Hemodynamics of collapsible vessels with tone: the vascular waterfall

A theoretical analysis is presented of pressure-flow relationships in arterioles based on the assumption that the presence of active tension produced by smooth muscle contraction causes a critical closing pressure which is itself a function of the magnitude of the active tension. This analysis differs from those previously carried out in that it uses the pressure-flow relationships of a waterfall rather than those described by Poiseuille's law to characterize the flow between arterioles and capillaries in the presence of active tension. It is suggested that, under some conditions, the driving pressure for the flow through arterioles is not the difference between the inflow pressure and outflow pressure of the arterioles, but rather the difference between the inflow pressure and the critical closing pressure. This seemingly slight modification causes marked differences in the interpretation of pressure-flow relationships and vascular resistance in the presence of active tone. Submitted on December 10, 1962