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Theses Doctoral

Mechanically Mediated Fatigue Failure in Articular Cartilage: Experimental, Theoretical, and Computational Models

Zimmerman, Brandon Kendrick

Osteoarthritis is a progressive degenerative disease which affects the cartilage in articulating joints. The progression of osteoarthritis is known to be mechanically mediated, though specific mechanical factors have yet to be identified. In particular, the effects of frictional interactions and altered mechanical homeostasis remain unknown, and the inability to link specific mechanisms to disease advancement hinders the development of treatment strategies. The overarching objective of this dissertation is to study the mechanically-mediated fatigue failure process in articular cartilage through a validated computational model to ascertain the relative importance of mechanical factors, including surface friction and bulk cyclic stresses, on progression of osteoarthritis.

Fatigue failure in cartilage progresses as a function of multiple mechanical and physicochemical interactions. Collagen fibrils are the primary constituents that fail under fatigue loading. As the collagen fails, homeostasis between osmotic pressure and collagen tension is disrupted and the cartilage imbibes water and swells, producing softening. This entire process occurs under frictional contact loading. From a modeling standpoint, several primary challenges arise: (1) Accounting for the osmotic swelling of cartilage, which has not been sufficiently characterized experimentally; (2) Developing finite element algorithms to handle frictional contact of charged multiphasic (solid-fluid-solute) materials such as cartilage; (3) Modeling fatigue mechanics with observable state variables representing measures of cartilage composition, such that imaging techniques may inform the theory; and (4) Formulating compatible plasticity theories to allow validation of the novel fatigue framework with the extensive literature on fatigue of metals. This dissertation addressed these challenges in pursuit of the overarching objective.

Direct experimental measurements revealed the osmotic swelling pressure in cartilage does not obey ideal Donnan law, which significantly overestimates the measured pressure by approximately a factor of three. The aggregate modulus in triphasic theory was found to vary strongly with the external concentration, increasing three- to five-fold between hypertonic and hypotonic solutions. These results allow us to capture the interaction of swelling with damage.

The fatigue process is coupled with swelling, and computer modeling must be performed in a multiphasic environment which accounts for flow of charged ions. To address this, a novel surface-to-surface finite element algorithm for frictional contact was developed, providing the capabilities of complex surface-smoothing algorithms while retaining the simplicity of node-to-segment methods. This powerful framework was adapted to model friction between porous-permeable tissues, resulting in the development, implementation, and validation of finite element algorithms for four different types (single-phase elastic, biphasic, biphasic-solute, and multiphasic) of frictional contact. For the latter three, our work represented the first algorithms of this type. These algorithms are applied to model cartilage friction.

By using constrained reactive mixture theory, we developed a reactive plasticity framework that reduced to classical Prandtl-Reuss plasticity theory in the limit of infinitesimal deformation, using only scalar state variables representing composition measures. Applying this reaction kinetics-based approach to model fatigue mechanics provided a valid theoretical framework for treating evolving damage, where measures of the mass composition of cartilage served as observable state variables. By incorporating reactive plasticity, our reactive fatigue theory was thoroughly validated against experimental data from metals and biological tissues, including human tendon and human cartilage.

These modeling efforts were then synthesized to develop a fully validated computational model of fatigue failure in articular cartilage. For the first time, the role of frictional interactions on the progression of fatigue in articular cartilage was quantified. Results demonstrate that friction has an effect, but it is relatively small compared to the magnitude of the damage which takes place due to contact loads raising the magnitude of stresses in the collagen matrix. The implication of this result is that fatigue accumulation in cartilage is more sensitive to contact loading rather than surface interactions such as friction. This key finding may have clinical implications regarding treatment strategies for early-stage osteoarthritis.

This dissertation has generated a novel suite of theoretical and computational tools which have facilitated the development of a fully validated computational model of fatigue failure in articular cartilage. Replicating previous experimental fatigue studies with the model has confirmed that bulk matrix stresses are responsible for the majority of fatigue-induced damage, and that friction plays a relatively minor role. Future work will apply these computational models to further analyze fatigue failure in fibrous biological tissues and study experimentally-generated hypotheses.

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More About This Work

Academic Units
Mechanical Engineering
Thesis Advisors
Ateshian, Gerard Agop
Degree
Ph.D., Columbia University
Published Here
July 13, 2020