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Multiscale Finite Element Modeling of the Trabeculated Embryonic Heart: Numerical Evaluation of the Constitutive Relations for the Trabeculated Myocardium

A numerical homogenization procedure for deriving the constitutive relations of the trabeculated embryonic myocardium is presented. This procedure is based on voxel modeling, nonlinear Finite Element analysis, and nonlinear data regression. Voxel reconstructions derived from digitized serial sections are used to construct local Finite Element meshes (called Representative Volume Elements) of the trabeculated myocardial wall. The orientation of the myofibrils is approximated by the geometrical skeleton of the voxel model. A 3-D nonlinear Finite Element research code, designed for modeling incompressible hyperelastic materials and capable of representing muscle activation and volumetric growth, is used to compute the mechanical response of the RVE. Bi-axial stretching experiments designed to generate tri-axial stress states are performed to compute the averaged stress-strain relations under passive and active conditions. New Strain Energy Density functions - both passive and active - are proposed for the RVE. A multi-dimensional Levenberg-Marquardt nonlinear regression is performed on the stress-strain data to yield the unknown parameters in the SED functions. The reliability and predictability of the computed functions is verified through additional tri-axial testing.