Minimal model for the dependence of stresses in the wall of a cerebral vessel on the parameters of a smooth muscle cell

Abstract

A minimal mathematical model of the wall of a small arterial vessel is described. This model is created based on the published results of experiments performed on rat cerebral vessels. It is assumed that the active stress has only a circumferential component and depends on the circumferential stretch, calcium concentration in the cytoplasm, and the membrane potential of smooth muscle cells. The presented model for a small artery can qualitatively reproduce the results of more sophisticated models for other vessels under normal physiological conditions. Unlike a similar model, that accounts for only one cellular parameter, the addition of membrane potential as one of the main parameters was crucial to reveal a qualitative change in the dependency of circumferential stress on stretch and the radial coordinate with an alteration in vascular tone. At fixed values of membrane potential and calcium concentration in the phase of a development of vascular tone, stress decreases as it approaches the outer wall of the vessel and increases as stretch increases, and after it is formed, the direction of changes in the circumferential stress reverses.