Cartilage Mechanics
Articular cartilage is the bearing material lining the articulating surfaces of bones. Its primary function is to provide low friction and wear under normal function. Cartilage degradation is one of the main events associated with osteoarthritis, a degenerative disease that impacts the quality of life significantly. Unlike fractured bone, cartilage is unable to heal on its own, and treatment modalities for osteoarthritis mostly represent palliative measures against pain. A fundamental understanding of cartilage mechanics is essential to the development of promising treatment modalities.
Articular cartilage forms a thin layer whose thickness varies from 0.1 mm to 7 mm, with most human joints exhibiting mean thickness values in the range of 1 to 3 mm. Therefore, in early studies of cartilage mechanics, the standard method for harvesting tissue samples consisted of coring out cylindrical plugs perpendicularly to the articular surface, or cutting rectangular strips tangentially to the surface. Cylindrical plugs were used for compressive testing and strips were used for tensile testing. Results demonstrated that the tensile modulus from strips was 10 to 100 times greater than the compressive modulus from plugs.
It was unclear from these studies whether the modulus of cartilage was simply greater in tension than compression, or whether cartilage was in fact anistropic, such that its modulus in the direction tangential to the articular surface was significantly different than along the direction normal to the surface, regardless of tension or compression. Therefore our laboratory conducted exhaustive testing of small cubic samples (1 mm x 1 mm x 1 mm) of articular cartilage under a microscope to measure strains accurately. Compressive loading was applied along one of the three principal directions of the cubic sample, which aligned with the tangential and normal directions to the articular surface. Results showed that the compressive modulus of cartilage was substantially similar along all three directions, demonstrating that tissue anisotropy could not explain the hundred-fold difference observed in earlier studies.
Furthermore, by subjecting the tissue to osmotic swelling, we were able to extract the properties of cartilage in the transitional range between tension and compression, along the three preferred material directions. These measurements clearly demonstrated the rapid transition of the cartilage modulus from small values in compression to very large values in tension. These studies, which conclusively established the large disparity between tensile and compressive properties of cartilage, represent major components of the doctoral dissertations of Drs. Changbin (Chris) Wang and Nadeen O. Chahine.
Within articulating joints, such as the knee or shoulder, cartilage is subjected to intermittent compressive loading, while the opposing articular layers slide and roll relative to each other. Despite the fact that the predominant mode of loading is compressive, the observation that cartilage exhibits a much higher modulus in tension than in compression was intriguing, and the significance of this disparity to the structure-function relationships of articular cartilage became a topic of great interest.
Research conducted in our laboratory has now demonstrated that this disparity, called tension-compression nonlinearity, considerably enhances the pressurization of the interstitial fluid of cartilage under various loading conditions. This discovery was first noted from theoretical analyses, and was subsequently verified from experimental measurements of interstitial fluid pressurization. These studies represent significant components of the doctoral dissertations of Drs. Michael A. Soltz and Seonghun Park.
When the interstitial fluid of cartilage pressurizes, it contributes to supporting the load transmitted across the articular layers. Therefore an important functional role for tension-compression nonlinearity is to enhance the compressive stiffness of cartilage under dynamic loading conditions. This interstitial fluid pressurization also plays a critical role in reducing the friction coefficient of articular cartilage.
Most biological soft tissues exhibit viscoelastic responses to loading, which means that part of the energy imparted to the tissue during loading gets dissipated into heat; therefore, when the tissue is unloaded, it can restore only the remaining part of the energy imparted to it. Since the interstitial fluid of articular cartilage pressurizes under loading, it flows through the tissue's porous collagenous matrix, and the frictional interaction between the fluid and solid constituents contributes significantly to this energy dissipation. This mechanism is thus described as flow-dependent viscoelasticity.
