[Mathematical modeling of non-stationary spatial gradients of nitric oxide in the muscle wall of blood vessels].

A mathematical description of the diffusion of low-mass uncharged molecules in homogenous biological medium was considered. The distribution of nitric oxide in vascular smooth muscles was taken as an example. The model makes it possible to describe the spatial-temporal gradient of NO near the surface of endothelium in terms of one-dimensional diffusion. In the case of the constant rate of nitric oxide production in endothelium, an analytical expression of nonstationary distribution of NO concentration was obtained. It was found that, if the diameter of blood vessel exceeds 800 microns, the concentration of nitric oxide on the outer border of vascular smooth muscle layer is less than the equilibrium dissociation constant (0.25 microM) of soluble guanylyl cyclase. Thus, the diffusion of nitric oxide produced in endothelium is insufficient to cause a relaxation of vascular smooth muscles in medium- and large-size blood vessels. In this case, the role of nitric oxide synthesized in vasa vasorum acquires a special significance for the regulation of vessel tone.