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With the arterial wall modeled as an initially-tensioned thin-walled orthotropic tube, this study aims to analyze radial and axial motion of the arterial wall and thereby reveal the role of axial motion and two initial tensions of the arterial wall in arterial pulse wave propagation. By incorporating related clinical findings into the pulse wave theory in the literature, a theoretical study is conducted on arterial pulse wave propagation with radial and axial wall motion. Since the Young wave is excited by pulsatile pressure and is examined in clinical studies, commonly measured pulsatile parameters in the Young wave are expressed in terms of pulsatile pressure and their values are calculated with the well-established values of circumferential elasticity (E) and initial tension (T0) and assumed values of axial elasticity (Ex) and initial tension (Tx0) at the ascending aorta and the carotid artery. The corresponding values with exclusion of axial wall motion are also calculated. Comparison of the calculated results between inclusion and exclusion of axial wall motion indicates that 1) axial wall motion does not affect radial wall motion and other commonly measured pulsatile parameters, except wall shear stress; 2) axial wall motion is caused by wall shear stress and radial wall displacement gradient with a factor of (Tx0T0), and enables axial power transmission through the arterial wall; and 3) while radial wall motion reflects E and T0, axial wall motion reflects Ex and (Tx0T0). 

With consideration of a full set of mechanical properties: elasticity, viscosity, and axial and circumferential initial tensions, and radial and axial motion of the arterial wall, this paper presents a theoretical study of pulse wave propagation in arteries and evaluates pulse wave velocity and transmission at the carotid artery (CA) and the ascending aorta (AA). The arterial wall is treated as an initially-tensioned, isotropic, thin-walled membrane, and the flowing blood in the artery is treated as an incompressible Newtonian fluid. Pulse wave propagation in arteries is formulated as a combination of the governing equations of radial and axial motion of the arterial wall, the governing equations of flowing blood in the artery, and the interface conditions that relate the arterial wall variables to the flowing blood variables. We conduct a free wave propagation analysis of the problem and derive a frequency equation. The solution to the frequency equation indicates two waves: Young wave and Lamb wave, propagating in the arterial tree. With the related values at the CA and the AA, we evaluate the influence of arterial wall properties on their wave velocity and transmission, and find the opposite effects of axial and circumferential initial tensions on transmission of both waves. Physiological implications of such influence are discussed.