On the Uncertainty Quantification and Non-Linear Hyper Elastic Simulation of Biological Tissues

A Dissertation Presented for the Doctor of Philosophy in Computational Engineering, The University of Tennessee at Chattanooga

Behrouz Shamsaei, August 2016

Abstract:
In this dissertation, a computational structural mechanics capability is developed for the simulation of biological tissues. These tissues may exhibit either linear or nonlinear material responses and, therefore, the resultant theory and computational implementation are presented. Various discretization methods of the systems of equations are possible, and in the current work Continuous Galerkin (CG) and the Discontinuous Galerkin (DG) approaches are employed. Additionally, due to natural variations in biophysical properties from person to person, uncertainty quantification may be used to ascertain the impact on deterministic simulation results when assuming mean values of these properties. To this end, a hyper elastic formulation for the nonlinear, transversely isotropic behavior of soft and hard tissue is utilized for the simulation and failure analysis of the proximal femur. Both linear and nonlinear material results are compared. The uncertainty in the failure analysis due to the selected biophysical properties is then examined using the First-Order Second-Moment (FOSM) method. Additionally, within Computational Fluid Dynamics (CFD) it is often necessary to adaptively move the mesh (e.g. moving boundary simulations, shape design optimization, generation of higher-order grids near curved boundaries, etc.). In these regards, linear elasticity is commonly used for adaptation by viewing the mesh as a solid. In some cases, such as for anisotropic meshes or for extremely large boundary movement, this approach to mesh movement has experienced difficulties in producing valid grids for simulation purposes. Thus, using the developed capability, the potential benefits of utilizing nonlinear material behavior for mesh movement is additionally examined.

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