Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation

The present study addresses constitutive modelling and implementation of transversely isotropic hyperelastic material models for the analysis of the mitral valve. This valve separates the left atrium and left ventricle in the heart. Two convex strain energy potentials are employed in derivation of stress tensors and elasticity tensors. The plane stress and incompressibility conditions are accounted for directly. The relationships are implemented in an implicit code (ABAQUS) via the user-defined interface. Numerical simulations of the valve motion during a part of the heart cycle are carried out and compared to ultrasound measurements of a healthy human valve. The significance of placement of chordae tendinae is illustrated. The implementation provides a tool for simulations of both healthy and pathological mitral valve conditions. Copyright q 2007 John Wiley & Sons, Ltd.