Minimal Model of the Dependence of Stresses in a Cerebral Vessel Wall on Smooth Muscle Cell Parameters

A minimal mathematical model of the wall of a small arterial vessel was created based on the published results of experiments with rat cerebral vessels. It was assumed that the active stress has only a circumferential component and depends on the circumferential stretch, the calcium concentration in the cytoplasm, and the membrane potential of smooth muscle cells. The model of a small artery qualitatively reproduces the results of more sophisticated models of other vessels under normal physiological conditions. Unlike in a similar model with a single cell parameter taken into account, the addition of the membrane potential as one of the main parameters made it possible to detect a qualitative change that occurs in the dependence of circumferential stress on the stretch and radial coordinate with a change in vascular tone. At fixed values of the membrane potential and calcium concentration in the phase of vascular tone development, the stress decreases towards the outer wall of the vessel and increases with the increasing stretch. Once the tone has formed, the direction of changes in circumferential stress reverses.