Understanding the Role of Longitudinal Arterial Wall Motion in Blood Circulation from the Perspective of a Piano String

This work is aimed to establish engineering theories of the coupled longitudinal and radial motion of the arterial wall. By treating the arterial wall as a piano string in the longitudinal direction and as a viscoelastic material in the circumferential direction, and considering pulsatile pressure and wall shear stress from axial blood flow in an artery, the fully-formed governing equations of the coupled motion of the arterial wall are obtained and are related to the engineering theories of axial blood flow for a unified engineering understanding of blood circulation in the cardiovascular (CV) system. The longitudinal wall motion and the radial wall motion are essentially a longitudinal elastic wave and a transverse elastic wave, respectively, traveling along the arterial tree, with their own propagation velocities dictated by the physical properties and geometrical parameters of the arterial wall. The longitudinal initial tension is essential for generating a transverse elastic wave in the arterial wall to accompany the pulsatile pressure wave in axial blood flow. Under aging and subclinical atherosclerosis, propagation of the two elastic waves and coupling of the two elastic waves weakens and consequently might undermine blood circulation.