Techniques for extended modeling of cardiac morphogenesis in the embryonic chick

Computational models that simulate the biophysical mechanisms of early cardiac morphogenesis in the embryonic chick heart have been used to demonstrate the influence of biomechanics in cardiac development. However, algorithms for the automatic coding of material subroutines that govern the constitutive relations of biological tissues, generating realistic: geometries, transferring solution results correctly during analysis continuation procedures, and for including advanced biomechanical components of the developing cardiac environment limit current models from demonstrating the role biomechanics has on normal cardiac development. The purpose of our work is to develop and demonstrate novel techniques to resolve each of the aforementioned limitations and use new techniques to model the hypothetical role of biormechanics in cardiac development.;First, we use the symbolic mathematics software Mathematica and nonlinear continuum mechanics to automatically generate FORTRAN based user material subroutines. The Mathematica notebook only requires the definition of a pseudoelastic strain energy function to generate the current Cauchy stress and Tensor of Elasticity for all integration points in the model. We demonstrate the accuracy of the automatically generated code using uniaxial, equibiaxial, and simple shear tests of materials defined by a Fung-Orthotropic pseudoelastic strain energy function. The code is also capable of modeling continuum growth, and we therefore test it by curling and twisting a bilayered bar. The Mathematica user material subroutine generator automatically generated user material subroutines that performed well for standard tests in hyperelasticity and complex problems in biomechanics. Therefore, we made the code freely available as supplemental material to an article we published in the Journal of Biomechanical Engineering.;We then describe the generation of realistic geometries by demonstrating the benefits and drawbacks to voxel based reconstructions. To resolve the limitations of the pure voxel based mesh, we present both results smoothing and mesh smoothing algorithms. We adapt the theory of membranes to design an algorithm, which recalculates the results on the boundaries of a pure voxel based mesh. Additionally, we implement Laplacian band-pass smoothing to modify the pure voxel based mesh, and thus generate a new smoothed geometric mesh. We conclude that results recalculation is only valid if the radius of curvatures represented in the model are large compared to voxel size. However, the mesh smoothing technique used here provides a realistic valid mesh, which can be used in nonlinear analyses.;Next we outline the standard technique for solution transfer and demonstrate its limitation when transferring field discontinuities. We develop a novel solution transfer scheme that reduces the diffusion of solution fields during analysis transfer. We demonstrate the benefits of our novel solution transfer technique in a simple growth based example that relates to cardiac morphogenesis.;Finally, we include the presence of the splanchnopleure, implement cohesive contact to simulate fusion of the omphalomesenteric veins, include element deletion to simulate the rupture of the dorsal mesocardium, and recast the developmental biomechanics of early cardiac morphogenesis using a nonlinear explicit dynamics solver. The new computational model extends previously studied mechanisms of cardiac morphogenesis to study c-looping in a single simulation. We maintain the growth stretches used to simulate normal development, while we independently eliminate the major structural components of the heart model to provide secondary validation of the hypothesized growth mechanisms of normal development. The predicted deformation, stress, and strain of the extended model are qualitatively and quantitatively agreeable compared to in vivo observations of cardiac development in the embryonic chick.;The algorithms we describe and implement in this work extend the capabilities of current computational models in describing the biomechanics of cardiac morphogenesis. We use a variety of numerical tools to overcome the limitations of current models, and though our focus is on cardiac development, these tools are beneficial for studying related problems in growth and remodeling.