# Physics of Within-Tissue Wave Propagation Generated by Pulse Propagation in the Carotid Artery
## 1 Introduction  
Cardiovascular disease (CVD) remains the leading cause of death worldwide and contributes substantially to morbidity, disability and death in patients [1]. Besides continued efforts to find more effective treatment, identifying subjects at risk of CVD--especially among those categorized as having a low risk according to classical risk factors (age, gender, blood pressure, lipid levels, smoking status... )--has received a lot of attention in pre-clinical research. A particular aim of such studies is to prevent the development of CVD at a young age [2; 3]. There is compelling evidence that arterial stiffness is a biomarker that carries prognostic power above and beyond these classical risk factors [4]. The clinical \"gold standard\" method for evaluating arterial stiffness is carotid-femoral pulse wave velocity (PWV\({}_{c}\)t), calculated as the ratio of the distance between the carotid and femoral measuring sites, and the time taken for the arterial pulse to propagate from the carotid to the femoral artery [5; 6; 7]. Different devices are available to measure these pulse waveforms, but current methods have methodological issues (there is no unequivocal path between the carotid and femoral artery, and the measurement basically excludes the most distensible proximal aorta). Furthermore, they arerelatively demanding to use (e.g., arterial applamation tonometry, ultrasound), requiring trained operators and, in the case of magnetic resonance imaging, are associated with high costs [8; 9]. These limitations justify the continued search for an accurate, low-cost and non-contact measurement device for PWV assessment that can easily be used in daily clinical practice. In the early stages of atherosclerotic disease, alteration of the arterial elastic properties starts in localized regions to then become more widespread. Thus, a local PWV value represents a more precise indicator of the ongoing arterial stiffening compared with the regional PWV value calculated by the most common commercial devices [8]. Therefore, an easy to use device which allows arterial PWV assessment locally is needed. Within this context, we are exploring laser Doppler vibrometry (LDV) as a method to locally measure PWV in the common carotid artery (CCA), a superficial large elastic artery known to be prone to remodel and stiffen with age and disease [10; 11; 12]. LDV allows optical measurement of out-of-plane skin displacements as a function of time, in which the mechanical perturbation caused by the arterial pressure pulse can be identified. This measurement is then performed in at least two different spatial locations along the carotid artery (CA) and PWV can consequently be calculated as the ratio of the distance between the laser beams and the time shift of the recorded displacement signals. Due to the limited distance between the laser beams and the total length of the CCA (a few centimeters), LDV provides a local estimation of PWV compared to the carotid-femoral PWV measurement. The technical feasibility of LDV as a technique for PWV assessment has been explored in some in vitro and in vivo studies [13; 14; 15; 16; 17]. Recent studies have also shown good correspondence between PWV evaluated with LDV and ultrasound-based pulse wave imaging (PWI) in a phantom, and demonstrated the potential of LDV to detect arterial wall stiffening [18]. Even though previous studies have shown promising results for LDV as screening tool for CVD, the understanding of the generated wave propagation mechanics between arterial wall and skin surface is still limited. Indeed, the waves are subjected to reflections, attenuation and interaction with the surrounding structures and organs, potentially leading to wave interference or wave mode conversions, complicating the relationship between the arterial pressure pulse and the corresponding skin displacement.