A mathematical description of the myogenic response in the microcirculation

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Abstract
A mathematical model for description of static and dynamic myogenic responses to change of vascular transmural pressure in the arterioles of skeletal muscle was developed for the purpose of elucidating some basic characteristics of the myogenic vascular control system which have proved difficult to reveal by physiological observations alone. The model, which is a refined version of a pervious one (Borgstrome and Grande 1979), is based on a force-equilibrium in the arteriolar wall, including passive forces related to vascular transmural pressure, wall elasticity and wall viscosity, an active force related to resting vascular tone, and the active static and dynamic myogenic forces considered to be related to and triggered by wall tension (force) and its rate of change as indicated by previous results. The effects of biological inertia of shifts along the length-tension curve of the smooth muscle and of pressure induced reactions in the more proximal arterial vessels, were taken into account in the present force-equilibrium equation for the arterioles. Arteriolar wall viscosity was assumed to decrease with increasing rate of wall movement, a behavior predicted by the model and corroborated by in vitro observations on larger vessels. The model was found capable of faithfully simulating microvascular myogenic responses in cat skeletal muscle in vivo in response to ramp as well as impulse transmural pressure stimuli over the entire biological range from maximum constriction to dilatation. With such characteristics, it can serve as a useful complement to physiological approaches in attempts to define more precisely the mode of operation of the myogenic control system and to reveal inherent complexities of biophysical factors and of interaction of other control mechanisms in microvascular regulation in vivo, as exemplified by presented tests and preliminary results.

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