Influence of orifice geometry and flow rate on effective valve area: an in vitro study

Fluid dynamics suggests that orifice geometry is a determinant of discharge properties and, therefore, should influence empiric constants in formulas (such as the Gorlin formula) to calculate stenotic valve area. An in vitro study utilizing a model of transmitral flow was conducted to investigate how the discharge coefficient changes with 1) orifice eccentricity (ratio of long to short diameter), 2) absolute area, 3) the presence of a nozzle-like inlet, and 4) varying flow. Twenty-three orifices with areas varying between 0.3 and 2.5 cm2 and eccentricities from 1:1, or circular, to 5:1, or elliptic, were tested. The calculated discharge coefficients ranged between 0.675 and 0.93. For a given area, the discharge coefficient decreased by a mean value (+/- SD) of 5.5 +/- 1.3% between circular orifices and 5:1 ellipses. Discharge coefficients increased by a mean of 8.9 +/- 3.5% from 0.3 to 2.5 cm2 area within each eccentricity class. A gradually tapering inlet (nozzle) raised the discharge coefficient by 8.8 +/- 3.9%, leading to a discharge coefficient between 0.81 and 0.93 for round orifices. The discharge coefficient did not change appreciably with flow. The concept of the discharge coefficient and its role in assessing restrictive orifices in general by hydraulic formulas (for example, the Gorlin and pressure half-time calculations) are discussed.