The material properties of the soft tissues of the knee are non-linear, anisotropic, and viscoelastic. These tissue structures also exhibit mechanical heterogeneity. The use of computational tools to examine knee biomechanics in healthy and diseased states, such as in osteoarthritic knees or anterior cruciate ligament (ACL) deficient knees, is becoming widely popular. However many computational models of the knee contain constitutive descriptions of the soft tissues that neglect one or more and sometimes all of these characteristics. The majority of computational efforts to date have focused on building accurate geometrical models and computationally efficient schemes, and advances in these areas have been remarkable. What has been lacking is sufficient attention to the complex biomechanics of the materials within those computational tools because of both the lack of adequate experimental data and the expertise to develop mathematical material models that are relevant for soft tissue. This talk will focus on two important soft tissues in the knee, the ACL and the tibial and femoral surface cartilages. The ACL is particularly challenging to experimentally characterize; in its anatomically relevant state, it is twisted and partially extended regardless of knee flexion angle. The ACL consists of two bundles that are not simultaneously unloaded under any configuration, and a novel approach to accurately characterize each bundle is described. Our experimental methods involve mechanically testing in uniaxial loading as well as anatomical positions using digital image correlation analysis to accurately describe the strain fields arising from mechanical heterogeneity in each experimental condition. We demonstrate that the anterior bundle of the ACL is functionally graded whereas the posterior bundle is mechanically homogeneous. We have developed a non-linear viscoelastic mathematical model of the ACL and implemented it into a finite element framework for computational analysis of the ACL during physiologically relevant loading conditions. In our computational environment we can transition from the uniaxial loading state to the anatomically correct loading state and predict the strain fields in the ACL during an anterior tibial translation. This motion is relevant to ACL injury as the ACL tears when the tibia anteriorly translates excessively relative to the femur. Our computational model is able to predict the location of ACL tears in the proximal third of the tissue. We also have measured the non-linear mechanical response of tibial and femoral cartilage of healthy female cadaveric specimens at a physiological strain rate as a function of position and found a persistent spatial dependency to both mechanics and thickness to exist. Our mechanical strain data demonstrate that non-linear elasticity dominates the response of cartilage at 1/sec, a strain rate consistent with a normal walking gait. Therefore, we neglected viscous effects at this strain rate and examined the ability of an anisotropic, non-linear elastic mathematical model to capture the response of cartilage throughout the tibial and femoral surfaces. We developed a modified form of an existing mathematical model and demonstrated that it was capable of describing the entire range of cartilage response with one adjustable parameter, the initial modulus. We implemented these mechanically graded tibial and femoral cartilage tissue models, along with the spatially varying thicknesses, into a finite element model of the human knee using the anisotropic, non-linear elastic mathematical model with a spatially varying initial modulus parameter. The purpose of this study was to examine the effects of non-linearity and inhomogeneity of cartilage properties on the ability to predict loading patterns, and therefore, disease and injury mechanisms in normal ACL-deficient and ACL-repaired knees. Our results indicate that in silico models that assume linear, homogeneous constitutive responses and uniform cartilage thickness may lead to inaccurate conclusions regarding the roles of geometric factors implicated in knee injuries and osteoarthritis. Moreover, our implementation of mechanical and physical heterogeneity and non-linearity involves little additional computational penalty as the non-linear, anisotropic cartilage model contains only one spatially varying parameter. It is clear that more biomechanically and physiologically relevant soft tissue models are required to advance our understanding of the mechanisms affecting knee injuries and disease states; the challenge is to retain tractability within the numerical framework. Our approach is attractive in that it offers a marked improvement in material model accuracy without an enormous computational penalty.
About the Speaker
Ellen M. Arruda, Ph.D. is a Professor of Mechanical Engineering at the University of Michigan. She also holds courtesy appointments in Biomedical Engineering and in Macromolecular Science and Engineering. She earned her B.S. degree in Engineering Science and her M.S. degree in Engineering Mechanics from The Pennsylvania State University, and her Ph.D. degree in Mechanical Engineering from the Massachusetts Institute of Technology. She joined the UM faculty in 1992. Professor Arruda teaches and conducts research in the areas of theoretical and experimental mechanics of macromolecular materials including polymers, elastomers, composites, soft tissues and proteins, and in tissue engineering of soft tissues and tissue interfaces. Her work has recently earned several honors and awards including the Ann Arbor Spark Best of Boot Camp Award 2012 and the 2012 Excellence in Research Award by the American Orthopaedic Society for Sports Medicine. She is a Fellow of the American Society of Mechanical Engineers, the American Academy of Mechanics and the Society of Engineering Science.
*Times, dates and titles are subject to change. Check mechanical.illinois.edu for updated information. These seminars count toward the requirements for ME 590 and TAM 500.