Pressure pulse velocity is related to the longitudinal elastic properties of the artery.

It is known that arteries in their natural position are always subject to a longitudinal stress. However, the effect of this strong longitudinal tension has seldom been addressed. In this paper, we point out that the traditional pulse wave velocity formulae considering only the circumferential elasticity fail to include all the important energies. We present a vigorous derivation of a pressure wave equation, the pressure wave equation with total energy, which considers all the important energies of the whole arterial system by treating the arterial wall and the blood as one system. Our model proposes that the energy transport in the main arterial system is primarily via the transverse vibration motion of the elastic wall. The final equation indicates that the longitudinal stress is essential and the high frequency phase velocity is related to the longitudinal tension along the arterial wall and its Young's shearing modulus. By applying this equation, we suggest that longitudinal elastic property is an important factor in hemodynamics and in the treatment of cardiovascular diseases.