Contribution of tissue composition and structure to mechanical response of articular cartilage under different loading geometries and strain rates

Mechanical function of articular cartilage in joints between articulating bones is dependent on the composition and structure of the tissue. The mechanical properties of articular cartilage are traditionally tested in compression using one of the three loading geometries, i.e., confined compression, unconfined compression or indentation. The aim of this study was to utilize a composition-based finite element model in combination with a fractional factorial design to determine the importance of different cartilage constituents in the mechanical response of the tissue, and to compare the importance of the tissue constituents with different loading geometries and loading rates. The evaluated parameters included water and collagen fraction as well as fixed charge density on cartilage surface and their slope over the tissue thickness. The thicknesses of superficial and middle zones, as based on the collagen orientation, were also included in the evaluated parameters. A three-level resolution V fractional factorial design was used. The model results showed that inhomogeneous composition plays only a minor role in indentation, though that role becomes more significant in confined compression and unconfined compression. In contrast, the collagen architecture and content had a more profound role in indentation than with two other loading geometries. These differences in the mechanical role of composition and structure between the loading geometries were emphasized at higher loading rates. These findings highlight how the results from mechanical tests of articular cartilage under different loading conditions are dependent upon tissue composition and structure.     

A comparison of cartilage stress-relaxation models in unconfined compression: QLV and stretched exponential in combination with fluid flow

Cartilage exhibits nonlinear viscoelastic behaviour. Various models have been proposed to explain cartilage stress relaxation, but it is unclear whether explicit modelling of fluid flow in unconfined compression is needed. This study compared Fung's quasi-linear viscoelastic (QLV) model with a stretched-exponential model of cartilage stress relaxation and examined each of these models both alone and in combination with a fluid-flow model in unconfined compression. Cartilage explants were harvested from bovine calf patellofemoral joints and equilibrated in tissue culture for 5 days before stress-relaxation testing in unconfined compression at 5% nominal strain. The stretched exponential models fit as well as the QLV models. Furthermore, the average stretched exponential relaxation time determined by this model lies within the range of experimentally measured relaxation times for extracted proteoglycan aggregates, consistent with the hypothesis that the stretched exponential model represents polymeric mechanisms of cartilage viscoelasticity.     

Experimental verification of the roles of intrinsic matrix viscoelasticity and tension-compression nonlinearity in the biphasic response of cartilage

A biphasic-CLE-QLV model proposed in our recent study [2001, J. Biomech. Eng., 123, pp. 410-417] extended the biphasic theory of Mow et al. [1980, J. Biomech. Eng., 102, pp. 73-84] to include both tension-compression nonlinearity and intrinsic viscoelasticity of the cartilage solid matrix by incorporating it with the conewise linear elasticity (CLE) model [1995, J. Elasticity, 37, pp. 1-38] and the quasi-linear viscoelasticity (QLV) model [Biomechanics: Its foundations and objectives, Prentice Hall, Englewood Cliffs, 1972]. This model demonstrates that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelastic effects, as well as tension-compression nonlinearity. The objective of this study is to directly test this biphasic-CLE-QLV model against experimental data from unconfined compression stress-relaxation tests at slow and fast strain rates as well as dynamic loading. Twelve full-thickness cartilage cylindrical plugs were harvested from six bovine glenohumeral joints and multiple confined and unconfined compression stress-relaxation tests were performed on each specimen. The material properties of specimens were determined by curve-fitting the experimental results from the confined and unconfined compression stress relaxation tests. The findings of this study demonstrate that the biphasic-CLE-QLV model is able to describe the strain-rate-dependent mechanical behaviors of articular cartilage in unconfined compression as attested by good agreements between experimental and theoretical curvefits (r2 = 0.966 +/- 0.032 for testing at slow strain rate; r2 = 0.998 +/- 0.002 for testing at fast strain rate) and predictions of the dynamic response (r2 = 0.91 +/- 0.06). This experimental study also provides supporting evidence for the hypothesis that both tension-compression nonlinearity and intrinsic viscoelasticity of the solid matrix of cartilage are necessary for modeling the transient and equilibrium responses of this tissue in tension and compression. Furthermore, the biphasic-CLE-QLV model can produce better predictions of the dynamic modulus of cartilage in unconfined dynamic compression than the biphasic-CLE and biphasic poroviscoelastic models, indicating that intrinsic viscoelasticity and tension-compression nonlinearity of articular cartilage may play important roles in the load-support mechanism of cartilage under physiologic loading.     

