A quasi-one-dimensional flow of a viscous Newtonian fluid in a small artery able to regulate its lumen by the level of the contractile activity of smooth muscle cells of the vascular wall is considered. Among the factors that influence the muscle contractility, mechanical stimuli, such as the pressure difference between the inner and outer surfaces of the vessel wall and wall shear stress, are of importance. The equations of the model are based on experiments on the brain vessels of laboratory rats. The calculations show that both the magnitude and direction of the radius response to a mechanical stimulus depend on the initial state of the vessel wall. Transient and oscillatory flows were considered and the degree of participation of each of the above-mentioned mechanical stimuli in the regulation of the vessel lumen and blood flow-rate was estimated.
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