Depth-dependent analysis of the role of collagen fibrils, fixed charges and fluid in the pericellular matrix of articular cartilage on chondrocyte mechanics

The pericellular matrix of articular cartilage has been shown to regulate the mechanical environment of chondrocytes. However, little is known about the mechanical role of collagen fibrils in the pericellular matrix, and how fibrils might help modulate strains acting on chondrocytes when cartilage is loaded. The primary objective was to clarify the effect of pericellular collagen fibrils on cell volume changes and strains during cartilage loading. Secondary objectives were to investigate the effects of pericellular fixed charges and fluid on cell responses. A microstructural model of articular cartilage, in which chondrocytes and pericellular matrices were represented with depth-dependent structural and morphological properties, was created. The extracellular matrix and pericellular matrices were modeled as fibril-reinforced, biphasic materials with swelling capabilities, while chondrocytes were assumed to be isotropic and biphasic with swelling properties. Collagen fibrils in the extracellular matrix were represented with an arcade-like architecture, whereas pericellular fibrils were assumed to run tangential to the cell surface. In the early stages of a stress-relaxation test, pericellular fibrils were found to sensitively affect cell volume changes, even producing a reversal from increasing to decreasing cell volume with increasing fibril stiffness in the superficial zone. Consequently, steady-state volume of the superficial zone cell decreased with increasing pericellular fibril stiffness. Volume changes in the middle and deep zone chondrocytes were smaller and opposite to those observed in the superficial zone chondrocyte. An increase in the pericellular fixed charge density reduced cell volumes substantially in every zone. The sensitivity of cell volume changes to pericellular fibril stiffness suggests that pericellular fibrils play an important, and as of yet largely neglected, role in regulating the mechanical environment of chondrocytes, possibly affecting matrix synthesis during cartilage development and degeneration, and affecting biosynthetic responses associated with articular cartilage loading.     

Collagen Network of Articular Cartilage Modulates Fluid Flow and Mechanical Stresses in Chondrocyte

The extracellular matrix of articular cartilage modulates the mechanical signals sensed by the chondrocytes. In the present study, a finite element model (FEM) of the chondrocyte and its microenvironment was reconstructed using the information from fourier transform infrared imaging spectroscopy. This environment consisted of pericellular, territorial (mainly proteoglycans), and inter-territorial (mainly collagen) matrices. The chondrocyte, pericellular, and territorial matrix were assumedto be mechanically isotropic and poroelastic, whereas the inter-territorial matrix, due to its high collagen content, was assumed to be transversely isotropic and poroelastic. Under instantaneous strain-controlled compression, the FEM indicated that the fluid pressure within the chondrocyte increased nonlinearly as a function of the in-plane Young’s modulus of the collagen network. Under instantaneous force-controlled compression, the chondrocyte experienced the highest fluid pressure when the in-plane Young’s modulus of the collagen network was ~4 MPa. Based on the present results, the mechanical characteristics of the collagen network of articular cartilage can modify fluid flow and stresses in chondrocytes. Therefore, the integrity of the collagen network may be an important determinant in cell stimulation and in the control of the matrix maintenance.     

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.     

The effect of matrix tension-compression nonlinearity and fixed negative charges on chondrocyte responses in cartilage

Thorough analyses of the mechano-electrochemical interaction between articular cartilage matrix and the chondrocytes are crucial to understanding of the signal transduction mechanisms that modulate the cell metabolic activities and biosynthesis. Attempts have been made to model the chondrocytes embedded in the collagen-proteoglycan extracellular matrix to determine the distribution of local stress-strain field, fluid pressure and the time-dependent deformation of the cell. To date, these models still have not taken into account a remarkable characteristic of the cartilage extracellular matrix given rise from organization of the collagen fiber architecture, now known as the tension-compression nonlinearity (TCN) of the tissue, as well as the effect of negative charges attached to the proteoglycan molecules, and the cell cytoskeleton that interacts with mobile ions in the interstitial fluid to create osmotic and electro-kinetic events in and around the cells. In this study, we proposed a triphasic, multi-scale, finite element model incorporating the Conewise Linear Elasticity that can describe the various known coupled mechanical, electrical and chemical events, while at the same time representing the TCN of the extracellular matrix. The model was employed to perform a detailed analysis of the chondrocytes' deformational and volume responses, and to quantitatively describe the mechano-electrochemical environment of these cells. Such a model describes contributions of the known detailed micro-structural and composition of articular cartilage. Expectedly, results from model simulations showed substantial effects of the matrix TCN on the cell deformational and volume change response. A low compressive Poisson's ratio of the cartilage matrix exhibiting TCN resulted in dramatic recoiling behavior of the tissue under unconfined compression and induced significant volume change in the cell. The fixed charge density of the chondrocyte and the pericellular matrix were also found to play an important role in both the time-dependent and equilibrium deformation of the cell. The pericellular matrix tended to create a uniform osmolarity around the cell and overall amplified the cell volume change. It is concluded that the proposed model can be a useful tool that allows detailed analysis of the mechano-electrochemical interactions between the chondrocytes and its surrounding extracellular matrix, which leads to more quantitative insights in the cell mechano-transduction.     

