Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression

Articular cartilage exhibits complex mechanical properties such as anisotropy, inhomogeneity and tension-compression nonlinearity. This study proposes and demonstrates that the application of compressive loading in the presence of osmotic swelling can be used to acquire a spectrum of incremental cartilage moduli (EYi) and Poisson's ratios (upsilon ij) from tension to compression. Furthermore, the anisotropy of the tissue can be characterized in both tension and compression by conducting these experiments along three mutually perpendicular loading directions: parallel to split-line (1-direction), perpendicular to split-line (2-direction) and along the depth direction (3-direction, perpendicular to articular surface), accounting for tissue inhomogeneity between the surface and deep layers in the latter direction. Tensile moduli were found to be strain-dependent while compressive moduli were nearly constant. The peak tensile (+) Young's moduli in 0.15M NaCl were E+Y1=3.1+/-2.3, E+Y2=1.3+/-0.3, E+Y3(Surface)=0.65+/-0.29 and E+Y3(Deep)=2.1+/-1.2 MPa. The corresponding compressive (-) Young's moduli were E-Y1=0.23+/-0.07, E-Y2=0.22+/-0.07, E-Y3(Surface)=0.18+/-0.07 and E-Y3(Deep)=0.35+/-0.11 MPa. Peak tensile Poisson's ratios were upsilon+12=0.22+/-0.06, upsilon+21=0.13+/-0.07, upsilon+31(Surface)=0.10+/-0.03 and upsilon+31(Deep)=0.20+/-0.05 while compressive Poisson's ratios were upsilon-12=0.027+/-0.012, upsilon-21=0.017+/-0.07, upsilon-31(Surface)=0.034+/-0.009 and upsilon-31(Deep)=0.065+/-0.024. Similar measurements were also performed at 0.015 M and 2 M NaCl, showing strong variations with ionic strength. Results indicate that (a) a smooth transition occurs in the stress-strain and modulus-strain responses between the tensile and compressive regimes, and (b) cartilage exhibits orthotropic symmetry within the framework of tension-compression nonlinearity. The strain-softening behavior of cartilage (the initial decrease in EYi with increasing compressive strain) can be interpreted in the context of osmotic swelling and tension-compression nonlinearity.     

Membrane transport properties of bovine articular cartilage

The thermodynamic parameters which define transport of nonelectrolytes through bovine articular cartilage membranes were evaluated. H³HO, glucose and sucrose were used as permeants. These solutes permeate more readily through the upper layers (near the articular surface) than through the denser deeper layers approaching bone. Cartilage is similar in many respects to a swollen cellulose gel. Viscous-flow contributes importantly to transprot within cartilage thus greatly enhancing the movement of nutrients.     

Injurious mechanical compression of bovine articular cartilage induces chondrocyte apoptosis

A bovine cartilage explant system was used to evaluate the effects of injurious compression on chondrocyte apoptosis and matrix biochemical and biomechanical properties within intact cartilage. Disks of newborn bovine articular cartilage were compressed in vitro to various peak stress levels and chondrocyte apoptotic cell death, tissue biomechanical properties, tissue swelling, glycosaminoglycan loss, and nitrite levels were quantified. Chondrocyte apoptosis occurred at peak stresses as low as 4.5 MPa and increased with peak stress in a dose-dependent manner. This increase in apoptosis was maximal by 24 h after the termination of the loading protocol. At high peak stresses (>20 MPa), greater than 50% of cells apoptosed. When measured in uniaxial confined compression, the equilibrium and dynamic stiffness of explants decreased with the severity of injurious load, although this trend was not significant until 24-MPa peak stress. In contrast, the equilibrium and dynamic stiffness measured in radially unconfined compression decreased significantly after injurious stresses of 12 and 7 MPa, respectively. Together, these results suggested that injurious compression caused a degradation of the collagen fibril network in the 7- to 12-MPa range. Consistent with this hypothesis, injurious compression caused a dose-dependent increase in tissue swelling, significant by 13-MPa peak stress. Glycosaminoglycans were also released from the cartilage in a dose-dependent manner, significant by 6- to 13-MPa peak stress. Nitrite levels were significantly increased above controls at 20-MPa peak stress. Together, these data suggest that injurious compression can stimulate cell death as well as a range of biomechanical and biochemical alterations to the matrix and, possibly, chondrocyte nitric oxide expression. Interestingly, chondrocyte programmed cell death appears to take place at stresses lower than those required to stimulate cartilage matrix degradation and biomechanical changes. While chondrocyte apoptosis may therefore be one of the earliest responses to tissue injury, it is currently unclear whether this initial cellular response subsequently drives cartilage matrix degradation and changes in the biomechanical properties of the tissue.     

Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression.

Compression tests have often been performed to assess the biomechanical properties of full-thickness articular cartilage. We tested whether the apparent homogeneous strain-dependent properties, deduced from such tests, reflect both strain- and depth-dependent material properties. Full-thickness bovine articular cartilage was tested by oscillatory confined compression superimposed on a static offset up to 45%. and the data fit to estimate modulus, permeability, and electrokinetic coefficient assuming homogeneity. Additional tests on partial-thickness cartilage were then performed to assess depth- and strain-dependent properties in an inhomogeneous model, assuming three discrete layers (i = 1 starting from the articular surface, to i = 3 up to the subchondral bone). Estimates of the zero-strain equilibrium confined compression modulus (H(A0)), the zero-strain permeability (kp0) and deformation dependence constant (M), and the deformation-dependent electrokinetic coefficient (ke) differed among individual layers of cartilage and full-thickness cartilage. HiA0 increased from layer 1 to 3 (0.27 to 0.71 MPa), and bracketed the apparent homogeneous value (0.47 MPa). ki(p0) decreased from layer 1 to 3 (4.6 x 10(-15) to 0.50 x 10(-15) m2/Pa s) and was less than the homogeneous value (7.3 x 10(-15) m2/Pa s), while Mi increased from layer 1 to 3 (5.5 to 7.4) and became similar to the homogeneous value (8.4). The amplitude of ki(e) increased markedly with compressive strain, as did the homogeneous value: at low strain, it was lowest near the articular surface and increased to a peak in the middle-deep region. These results help to interpret the biomechanical assessment of full-thickness articular cartilage.     

A microstructural model of elastostatic properties of articular cartilage in confined compression

A microstructural model of cartilage was developed to investigate the relative contribution of tissue matrix components to its elastostatic properties. Cartilage was depicted as a tensed collagen lattice pressurized by the Donnan osmotic swelling pressure of proteoglycans. As a first step in modeling the collagen lattice, two-dimensional networks of tensed, elastic, interconnected cables were studied as conceptual models. The models were subjected to the boundary conditions of confined compression and stress-strain curves and elastic moduli were obtained as a function of a two-dimensional equivalent of swelling pressure. Model predictions were compared to equilibrium confined compression moduli of calf cartilage obtained at different bath concentrations ranging from 0.01 to 0.50 M NaCl. It was found that a triangular cable network provided the most consistent correspondence to the experimental data. The model showed that the cartilage collagen network remained tensed under large confined compression strains and could therefore support shear stress. The model also predicted that the elastic moduli increased with increasing swelling pressure in a manner qualitatively similar to experimental observations. Although the model did not preclude potential contributions of other tissue components and mechanisms, the consistency of model predictions with experimental observations suggests that the cartilage collagen network, prestressed by proteoglycan swelling pressure, plays an important role in supporting compression.     

Frictional behaviour of bovine articular cartilage

The experimentally measured indentation displacement and friction of normal and degraded (treated with chondroitinase AC) bovine articular cartilage plugs against a smooth steel plate were compared with the predictions based on the biphasic theory using the finite element method. It was found that the measured indentation displacement of both cartilage specimens could be predicted from the biphasic theory and the permeability for the degraded cartilage specimen was increased approximately three times. However, the measured friction coefficient was much lower for short period of loading, and the difference in the finite element prediction of friction coefficient between the normal and degraded cartilage specimens was not observed in the experiment. Therefore, it was concluded that both biphasic and other mechanisms were important in controlling the frictional and lubricating characteristics of articular cartilage in mixed and boundary lubrication regimes.     

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.     

