of the band. The 3D reconstruction does not add to this, but makes it visible, it is the identification, not the presence of artefacts that are influenced by this method.
Strain rate is sensitive to random noise, and smoothing of curves has to be applied, resulting in loss of temporal resolution. This might lead to underestimation of peak values, but in parametric imaging, being semi-quantitative, this is less important.
3D reconstruction is a method for quick visualisation of global distribution of deformation. Infarctions were visible as dyssynergy in the typical anteroapical or inferior locations, and colour display of mid systolic strain rate and end systolic strain were equally sensitive. Post-systolic shortening , was an additional finding in all infarcts. Thus, it represents an additional diagnostic criterion, facilitating visual diagnosis of acute infarction. The mechanism for the phenomenon is incompletely understood, but has been clearly documented as a marker of acute ischemia [21, 22]. It is interesting that the area of post-systolic shortening was larger than the area with hypo- to dyskinesia in all patients. The difference may show an additional area of partly ischemic myocardium, visualising the border zone at risk. This has been visible by curved M-mode alone in previous studies as well [8, 9], although not commented on. Post systolic shortening was visible in both strain rate and strain curves, but only in strain rate colour display.
Reverberations were easily identified. On M-mode they did show up as horizontal bands, on the bull's eye as ring shaped structures. The location, shape and temporal sequence differed from the typical vascular areas, and were thus discerned from true pathology, as shown in fig. 5. The artefacts were not so obvious from the curves alone. Basal artefacts are due to either angle distortion or inclusion of part of the mitral ring or pericardium during initial processing. It is important that in three out of six normal subjects, reverberation noise was visible. This high incidence of artefacts has not been reported previously, and may have important implications for the validity and accuracy of quantitative data in clinical practice.
By identifying regions with artefacts, the colour display may aid in avoiding quantitative measurements in those, and thus may also increase the specificity of quantitative strain rate/strain in clinical practice.
Strain rate vs. strain
Deformation imaging is better in identifying regions of dyssynergy than motion imaging, due to tethering effects. Velocities decrease from base to apex  while peak strain rate is the same in all three levels [10, 14, 19, 20].
Peak strain rate was the only quantitative parameter in this study able to identify the infarct areas, while neither mid systolic strain rate nor end systolic/peak strain could do this. This demonstrates a basic limitation of 3D reconstruction. In 3D display, all parts of the ventricle are (in theory), displayed at the same instance of the heart cycle. All previous works in strain rate, however, have concentrated on peak strain rate, but peak strain rate has not been demonstrated to be simultaneous in all parts of the ventricle. Thus, mid-systolic strain rate (or strain rate at any other point in systole) is not equivalent to peak strain rate. Systolic strain is maximal in end systole in normals, and peak strain thus simultaneous. In theory this should be an advantage in 3D reconstruction, but the presence of reverberations eliminated this.
There was no difference between strain and strain rate in the sensitivity to reverberations and dropouts (fig. 4). Smoothing of strain rate data results in reduction in measured peak values, but the temporal resolution is still better in colour strain rate than strain, due to the shifts between positive and negative values as evidenced by the visualisation of post-systolic shortening. Thus, strain rate is best suited to colour display.
Limitations and advantages of the processing method and 3D display
It may be considered a major limitation that the circumferential resolution is limited to three planes, and that most of the information displayed is interpolation. However, the main point of this method is about display of data. The 16-segment model of the left ventricle  is the basis of all analysis of regional function in clinical cardiology, wall motion scoring as well as quantitative measurement by velocity, displacement and strain rate/strain imaging. In all these modalities, measurements are taken as representative of a whole segment, resulting in a circumferential resolution of 60°. This is true of any Bull's eye plot, whether of wall motion score or numerical measurements. Reconstruction to Bull's eye alone, does not add more information, but rather displays it in a more accessible form. The method itself, however, is not limited to three planes, but more planes will be non-standard, however. With a gated rotational probe, the number of planes could be increased, but the post processing time would increase proportionately. However, doubling the number of planes, the whole post processing time would still be less than five minutes. The impact of the number of planes has been extensively studied previously . Three planes result in a correct average of volume and surface area, even in asymmetric ventricles. Variability is high, and decreases substantially with an increase to four planes, and little is gained by further increase. Concerning regional dyssynchrony, more planes would increase the exact delineation of the areas. This, however, applies to the whole concept of segmental analysis.
