# Physics of Within-Tissue Wave Propagation Generated by Pulse Propagation in the Carotid Artery
## 5 Discussion
It is generally known that soft tissue is more viscoelastic than PVA-material and this will have an extra damping effect on the wave patterns reducing all high frequency patterns. Also, the boundary conditions to minimize wave reflections did not work optimally due to the nature of the infinite elements (see Figure 1). The loading conditions did not replicate the shape of a physiological pulse nor its periodic course, therefore the actual mechanical interaction of the pressure pulse and the lumen wall was not realistically simulated. In addition, we did not account for the fluid-structure interaction or any vibrations that may arise from instabilities in the flow field, propagating to the wall and skin. It should be kept in mind that the accuracy of the presented results depends on the chosen finite element mesh size, interpolation grids in Matlab and the projection angle of the Radon transform. This is also related to the available computer power and performance requirements, which were very demanding for the FEM simulations of the patient-specific model (72 h on a Linux cluster using a single computing node containing two Intel E5-2670 processors each with 8 cores, 2.60  GHz processor base frequency, 64 GB of memory and Fourteen Data Rate InfiniBand). The main limitation of the current modeling environment is the lack of validation. However, we believe that the good correspondence between simulation and theoretical results for shear and surface wave propagation (see Table 1 and Figure 3) lends confidence to the current modeling results. The developed finite element model offers the advantage of visualizing and investigating the within-tissue wave propagation mechanics between lumen and skin, generated by the traveling pulse wave, which is difficult to obtain from experiments. Furthermore, it allows one to analyze multiple components of the displacements in 3D and gives access to other variables such as stresses. Compared to the LDV technique, the simulations provided a higher spatial resolution and adjustable temporal resolution (10 kHz and 0.2 mm over a 50 mm vs. 500 kHz and 15 mm over 45 mm [18]) and are not contaminated with any measurement noise. This high spatial resolution allowed us to employ an alternative method to the traditional LDV algorithms to estimate PWV, i.e., the Radon transform, an approach which is commonly used in the field of elastography to estimate wave speeds [33]. In contrast to the available methods for the LDV technique, this method provides a robust way of estimating wave speeds by yielding a linear wave trajectory based on the maximal Radon-projected displacements generated by the propagating wave. As this method requires a higher spatial and temporal resolution in combination with more measurement points, it might be more productive in the context of the recently developed LDV system consisting of 6-beams spaced 5 mm apart (total length 25 mm) by [PERSON] et al. [34]. Nevertheless, the developed simulation framework in this study can act as a validation tool for newly proposed LDV-processing techniques, since the simulated displacement data are not contaminated by any of the complexities present in an actual experiment (noise, limited spatial and temporal resolution, etc.) and it offers direct access to the actual PWV in the lumen. In addition to patient-specific intrinsic factors affecting the wave propagation from lumen to skin (e.g., carotid depth--as considered in this study), there are also some technical and operator-dependent factors influencing the LDV measured PWV value such as laser signal strength and the localization of the measurement points. The latter issue might be improved by providing a real-time data visualization of the spatio-temporal plots to the operator that demonstrates wave propagation at the skin, as shown in the results section of our model.