Depth-dependent biomechanical and biochemical properties of fetal, newborn, and tissue-engineered articular cartilage

Adult articular cartilage has depth-dependent mechanical and biochemical properties which contribute to zone-specific functions. The compressive moduli of immature cartilage and tissue-engineered cartilage are known to be lower than those of adult cartilage. The objective of this study was to determine if such tissues exhibit depth-dependent compressive properties, and how these depth-varying properties were correlated with cell and matrix composition of the tissue. The compressive moduli of fetal and newborn bovine articular cartilage increased with depth (p<0.05) by a factor of 4-5 from the top 0.1 mm (28+/-13 kPa, 141+/-10 kPa, respectively) to 1 mm deep into the tissue. Likewise, the glycosaminoglycan and collagen content increased with depth (both p<0.001), and correlated with the modulus (both p<0.01). In contrast, tissue-engineered cartilage formed by either layering or mixing cells from the superficial and middle zone of articular cartilage exhibited similarly soft regions at both construct surfaces, as exemplified by large equilibrium strains. The properties of immature cartilage may provide a template for developing tissue-engineered cartilage which aims to repair cartilage defects by recapitulating the natural development and growth processes. These results suggest that while depth-dependent properties may be important to engineer into cartilage constructs, issues other than cell heterogeneity must be addressed to generate such tissues.     

Extraction of mechanical properties of articular cartilage from osmotic swelling behavior monitored using high frequency ultrasound

Articular cartilage is a biological weight-bearing tissue covering the bony ends of articulating joints. Negatively charged proteoglycan (PG) in articular cartilage is one of the main factors that govern its compressive mechanical behavior and swelling phenomenon. PG is nonuniformly distributed throughout the depth direction, and its amount or distribution may change in the degenerated articular cartilage such as osteoarthritis. In this paper, we used a 50 MHz ultrasound system to study the depth-dependent strain of articular cartilage under the osmotic loading induced by the decrease of the bathing saline concentration. The swelling-induced strains under the osmotic loading were used to determine the layered material properties of articular cartilage based on a triphasic model of the free-swelling. Fourteen cylindrical cartilage-bone samples prepared from fresh normal bovine patellae were tested in situ in this study. A layered triphasic model was proposed to describe the depth distribution of the swelling strain for the cartilage and to determine its aggregate modulus H(a) at two different layers, within which H(a) was assumed to be linearly dependent on the depth. The results showed that H(a) was 3.0+/-3.2, 7.0+/-7.4, 24.5+/-11.1 MPa at the cartilage surface, layer interface, and deep region, respectively. They are significantly different (p<0.01). The layer interface located at 70%+/-20% of the overall thickness from the uncalcified-calcified cartilage interface. Parametric analysis demonstrated that the depth-dependent distribution of the water fraction had a significant effect on the modeling results but not the fixed charge density. This study showed that high-frequency ultrasound measurement together with triphasic modeling is practical for quantifying the layered mechanical properties of articular cartilage nondestructively and has the potential for providing useful information for the detection of the early signs of osteoarthritis.     

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.     

The effect of storage on the biomechanical behavior of articular cartilage--a large strain study.

The transplantation of stored shell osteochondral allografts is a potentially useful alternative to total joint replacements for the treatment of joint ailments. The maintenance of normal cartilage properties of the osteochondral allografts during storage is important for the allograft to function properly and survive in the host joint. Since articular cartilage is normally under large physiological stresses, this study was conducted to investigate the biomechanical behavior under large strain conditions of cartilage tissue stored for various time periods (i.e., 3, 7, 28, and 60 days) in tissue culture media. A biphasic large strain theory developed for soft hydrated connective tissues was used to describe and determine the biomechanical properties of the stored cartilage. It was found that articular cartilage stored for up to 60 days maintained the ability to sustain large compressive strains of up to 40 percent or more, like normal articular cartilage. Moreover, the equilibrium stress-strain behavior and compressive modulus of the stored articular cartilage were unchanged after up to 60 days of storage.     

