The tensile properties of the cartilage of human femoral condyles related to the content of collagen and glycosaminoglycans

A method is described of measuring the tensile stiffness and fracture stress of human femoral condylar cartilage in planes parallel to and at increasing depth below the articular surface. The axis of tension was either parallel or perpendicular to the predominant collagen fibre direction in the superficial zone. Specimens were analysed for their collagen and glycosaminoglycan contents and partial correlation coefficients were determined between the tensile properties and each of the chemical constituents.The correlations between the tensile properties and the collagen content of specimens oriented parallel to the collagen fibre direction was statistically significant in the superficial zone but the significance level decreased with increasing depth. In specimens which were oriented perpendicularly to the collagen fibre direction the correlations between the above variables were less significant.There was no significant correlation between the tensile properties and the glycosaminoglycans in cartilage.Visibly normal specimens from the superficial layer which were situated adjacent to visibly degenerate cartilage were weaker and less stiff than specimens situated on normal joints or remote from visibly degenerate cartilage. Such differences decreased with depth below articular surface and were greater in parallel-oriented specimens.     

The effects of proteolytic enzymes on the mechanical properties of adult human articular cartilage.

The effects of the lysosomal proteinase cathepsin D on the mechanical properties of adult human articular cartilage were examined in detail in 7 joints within the age range 21 to 72 years. The results of a preliminary study on the effects of the lysosomal proteinase cathepsin B1 and clostridial collagenase on the mechanical properties of cartilage are also presented. Cartilage which had been incubated with either cathepsin D or cathepsin B1 showed increased deformation in uniaxial compression perpendicular to the articular surface. The enzyme-treated cartilage also showed decreased tensile stiffness at low values of stress. This effect was more pronounced in specimens from the deeper zone of cartilage than in specimens from the superficial zone. It was also more pronounced in specimens which were aligned perpendicular to the predominant alignment of the collagen fibres in the superficial zone than in specimens which were parallel to the collagen fibres. At higher stresses the tensile stiffness of the treated cartilage was not significantly different from that of the untreated tissue. The tensile fracture stress of the cartilage was also not significantly reduced by the action of cathepsin D. In contrast to the effects observed with the cathepsins, the preliminary results obtained by incubating cartilage for 24 h with clostridial collagenase showed that both the tensile stiffness and the fracture stress were considerably lower than the corresponding values for the untreated tissue. Biochemical analysis of the incubation media, and the specimens, revealed that a large proportion of the proteoglycans was released from the cartilage by each of the three enzymes. The proportion of the total collagen which was released from the cartilage was different for each enzyme: cathepsin D released between 0 and 1.5 per cent, cathepsin B1 released between 2.3 and 4.3 per cent and collagenase released between 5.3 and 27.8 per cent of the collagen after 24 h.     

Inhomogeneous cartilage properties enhance superficial interstitial fluid support and frictional properties, but do not provide a homogeneous state of stress

It has been well established that articular cartilage is compositionally and mechanically inhomogenous through its depth. To what extent this structural inhomogeneity is a prerequisite for appropriate cartilage function and integrity is not well understood. The first hypothesis to be tested in this study was that the depth-dependent inhomogeneity of the cartilage acts to maximize the interstitial fluid load support at the articular surface, to provide efficient frictional and wear properties. The second hypothesis was that the inhomogeneity produces a more homogeneous state of elastic stress in the matrix than would be achieved with uniform properties. We have, for the first time, simultaneously determined depth-dependent tensile and compressive properties of human patellofemoral cartilage from unconfined compression stress relaxation tests. The results show that the tensile modulus increases significantly from 4.1 +/- 1.9 MPa in the deep zone to 8.3 +/- 3.7 MPa at the superficial zone, while the compressive modulus decreases from 0.73 +/- 0.26 MPa to 0.28 +/- 0.16 MPa. The experimental measurements were then implemented with the finite-element method to compute the response of an inhomogeneous and homogeneous cartilage layer to loading. The finite-element models demonstrate that structural inhomogeneity acts to increase the interstitial fluid load support at the articular surface. However, the state of stress, strain, or strain energy density in the solid matrix remained inhomogeneous through the depth of the articular layer, whether or not inhomogeneous material properties were employed. We suggest that increased fluid load support at the articular surface enhances the frictional and wear properties of articular cartilage, but that the tissue is not functionally adapted to produce homogeneous stress, strain, or strain energy density distributions. Interstitial fluid pressurization, but not a homogeneous elastic stress distribution, appears thus to be a prerequisite for the functional and morphological integrity of the cartilage.     

