Material characterization of cardiovascular biomaterials using an inverse finite-element method and an explicit solver

The ability to accurately model soft tissue behavior, such as that of heart valve tissue, is essential for developing reliable numerical simulations and determining patient-specific care options. Although several material models can predict soft tissue behavior, complications may arise when these models are implemented into finite element (FE) programs, due to the addition of an arbitrary penalty parameter for numerically enforcing material incompressibility. Herein, an inverse methodology was developed in MATLAB to use previously published stress-strain data from experimental planar equibiaxial testing of five biomaterials used in heart valve cusp replacements, in conjunction with commercial explicit FE solver LS-DYNA, to optimize the material parameters and the penalty parameter for an anisotropic hyperelastic strain energy function. A two-parameter optimization involving the scaling constant of the strain energy function and the penalty parameter proved sufficient to produce acceptable material responses when compared with experimental behaviors under the same testing conditions, as long as analytically derived material constants were available for the other non-optimized parameters and the actual tissue thickness was not much less than 1 mm. Variations in the penalty parameter had a direct effect on the accuracy of the simulated responses, with a practical range determined to be 5×108-9×108 times the scaling constant of the strain energy function.