## 4 Discussion
### Effect of Ultrafast Imaging on SWE in the Studied Left Ventricular Model
Nevertheless, the shear modulus estimates are depth-dependent for all applied material characterization methods, as can be seen in the spread of the boxplots in Figure 6. For the group velocity analysis (discarding 5 data points), this is mainly due to the difference in the shear wave propagation pattern at the upper and lower boundaries of the phantom (\(\pm 0\)-\(25\%\) and \(\pm 75\)-\(100\%\) depth) compared to the middle segment of the phantom (\(\pm 25\)-\(75\%\) depth), as visible in Figure S1. This group speed-derived stiffness difference between the boundaries and center of a tissue-mimicking medium was experimentally studied by [PERSON] et al. [44], in which they identified the presence of Scholte surface waves at the fluid-solid interface as the primary reason for this discrepancy. For the phase velocity analysis, the cause of the depth-dependency of the stiffness estimates is less straightforward, as the extracted frequency characteristics of the primary mode across depth were very similar (see Figure 5). However, as also shown in [23], characterizing deeper shear waves via the phase velocity analysis is more challenging as their 2D FFT energy content is smaller (fewer data points to fit) and their velocity amplitude is lower (lower signal-to-noise ratio), leading to less reliable shear modulus estimates. Phase velocity analysis provided a more robust and correct estimate for both the biomechanics and imaging simulations, as spectral characteristics of the tracked primary mode (fitted to the theoretical A0-mode) for all acquisitions are very similar, as shown in Figure 5. Furthermore, for both experiment and simulation, the true tissue stiffness was underestimated by the TOF method, independent of the number of considered data points, whereas phase velocity analysis provided a better estimate of the mechanically determined stiffness. This is in accordance with our previous findings of experimental work on the same ventricular model in which we only applied single PWI [23]. Nevertheless, if the stiffness estimation technique is chosen based on observed shear wave physics (i.e., TOF method for compounded images visualizing almost no dispersion and phase velocity analysis for single plane wave images depicting dispersion), differences of minimally 5.9 kPa and 9.3 kPa are obtained for measurements and simulations, respectively. This is about 25% of the value of the actual shear modulus, and non-negligible. Therefore, when studying low viscous settings evoking guided wave dispersion due to geometry, one should be cautious when selecting a tissue characterization method based on the observed shear wave pattern as this might be affected by the applied imaging set-up. In these cases, it might be relevant to also study phase velocity next to group velocity. It should be noted that the primary objective of this work was not to compare the performance of single and compounded PWI, as this requires (i) the study of multiple configurations and material models, (ii) the use of more complex SWE-based material characterization and (iii) the inclusion of noise in the numerical models. However, this work shows the potential of computational modeling in identifying potential pitfalls in shear wave visualization and characterization with SWE, demonstrated through a case study of an idealized SWE setting with little amount of noise (as shown by the good correspondence between experiment and simulation). Future research should focus on applying the current modeling technique to different settings to further study the performance of single and compounded PWI.