Insights from three-dimensional echocardiographic laser stereolithography : Effect of leaflet funnel geometry on the coefficient of orifice contraction, pressure loss, and the gorlin formula in mitral stenosis

Three-dimensional echocardiography can allow us to address uniquely three-dimensional scientific questions, for example, the hypothesis that the impact of a stenotic valve depends not only on its limiting orifice area but also on its three-dimensional geometry proximal to the orifice. This can affect the coefficient of orifice contraction (Cc = effective/anatomic area), which is important because for a given flow rate and anatomic area, a lower Cc gives a higher velocity and pressure gradient, and Cc, routinely assumed constant in the Gorlin equation, may vary with valve shape (60% for a flat plate, 100% for a tube). To date, it has not been possible to study this with actual valve shapes in patients. Three-dimensional echocardiography reconstructed valve geometries typical of the spectrum in patients with mitral stenosis: mobile doming, intermediate conical, and relatively flat immobile valves. Each geometry was constructed with orifice areas of 0.5, 1.0 and 1.5 cm2 by stereolithography (computerized laser polymerization) (total, nine valves) and studied at physiological flow rates. Cc varied prominently with shape and was larger for the longer, tapered dome (more gradual flow convergence proximal and distal to the limiting orifice): for an anatomic orifice of 1.5 cm2, Cc increased from 0.73 (flat) to 0.87 (dome), and for an area of 0.5 cm2, from 0.62 to 0.75. For each shape, Cc increased with increasing orifice size relative to the proximal funnel (more tubelike). These variations translated into important differences of up to 40% in pressure gradient for the same anatomic area and flow rate (greatest for the flattest valves), with a corresponding variation in calculated Gorlin area (an effective area) relative to anatomic values. The coefficient of contraction and the related net pressure loss are importantly affected by the variations in leaflet geometry seen in patients with mitral stenosis. Three-dimensional echocardiography and stereolithography, with the use of actual information from patients, can address such uniquely three-dimensional questions to provide insight into the relations between cardiac structure, pressure, and flows.