# Physics of Within-Tissue Wave Propagation Generated by Pulse Propagation in the Carotid Artery
## 5 Discussion  
In the last decade, few studies have investigated the potential of LDV-based methods to assess local PWV estimation from skin vibrations generated by the pressure pulse traveling inside the underlying artery. LDV measurements have been performed with a two-beam LDV both in vitro (phantom set up mimicking arterial pulse propagation), and in vivo (CCA in healthy volunteers) [16; 17]. Preliminary results have assessed the technical feasibility of LDV to accurately measure the displacement waveform at two skin locations, but also emphasized that the complexity of the skin motion prevented accurate estimation of the pulse transit time between the two measurement sites, resulting in an uncertainty in the PWV results. The transit-time error depends on many factors: shape differences between the two recorded pulses, perturbations of the LDV outputs due to a non-optimal or too weak a degree of light reflection, the existence of spurious reflections, artifacts due to secondary sources of motion (e.g., swallowing, any involuntary body movement, movement of the LDV and vibrations coming from the environment) as well as limitations of the algorithm used to estimate pulse transit time [16]. An in vivo study on 48 patients [27] has shown that signal analysis is still the most difficult challenge to validate local PWV through an LDV-based method. As expected pulse transit times are small (ranging from 2.5 to 1 ms for a beam separation of 10 mm when assuming a PWV between 4-10 m/s). Thus, a small inaccuracy in the pulse transit time estimation can lead to a considerable error in PWV estimation. Several algorithms are currently available to determine the pulse transit time. Some of them use the first or second derivative of the displacement signal (e.g., second derivative method, tangent-intersect method) but these methods are sensitive to noise [28]. The cross-correlation method measures the similarity of two waveforms as a function of a time-lag applied to one of them but fails when comparing signals with shapes that are too different [17]. Common algorithms to estimate the pulse transit time from in vivo measurements are based on the identification of a reference point, typically the dicrotic notch or the systolic foot [29]. However, the identification of the reference point can often not be assessed unambiguously in a substantial portion of the data [27]. Further studies have tried to improve local PWV estimation by increasing the number of measuring points from two to four with 15 mm spacing between them. PWV obtained by such LDV measurements in an in vitro set-up consisting of an elastic tube embedded in tissue-mimicking materials, showed a good agreement with measurements performed by the more established ultrasound-based pulse wave imaging [18]. The LDV technique was also able to distinguish phantoms with greater stiffness (higher PWV) but not to determine the precise location of a stiffer inclusion due to the low spatial resolution of the measurements. In this work, we have presented a finite element model to gain a more fundamental understanding of wave propagation from mechanical perturbations initiated by arterial pressure pulses in a healthy carotid artery model, to the skin surface (measured by the LDV-technique). As explained in Section 3.1.2, the choice of numerical settings such as time increment size, numerical damping and mesh size, together with the material parameters (e.g., Poisson's ratio) highly influenced the computational efficiency and the reliability of the wave propagation simulations. Therefore, the appropriateness of the chosen numerical settings was initially verified by comparing the simulated displacement patterns of waves where a theoretical solution was at hand (shear and Rayleigh waves, as described in Section 2). It should be noted that these analytical solutions assume an infinite (shear waves) and semi-infinite (Rayleigh waves) isotropic linear elastic material, whereas our final model did not meet these geometrical requirements.