Radial and Longitudinal Motion of the Arterial Wall: Their Relation to Pulsatile Pressure and Flow in the Artery

The aim of this paper is to analyze the radial and longitudinal motion of the arterial wall in the context of pulsatile pressure and flow, and to understand their physiological implications for the cardiovascular system. A reexamination of the well-established one-dimensional governing equations for axial blood flow in the artery and the constitutive equation for the radial dilation of the arterial wall shows that two waves—a pulsatile pressure wave in the artery and a radial displacement wave in the arterial wall—propagate simultaneously along the arterial tree with the same propagation velocity, explaining why this velocity combines the physical properties and geometries of both the blood and the arterial wall. With consideration of their coupling, the governing equations for the radial motion and longitudinal motion of the arterial wall are derived separately. The driving force for the radial motion of the arterial wall arises from its longitudinal motion. The longitudinal motion of the arterial wall is the standard longitudinal elastic wave with two driving forces: one associated with the pulsatile flow rate and the other associated with the radial motion. These derived governing equations shed insights on some recent experimental findings in the literature, including the correlation of measured arterial wall stiffness (solely based on the radial motion) to its longitudinal motion, the decreasing trend of arterial wall distensibility from the aorta to the periphery, the underlying mechanism of the longitudinal motion pattern of the common carotid arterial wall, and the motion pattern variation in longitudinal motion with aging and diseases