DIAGNOSTIC METHODS VALVUIAR HEART DISEASE Hydraulic estimation of stenotic orifice area: a correction of the Gorlin formula

To determine the source of errors in the Gorlin formula for estimating stenotic valvular orifice area, we used a pulsatile flow model that emulated left ventricular and aortic pressures and flow and allowed control of ventricular outflow orifice area. After comparing orifice areas calculated by the Gorlin formula with actual orifice areas, the Gorlin formula constant (k) was found to be highly correlated with the square root of the mean transvalvular gradient (r -= .95). A new formula was derived empirically aid predicted areas more accurately and with smaller standard errors than the Gorlin formula in the model (r .98, SEE = 0. 1 1 and r = .87, SEE = 0.28, respectively) in a series of 19 patients with Hancock porcine xenograft valves (r = .89, SEE = 0.07 and r = .60, SEE = 0. 12, respectively) and 1n the original series of patients reported by Gorlin and Gorlin in proposing the Gorlin formula (r = .93, SEE = 0.11 and r = .91, SEE = 0. 12, respectively). Circulation 71, No. 6, 1170-1178, 1985. THE GORLIN FORMULA,' introduced in 1951 and later modified in 1972,2 has become the standard method of estimating valvular orifice areas in the presence of stenosis. Unfortunately, significant questions exist concerning its accuracy. Several investigators3-9 have noted apparertierrors in valve area calculations made with the Gorlin formula (involving both patient studies in vivo and models in vitro), particularly in the presence of extremes of pressure gradient or flow. After studying hemodynamic data from 175 patients with mitral xenografts who underwent catheterization shortly after surgery, Ubago et al.3 noted a wide disparity between valve areas calculated with the Gorlin formula and actual valve areas. This same disparity was reported by Bache et al.', who found questionable increases in valve areas calculated with the Gorlin formula during exercise in patients with significant native aortic stenosis. Richter5 suggested that errors may be as great as 100% in patients with low valvular flows and pressure gradients. The Gorlin formula was derived from two simplified From the Department of Computer Science, Utah State University, Logan, UT, and the Department of Medicine, University of Texas Health Science Center, Audie Murphy Veterans Hospital, San Antonio, TX. Supported in part by the American Heart Association, Texas Affiliate, and the Veterans Administration. Address for correspondence: Scott R. Cannon, Ph.D., Department of Computer Science, UMC-42, Utah State University, Logan, UT 84322. Received Jan. 23, 1985; accepted March 7, 1985. 1170 equations describing steady-state flow through an orifice: