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. The model is based on the experimental data obtained for cerebral arteries, but may be used for any other resistive vessel. The model not only describes the regulation of the vascular lumer by transmural pressure but also shows realistic behaviour of the radius and intracellular cytosolic Ca2+ concentration at different velocities of pressure change. Possible variations of the radius along the vessel as a consequence of the Bayliss effect are considered.
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