Electromechanical response of articular cartilage in indentation--considerations on the determination of cartilage properties during arthroscopy

A finite element formulation of streaming potentials in articular cartilage was incorporated into a fibril-reinforced model using the commercial software ABAQUS. This model was subsequently used to simulate interactions between an arthroscopic probe and articular cartilage in a knee joint. Fibril reinforcement was found to account for large fluid pressure at considerable strain rates, as has been observed in un-confined compression. Furthermore, specific electromechanical responses were associated with specific changes in tissue properties that occur with cartilage degeneration. For example, the strong strain-rate dependence of the load response was only observed when the collagen network was intact. Therefore, it is possible to use data measured during arthroscopy to evaluate the degree of cartilage degeneration and the source causing changed properties. However, practical problems, such as the difficulty of controlling the speed of the hand-held probe, may greatly reduce the reliability of such evaluations. The fibril-reinforced electromechanical model revealed that high-speed transient responses were associated with the collagen network, and equilibrium response was primarily determined by proteoglycan matrix. The results presented here may be useful in the application of arthroscopic tools for evaluating cartilage degeneration, for the proper interpretation of data, and for the optimization of data collection during arthroscopy.     

Depth-dependent strain of patellofemoral articular cartilage in unconfined compression

This biomechanical study reports strain gradients in patellofemoral joint cross-sections of seven porcine specimens in response to 1% unconfined axial compression subsequent to specific amounts of off-set strain. Strain distributions were quantified with a customized laser-based electronic speckle pattern interferometry (ESPI) system in a non-contact manner, delivering high-resolution, high-sensitivity strain maps over entire patellofemoral cartilage cross-sections. Strain reports were evaluated to determine differences in strain magnitudes between the superficial, middle, and deep cartilage layers in femoral and patellar cartilage. In addition, the effect of 5%, 10%, 15%, and 20% off-set strain on depth-dependent strain gradients was quantified. Regardless of the amount of off-set strain, the superficial layer of femoral cartilage absorbed the most strain, and the deep layer absorbed the least strain. These depth-dependent strain gradients were most pronounced for 5% off-set strain, at which the superficial layer absorbed on average 5.7 and 23.7 times more strain as compared to the middle and deep layers, respectively. For increased off-set strain levels, strain gradients became less pronounced. At 20% off-set strain, differences in layer-specific strain were not statistically significant, with the superficial layer showing a 1.4 fold higher strain as the deep layer. Patellar cartilage exhibited similar strain gradients and effects of off-set strain, although the patellar strain was on average 19% larger as compared to corresponding femoral strain reports. This study quantified for the first time continuous strain gradients over patellofemoral cartilage cross-sections. Next to provision of a detailed functional characterization of normal diarthrodial joints, this novel experimental approach holds considerable attraction to investigate joint degenerative processes.     

Strain-rate dependent stiffness of articular cartilage in unconfined compression

The stiffness of articular cartilage is a nonlinear function of the strain amplitude and strain rate as well as the loading history, as a consequence of the flow of interstitial water and the stiffening of the collagen fibril network. This paper presents a full investigation of the interplay between the fluid kinetics and fibril stiffening of unconfined cartilage disks by analyzing over 200 cases with diverse material properties. The lower and upper elastic limits of the stress (under a given strain) are uniquely established by the instantaneous and equilibrium stiffness (obtained numerically for finite deformations and analytically for small deformations). These limits could be used to determine safe loading protocols in order that the stress in each solid constituent remains within its own elastic limit. For a given compressive strain applied at a low rate, the loading is close to the lower limit and is mostly borne directly by the solid constituents (with little contribution from the fluid). In contrast, however in case of faster compression, the extra loading is predominantly transported to the fibrillar matrix via rising fluid pressure with little increase of stress in the nonfibrillar matrix. The fibrillar matrix absorbs the loading increment by self-stiffening: the quicker the loading the faster the fibril stiffening until the upper elastic loading limit is reached. This self-protective mechanism prevents cartilage from damage since the fibrils are strong in tension. The present work demonstrates the ability of the fibril reinfored poroelastic models to describe the strain rate dependent behavior of articular cartilage in unconfined compression using a mechanism of fibril stiffening mainly induced by the fluid flow.     

