## 4 Discussion  
### Multiphysics Modeling  
In this work, a SWE multiphysics modeling approach incorporating the biomechanics and imaging physics of the shear wave propagation problem was presented, providing valuable insights into how the ultrafast US sequence and signal processing affects the true shear wave's characteristics in the time and frequency domain, and the subsequent shear modulus characterization. Furthermore, a modeling approach offers the benefits of full flexibility at the level of the tissue mechanics (tissue geometry, material properties and tissue surrounding) and ultrasound physics (ARF configuration, imaging settings and processing techniques). This approach was applied to a low-viscous pediatric ventricular phantom model, displaying clear shear wave dispersion as can be seen from the frequency-dependent phase velocity in the Fourier spectra and the split shear wave front in the temporal shear wave pattern for both experiment and biomechanics model [23]. The ventricular geometry was mainly the cause of the observed dispersion, as incorporating the measured viscoelastic material properties in the model did not significantly alter the shear wave characteristics (see [23] for details). A similar multiphysics approach has already been used by [PERSON] et al. [40] to study jitter errors and displacement underestimation in unbounded media, also in combination with experiments. Another study [41] used these same tools to investigate how parameters related to shear wave excitation and tracking affected the quality of shear wave speed images. However, both studies mimicked a different elastography technique, called Acoustic Radiation Force Imaging (ARFI), which employs conventional line-by-line scanning instead of plane wave imaging to visualize the shear wave propagation. Figure 6: Comparison of estimated shear modulus via material characterization methods based on group and phase velocity for the numerical (biomechanics and ultrasound simulations with single and compounded plane wave imaging (PWI)) and experimental shear wave acquisitions (single and compounded PWI). The mechanically determined shear modulus \(\mu_{\text{mech}}\) of 24.3 kPa is also indicated in this figure, corresponding to the modeled stiffness. The boxplot represents the variation in shear modulus estimation throughout depth (\(n=10\)), where the box displays first, second (median) and third quartiles and the whiskers indicate minima and maxima. In general, the multiphysics model was capable of reproducing the experimental results (see Figures 3-6), indicating that the simulated biomechanical ground truth is a good representation of the actual shear wave physics occurring in the PVA phantom. However, there were also some discrepancies in shear wave visualization and characterization. For the shear wave's characteristics in the time and frequency domain, we firstly noticed a different axial velocity magnitude (see Figures 3 and 4) and Fourier energy amplitude (see Table 3) as a result of scaling the time-averaged acoustic intensity to 1500 W/cm\({}^{2}\) when calculating the numerical ARF. For the virtual compounded acquisition, there was the additional effect of large shear wave travel in between ultrasound frames in combination with the presence of high relaxation velocities (blue in Figure 4) in the biomechanical simulation, indicating that compounding in the simulation reduces the downward velocities (red in Figure 4) more than in the experiment. Secondly, there were also differences in the temporal axial velocity pattern (e.g., larger relaxation peak at the center of the phantom for the simulations) and frequency spectra (e.g., more secondary mode excitation at 40% tissue thickness in the simulations).