Soft Tissue Constitutive Forms and Their Implications for Whole Knee Computational Models

Abstract

This work sought to determine the extent to which approximations in the constitutive theories and geometric representations of individual soft tissues affected the predictive power of computational knee models. Two tissue systems were evaluated: articular cartilage and structural ligaments, particularly focusing on the anterior cruciate ligament (ACL). These tissues were selected due to the rates and debilitating effects of their associated injuries and diseases, as well as their ubiquitous inclusion in computational knee models.

The mechanical consequences of various levels of articular cartilage constitutive complexity were investigated during physiologically representative loading. Additional complexity, compared to the common assumption of linear elasticity, was introduced through the systematic incorporation of nonlinear, directional, and spatially heterogeneous mechanical properties. Failure to include experimentally motivated cartilage material models resulted in overpredictions of joint motion and local tissue deformation. There were some diminishing returns with increasing complexity. In particular, there was a relatively small effect corresponding to the specific interpolation method used in the construction of each spatially heterogeneous mechanical property field. After determining the sensitivity of the representative computational knee model to cartilage constitutive behavior, the impacts of articular cartilage focal defect size and location were analyzed. Cartilage focal defects were shown to have a large effect on deformation in the neighborhood around their perimeters, though no consistent trends of altered deformation were observed in adjacent and opposing tissues. A defect of increased size was also shown to alter joint kinematics, while small defects, independent from their location, were found to have a minimal effect.

There has been a tremendous body of work directed at describing the deformation of ligaments. This work is largely built on the assumption that ligaments behave as transversely isotropic solids; however, there are limited and conflicting mechanical characterization data available for ligaments. Various constitutive theories were assessed on their ability to represent the stress-strain responses of structural ligaments in multiple loading configurations. Traditionally and commonly accepted transversely isotropic, hyperelastic constitutive theories proved incapable of describing the mechanical response of ligaments, predominantly failing in the transverse direction. Therefore, a new constitutive theory was developed and shown to have superior accuracy in describing the breadth of experimental stress-strain responses from multiple loading directions. With this new understanding related to the deformation of ligaments, the internal loading and detailed anatomy of the ACL were evaluated. Specifically, the double bundled, prestrained structure of the ACL was quantified computationally for the first time, and its effect on joint motion and local tissue deformation during normal clinical assessments was examined. The incorporation of prestrain was shown to be an important mechanical feature of knee stability, bringing predicted joint motions within the acceptable ranges of healthy knees.