Myogenic response of the cerebral vessel: a mathematical model

The myogenic response is most typical for small arterial vessels and consists in constriction of the vessel with an increase in transmural pressure, the pressure difference between the inner and outer surfaces of the vascular wall. There are many models describing this response. In models of last decades, in addition to macrostretchings and macrostrains, their microanalogues are introduced into consideration, that significantly complicates the description. In the presented work a simple model of the wall of the small cerebral artery is described, which includes the main parameters that control the myogenic response and corresponds to physiological processes underlining this response. It is believed that active stresses depend on stretching and the concentration of free calcium ions in the cytoplasm of the smooth muscle cell. In turn, the calcium content depends on the membrane potential, determined by the pressure. An axisymmetric stationary problem is considered; the wall material in the non-activated state is assumed to be pseudoelastic. Calculations showed a qualitative difference in the dependence of active stress on stretching and its distribution in the radial direction before and after the development of the vascular response. The calculated diameter values before and after exposure to substances affecting the polarization of the smooth muscle cell membrane are within the range of experimental values. These results indicate that the introduction of the dependence of calcium concentration on membrane potential expands the area of applicability of simple models of this kind for evaluating the value of vascular diameter.