[Mathematical modeling of the response of a resistive vessel to pressure].

The response of small arterial vessels to internal pressure makes an essential contribution to autoregulation in the vascular bed. It is believed that intracellular cytosolic Ca2+ concentration plays a pivotal role in the regulation of smooth muscle contractility and hence of vascular lumen. A simple mathematical model of blood flow in a resistive vessel is suggested.

[Mathematical models of nitric oxide transport in a blood vessel].

The appearance of this review concerning the nitric oxide transport in a blood vessel wall is connected with the authors' interest in vessel tone regulation. The introductory part contains basic equations for resistive vessels, an outline of processes occurring in smooth muscle and endothelial cells, and the simulation of these processes. As a rule, the description of nitric oxide diffusion and reactions in blood vessels is given in the order of increasing complication of the models.

[A simple model of a vessel with a wall sensitive to mechanical stimuli].

Smooth muscles in the walls of small blood vessels under normal conditions are always moderately active, so that there is a certain reserve for blood flow adaptation to changed conditions by either narrowing or expanding of the vessel lumen. The previous studies of small vessel hydrodynamics have shown that the activity can cause specific instability of vessel steady states. In order to trace qualitatively the influence of numerous factors on the active state of the vessel, a simplified model of the vessel was proposed, which is reduced to a nonlinear ordinary equation of the first order with delayed argument.