Stress distributions and material properties determined in articular cartilage from MRI-based finite strains

The noninvasive measurement of finite strains in biomaterials and tissues by magnetic resonance imaging (MRI) enables mathematical estimates of stress distributions and material properties. Such methods allow for non-contact and patient-specific modeling in a manner not possible with traditional mechanical testing or finite element techniques. Here, we employed three constitutive (i.e. linear Hookean, and nonlinear Neo-Hookean and Mooney-Rivlin) relations with known loading conditions and MRI-based finite strains to estimate stress patterns and material properties in the articular cartilage of tibiofemoral joints. Displacement-encoded MRI was used to determine two-dimensional finite strains in juvenile porcine joints, and an iterative technique estimated stress distributions and material properties with defined constitutive relations. Stress distributions were consistent across all relations, although the stress magnitudes varied. Material properties for femoral and tibial cartilage were found to be consistent with those reported in literature. Further, the stress estimates from Hookean and Neo-Hookean, but not Mooney-Rivlin, relations agreed with finite element-based simulations. A nonlinear Neo-Hookean relation provided the most appropriate model for the characterization of complex and spatially dependent stresses using two-dimensional MRI-based finite strain. These results demonstrate the feasibility of a new and computationally efficient technique incorporating MRI-based deformation with mathematical modeling to non-invasively evaluate the mechanical behavior of biological tissues and materials.     

Turnover of proteoglycans in cultures of bovine articular cartilage

Proteoglycans in cultures of adult bovine articular cartilage labeled with [35S]sulfate after 5 days in culture and maintained in medium containing 20% fetal calf X serum had longer half-lives (average 11 days) compared with those of the same tissue maintained in medium alone (average 6 days). The half-lives of proteoglycans in cultures of calf cartilage labeled after 5 days in culture and maintained in medium with serum were considerably longer (average 21 days) compared to adult cartilage. If 0.5 mM cycloheximide was added to the medium of cultures of adult cartilage, or the tissue was maintained at 4 degrees C after labeling, the half-lives of the proteoglycans were greater, 24 and greater than 300 days, respectively. Analyses of the radiolabeled proteoglycans remaining in the matrix of the tissue immediately after labeling the tissue and at various times in culture revealed two main populations of proteoglycans; a large species eluting with Kav of 0.21-0.24 on Sepharose CL-2B, of high bouyant density and able to form aggregates with hyaluronate, and a small species eluting with a Kav of 0.63-0.70 on Sepharose CL-2B, of low buoyant density, containing only chondroitin sulfate chains, and unable to form aggregates with hyaluronate. The larger proteoglycan had shorter half-lives than the smaller proteoglycan; in cartilage maintained with serum, the half-lives were 9.8 and 14.5 days, respectively. Labeling cartilage with both [3H]leucine and [35S]sulfate showed the small proteoglycan to be a separate synthetic product. The size distribution of 35S-labeled proteoglycans lost into the medium was shown to be polydisperse on Sepharose CL-2B, the majority eluting with a Kav of 0.27 to 0.35, of high buoyant density, and unable to aggregate with hyaluronate. The size distribution of glycosaminoglycans from 35S-labeled proteoglycans appearing in the medium did not differ from that associated with labeled proteoglycans remaining in the matrix.     

Ultrasound indentation of bovine knee articular cartilage in situ

We have earlier developed a handheld ultrasound indentation instrument for the diagnosis of articular cartilage degeneration. In ultrasound indentation, cartilage is compressed with the ultrasound transducer. Tissue thickness and deformation are calculated from the A-mode ultrasound signal and the stress applied is registered with the strain gauges. In this study, the applicability of the ultrasound indentation instrument to quantify site-dependent variation in the mechano-acoustic properties of bovine knee cartilage was investigated. Osteochondral blocks (n=6 per site) were prepared from the femoral medial condyle (FMC), the lateral facet of the patello-femoral groove (LPG) and the medial tibial plateau (MTP). Cartilage stiffness (dynamic modulus, E(dyn)), as obtained with the ultrasound indentation instrument in situ, correlated highly linearly (r=0.913, p<0.01) with the values obtained using the reference material-testing device in vitro. Reproducibility (standardized coefficient of variation) of the ultrasound indentation measurements was 5.2%, 1.7% and 3.1% for E(dyn), ultrasound reflection coefficient of articular surface (R) and thickness, respectively. E(dyn) and R were site dependent (p<0.05, Kruskall-Wallis H test). E(dyn) was significantly higher (p<0.05, Kruskall-Wallis Post Hoc test) in LPG (mean+/-SD: 10.1+/-3.1MPa) than in MTP (2.9+/-1.4MPa). In FMC, E(dyn) was 4.6+/-1.3MPa. R was significantly (p<0.05) lower at MTP (2.0+/-0.7%) than at other sites (FMC: 4.2+/-0.9%; LPG: 4.4+/-0.8%). Cartilage glycosaminoglycan concentration, as quantified with the digital densitometry, correlated positively with E(dyn) (r=0.678, p<0.01) and especially with the equilibrium Young's modulus (reference device, r=0.874, p<0.01) but it was not associated with R (r=0.294, p=0.24). We conclude that manual measurements are reproducible and the instrument may be used for detection of cartilage quality in situ. Especially, combined measurement of thickness, E(dyn) and R provides valuable diagnostic information on cartilage status.     

