Dynamic simulation of heart mitral valve with transversely isotropic material model

Abstract

This thesis develops two methods for simulating, in the finite element setting, the material behavior of heart mitral valve leaflet tissue. First, a mixed pressure-displacement formulation is used to implement the constitutive material behavior with general 3D elements. Second, a shell is formulated that incorporates the 3D material behavior by use of a local plane stress iteration method. Both of these works are based on an existing invariant-based strain energy function that has been experimentally determined for the mitral valve leaflet tissue. Since this material is considered to be nearly incompressible, a mixed pressure-displacement (u/p) formulation is needed to apply the material model in 3D elements. The standard (u/p) formulation is; employed with a modification to ensure positive definiteness of the constitutive tensor at low strains. The shell formulation is introduced as a computationally less expensive alternative to the use of 3D elements. A 4-node shell with mixed interpolation of transverse shears is implemented. To incorporate the 3D material model into this shell, a local plane stress iteration is used to enforce that the shell stress assumption at each integration point. Comparisons of numerical results to analytical predictions verify the accuracy of both the (u/p) formulation and shell element. These methods provide useful bases for finite element simulations of mitral heart valve behavior.