# Shear Wave Elastography Implementation on a Portable Research Ultrasound System: Initial Results
## 4 Discussion
### Phantom Experiments
In general, for all techniques and all inclusion types, the absolute bias increased as the inclusion diameter became smaller. For the largest target dimension that was used (\(16.7\,\mathrm{mm}\)), the observed bias was in the range of \(-9.6\) to \(-7.9\%\) for type IV inclusions, \(1.8\) to \(4\%\) for type III inclusions and \(14.8\) to \(16.4\%\) for type II inclusions. Furthermore, it should be noted that the SWS bias resulted in an even higher bias in the elasticity maps because the Young's modulus was proportional to the square of the SWS (see Equation (2)). In this work, the values that were provided by the phantom manufacturer were treated as the nominal values. Those values had a \(5\%\) tolerance for a given stiffness. Nevertheless, in the homogeneous case, all of the estimated average SWS values that were obtained by all three techniques were beyond this margin, which was a \(2.41\,\mathrm{m/s}\) maximum for background material. The same applied to heterogeneous phantom results in the majority of cases. Assuming that the real SWS values were within the margins provided by the manufacturer, this led to the conclusion that there were one or more bias sources present in the system. The bias effects in the SWE technique were investigated in works by other research groups, in which it was confirmed that the SWS values that were produced with the ARF and ToF approaches depend on the transducer, aperture size and pixel position. One possible cause of bias could be an undesired push beam intensity field as wide beam widths in the elevation direction can generate significant out-of-plane shear waves that bias the SWS estimates high [29]. It has been reported that this effect is stronger when in close proximity to the push beam axis in the lateral direction and with an increasing distance from the beam focus in the axial direction. In this study, the push beam focal point depth was set close to the probe elevation focus depth (\(25\,\mathrm{mm}\)) and SWS estimates that were close to the shear wave sources were not used. Although those measures could minimize the bias, the effects could not be dismissed entirely. Diffraction could be another cause of the bias. For a push beam, diffraction produces an acoustic intensity before and beyond the depth of focus, which generates additional shear waves in non-focal regions and interferes with shear waves from the focal point, thereby biasing the results high [29]. This effect is stronger for wider apertures. Furthermore, it was assumed in the data processingimplementation that the shear waves would only propagate in the lateral direction, which was reported to be another possible reason for bias [21]. Finally, the biased results could be also caused by system-dependent parameters, such as PRF error and transducer parameter mismatches between the real values and those used in the software or phase aberration [30]. Interestingly, similar levels of bias have been reported in other studies that used the same phantom and commercial systems [31; 32]. In summary, the reconstruction of SWS maps is a complex multi-step process and bias can arise at each processing stage. This then propagates through the processing pipeline, resulting in errors in the estimated SWS maps. Identifying the bias source could require a detailed analysis and was beyond the scope of this article. The same applies to the estimate variance. Exploring the effects of various system components on the bias and accuracy will be the subject of future work. No systematic evaluation of the SWS map resolution was performed in this study. The resolution depends on many factors that are related to shear wave excitation, SWS estimation method and the parameters that are used for its calculation [6]. Importantly, there is a trade-off between the accuracy and spatial resolution that is adjusted by the lateral correlation window sizes that are used in the SWS estimation [6; 28]. In this study, only a single lateral correlation window size was used (2.8 mm) in the heterogeneous experiments, which was found experimentally.