Synthesis of hyaluronate in cultured bovine articular cartilage.

The synthesis and distribution of hyaluronate and proteoglycan were studied in bovine articular cartilage in short-term explant culture with [3H]acetate and H2(35)SO4 as precursors. The incorporation of [3H]acetate into hyaluronate and sulphated glycosaminoglycans was linear with time, except that hyaluronate synthesis showed a marked lag at the beginning of the incubation. [3H]Hyaluronate represented 4-7% of the total [3H]glycosaminoglycans synthesized over a 6 h period. However, the distributions of [3H]hyaluronate and 3H-labelled sulphated glycosaminoglycans were different: about 50% of the newly synthesized [3H]hyaluronate appeared in the medium, compared with less than 5% of the 3H-labelled sulphated proteoglycans. A pulse-chase experiment revealed that the release of newly synthesized [3H]hyaluronate from cartilage was rapid. No difference was observed in the distribution of [3H]hyaluronate between medium and tissue by cartilage from either the superficial layer or the deep layer of articular cartilage. When articular cartilage was incubated with 0.4 mM-cycloheximide, proteoglycan synthesis was markedly inhibited, whereas the synthesis of hyaluronate was only partially inhibited and resulted in more of the newly synthesized hyaluronate being released into the medium. Analysis of the hydrodynamic size of [3H]hyaluronate isolated from cartilage on Sephacryl-1000 revealed one population that was eluted as a broad peak (Kav. less than 0.7), compared with two populations (Kav. greater than 0.5 and less than 0.5) appearing in the medium of cultures. These data suggest that hyaluronate is synthesized in excess of proteoglycan synthesis and that the hyaluronate that is not complexed with proteoglycans is rapidly lost from the tissue.     

Comparison of proteoglycans from bovine articular cartilage.

Four bovine articular cartilages have been compared with regard to the chemical composition of the whole cartilages, the amount of proteoglycan selectively extracted with 3 M MGCl2 or with 3 M guanidine-HCl, and the compositions and physical properties of the isolated proteoglycans. The whole cartilages differ but slightly in composition. Occipital condylar cartilage, a thin cartilage from the smallest joint, contains 4% more collagen and proportionately less proteoglycan than proximal humeral, the thickest cartilage from the largest joint. Each cartilage contains a pool of proteoglycan that resists extraction with 3 M MgCl2 but is extracted with 3 M guanidine-HCl. The proteoglycan extracted from each cartilage with 3 M guanidine-HCl contains a high molecular weight proteoglycan-collagen complex demonstrated by analytical ultracentrifugation and by the turbidity of its visible and ultra-violet spectra. The four cartilages appear to differ most remarkably in the fraction of total proteoglycan extracted from each as proteoglycan-collagen complex.     

Biomechanical properties of knee articular cartilage

Structure and properties of knee articular cartilage are adapted to stresses exposed on it during physiological activities. In this study, we describe site- and depth-dependence of the biomechanical properties of bovine knee articular cartilage. We also investigate the effects of tissue structure and composition on the biomechanical parameters as well as characterize experimentally and numerically the compression-tension nonlinearity of the cartilage matrix. In vitro mechano-optical measurements of articular cartilage in unconfined compression geometry are conducted to obtain material parameters, such as thickness, Young's and aggregate modulus or Poisson's ratio of the tissue. The experimental results revealed significant site- and depth-dependent variations in recorded parameters. After enzymatic modification of matrix collagen or proteoglycans our results show that collagen primarily controls the dynamic tissue response while proteoglycans affect more the static properties. Experimental measurements in compression and tension suggest a nonlinear compression-tension behavior of articular cartilage in the direction perpendicular to articular surface. Fibril reinforced poroelastic finite element model was used to capture the experimentally found compression-tension nonlinearity of articular cartilage.