A theoretical investigation of low frequency diameter oscillations of muscular arteries

Abstract

Spontaneous low frequency diameter oscillations have been observedin vivo in some muscular arteries. The aim of this paper is to propose a possible mechanism for their appearance. A lumped parameter mathematical model for the mechanical response of an artery perfused with constant flow is proposed, which takes into account the active behavior of the vascular smooth muscle. The system of governing equations is reduced into two nonlinear autonomous differential equations for the arterial circumferential stretch ratio, and the concentration of calcium ions, Ca²⁺, within the smooth muscle cells. Factors controlling the muscular tone are taken into account by assuming that the rate of change of Ca²⁺ depends on arterial pressure and on shear stress acting on the endothelium. Using the theory of dynamical systems, it was found that the stationary solution of the set of governing equations may become unstable and a periodic solution arises, yielding self-sustained diameter oscillations. It is found that a necessary condition for the appearance of diameter oscillations is the existence of a negative slope of the steady state pressure-diameter relationship, a phenomenon known to exist in arterioles. A numerical parametric study was performed and bifurcation diagrams were obtained for a typical muscular artery. Results show that low frequency diameter oscillations develop when the magnitude of the perfused inflow, the distal resistance, as well as the length of the artery are within a range of critical values.