A continuum model and simulations for large deformation of anisotropic fiber-matrix composites for cardiac tissue engineering.

Cardiac patch therapies promise to restore heart function and lower the risk of heart failure after heart attack. Fiber-matrix engineered tissue scaffolds have gained significant attention due to their tunable micro-structures, providing nonlinear mechanical properties similar to native anisotropic heart tissues. Mechanical properties of engineered scaffolds directly affect the stress fields generated inside and around the tissue scaffolds and have significant impact on the tissue functionality. Currently, biomedical cardiac patches are designed through experimentation and there exists a need for an accurate model that will allow micro-structural design optimization and analysis of effectiveness of the implanted patches. We have developed a three-dimensional large strain continuum model that can predict nonlinear, anisotropic mechanical response of engineered tissue scaffolds that have two orientation families of fibers inside a bulk hydrogel matrix. We have validated the predictive capability of our continuum model for the fiber-matrix composite using selected experiments and a suite of detailed finite element analysis that incorporated the micro-structural details of the composites. Comparing the continuum model predictions (1 element) against the representative volume micro-structural geometry finite element simulations (with greater than 4,00,000 elements), we show that the proposed model can accurately predict nonlinear mechanical behavior of highly anisotropic tissue scaffolds in both the longitudinal and transverse directions, as a function of the critical design parameters inter-fiber angle and fiber spacing. We show that the model can also capture native heart tissue's anisotropic large strain mechanical response. We implemented our model in the finite element software Abaqus by writing a user material subroutine UANISOHYPER and demonstrated its predictive abilities by conducting a full three-dimensional analysis of engineered tissue patch application on an infarcted heart.