Articular cartilage is the soft tissue consisting mostly of extracellular matrix biopolymers and water that covers the ends of bones in synovial joints. Cartilage functions mechanically: it provides lowfriction surfaces for articulation and deforms during joint contact to decrease contact pressure and increase joint stability. As such, understanding the specific molecular origins of cartilage resistance to deformation is necessary to understand cartilage mechanical function.
Most previous cartilage mechanics research has focused on macroscale continuum models, but recent advances have enabled the description and determination of microscale polymeric behavior. The theory of polymer dynamics uses statistical physics to describe the motions and interactions of entangled polymers. The objective of this project was to determine if polymer dynamics is a relevant mechanism in cartilage viscoelasticity, with the underlying hypothesis that modifications to cartilage molecules will result in changes in tissue-level mechanical properties that are predicted by polymer dynamics theory. Most experiments consisted of stress-relaxation tests performed on various experimental groups subjected to modified or control conditions. A time constant for stress-relaxation was determined by fitting a stretched exponential model to the experimental data. Chapter 3 details a novel method of fitting this model.
Chapter 2 details comparisons between and modeling of cartilage viscoelasticity from both flow-dependent and flow-independent mechanisms. The results show that the best description of the data utilizes both flow-dependent and flow-independent (e.g. polymer dynamics) mechanisms. However, very small differences in fit quality were observed between the flow-independent and flow-dependent models. Additionally, there is no significant change in parameters when the stretched exponential model is fit with or without terms describing fluid flow. Furthermore, experiments examining cartilage stress-relaxation under varying strain levels show that stress-relaxation proceeds slower at higher compressive strains. This may result from either increased resistance to fluid flow or decreased polymer mobility. The experimentally observed dynamics are predominantly faster than those predicted for fluid flow mechanisms, but consistent with polymer dynamics theory.
Chapter 4 examines the temperature-dependence of cartilage stress-relaxation, and includes the novel observation that cartilage generates increases compressive stress upon temperature increase. Stress-relaxation proceeded faster at higher temperature, consistent with the Arrhenius behavior predicted by polymer theory. Further more the observed temperature-induced stress-increase is consistent with thermal polymer motion as a source of deformation resistance.
Chapter 5 used specific digestion of cartilage matrix molecules to determine if changes in molecular length resulted in changes in cartilage viscoelasticity. The stretched exponential time constant exhibited greater decreases for samples exposed to enzymatic digestion than for samples under control conditions. The absence of this result would have invalidated polymer dynamics as a mechanism of cartilage viscoelasticity. However, this result is predicted by polymer dynamics theory.
Chapter 6 examined cartilage viscoelastic properties under different solution ion concentrations and cation valences. Notably, stress-relaxation proceeded faster under higher ion concentration. Previous research has shown that aggrecan (a major component of the cartilage extracellular matrix) stiffness decreases with increased ion concentration, and this data implicates aggrecan stiffness in tissuelevel viscoelasticity. The polymer dynamics interpretation is that more compliant (i.e. less stiff) molecules are more mobile and can therefore equilibrate more quickly to the applied deformation of the stress-relaxation experiment.
Chapter 7 utilized nuclear magnetic resonance spectroscopy to examine the relationships between the transverse nuclear magnetic relaxation times (T2 values) of collagen and glycosaminoglycan and parameters describing the stress-relaxation data. Notably, there was a significant negative correlation between the collagen T2 value and the stretched exponential time constant, as predicted by polymer dynamics theory. However, no such correlation was observed for the glycosaminoglycan T2 value. This observation suggests that the molecular mobility of collagen is a stronger determinant of cartilage stress-relaxation dynamics than is glycosaminoglycan mobility. Importantly, collagen may sufficiently restrain glycosaminoglycan motion leading to the observed slow glycosaminoglycan T2 relaxation.
These data present a complex picture of cartilage mechanics and the polymer dynamics interpretation is consistent with the role of matrix viscoelasticity developed in previous cartilage mechanics studies. Fluid flow appears to be a slow mechanism of cartilage viscoelasticity, and polymer motion may be a mechanism of the faster stress-relaxation which is observed experimentally. Significant further research remains to fully understand how the motions and interactions of specific matrix molecules in conjunction with fluid flow result in the nonlinear viscoelasticity of cartilage.
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