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.