Investigation of the Influence of Smooth Muscle Contractions on the Properties of the Wall of a Small Arterial Vessel

The plane problem of the effect of contractions of smooth muscle cells in the wall of a resistance vessel under the action of transmural pressure on the radius and the distribution of stresses in the vascular wall is considered. It is assumed that in the inactivated state the vessel wall is hyperelastic, and the contraction of smooth muscle cells as a result of activation contributes to the circumferential stress alone. Based on the model and published experimental data, a functional dependence of the active stress on the concentration of the activator of smooth muscle contraction is obtained. Calculations show that the total stress in the wall is determined mainly by the active component. With increasing pressure, contractions of smooth muscle cells lead to decrease in stresses, while the pattern of the distribution of circumferential stresses changes. The circumferential stretch ratios also decrease with activation and their distribution becomes more homogeneous. In both passive and active vessels, the modulus of the ratio of the radial to circumferential stress decreases with increase in tension, this ratio being several times greater in the active vessel than in the passive one.