Contribution of postnatal collagen reorientation to depth-dependent mechanical properties of articular cartilage

The collagen fibril network is an important factor for the depth-dependent mechanical behaviour of adult articular cartilage (AC). Recent studies show that collagen orientation is parallel to the articular surface throughout the tissue depth in perinatal animals, and that the collagen orientations transform to a depth-dependent arcade-like structure in adult animals. Current understanding on the mechanobiology of postnatal AC development is incomplete. In the current paper, we investigate the contribution of collagen fibril orientation changes to the depth-dependent mechanical properties of AC. We use a composition-based finite element model to simulate in a 1-D confined compression geometry the effects of ten different collagen orientation patterns that were measured in developing sheep. In initial postnatal life, AC is mostly subject to growth and we observe only small changes in depth-dependent mechanical behaviour. Functional adaptation of depth-dependent mechanical behaviour of AC takes place in the second half of life before puberty. Changes in fibril orientation alone increase cartilage stiffness during development through the modulation of swelling strains and osmotic pressures. Changes in stiffness are most pronounced for small stresses and for cartilage adjacent to the bone. We hypothesize that postnatal changes in collagen fibril orientation induce mechanical effects that in turn promote these changes. We further hypothesize that a part of the depth-dependent postnatal increase in collagen content in literature is initiated by the depth-dependent postnatal increase in fibril strain due to collagen fibril reorientation.     

The C5 domain of Col6A3 is cleaved off from the Col6 fibrils immediately after secretion.

In articular cartilage, type VI collagen is concentrated in the pericellular matrix compartment. During protein synthesis and processing at least the alpha3(VI) chain undergoes significant posttranslational modification and cleavage. In this study, we investigated the processing of type VI collagen in articular cartilage. Immunostaining with a specific polyclonal antiserum against the C5 domain of alpha3(VI) showed strong cellular staining seen in nearly all chondrocytes of articular cartilage. Confocal laser-scanning microscopy and immunoelectron microscopy allowed localization of this staining mainly to the cytoplasm and the immediate pericellular matrix. Double-labeling experiments showed a narrow overlap of the C5 domain and the pericellular mature type VI collagen. Our results suggest that at least in human adult articular cartilage the C5 domain of alpha3(VI) collagen is synthesized and initially incorporated into the newly formed type VI collagen fibrils, but immediately after secretion is cut off and is not present in the mature pericellular type VI matrix of articular cartilage.     

Retention of the native chondrocyte pericellular matrix results in significantly improved matrix production.

The interaction of the cell with its surrounding extracellular matrix (ECM) has a major effect on cell metabolism. We have previously shown that chondrons, chondrocytes with their in vivo-formed pericellular matrix, can be enzymatically isolated from articular cartilage. To study the effect of the native chondrocyte pericellular matrix on ECM production and assembly, chondrons were compared with chondrocytes isolated without any pericellular matrix. Immediately after isolation from human cartilage, chondrons and chondrocytes were centrifuged into pellets and cultured. Chondron pellets had a greater increase in weight over 8 weeks, were more hyaline appearing, and had more type II collagen deposition and assembly than chondrocyte pellets. Minimal type I procollagen immunofluorescence was detected for both chondron and chondrocyte pellets. Chondron pellets had a 10-fold increase in proteoglycan content compared with a six-fold increase for chondrocyte pellets over 8 weeks (P<0.0001). There was no significant cell division for either chondron or chondrocyte pellets. The majority of cells within both chondron and chondrocyte pellets maintained their polygonal or rounded shape except for a thin, superficial edging of flattened cells. This edging was similar to a perichondrium with abundant type I collagen and fibronectin, and decreased type II collagen and proteoglycan content compared with the remainder of the pellet. This study demonstrates that the native pericellular matrix promotes matrix production and assembly in vitro. Further, the continued matrix production and assembly throughout the 8-week culture period make chondron pellet cultures valuable as a hyaline-like cartilage model in vitro.     

