Modeling prosthetic heart valves for numerical analysis of blood flow in the heart

This paper extends our previous work on numerical analysis of blood flow in the heart. In that work the boundary forces were evaluated by solving a fixed-point problem, which we now reformulate as a problem in optimization. This optimization problem, which involves the energy function from which the boundary forces are derived, is solved by Murray's modification of Newton's method. The energy function turns out to be an extremely useful tool in modeling prosthetic heart valves. To enforce a constraint on the valve, we use an energy function which is zero when the constraint is satisfied and positive otherwise. The energy function must be invariant under translation and rotation so that conservation of momentum and angular momentum will be satisfied. We use this technique to construct computer models of several prosthetic valves, and we study the flow patterns of these valves in our computer test chamber.