An automated approach for direct measurement of two-dimensional strain distributions within articular cartilage under unconfined compression

An automated approachfor measuring in situ two-dimensional strain fields was developed and validated for its application to cartilage mechanics. This approach combines video microscopy, optimized digital image correlation (DIC), thin-plate spline smoothing (TPSS) and generalized cross-validation (GCV) techniques to achieve the desired efficiency and accuracy. Results demonstrate that sub-pixel accuracies can be achieved for measuring tissue displacements with this methodology with a measurement uncertainty ranging from 0.25 to 0.30 pixels. The deformational gradients (from which the strains are determined) can be evaluated directly using the optimized DIC, with a measurement uncertainty of 0.017 to approximately 0.032. In actual measurements of strain in cartilage, TPSS and differentiation can be used to achieve a more accurate measurement of the gradients from the displacement data. Using this automated approach, the two-dimensional strain fields inside immature bovine carpometacarpal joint cartilage specimens under unconfined compression were characterized (n=21). The depth-dependent apparent elastic modulus and Poisson's ratio were also determined and found to be smallest at the articular surface and increasing with depth. The apparent Poisson's ratio is found to decrease with increasing compressive strain, with values as low as 0.01 observed near the articular surface at 25% compression. The variation of the apparent Poisson's ratio with depth is found to be consistent with a theoretical model of cartilage which accounts for the disparity in its tensile and compressive moduli.     

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.     

Electrostatic and non-electrostatic contributions of proteoglycans to the compressive equilibrium modulus of bovine articular cartilage

This study presents direct experimental evidence for assessing the electrostatic and non-electrostatic contributions of proteoglycans to the compressive equilibrium modulus of bovine articular cartilage. Immature and mature bovine cartilage samples were tested in unconfined compression and their depth-dependent equilibrium compressive modulus was determined using strain measurements with digital image correlation analysis. The electrostatic contribution was assessed by testing samples in isotonic and hypertonic saline; the combined contribution was assessed by testing untreated and proteoglycan-depleted samples.Though it is well recognized that proteoglycans contribute significantly to the compressive stiffness of cartilage, results demonstrate that the combined electrostatic and non-electrostatic contributions may add up to more than 98% of the modulus, a magnitude not previously appreciated. Of this contribution, about two thirds arises from electrostatic effects. The compressive modulus of the proteoglycan-depleted cartilage matrix may be as low as 3 kPa, representing less than 2% of the normal tissue modulus; experimental evidence also confirms that the collagen matrix in digested cartilage may buckle under compressive strains, resulting in crimping patterns. Thus, it is reasonable to model the collagen as a fibrillar matrix that can sustain only tension. This study also demonstrates that residual stresses in cartilage do not arise exclusively from proteoglycans, since cartilage remains curled relative to its in situ geometry even after proteoglycan depletion. These increased insights on the structure–function relationships of cartilage can lead to improved constitutive models and a better understanding of the response of cartilage to physiological loading conditions.     

Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis

Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.     

Two-dimensional strain fields on the cross-section of the bovine humeral head under contact loading

The objective of this study was to provide a detailed experimental assessment of the two-dimensional cartilage strain distribution on the cross-section of immature and mature bovine humeral heads subjected to contact loading at a relatively rapid physiological loading rate. Six immature and six mature humeral head specimens were loaded against glass and strains were measured at the end of a 5s loading ramp on the textured articular cross-section using digital image correlation analysis. The primary findings indicate that elevated tensile and compressive strains occur near the articular surface, around the center of the contact region. Few qualitative or quantitative differences were observed between mature and immature joints. Under an average contact stress of approximately 1.7 MPa, the peak compressive strains averaged -0.131+/-0.048, which was significantly less than the relative change in cartilage thickness, -0.104+/-0.032 (p<0.05). The peak tensile strains were significantly smaller in magnitude, at 0.0325+/-0.013. These experimental findings differ from a previous finite element analysis of articular contact, which predicted peak strains at the cartilage-bone interface even when accounting for the porous-hydrated nature of the tissue, its depth-dependent inhomogeneity, and the disparity between its tensile and compressive properties. These experimental results yield new insights into the local mechanical environment of the tissue and cells, and suggest that further refinements are needed in the modeling of contacting articular layers.     

