Estimation of depth-dependent material properties of biphasic soft tissues through finite element optimization and sensitivity analysis

Abstract

A knowledge of material properties of soft tissue, such as articular cartilage, is essential to assess its mechanical function. It is also increasingly more evident that the inhomogeneity of the tissues plays a significant role in its in vivo functioning. Hence, efficient and reliable tools are needed to accurately characterize the inhomogeneity of the soft tissue mechanical properties. The objective of this research is to propose a finite element optimization procedure to determine depth-dependent material properties of articular cartilage by processing experimental data. Cartilage is modeled as a biphasic continuum with a linear elastic solid phase. The optimization method is based on a sensitivity analysis where the sensitivity of the finite element results to a variation in the material properties is analytically evaluated. The elastic modulus and permeability of the tissue are assumed to vary either linearly or quadratically through the thickness of the cartilage layer. After adopting some initial estimates, these material properties are updated iteratively based on their sensitivities to the current results, and the difference between the actual experimental data and computational experimental data. The optimization method has been tested in two common experimental configurations of cartilage and found to be efficient to estimate the material properties.