Nonlinear tensile properties of bovine articular cartilage and their variation with age and depth

Tensile stiffness of articular cartilage is much greater than its compressive stiffness and plays an essential role even in compressive properties by increasing transient fluid pressures during physiological loading. Recent studies of nonlinear properties of articular cartilage in compression revealed several physiologically pertinent nonlinear behaviors, all of which required that cartilage tensile stiffness increase significantly with stretch. We therefore performed sequences of uniaxial tension tests on fresh bovine articular cartilage slices using a protocol that allowed several hours to attain equilibrium and measured longitudinal and transverse tissue strain. By testing bovine cartilage from different ages (6 months to 6 years) we found that equilibrium and transient tensile modulus increased significantly with maturation and age, from 0 to 15 MPa at equilibrium and from 10 to 28 MPa transiently. Our results indicate that cartilage stiffens with age in a manner similar to other highly hydrated connective tissues, possibly due to age-dependent content of enzymatic and nonenzymatic collagen cross links. The long relaxation period used in our tests (5-10 hours) was necessary in order to attain equilibrium and avoid a very significant overestimation of equilibrium modulus that occurs when much shorter times are used (15-30 minutes). We also found that equilibrium and transient tensile modulus increased nonlinearly when cartilage is stretched from 0 to 10% strain without any previous tare load. Although our results estimate a nonlinear increase in tensile stiffness with stretch that is an order of magnitude lower than that required to predict nonlinear properties in compression, they are in agreement with previous results from other uniaxial tension tests of collagenous materials. We therefore speculate that biaxial tensile moduli may be much higher and thereby more compatible with observed nonlinear compressive properties.     

The effects of proteolytic enzymes on the mechanical properties of adult human articular cartilage

The effects of the lysosomal proteinase cathepsin D on the mechanical properties of adult human articulage were examined in detail in 7 joints within the age rangee 21 to 72 years. The results of preliminary study on the effects of the lysosomal proteinase cathepsin B1 and clostridial collagenase on the mechanical properties of cartilage are also presented.Cartilage which had been incubated with either cathepsin D or cathepsin B1 showed increased deformation in unixial compression perpendicular to the articular surface.The enzyme-treated cartilage also showed decreased tensile stiffness at low values of stress. This effect was more pronounced in specimens from the deeper zone of cartilage than in specimens from the superficial zone. It was also more pronounced in specimens which were aligned perpendicular to the predominant alignment of the collagen fibres in the superficial zone than in specimens which were parallel to the collagen fibres.At higher stresses the tensile stiffness of the treated cartilage was not significantly different from that of the untreated tissue. The tensile fracture stress of the cartilage was not significantly reduced by the action of cathepsin D.In contrast to the effects observed with the cathepsins, the preliminary results obtained by incubating cartilage for 24 h with clostridial collagenase showed that both the tensile stiffness and the fracture stress were considerably lower than the corresponding values for the untreated tissue.Biochemical analysis of the incubation media, and the specimens, reveled that a large proportion of the proteoglycans was released from the cartilage by each of the freeze enzymes. The proportion of the total collagen which was released from the cartilage was different for each enzyme: cathepsin D released between 0 and 1.5 per cent, cathepsin B1 released between 2.3 and 4.3 per cent and collagenase relesed between 5.3 and 27.8 per cent of the collagen after 24 h.     

Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus

Nonlinear, linear and failure properties of articular cartilage and meniscus in opposing contact surfaces are poorly known in tension. Relationships between the tensile properties of articular cartilage and meniscus in contact with each other within knee joints are also not known. In the present study, rectangular samples were prepared from the superficial lateral femoral condyle cartilage and lateral meniscus of bovine knee joints. Tensile tests were carried out with a loading rate of 5 mm/min until the tissue rupture. Nonlinear properties of the toe region, linear properties in larger strains, and failure properties of both tissues were analysed. The strain-dependent tensile modulus of the toe region, Young's modulus of the linear region, ultimate tensile stress and toughness were on average 98.2, 8.3, 4.0 and 1.9 times greater (p<0.05) for meniscus than for articular cartilage. In contrast, the toe region strain, yield strain and failure strain were on average 9.4, 3.1 and 2.3 times greater (p<0.05) for cartilage than for meniscus. There was a significant negative correlation between the strain-dependent tensile moduli of meniscus and articular cartilage samples within the same joints (r=−0.690, p=0.014). In conclusion, the meniscus possesses higher nonlinear and linear elastic stiffness and energy absorption capability before rupture than contacting articular cartilage, while cartilage has longer nonlinear region and can withstand greater strains before failure. These findings point out different load carrying demands that both articular cartilage and meniscus have to fulfil during normal physiological loading activities of knee joints.     

