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Adaptive Finite Element Analysis of the Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics

Abstract The nonlinear partial differential equations of the anisotropic biphasic theory of tissue-equivalent mechanics are solved with axial symmetry by an adaptive finite element system. The adaptive procedure operates within a method-of-lines framework using finite elements in space and backward difference software in time. Spatial meshes are automatically refined, coarsened, and relocated in response to error indications and material deformation. Problems with arbitrarily complex two-dimensional regions may be addressed. With meshes graded in high-error regions, the adaptive solutions have fewer degrees of freedom than solutions with comparable accuracy obtained on fixed quasi-uniform meshes. The adaptive software is used to address problems involving an isometric cell traction assay, where a cylindrical tissue equivalent is adhered at its end to fixed circular platens; a prototypical bioartificial artery; and a novel configuration that is intended as an initial step in a study to determine bioartificial arteries having optimal collagen and cell concentrations.