Dynamic measurement of internal solid displacement in articular cartilage using ultrasound backscatter

Mechanics of articular cartilage can be represented using poroelastic theories where fluid and solid displacements are viscously coupled to create a time-dependent spatially heterogeneous behavior. In recent models of this tissue, finite element methods have been used to predict tissue deformation as a function of time for adult articular cartilage bearing a characteristic depth-dependent structure and composition. However, current experimental methods are limited in providing verification of these predictions. The current study presents an apparatus for imaging the radial displacement profile of cartilage in unconfined compression using an ultrasound technique called elastography. We acquired ultrasound A-scans across the lateral diameter of full-thickness cartilage disks containing a thin layer of underlying bone, during axial compression. Elastography was then applied to correlate temporally sequential A-scans to estimate the solid radial displacement profile in articular cartilage while it undergoes compression and stress-relaxation. Both time-dependent and depth-dependent solid radial displacement profiles were obtained with a precision better than 0.2 micro The results generally agree with predictions of poroelastic models, demonstrating lateral expansion with an effective Poisson's ratio just after completion of the compression phase of the mechanical tests reaching values from 0.18 to 0.4 (depending on compression speed), followed by contraction to lower values. A more restricted movement was observed at both the articular surface and near to the subchondral bone than at regions midway between these two locations.     

Characterization of articular cartilage by combining microscopic analysis with a fibril-reinforced finite-element model

Load-bearing characteristics of articular cartilage are impaired during tissue degeneration. Quantitative microscopy enables in vitro investigation of cartilage structure but determination of tissue functional properties necessitates experimental mechanical testing. The fibril-reinforced poroviscoelastic (FRPVE) model has been used successfully for estimation of cartilage mechanical properties. The model includes realistic collagen network architecture, as shown by microscopic imaging techniques. The aim of the present study was to investigate the relationships between the cartilage proteoglycan (PG) and collagen content as assessed by quantitative microscopic findings, and model-based mechanical parameters of the tissue. Site-specific variation of the collagen network moduli, PG matrix modulus and permeability was analyzed. Cylindrical cartilage samples (n=22) were harvested from various sites of the bovine knee and shoulder joints. Collagen orientation, as quantitated by polarized light microscopy, was incorporated into the finite-element model. Stepwise stress-relaxation experiments in unconfined compression were conducted for the samples, and sample-specific models were fitted to the experimental data in order to determine values of the model parameters. For comparison, Fourier transform infrared imaging and digital densitometry were used for the determination of collagen and PG content in the same samples, respectively. The initial and strain-dependent fibril network moduli as well as the initial permeability correlated significantly with the tissue collagen content. The equilibrium Young's modulus of the nonfibrillar matrix and the strain dependency of permeability were significantly associated with the tissue PG content. The present study demonstrates that modern quantitative microscopic methods in combination with the FRPVE model are feasible methods to characterize the structure-function relationships of articular cartilage.     

Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal,proteoglycan depleted and collagen degraded articular cartilage

Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (-64+/-28%) and a minor decrease of the fibril network modulus (-11+/-9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (-69+/-5%) and a decrease of the drained porous matrix modulus (-44+/-18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.     

The Mechanical Behaviour of Chondrocytes Predicted with a Micro-structural Model of Articular Cartilage