Age-related changes in the tensile properties of human articular cartilage: a comparative study between the femoral head of the hip joint and the talus of the ankle joint

Specimens of articular cartilage from the superficial and mid-depth zones of the human femoral head and the talus of the ankle joint were tested in tension in planes parallel to the articular surface and parallel to the predominant orientation of the superficial collagen fibrils. The tensile fracture stress of cartilage from both the superficial and mid-depth zones of the femoral head decreased considerably with age. The superficial zone decreased from 33 MPa at 7 years to 10 MPa by the age of 90 years, while the mid-depth zone decreased from 32 MPa at 7 years to 2 MPa by the age of 85 years. In contrast the fracture stress of both levels of cartilage from the talus of the ankle did not decrease significantly with increasing age. The tensile stiffness at 10 MPa of both the superficial and mid-depth zones of the femoral head decreased with age. That of the superficial zone decreased from 150 MPa at 7 years to 80 MPa at 90 years, while the mid-depth zone decreased from 60 MPa at 7 years to 10 MPa at 60 years. The stiffness of talar cartilage from the superficial zone decreased by 20%, while that of the mid-depth zone showed a slight increase in stiffness at 10 MPa with increasing age. There was no significant decrease in the tensile stiffness at 1 MPa with age for either the femoral head or talar cartilage. Based on the results of previous studies it is possible to conclude that the decrease in tensile properties seen in the femoral head results from a deterioration in the tensile properties of the network of collagen fibrils. It is suggested that progressive fatigue failure, perhaps with associated changes in the structure of cartilage due to altered chondrocyte metabolism, causes the reduction in tensile properties with age. The results offer a potential explanation for the observation that osteoarthritis commonly occurs in the hip and knee joints at an increasing incidence as age increases, while the condition only rarely occurs in the ankle joint except as a secondary event to trauma.     

The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation

The relative importance of fluid-dependent and fluid-independent transient mechanical behavior in articular cartilage was examined for tensile and unconfined compression testing using a fibril reinforced model. The collagen matrix of articular cartilage was modeled as viscoelastic using a quasi-linear viscoelastic formulation with strain-dependent elastic modulus, while the proteoglycan matrix was considered as linearly elastic. The collagen viscoelastic properties were obtained by fitting experimental data from a tensile test. These properties were used to investigate unconfined compression testing, and the sensitivity of the properties was also explored. It was predicted that the stress relaxation observed in tensile tests was not caused by fluid pressurization at the macroscopic level. A multi-step tensile stress relaxation test could be approximated using a hereditary integral in which the elastic fibrillar modulus was taken to be a linear function of the fibrillar strain. Applying the same formulation to the radial fibers in unconfined compression, stress relaxation could not be simulated if fluid pressurization were absent. Collagen viscoelasticity was found to slightly weaken fluid pressurization in unconfined compression, and this effect was relatively more significant at moderate strain rates. Therefore, collagen viscoelasticity appears to play an import role in articular cartilage in tensile testing, while fluid pressurization dominates the transient mechanical behavior in compression. Collagen viscoelasticity plays a minor role in the mechanical response of cartilage in unconfined compression if significant fluid flow is present.     

Do changes in the mechanical properties of articular cartilage promote catabolic destruction of cartilage and osteoarthritis?

