A tri-leaflet prosthetic cardiac valve with leaflets having an analytic shape in a selected position. The leaflets are connected to a valve body at attachment curves. The shape of the leaflet is selected from a set of geometries that can be represented mathematically. The attachment curve is selected to improve the durability of the tri-leaflet valve by moving the point of maximum loaded stress along the attachment curve away from the commissures. An inner wall of the valve body is given a non-circular shape near the attachment curve, the shape of the inner wall corresponding to the attachment curve. Also, a method of making a valve by selecting an analytic leaflet shape, selecting an attachment curve to improve durability of the valve by moving the point of maximum loaded stress along the attachment curve away from the commissures, and forming a valve body to support one or more leaflets, the valve body having a non-circular inner wall conforming to the attachment curve.
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