## 4 Discussion
### Effect of Ultrafast Imaging on SWE in the Studied Left Ventricular Model  
We studied the effect of ultrafast imaging on SWE by comparing shear wave visualization and characterization obtained from US and CSM simulations of our left ventricular phantom model. When analyzing the temporal shear wave patterns of all simulations in Figure 4, a clear broadening of the shear wave front and underestimation of axial velocities is noticeable for both imaging acquisitions. A similar negative velocity bias was also recently reported when using coherent plane wave compounding for Doppler imaging [42]. Furthermore, the plane wave compounded images revealed a shear wave pattern different than the single plane wave images: the split shear wave front, clearly visible in the single plane wave acquisition, was less observable in the compounded images (Figure 4). Furthermore, the experimental compounded images in Figure 3 showed a completely merged wave front instead of the split wave front as observed in the single plane wave images. Even though this observation was less clearly noticeable in the simulations (due to the presence of a larger relaxation peak in between the split wave front compared to the measurements, as mentioned in Section 4.1), the multiphysics model still demonstrated that these observed differences in temporal characteristics of the shear wave are mainly attributed to the chosen imaging parameters, as both virtual imaging acquisitions were derived from the same true mechanical wave propagation (see Figure 4). We also investigated the subsequent changes in the shear wave's frequency characteristics, which showed that the detected excited frequencies, amplitudes and modes did not necessarily correspond to the ones excited in the biomechanical model. Indeed, the biomechanical frequency spectra are solely dependent on the model characteristics and the ARF properties [43], whereas the imaged spectra are also affected by plane wave imaging, acting as a low-pass filter, and by image processing techniques such as pixel averaging and slow time up-sampling. Next to this qualitative investigation, we also quantitatively studied the effect of ultrafast imaging on the performance of SWE by comparing the SWE-derived shear modulus for both US and CSM simulations (see Figure 6). This study showed that ultrafast imaging had mainly an effect on stiffness characterization through the group speed method: single and compounded PWI simulations led to median stiffness underestimations of \(-2.2\) kPa (\(-4.0\) kPa when discarding 20 data points) and \(-1.1\) kPa (\(-6.2\) kPa when discarding 20 data points) respectively compared to the SWE-derived stiffness estimates from the biomechanical simulations. Additionally, the results of the TOF method when discarding 20 edge elements were very depth-dependent for the single PWI simulation. This was also observed for the experiments in Figure 6. This large dissimilarity in depth-dependency of the stiffness estimates is due to a difference in meaning of the fitted linear relationship in the TOF method when discarding more or less data points for the single PWI acquisition. When 20 data points are discarded during the fitting procedure, the fitted linear relationship represents the true non-shifted shear wave position throughout time which varies a lot across depth, whereas it depicts an averaged shear wave position in time when only 5 data points are discarded (Figure S1). The latter corresponds to the TOF shear wave characterization with compounded PWI (as can be seen in Figure 6 and Figure S1), as the compounded images already visualize the averaged shear wave behavior.