Mass-spring vs. Finite Element Models of Anisotropic Heart Valves: Speed and Accuracy

INTRODUCTION Heat valve dysfunction can lead to heart failure and death, and surgery is the standard treatment. Valve repair surgery is performed under cardiopulmonary bypass making it difficult for the surgeon to know if a surgical modification will be effective when blood flow is restored. A surgical planning system has been proposed to improve surgical outcomes by allowing a surgeon to explore valve repair strategies on a computer model of a patient’s valve (1). Many groups have published computational models of heart valves based on the finite element (FE) method, but they are prohibitively slow for simulating valve mechanics in an interactive setting. Massspring (MS) networks have been used as an alternative to FE methods for modeling deformable bodies, trading off accuracy for speed. In this study, we assess the trade-off between speed and accuracy in an anisotropic MS model of aortic valve leaflets. We compare accuracy and computational cost of a MS model to a FE model of a membrane formulated for large deformations. We first compare stress-strain curves of simulated square patches of membrane under biaxial loading to stress-strain curves calculated directly from the constitutive law. Then, to assess accuracy in a way that is more relevant to heart valve loading, we simulate deformation of a semicircular membrane under typical pressure experienced by the aortic valve under peak load.