However, stored energy may also be dissipated within the solid matrix of cartilage, due to formation and breaking of temporary bonds between the matrix molecules. This mechanism is described as flow-independent or intrinsic viscoelasticity of the solid matrix. Intrinsic viscoelasticity also contributes to stiffening cartilage under dynamic loading conditions. Therefore, an understanding of the contribution of each mechanism would provide greater insight into the structure-function relationships in cartilage. Experimentally, it is not possible to differentiate between these two modes of energy dissipation because they produce similar alterations to the tissue's mechanical response. They both produce creep and stress-relaxation behaviors, and a hysteretic response under loading and unloading.
In articular cartilage, our theoretical studies demonstrated that flow-dependent viscoelasticity manifests itself most significantly under compressive loading. However, when subjected to uniaxial tensile loading, the interstitial fluid pressurization of cartilage would be negligible due to tension-compression nonlinearity; thus it would not contribute to flow-dependent viscoelasticity under this particular loading configuration. This fortuitous discovery from theoretical analyses implied that experimental measurements of the tensile response of cartilage would exclusively yield the flow-independent viscoelasticity of the solid matrix, and we proceeded to perform such measurements in our laboratory. These studies represent significant components of the doctoral dissertations of Drs. Chun-Yuh (Charles) Huang and Seonghun Park.
Despite the fact that studies of cartilage mechanics have been conducted for many decades, there is surprisingly limited information on the magnitude of strains to which articular cartilage is subjected under physiological loading conditions. Many investigators have reported on the magnitude of loads transmitted across the joints, and the magnitude and distribution of contact stresses at the articular surfaces. The relative change in thickness of cartilage under loading has also been reported, however this represents only an average measure of the strain distribution.
Therefore, our laboratory has conducted measurements of the two-dimensional strain distribution over the cross-section of the human patellofemoral joint, under physiological load magnitudes representing activities of daily living. These studies have demonstrated that peak strains in articular layers are on the order of 12% to 16% under such loading conditions. These values are surprisingly smaller than would be expected based on estimations from joint contact stresses and various measurements of the cartilage compressive modulus. This outcome emphasizes that the flow-dependent and flow-independent viscoelasticity of cartilage play a critical role in the stiffening of articular layers under dynamic loading, thereby producing relatively small strains despite the large joint loads. These studies represent a significant component of the doctoral dissertation of Dr. Clare Canal Guterl.
Electrostatic and Non-Electrostatic Contributions of Proteoglycans
Proteoglycans are macromolecules enmeshed within the collagen matrix of articular cartilage. Their negatively charged glycosaminoglycan chains interact with electrolytes in the interstitial fluid to produce a Donnan osmotic pressure relative to the external bathing solution of the tissue. This internal pressurization swells the tissue and contributes to resisting compressive loads on cartilage. It has long been known that proteoglycans contribute significantly to the compressive modulus of articula cartilage. However, a precise prediction of this contribution remains elusive to this day.
The osmotic pressure that proteoglycans may induce in salt solutions of various concentrations has only been reported by one other group of investigators. In our laboratory, we designed and built a custom membrane osmometer to measure the osmotic pressure of chondroitin sulfate, which is the dominant glycosaminoglycan constituent of cartilage proteoglycans. Using these measurements, we estimated the extent by which proteoglycans might contribute to the overall compressive stiffness of articular cartilage if this contribution only arises from the osmotic pressure alone. This analysis predicted that osmotic effects contribute approximately one-third of the compressive modulus of cartilage, consistent with prior literature reports based on measuring properties of cartilage in isotonic and hypertonic salt solutions.
To further explore whether proteoglycans may also contribute structurally to the compressive modulus, we performed measurements before and after complete digestion of proteoglycans from immature and mature bovine articular cartilage. Surprisingly, it was found that the modulus of digested cartilage drops by up to 98% relative to the control samples, indicating that these macromolecules may contribute far more significantly to the compressive modulus than suggested from Donnan osmotic effects alone. This finding heightens our interest in understanding how proteoglycans may contribute so significantly to the compressive modulus of the tissue, and elucidate all the mechanisms by which this occurs. The study of chondroitin sulfate osmotic pressure with membrane osmometry was a component of Dr. Nadeen Chahine's doctoral dissertation, and the study of complete proteoglycan digestion was a component of Dr. Clare Canal Guterl's dissertation.