Nonlinear Material Parameter Estimation Using Inverse Finite Element Analysis

Constitutive parameters for biological materials are ideally regressed against data from well-designed experiments in which the loading and boundary conditions give rise to a homogeneous region of deformation. Such conditions may exist for healthy tissue within the context of in vitro tests, but rarely are met when attempting to measure parameters physiologically or noninvasively, due to complex boundary conditions or heterogeneous material structure and properties. The ability to estimate parameters in these situations is essential in many clinically relevant studies, including determination of tendon/ligament parameters in whole knee studies, non-destructive evaluation of evolving material parameters in laboratory studies, and estimation of heterogeneous parameters due to local normal or pathologic disruptions in tissue microstructure. In such cases, computational algorithms must be used to regress material parameters for a given constitutive model against the available data, in which the experimental conditions are modeled as accurately as possible without significant regard to complexity. The work presented here is focused on development of an iterative, inverse finite element (FE) algorithm for estimation of material parameters from experimental data obtained from tests with nonlinear complexities from contact, large deformations, and constitutive models.