Zonal changes in the three-dimensional morphology of the chondron under compression: the relationship among cellular, pericellular, and extracellular deformation in articular cartilage

The pericellular matrix (PCM) is a narrow region of tissue that completely surrounds chondrocytes in articular cartilage. Previous theoretical models of the "chondron" (the PCM with enclosed cells) suggest that the structure and properties of the PCM may significantly influence the mechanical environment of the chondrocyte. The objective of this study was to quantify changes in the three-dimensional (3D) morphology of the chondron in situ at different magnitudes of compression applied to the cartilage extracellular matrix. Fluorescence immunolabeling for type-VI collagen was used to identify the boundaries of the cell and PCM, and confocal microscopy was used to form 3D images of chondrons from superficial, middle, and deep zone cartilage in explants compressed to 0%, 10%, 30%, and 50% surface-to-surface strain. Lagrangian tissue strain, determined locally using texture correlation, was highly inhomogeneous and revealed depth-dependent compressive stiffness and Poisson's ratio of the extracellular matrix. Compression significantly decreased cell and chondron height and volume, depending on the zone and magnitude of compression. In the superficial zone, cellular-level strains were always lower than tissue-level strains. In the middle and deep zones, however, tissue strains below 25% were amplified at the cellular level, while tissue strains above 25% were decreased at the cellular level. These findings are consistent with previous theoretical models of the chondron, suggesting that the PCM can serve as either a protective layer for the chondrocyte or a transducer that amplifies strain, such that cellular-level strains are more homogenous throughout the tissue depth despite large inhomogeneities in local ECM strains.     

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.     

Ultrasonic measurement of depth-dependent transient behaviors of articular cartilage under compression

We previously reported an ultrasound method for measuring the depth-dependent equilibrium mechanical properties of articular cartilage using quasi-static compression. The objective of this paper was to introduce our recent development for nondestructively measuring the transient depth-dependent strains of full-thickness articular cartilage specimens prepared from bovine patellae. A 50 MHz focused ultrasound transducer was used to collect ultrasound echoes from articular cartilage specimens (n=8) and sponge phantoms with open pores (n=10) during tests of compression and subsequent stress-relaxation. The transient displacements of the tissues at different depths along the compression direction were calculated from the ultrasound echoes using a cross-correlation tracking technique. An LVDT sensor and a load cell were used to measure the overall deformation of the tissue and the applied force, respectively. Results showed that the tissues inside the cartilage layer continued to move during the stress-relaxation phase after the compression was completed. In the equilibrium state, the displacements of the cartilage tissues at the depths of 1/4, 1/2, and 3/4 of the full-thickness reduced by 51%+/-22%, 54%+/-17%, and 50+/-17%, respectively, in comparison with its peak value. However, no similar phenomenon was observed in the sponge phantoms. Our preliminary results demonstrated that this ultrasound method may provide a potential tool for the nondestructive measurement of the transient depth-dependent processes involved in biological and bioengineered soft tissues as well as soft biomaterials under dynamic loading.     

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.     

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.     

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.     

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.     

Nonuniform swelling-induced residual strains in articular cartilage

Swelling effects in cartilage originate from an interstitial osmotic pressure generated by the presence of negatively charged proteoglycans in the tissue. This swelling pressure gives rise to a non-zero residual strain in the cartilage solid matrix in the absence of externally applied loads. Previous studies have quantified swelling effects in cartilage as volumetric or dimensional change of excised samples in varying osmotically active solutions. This study presents a new optical technique for measuring two-dimensional swelling-induced residual strain fields in planar samples of articular cartilage attached to the bone (i.e., in situ). Osmotic loading was applied to canine cartilage bone samples by equilibration in external baths of varying NaCl concentration. Non-zero swelling-induced strains were measured in physiological saline, giving evidence of the existence of residual strains in articular cartilage. Only one component of planar strain (i.e., in thickness direction) was found to be non-zero. This strain was found to be highly non-uniform in the thickness direction, with evidence of compressive strain in the deep zone of cartilage and tensile strain in the middle and surface zones. The obtained results can be used to characterize the material properties of the articular cartilage solid matrix, with estimated values of 26 M Pa for the tensile modulus for middle zone cartilage. The method provides the basis to obtain material properties of the cartilage solid matrix from a simple, free-swelling test and may be useful for quantifying changes in cartilage properties with injury, degeneration and repair.     

Application of the u-p finite element method to the study of articular cartilage.

The finite element method using the principle of virtual work was applied to the biphasic theory to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (mu) and true fluid pressure (p) as the unknown variables at the element nodes. Both small and large strain conditions were considered. The algorithms and computer code for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases were developed. The u-p finite element numerical procedure demonstrated excellent agreement with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The model was also used to examine the behavior of a repaired articular surface. The differences in material properties between the repair tissue and normal cartilage resulted in significant deformation gradients across the repair interface as well as increased fluid efflux from the tissue.     

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.     

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.