Using three planes, the average angular separation is 60°. This is in accordance with the standard representation of bull's eye, and was chosen for the visual display. The true position of the planes is closer to 0, 62 and 101°. These values could be implemented into the model at need, but previous analysis have shown that a variation of ± 15° results in less than 2% error , so the practical advantage of this correction is dubious.
The radial resolution (along the ultrasound beams) is a little more than strain offset length, around 15 mm; i.e. about twice as good as that of the 16-segment model.
Bull's eye and M-mode array could be obtained more directly, without the 3D reconstruction. The 3D surface model, however, incorporates the curvature data, which truly adds new information. The main advantage of this is giving an approximate representation of the true area. By subjective assessment, it was an additional help in differentiating infarct areas from basal artefacts in two patients, as it gave a more correct display of the shape and size of the infarct area. The method has further possibilities of true quantitative infarct area measurement, subject to validation studies.
The 3D surface model gives a more intuitive visualisation of the left ventricle, for clinicians unaccustomed to bull's eye or curved M-mode. However, this is also a potential source of pitfalls. The processing method will result in a grid, whether there are tissue data or dropouts. Appropriate blanking of the apical area should be applied to avoid interpretation of angle distortion in the apex as dyskinesia, but as already discussed; this region is far smaller than the extent of the apical segments. Finally, the representation still only shows longitudinal deformation, but as discussed previously this may reflect compound deformation in more than one dimension.
Combining data in a four-dimensional data set results in versatility. The method described may be seen as a method for storing data, where any desired derived parameter and display method can be extracted. Segmental waveform analysis, as well as any kind of parametric display modality as is M-mode, bull's eye and 3D surface is then available. As shown, each type of display contributes to the total information: Bull's eye by showing the whole of the surface, M-mode by showing space – time relations and 3D surface by displaying the anatomy of the surface and the correct area.
Compensation for HR variability during examination
With varying HR, the RR-interval will vary too. Systole and diastole varies differently, so a simple linear correction ("stretching") by the end points of the heart cycle is insufficient. A better approximation would be to correct systole and diastole separately, by identifying a point in end-systole, and then fit the two parts of the cycle separately – a three point correction. The present algorithm instead uses a 200-point correction by ECG, so the correction should in theory be correct down to 5 ms, but the use of ECG makes it vulnerable to noisy ECG curves and to variations in automatic trigging. That this approach is less than perfect can be seen in figs 1 and 3.
Limitations of the study
The present study is a feasibility study only, with limited numbers, but allowing a more detailed discussion of technical detail and individual findings. The prevalence of artefacts in a normal population, as well as the identification of those in patients, and the resulting diagnostic accuracy should be addressed in larger studies. It is still evident that interpretation of colour images is experience dependent, and influences reproducibility of diagnosis. Small numbers may also explain lack of significant differences shown in table 1, but findings that need larger numbers for significance have limited clinical value.
In this study, care was taken not to exclude artefacts from the quantitative analysis, to show the impact of those. As the study has demonstrated, colour imaging assists in identifying the artefacts, and the impact of identifying and eliminating artefacts before quantitative analysis has to be studied prospectively.
Post-systolic shortening, or thickening in the transverse direction  is generally defined as shortening after closure of the aortic annulus. In quantitative analysis, especially in strain, the exact location of end systole is important, to identify and measure peak value. In colour imaging, especially in 3D reconstruction, this is not equally important. The post-systolic shortening has a definite duration, extending into the early filling period, where elongation in other areas is visible. The exact location of the time of peak is not important.
Possible applications and further development
There are two main areas of application. In acute infarction, infarct area is important in prognosis. In addition, identification of an area at risk, may be important in clinical decisions, although the utility of this need to be established.
The other main area is in stress echocardiography. The experienced stress echo cardiographer does a quick visual assessment of the whole cine loop, before scoring in individual segments. This results in quick a decision reached of whether dyssynergy is present or not, and whether segmental scoring is necessary. Colour parametric imaging may to some degree duplicate this by making it possible to evaluate the homogeneity of colour, in one glance, and further to identify the segments where measurement is necessary. Colour display may also facilitate the learning of stress echo interpretation.