Biomechanical modeling and nonlinear finite element analysis of the embryonic heart during early cardiac morphogenesis

This dissertation addresses the problem of biomechanical modeling of growth and morphogenesis in the embryonic chick heart during Hamburger-Hamilton stages 10 through 16. The objectives are: (1) the development of a three-dimensional (3D) nonlinear Finite Element (FE) formulation capable of modeling cardiac tissue growth and activation, and of representing separately active and passive response; (2) the systematic FE study of the biomechanical role of cardiac jelly (CJ); and (3) the development of a theoretical growth law for the smooth walled tubular heart incorporating the effect of diastolic and systolic loading.; Extending an earlier Updated Lagrangian hyperelastic FE formulation developed at the University of Rochester, we introduce a new two-component element that models myocardial tissue as the superposition of a passive incompressible matrix and an active compressible counterpart consisting of contractile fibers oriented along locally defined tangent vectors. Distinct active and passive strain energy density functions as well as grown and active stress-free reference configurations are used in the FE equations. Growth and activation are modeled using formally identical stretch tensors, and can be combined with residual strains.; We quantify the biomechanical effects of the CJ under muscle activation through a systematic FE study conducted on a series of stage 10 cross-sectional models. The presence and the shape of the CJ layer substantially affect transmural stresses and cross-sectional deformations, thereby increasing the heart pumping efficiency.; A myocardial stress- and stretch-dependent growth law is proposed for circumferential and radial volumetric growth, and extensively tested on stage 10 models. The law is based on the hypothesis that the increasing volume requirements of the growing embryo and the increasing wall stresses induced by rising pressures and activation stimulate growth of the cardiac muscle. Growth computations are carried out using an iterative FE time-stepping scheme incorporating a procedure for computing opening angles due to residual strains. Applied diastolic and systolic loads for normal and pressure-overload conditions drive the growth simulations. The computed growth response is stable and predicts wall thickening, lumen enlargement, and residual strain patterns for the stage 10 myocardium which are consistent with experimental observations.