The integrity of articular cartilage depends on the proper functioning and mechanical stimulation of chondrocytes, the cells that synthesize extracellular matrix and maintain tissue health. The biosynthetic activity of chondrocytes is influenced by genetic factors, environmental influences, extracellular matrix composition, and mechanical factors. The mechanical environment of chondrocytes is believed to be an important determinant for joint health, and chondrocyte deformation in response to mechanical loading is speculated to be an important regulator of metabolic activity. In previous studies of chondrocyte deformation, articular cartilage was described as a biphasic material consisting of a homogeneous, isotropic, linearly elastic solid phase, and an inviscid fluid phase. However, articular cartilage is known to be anisotropic and inhomogeneous across its depth. Therefore, isotropic and homogeneous models cannot make appropriate predictions for tissue and cell stresses and strains. Here, we modelled articular cartilage as a transversely isotropic, inhomogeneous (TI) material in which the anisotropy and inhomogeneity arose naturally from the microstructure of the depth-dependent collagen fibril orientation and volumetric fraction, as well as the chondrocyte shape and volumetric fraction. The purpose of this study was to analyse the deformation behaviour of chondrocytes using the TI model of articular cartilage. In order to evaluate our model against experimental results, we simulated indentation and unconfined compression tests for nominal compressions of 15%. Chondrocyte deformations were analysed as a function of location within the tissue. The TI model predicted a non-uniform behaviour across tissue depth: in indentation testing, cell height decreased by 43% in the superficial zone and between 11 and 29% in the deep zone. In unconfined compression testing, cell height decreased by 32% in the superficial zone, 25% in the middle, and 18% in the deep zones. This predicted non-uniformity is in agreement with experimental studies. The novelty of this study is the use of a cartilage material model accounting for the intrinsic inhomogeneity and anisotropy of cartilage caused by its microstructure.     

Biomechanical properties of human articular cartilage under compressive loads

The function of articular cartilage is to support and distribute loads and to provide lubrication in the diarthrodial joints. Cartilage function is described by proper mechanical and rheological properties, strain and depth-dependent, which are not completely assessed. Unconfined and confined compression are commonly used to evaluate the Young's modulus (E) and the aggregate modulus (H(A)), respectively. The Poisson's ratio (nu) can be calculated indirectly from the equilibrium compression data, or using the biphasic indentation technique; it has recently been optically evaluated by using video microscopy during unconfined compression. The transient response of articular cartilage during confined compression depends on its permeability k; a constant value of k can be easily identified by a simple analytical model of confined compression tests, whereas more complex models or direct measurements (permeation tests) are needed to study the permeability dependence on deformation. A poroelastic finite element model of articular cartilage was developed for this purpose. The elastic parameters (E,nu) of the model were evaluated performing unconfined compression creep tests on human articular cartilage disks, whereas k was identified from the confined test response. Our combined experimental and computational method can be used to identify the parameters that define the permeability dependence on deformation, as a function of depth from articular surface.     

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.     

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.     

The importance of superficial collagen fibrils for the function of articular cartilage

It has been proposed that the superficial tangential zone (STZ) of articular cartilage is essential to the tissue’s load-distributing function. However, the exact mechanism by which the STZ fulfills this function has not yet been revealed. Using a channel-indentation experiment, it was recently shown that compared to intact tissue, cartilage without STZ behaves slightly stiffer and deforms significantly different in regions adjacent to mechanically compressed areas (Bevill et al. in Osteoarthr Cartil 18:1310–1318, 2010). We aim to further explore the role of STZ in the load-transfer mechanism of AC by thorough biomechanical analysis of these experiments. Using our previously validated fibril-reinforced swelling model of articular cartilage, which accounts for the depth-dependent collagen structure and biochemical composition of articular cartilage, we simulated the above-mentioned channel-indenter compression experiments for both intact and STZ-removed cartilage. First, we show that the composition of the deep zone in cartilage is most effective in carrying cartilage compression, which explains the apparent tissue stiffening after STZ removal. Second, we show that tangential fibrils in the STZ are responsible for transferring compressive loads from directly loaded regions to adjacent tissue. Cartilage with an intact STZ has superior load-bearing properties compared to cartilage in which the STZ is compromised, because the STZ is able to recruit a larger area of deep zone cartilage to carry compressive loads.     

Prediction of biomechanical properties of articular cartilage with quantitative magnetic resonance imaging

Quantitative magnetic resonance imaging (MRI) is the most potential non-invasive means for revealing the structure, composition and pathology of articular cartilage. Here we hypothesize that cartilage mechanical properties as determined by the macromolecular framework and their interactions can be accessed by quantitative MRI. To test this, adjacent cartilage disk pairs (n=32) were prepared from bovine proximal humerus and patellofemoral surfaces. For one sample, the tissue Young's modulus, aggregate modulus, dynamic modulus and Poisson's ratio were determined in unconfined compression. The adjacent disk was studied at 9.4T to determine the tissue T(2) relaxation time, sensitive to the integrity of the collagen network, and T(1) relaxation time in the presence of Gd-DTPA, a technique developed for the estimation of cartilage proteoglycan (PG) content. Quantitative MRI parameters were able to explain up to 87% of the variations in certain biomechanical parameters. Correlations were further improved when data from the proximal humerus was assessed separately. MRI parameters revealed a topographical variation similar to that of mechanical parameters. Linear regression analysis revealed that Young's modulus of cartilage may be characterized more completely by combining both collagen- and PG-sensitive MRI parameters. The present results suggest that quantitative MRI can provide important information on the mechanical properties of articular cartilage. The results are encouraging with respect to functional imaging of cartilage, although in vivo applicability may be limited by the inferior resolution of clinical MRI instruments.     

Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes

The collagen network and proteoglycan matrix of articular cartilage are thought to play an important role in controlling the stresses and strains in and around chondrocytes, in regulating the biosynthesis of the solid matrix, and consequently in maintaining the health of diarthrodial joints. Understanding the detailed effects of the mechanical environment of chondrocytes on cell behavior is therefore essential for the study of the development, adaptation, and degeneration of articular cartilage. Recent progress in macroscopic models has improved our understanding of depth-dependent properties of cartilage. However, none of the previous works considered the effect of realistic collagen orientation or depth-dependent negative charges in microscopic models of chondrocyte mechanics. The aim of this study was to investigate the effects of the collagen network and fixed charge densities of cartilage on the mechanical environment of the chondrocytes in a depth-dependent manner. We developed an anisotropic, inhomogeneous, microstructural fibril-reinforced finite element model of articular cartilage for application in unconfined compression. The model consisted of the extracellular matrix and chondrocytes located in the superficial, middle, and deep zones. Chondrocytes were surrounded by a pericellular matrix and were assumed spherical prior to tissue swelling and load application. Material properties of the chondrocytes, pericellular matrix, and extracellular matrix were obtained from the literature. The loading protocol included a free swelling step followed by a stress-relaxation step. Results from traditional isotropic and transversely isotropic biphasic models were used for comparison with predictions from the current model. In the superficial zone, cell shapes changed from rounded to elliptic after free swelling. The stresses and strains as well as fluid flow in cells were greatly affected by the modulus of the collagen network. The fixed charge density of the chondrocytes, pericellular matrix, and extracellular matrix primarily affected the aspect ratios (height/width) and the solid matrix stresses of cells. The mechanical responses of the cells were strongly location and time dependent. The current model highlights that the collagen orientation and the depth-dependent negative fixed charge densities of articular cartilage have a great effect in modulating the mechanical environment in the vicinity of chondrocytes, and it provides an important improvement over earlier models in describing the possible pathways from loading of articular cartilage to the mechanical and biological responses of chondrocytes.     

Dynamic response of immature bovine articular cartilage in tension and compression, and nonlinear viscoelastic modeling of the tensile response

Very limited information is currently available on the constitutive modeling of the tensile response of articular cartilage and its dynamic modulus at various loading frequencies. The objectives of this study were to (1) formulate and experimentally validate a constitutive model for the intrinsic viscoelasticity of cartilage in tension, (2) confirm the hypothesis that energy dissipation in tension is less than in compression at various loading frequencies, and (3) test the hypothesis that the dynamic modulus of cartilage in unconfined compression is dependent upon the dynamic tensile modulus. Experiment 1: Immature bovine articular cartilage samples were tested in tensile stress relaxation and cyclical loading. A proposed reduced relaxation function was fitted to the stress-relaxation response and the resulting material coefficients were used to predict the response to cyclical loading. Adjoining tissue samples were tested in unconfined compression stress relaxation and cyclical loading. Experiment 2: Tensile stress relaxation experiments were performed at varying strains to explore the strain-dependence of the viscoelastic response. The proposed relaxation function successfully fit the experimental tensile stress-relaxation response, with R2 = 0.970+/-0.019 at 1% strain and R2 = 0.992+/-0.007 at 2% strain. The predicted cyclical response agreed well with experimental measurements, particularly for the dynamic modulus at various frequencies. The relaxation function, measured from 2% to 10% strain, was found to be strain dependent, indicating that cartilage is nonlinearly viscoelastic in tension. Under dynamic loading, the tensile modulus at 10 Hz was approximately 2.3 times the value of the equilibrium modulus. In contrast, the dynamic stiffening ratio in unconfined compression was approximately 24. The energy dissipation in tension was found to be significantly smaller than in compression (dynamic phase angle of 16.7+/-7.4 deg versus 53.5+/-12.8 deg at 10(-3) Hz). A very strong linear correlation was observed between the dynamic tensile and dynamic compressive moduli at various frequencies (R2 = 0.908+/-0.100). The tensile response of cartilage is nonlinearly viscoelastic, with the relaxation response varying with strain. A proposed constitutive relation for the tensile response was successfully validated. The frequency response of the tensile modulus of cartilage was reported for the first time. Results emphasize that fluid-flow dependent viscoelasticity dominates the compressive response of cartilage, whereas intrinsic solid matrix viscoelasticity dominates the tensile response. Yet the dynamic compressive modulus of cartilage is critically dependent upon elevated values of the dynamic tensile modulus.     