Osteoarthritis (OA) is a joint disease characterized by cartilage degeneration, a thickening of subchondral bone, and formation of marginal osteophytes. Previous mechanical characterization of cartilage in our laboratory suggests that energy storage and dissipation is reduced in osteoarthritis as the extent of fibrillation and fissure formation increases. It is not clear whether the loss of energy storage and dissipation characteristics is a result of biochemical and/or biophysical changes that occur to hyaline cartilage in joints. The purpose of this study is to present data, on the strain rate dependence of the elastic and viscous behaviors of cartilage, in order to further characterize changes that occur in the mechanical properties that are associated with OA. We have previously hypothesized that the changes seen in the mechanical properties of cartilage may be due to altered mechanochemical transduction by chondrocytes. Results of incremental tensile stress-strain tests at strain rates between 100%/min and 10,000%/min conducted on OA cartilage indicate that the slope of the elastic stress-strain curve increases with increasing strain rate, unlike the reported behavior of skin and self-assembled collagen fibers. It is suggested that the strain-rate dependence of the elastic stress-strain curve is due to the presence of large quantities of proteoglycans (PGs), which protect articular cartilage by increasing the apparent stiffness. The increased apparent stiffness of articular cartilage at high strain rates may limit the stresses borne and prolong the onset of OA. It is further hypothesized that increased compressive loading of chondrocytes in the intermediate zone of articular cartilage occurs as a result of normal wear to the superficial zone or from excessive impact loading. Once the superficial zone of articular cartilage is worn away, the tension is decreased throughout all cartilage zones leading to increased chondrocyte compressive loading and up-regulation of mechanochemical transduction processes that elaborate catabolic enzymes.     

Anisotropy, inhomogeneity, and tension-compression nonlinearity of human glenohumeral cartilage in finite deformation

The tensile and compressive properties of human glenohumeral cartilage were determined by testing 120 rectangular strips in uniaxial tension and 70 cylindrical plugs in confined compression, obtained from five human glenohumeral joints. Specimens were harvested from five regions across the articular surface of the humeral head and two regions on the glenoid. Tensile strips were obtained along two orientations, parallel and perpendicular to the split-line directions. Two serial slices through the thickness, corresponding to the superficial and middle zones of the cartilage layers, were prepared from each tensile strip and each compressive plug. The equilibrium tensile modulus and compressive aggregate modulus of cartilage were determined from the uniaxial tensile and confined compression tests, respectively. Significant differences in the tensile moduli were found with depth and orientation relative to the local split-line direction. Articular cartilage of the humeral head was significantly stiffer in tension than that of the glenoid. There were significant differences in the aggregate compressive moduli of articular cartilage between superficial and middle zones in the humeral head. Furthermore, tensile and compressive stress-strain responses exhibited nonlinearity under finite strain, while the tensile modulus differed by up to two orders of magnitude from the compressive aggregate modulus at 0% strain, demonstrating a high degree of tension-compression nonlinearity. The complexity of the mechanical properties of human glenohumeral cartilage was exposed in this study, showing anisotropy, inhomogeneity, and tension-compression nonlinearity within the same joint. The observed differences in the tensile properties of human glenohumeral cartilage suggest that the glenoid may be more susceptible to cartilage degeneration than the humeral head.     

Elastic energy storage in human articular cartilage: estimation of the elastic modulus for type II collagen and changes associated with osteoarthritis.

The viscoelastic mechanical properties of normal and osteoarthritic articular were analyzed based on data reported by Kempson [in: Adult Articular Cartilage (1973)] and Silver et al. (Connect. Tissue Res., 2001b). Results of the analysis of tensile elastic stress-strain curves suggest that the elastic modulus of cartilage from the superficial zone is approximately 7.0 GPa parallel and 2.21 GPa perpendicular to the cleavage line pattern. Collagen fibril lengths in the superficial zone were found to be approximately 1265 microm parallel and 668 microm perpendicular to the cleavage line direction. The values for the elastic modulus and fibril lengths decreased with increased extent of osteoarthritis. The elastic modulus of type II collagen parallel to the cleavage line pattern in the superficial zone approaches that of type I collagen in tendon, suggesting that elastic energy storage occurs in the superficial zone due to the tensile pre-tension that exists in this region. Decreases in the elastic modulus associated with osteoarthritis reflect decreased ability of cartilage to store elastic energy, which leads to cartilage fibrillation and fissure formation. We hypothesize that under normal physiological conditions, collagen fibrils in cartilage function to store elastic energy associated with weight bearing and locomotion. Enzymatic cleavage of cartilage proteoglycans and collagen observed in osteoarthritis may lead to fibrillation and fissure formation as a result of impaired energy storage capability of cartilage.     

