HEMODYNAMICS OF ARTERIAL STENOSESTHE DEVELOPMENT of a stenosis in a major artery may significantly alter the blood supply to the peripheral vascular beds supplied by the artery. Since the early work of Mann et al., 1 much attention has been given to thisFrom the Department of Engineering Science and Mechanics, Biomedical Engineering Program, and the Department of Veterinary Anatomy, Physiology, and Pharmacology, Iowa State University, Ames, Iowa.Supported by the Engineering Research Institute, Iowa State Univerproblem, with special consideration given to the concept of the "critical stenosis," which generally has been defined as one for which a small, further increase in the severity of the stenosis will cause a significant reduction in blood VOL. 41, No. 1,JULY 1977 flow. This definition of a critical stenosis is not complete since the effect of a stenosis is influenced not only by the severity of the stenosis, but also by other geometric factors such as length, 2 "" 1 the peripheral resistance of the distal beds, 5 " 8 and collateral flow.9 "" The interaction between the flow through a stenosed artery, collateral flow, and peripheral resistance can be illustrated through the consideration of the simplified, but useful, hydraulic model shown in Figure 1. For this model it is assumed that the resistance of all peripheral beds distal to the stenosis can be considered as a lumped resistance R p . The time-averaged flow through the stenosis is Q s , net collateral flow is Q c , and the flow actually supplied to the distal beds is Q = Q s + Q c . The arterial pressure proximal to the stenosis is p a , and the venous pressure, p v , will be assumed to be zero. The bar over a symbol signifies its time-averaged value, i.e., the average value of the quantity taken over one cardiac cycle.In a normal vessel the commonly used relationship between pressure, flow, and peripheral resistance is 0 = Pa/Rp,which demonstrates that the flow is a function of the driving pressure p a and the resistance Rp. Furthermore, under normal flow conditions the collateral flow is expected to be negligible because the collateral resistance is large compared to the resistance of an unobstructed artery.As a stenosis develops, a pressure drop Ap = p a -pi is created across the stenosis, so that the driving pressure for flow to the peripheral beds is now p, rather than p a , and it is clear that the flow to the peripheral beds will be reduced unless the peripheral resistance can be reduced to compensate for the reduction in driving pressure or adequate collateral flow develops. In equation form Q = p,/R p = (p a -Ap~)/R P = ( Pa /R P )(l -Ap7p a ), (2) and this relationship shows how the pressure drop across the stenosis interacts with the peripheral resistance and arterial pressure to control the flow to the distal beds. A complicating feature of Equation 2 is the fact that the term Ap is a function of the flow through the stenosis. Thus, the effective resistance of the stenosis, as evidenced by Ap, changes the flow and, in fact, Ap increases...