Physiological Basis of Flow Dependence of Gorlin Formula Valve Area in Aortic Stenosis: Analysis Using an Hydraulic Model of Pulsatile Flow
Robert D. Rifkin MD

To assess whether cardiac output dependence of Gorlin formula valve area in aortic stenosis is due to a deficiency in the Gorlin formula, we devised a numerical model of pulsatile flow in which total pressure gradient was the sum of the convective (Bernoulli) gradient and pressure recovery plus an additional term representing viscous drag which we based upon orifice discharge coefficient data published in the hydraulic engineering literature. With this model, we calculated mean systolic gradient in numerically simulated pulsatile flow using various time-velocity flow profiles over a broad range of flow rates for valves with true valve areas between 0.5 and 2.0 cm2. Apparent Gorlin valve area at any cardiac output was then found by substituting the mean gradient given by the model at that output into the Gorlin formula. For true valve areas ≤1.5 cm2, apparent Gorlin valve area decreased very little when cardiac output fell from 5 to 2.5 l/min. For larger valve areas, flow dependence was much greater, but still not large enough to alter management decisions regarding valve replacement. We conclude that clinically reported flow dependence in low flow states is not due to a deficiency in the Gorlin formula and that true anatomic valve area changes are more likely to account for reported flow dependence of Gorlin valve area in these situations.

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