The effects of leucocyte elastase on the mechanical properties of adult human articular cartilage in tension

The effects of leucocyte elastase on the tensile properties of adult human articular cartilage were examined in detail in 99 specimens from hip, knee and ankle joints in the age range 16–83 years. The results showed that elastase reduced the tensile stiffness of cartilage, both at low stress and at fracture. The tensile strength of cartilage was also considerably reduced by the action of elastase. Biochemical analysis of the incubation media, and the specimens, revealed that 90%, or more, of the proteoglycan was released from the cartilage, whilst the release of collagen was negligible. Leucocyte elastase is known to degrade the non-helical terminal peptides of cartilage collagen molecules and thereby disrupt the main intermolecular cross-links in collage fribrils. A previous study (Kempson, G.E., Tuke, M.A., Dingle, J.T., Barrett, A.J. and Horsfield, P.H. (1976) Biochim. Biophys. Acta 428, 741–760) showed the lack of effect of proteoglycan degradation alone on the tensile strength and stiffness of cartilage. The reduction in strength and stiffness recorded in the present study can, therefore, be attributed to the action of elastase on the collagen in cartilage and it emphasises the important of covalent intermolecular cross-links to the mechanical properties of collagen fibrils.     

Elastic anisotropy of articular cartilage is associated with the microstructures of collagen fibers and chondrocytes

Chondrocyte shape and volumetric concentration change as a function of depth in articular cartilage. A given chondrocyte shape produces different effects on the global material properties depending on the structure of the collagen fiber network. The shape and volumetric concentration of chondrocytes in articular cartilage appear to be related to the mechanical stability of the matrix. The present study was aimed to investigate, theoretically, the effects of the structural arrangement of the collagen fiber network, and the shape and distribution of chondrocytes, on the global material behavior of articular cartilage. Articular cartilage was assumed to be a four-phasic composite comprised of a matrix (associated with the properties of the proteoglycan structure), vertically and horizontally distributed collagen fibers, and spheroidal inclusions representing chondrocytes. A solution for composite materials was used to estimate the global, effective material properties of cartilage. Only the elasticity of the solid phase was investigated in the present study. Our simulations suggest that a soft, spheroidal cell inclusion in a fiber-reinforced proteoglycan matrix affects the material properties differently depending on the shape of the spheroidal inclusions. If the long axis of the inclusions is parallel to the collagen fibers, as in the deep zone, the soft inclusions increase the stiffness of the composite in the fiber direction, and reduce the stiffness of the composite in the direction normal to the fibers. Furthermore, we found that Young's modulus normal to the contact surface increases from the superficial to the deep zone in articular cartilage by a factor of 10-50, a finding that agrees well with experimental observations. Our analysis suggests that the combination of proteoglycan matrix, fiber orientation, and shape of chondrocytes are intimately related and are likely adapted to optimize the mechanical stability and load carrying capacity of the structure.     

Tensile fatigue behaviour of articular cartilage

Although fatigue has been implicated in cartilage failure there are only two studies by the same author, and in both of which cartilage was tested in the direction parallel to the collagen orientation in the surface layer. In the present work articular cartilage was tested also along the perpendicular direction, being the direction in which cartilage possesses lower tensile strength.Specimens were tested under cyclic tensile load. Number of cycles at failure was recorded as well as elongation of the specimen. To date 72 specimens have been tested all from one knee joint.The number of cycles to failure ranged between two and 1.5 million. The surface and deep layers have better fatigue properties whether tested in the parallel or the perpendicular direction, while the middle layer was far weaker. Better fatigue behaviour was observed with specimens tested in parallel than in perpendicular direction to the fibres.     

Relative contribution of articular cartilage’s constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.     

The "instantaneous" deformation of cartilage: effects of collagen fiber orientation and osmotic stress

The present study was undertaken with two objectives in view. The first was to distinguish between the "instantaneous" deformation and creep of articular cartilage when subjected to a step loading in unconfined compression. This was done by observing changes in the specimen's diameter rather than its thickness. The second objective was to investigate experimentally the anisotropic behaviour of cartilage in a compressive loading mode, corresponding to the physiological situation. An apparatus was thus developed and constructed which enabled us to follow the "instantaneous" changes of the surface area of the sample as the latter was being loaded in unconfined compression. Specimens of human articular cartilage from normal femoral heads and condyles were tested. Full thickness specimens were tested with and without the underlying bone, as well as partial thickness specimens, characterizing the different zones of cartilage. Solutions of different ionic strength were used to vary the osmotic stress and specimens covering a considerable range of proteoglycan concentrations were selected. The effects of hydration and proteoglycan removal on the "instantaneous" deformation were also studied. The "instantaneous" deformation was found to be of a strongly anisotropic nature in all zones. The deformation was always smaller along the Indian-ink prick pattern than at 90 degrees to it, and this effect was most pronounced in the superficial zone of cartilage. The results reveal an analogy with the tensile properties of cartilage and indicate that the collagen network is mainly responsible for controlling the "instantaneous" deformation. The proteoglycans play an indirect role by modulating the stiffness of the collagen network through their osmotic pressure.     