Acoustic properties of articular cartilage under mechanical stress

Mechano-acoustic and elastographic techniques may provide quantitative means for the in vivo diagnostics of articular cartilage. These techniques assume that sound speed does not change during tissue loading. As articular cartilage shows volumetric changes during compression, acoustic properties of cartilage may change affecting the validity of mechano-acoustic measurements. In this study, we examined the ultrasound propagation through human, bovine and porcine articular cartilage during stress-relaxation in unconfined compression. The time of flight (TOF) technique with known cartilage thickness (true sound speed) as well as in situ calibration method [Suh, Youn, Fu, J. Biomech. 34 (2001), 1347-1353] were used for the determination of sound speed. Ultrasound speed and attenuation decreased in articular cartilage during ramp compression, but returned towards the level of original values during relaxation. Variations in ultrasound speed induced an error in strain and compressive moduli provided that constant ultrasound speed and time-of-flight data was used to determine the tissue thickness. Highest errors in strain (-11.8 +/- 12.0%) and dynamic modulus (15.4 +/- 17.9%) were recorded in bovine cartilage. TOF and in situ calibration methods yielded different results for changes in sound speed during compression. We speculate that the variations in acoustic properties in loaded cartilage are related to rearrangement of the interstitial matrix, especially to that of collagen fibers. In human cartilage the changes, are, however relatively small and, according to the numerical simulations, mechano-acoustic techniques that assume constant acoustic properties for the cartilage will not be significantly impaired by this phenomenon.     

Unconfined compression of articular cartilage: nonlinear behavior and comparison with a fibril-reinforced biphasic model

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample's radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models.     

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.     

Mechano-acoustic determination of Young's modulus of articular cartilage

The compressive stiffness of an elastic material is traditionally characterized by its Young's modulus. Young's modulus of articular cartilage can be directly measured using unconfined compression geometry by assuming the cartilage to be homogeneous and isotropic. In isotropic materials, Young's modulus can also be determined acoustically by the measurement of sound speed and density of the material. In the present study, acoustic and mechanical techniques, feasible for in vivo measurements, were investigated to quantify the static and dynamic compressive stiffness of bovine articular cartilage in situ. Ultrasound reflection from the cartilage surface, as well as the dynamic modulus were determined with the recently developed ultrasound indentation instrument and compared with the reference mechanical and ultrasound speed measurements in unconfined compression (n=72). In addition, the applicability of manual creep measurements with the ultrasound indentation instrument was evaluated both experimentally and numerically. Our experimental results indicated that the sound speed could predict 47% and 53% of the variation in the Young's modulus and dynamic modulus of cartilage, respectively. The dynamic modulus, as determined manually with the ultrasound indentation instrument, showed significant linear correlations with the reference Young's modulus (r(2)=0.445, p<0.01, n=70) and dynamic modulus (r(2)=0.779, p<0.01, n=70) of the cartilage. Numerical analyses indicated that the creep measurements, conducted manually with the ultrasound indentation instrument, were sensitive to changes in Young's modulus and permeability of the tissue, and were significantly influenced by the tissue thickness. We conclude that acoustic parameters, i.e. ultrasound speed and reflection, are indicative to the intrinsic mechanical properties of the articular cartilage. Ultrasound indentation instrument, when further developed, provides an applicable tool for the in vivo detection of cartilage mechano-acoustic properties. These techniques could promote the diagnostics of osteoarthrosis.