# Physics of Within-Tissue Wave Propagation Generated by Pulse Propagation in the Carotid Artery
## 5 Discussion
The estimated wave speed corresponded best with the imposed PWV (1.3%) in the proximal part of the model (z \(<\) 20 mm), since the geometry of the upper wall and centerline is then very similar (see Figure 1b). At the skin level, almost no effect of this split wave front was observed and traveling wave fronts V\({}_{1}\) and V\({}_{2}\) were tracked by a single line. Similarly to the CCA model, estimated wave speed at the skin corresponded best with the imposed V\({}_{\mathrm{z}}\) when considering a PWV of 7 m/s (-3.1%). The deviation was higher for a V\({}_{\mathrm{z}}\) of 4 m/s (47.0%) and a V\({}_{\mathrm{z}}\) of 10 m/s (36.0%). Figure 11 shows a large range in estimated speeds for the secondary waves in all simulation cases. It should be noted that in some cases, i.e., the CCA model with shock impulse loading condition and the patient-specific CA model with imposed PWV of 10 m/s, the speed of the secondary wave corresponded better with the expected or imposed velocity than the velocity of the main wave at the skin surface. These results suggest that the main wave front at the lumen level not necessarily translates into a main wave front at the skin level. However, these results again need to be interpreted with care as the modeled geometry and boundary conditions also have an effect. In other simulation cases, the nature of these secondary waves might be related to the propagation of the free vibrations of the surrounding tissue that is excited during the pulse transmission; However future work should include a more in-depth study of all displacement components and the application of advanced wave analysis techniques to better understand the nature of these secondary waves. Results supported the conclusion that the skin displacement is not a simple overlapping of free and induced waves, but the result of a combination of multiple reflections and re-combinations which iterate along the model's length in time, and are thus hard to predict and interpret. Therefore, we can conclude that the transmission of a single pulse creates a complex skin displacement pattern that manifests with changes in displacement amplitude, spatial lag and propagation velocities (V\({}_{1}\) and V\({}_{2}\)). Our results can be considered as an initial step towards a better understanding of the LDV-measured skin vibration signals by studying the wave propagation physics between the lumen and the skin. The model showed that the correspondence between the actual PWV in the lumen and the PWV measured at the skin surface depended on the magnitude of the PWV in the lumen and the studied subject (arterial depth and geometry). To the best of our knowledge, this work represents the first computational study that has investigated in detail the induced skin displacement in a structural model of a healthy artery for the estimation of pulse wave propagation speed. Indeed, until now in this context, a fluid-structure finite element approach has been adopted only to study the sound generated in a stenosed artery and transmitted through biological tissues to the skin, to investigate the possibility of using the LDV technique for arterial stenosis detection [30; 31; 32]. Although the developed numerical model has allowed us to study the propagation of a single traveling impulse under prescribed conditions in a simplified environment, it rests on several assumptions. For instance, the artery was approximated as a straight cylinder in the CCA model without any wall thickness. The absence of modeling the arterial wall did not allow the control of arterial stiffness in a direct way (e.g., increasing the Young's modulus of the material), thus arterial stiffening was indirectly simulated by varying the speed of the propagating pulse. Moreover, the effect of the surrounding biological structures (e.g., muscle, fat, bones) was not reproduced and the soft tissue was modeled as an isotropic homogenous viscoelastic medium without any biological discontinuities.