Cartilage interstitial fluid load support in unconfined compression

Under physiological conditions of loading, articular cartilage is subjected to both compressive strains, normal to the articular surface, and tensile strains, tangential to the articular surface. Previous studies have shown that articular cartilage exhibits a much higher modulus in tension than in compression, and theoretical analyses have suggested that this tension–compression nonlinearity enhances the magnitude of interstitial fluid pressurization during loading in unconfined compression, above a theoretical threshold of 33% of the average applied stress. The first hypothesis of this experimental study is that the peak fluid load support in unconfined compression is significantly greater than the 33% theoretical limit predicted for porous permeable tissues modeled with equal moduli in tension and compression. The second hypothesis is that the peak fluid load support is higher at the articular surface side of the tissue samples than near the deep zone, because the disparity between the tensile and compressive moduli is greater at the surface zone. Ten human cartilage samples from six patellofemoral joints, and 10 bovine cartilage specimens from three calf patellofemoral joints were tested in unconfined compression. The peak fluid load support was measured at 79±11% and 69±15% at the articular surface and deep zone of human cartilage, respectively, and at 94±4% and 71±8% at the articular surface and deep zone of bovine calf cartilage, respectively. Statistical analyses confirmed both hypotheses of this study. These experimental results suggest that the tension–compression nonlinearity of cartilage is an essential functional property of the tissue which makes interstitial fluid pressurization the dominant mechanism of load support in articular cartilage.     

Mapping the depth dependence of shear properties in articular cartilage

Determining the depth dependence of the shear properties of articular cartilage is essential for understanding the structure-function relation in this tissue. Here, we measured spatial variations in the shear modulus G of bovine articular cartilage using a novel technique that combines shear testing, confocal imaging and force measurement. We found that G varied by up to two orders of magnitude across a single sample, exhibited a global minimum 50-250 microm below the articular surface in a region just below the superficial zone and was roughly constant at depths > 1000 microm (the "plateau region"). For plateau strains gamma(plateau) approximately 0.75% and overall compressive strains epsilon approximately 5%, G(min) and G(plateau) were approximately 70 and approximately 650 kPa, respectively. In addition, we found that the shear modulus profile depended strongly on the applied shear and axial strains. The greatest change in G occurred at the global minimum where the tissue was highly nonlinear, stiffening under increased shear strain, and weakening under increased compressive strain. Our results can be explained through a simple thought model describing the observed nonlinear behavior in terms of localized buckling of collagen fibers and suggest that compression may decrease the vulnerability of articular cartilage to shear-induced damage by lowering the effective strain on individual collagen fibrils.     

Time and depth dependent poisson’s ratio of cartilage explained by an inhomogeneous orthotropic fiber embedded biphasic model

A time- and depth-dependent Poisson’s ratio has been observed during unconfined compression experiments on articular cartilage, but existing cartilage models have not fully addressed these phenomena. The goal of this study was to develop a model which is able to predict and explain these phenomena, while also being able to fit other experimental scenarios on full depth cartilage specimens such as confined and unconfined compressions. A biphasic (poroelastic), fiber-embedded cartilage model was developed. The heterogeneous material properties of the cartilage (aggregate modulus, void ratio tensile modulus) were extracted from reported experiments on individual layers of bovine articular cartilage. The nonlinear permeability material constants were found by fitting the overall response to published experimental data from confined compression. The matrix of the cartilage was modelled as an inhomogeneous isotropic biphasic material with nonlinear strain dependent permeability. Orthotropic layers were added as embedded elements to represent collagen fibers. Material parameters for these layers were derived from tensile tests of different layers of cartilage. With these predefined tensile parameters, the model showed a good fit with multi-step confined and unconfined compression experiments (R²=0.984 and 0.977, respectively) and could also predict the depth-dependent Poisson’s ratio (R²=0.981). The highlight of the model is the ability to explain the time-depth dependent Poisson's ratio and, by association, the strong effect of material inhomogeneity on local stress and strain patterns within the cartilage layer. This material model’s response may provide valuable new insight into potential initiation of cartilage fibrillation or delamination in whole-joint simulations.