Multi-scale modeling and nonlinear finite element analysis of the trabeculated embryonic heart

This dissertation addresses the problem of biomechanical modeling of the trabeculated embryonic chick heart at Hamburger-Hamilton (HH) stage 21. The objectives are: (1) the development of a multi-scale Finite Element (FE) modeling and simulation system for the trabeculated heart; (2) the derivation of effective mechanical properties of the trabeculated myocardium; (3) the systematic FE study of the mechanics of a HH21 heart and the preliminary investigation on functional roles of the trabeculated myocardium.; Based on a novel de-coupled myocardial tissue modeling concept, a set of Updated Lagrangian incremental FE formulations, and a residual deformation approach for simulating tissue growth and activation, we design and implement a specialized nonlinear FE analysis procedure with extensive capabilities of performing stress analyses on embryonic cardiac systems.; We integrate a new parallel 3D image thinning procedure, a voxel meshing procedure, the nonlinear FE analysis procedure, and a nonlinear data regression procedure to construct a sophisticated computational system that operates on local representative volume elements of the trabeculated myocardium. Employing this local computational system, we systematically study the effective mechanical properties of trabeculated myocardium. Results obtained in the local analysis are incorporated into homogenized global FE models of a HH21 heart.; Using a 3D image based modeling procedure, we reconstruct the smoothed geometry and create a series of global FE models of an entire HH21 heart. In order to determine appropriate parameters in global FE models, we carry out a comprehensive model calibration based on the experimental ventricular pressure-volume relations. We then simulate a complete cardiac cycle and extensively study the mechanics of a HH21 heart under normal in vivo conditions. We validate the FE simulation results by comparing the predicted epicardial strains to those derived from video sequences. Finally, we perform additional comparative FE simulations in order to gain insights into functional roles of trabeculated myocardium. Results support hypotheses that ventricular trabeculation is triggered by the increasing demand of oxygen delivery to the thickening myocardium, and might improve the overall performance of HH21 heart as a pump.