Recent computational methods enabling patient-specific simulations of native and prosthetic heart valves are reviewed. Emphasis is placed on two critical components of such methods: (1) anatomically realistic finite element models for simulating the structural dynamics of heart valves; and (2) fluid structure interaction methods for simulating the performance of heart valves in a patient-specific beating left ventricle. It is shown that the significant progress achieved in both fronts paves the way toward clinically relevant computational models that can simulate the performance of a range of heart valves, native and prosthetic, in a patient-specific left heart environment. The significant algorithmic and model validation challenges that need to be tackled in the future to realize this goal are also discussed.
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