How changes in interconnectivity affect the bulk properties of articular cartilage: a fibre network study

The remarkable compressive strength of articular cartilage arises from the mechanical interactions between the tension-resisting collagen fibrils and swelling proteoglycan proteins within the tissue. These interactions are facilitated by a significant level of interconnectivity between neighbouring collagen fibrils within the extracellular matrix. A reduction in interconnectivity is suspected to occur during the early stages of osteoarthritic degeneration. However, the relative contribution of these interconnections towards the bulk mechanical properties of articular cartilage has remained an open question. In this study, we present a simple 2D fibre network model which explicitly represents the microstructure of articular cartilage as collection of discrete nodes and linear springs. The transverse stiffness and swelling properties of this fibre network are studied, and a semi-analytic relationship which relates these two macroscopic properties via microscopic interconnectivity is derived. By comparing this derived expression to previously published experimental data, we show that although a reduction in network interconnectivity accounts for some of the observed changes in the mechanical properties of articular cartilage as degeneration occurs, a decrease in matrix interconnectivity alone do not provide a full account of this process.     

The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage

Mechanical compression of the cartilage extracellular matrix has a significant effect on the metabolic activity of the chondrocytes. However, the relationship between the stress–strain and fluid-flow fields at the macroscopic “tissue” level and those at the microscopic “cellular” level are not fully understood. Based on the existing experimental data on the deformation behavior and biomechanical properties of articular cartilage and chondrocytes, a multi-scale biphasic finite element model was developed of the chondrocyte as a spheroidal inclusion embedded within the extracellular matrix of a cartilage explant. The mechanical environment at the cellular level was found to be time-varying and inhomogeneous, and the large difference (3 orders of magnitude) in the elastic properties of the chondrocyte and those of the extracellular matrix results in stress concentrations at the cell–matrix border and a nearly two-fold increase in strain and dilatation (volume change) at the cellular level, as compared to the macroscopic level. The presence of a narrow “pericellular matrix” with different properties than that of the chondrocyte or extracellular matrix significantly altered the principal stress and strain magnitudes within the chondrocyte, suggesting a functional biomechanical role for the pericellular matrix. These findings suggest that even under simple compressive loading conditions, chondrocytes are subjected to a complex local mechanical environment consisting of tension, compression, shear, and fluid pressure. Knowledge of the local stress and strain fields in the extracellular matrix is an important step in the interpretation of studies of mechanical signal transduction in cartilage explant culture models.     

A Mechano-chemical Model for the Passive Swelling Response of an Isolated Chondron under Osmotic Loading

The chondron is a distinct structure in articular cartilage that consists of the chondrocyte and its pericellular matrix (PCM), a narrow tissue region surrounding the cell that is distinguished by type VI collagen and a high glycosaminoglycan concentration relative to the extracellular matrix. We present a theoretical mechano-chemical model for the passive volumetric response of an isolated chondron under osmotic loading in a simple salt solution at equilibrium. The chondrocyte is modeled as an ideal osmometer and the PCM model is formulated using triphasic mixture theory. A mechano-chemical chondron model is obtained assuming that the chondron boundary is permeable to both water and ions, while the chondrocyte membrane is selectively permeable to only water. For the case of a neo-Hookean PCM constitutive law, the model is used to conduct a parametric analysis of cell and chondron deformation under hyper- and hypo-osmotic loading. In combination with osmotic loading experiments on isolated chondrons, model predictions will aid in determination of pericellular fixed charge density and its relative contribution to PCM mechanical properties.     

Distribution of newly synthesized aggrecan in explant cultures of bovine cartilage treated with retinoic acid.

This paper describes temporal changes in the metabolism and distribution of newly synthesized aggrecan and the organization of the extracellular matrix when explant cultures of articular cartilage maintained in the presence of fetal calf serum were exposed to retinoic acid for varying periods of time. Explant cultures of articular cartilage were incubated with radiolabeled sulfate prior to exposure to retinoic acid. The radiolabeled and chemical aggrecan present in the tissue and appearing in the culture medium was studied kinetically. Changes in the localization of radiolabeled aggrecan within the extracellular matrix were monitored by autoradiography in relation to type VI collagen distribution in the extracellular matrix. In control cultures where tissue levels of aggrecan remain constant the newly synthesized aggrecan remained closely associated with the territorial matrix surrounding the chondrocytes. Exposure of cultures to retinoic acid for the duration of the experiment, resulted in the extensive loss of aggrecan from the tissue and the redistribution of the remaining radiolabeled aggrecan from the chondron and territorial matrix into the inter-territorial matrix. These changes preceded alterations in the organization of type VI collagen in the extracellular matrix that involved the remodeling of the chondron and the appearance of type VI collagen in the inter-territorial matrix; there was also evidence of chondrocyte proliferation and clustering. In cartilage explant cultures exposed to retinoic acid for 24 h there was no loss of aggrecan from the matrix but there was an extensive redistribution of the radiolabeled aggrecan into the inter-territorial matrix. This work shows that maintenance of the structure and organization of the extracellular matrix that comprises the chondron and pericellular microenvironment of chondrocytes in articular cartilage is important for the regulation of the distribution of newly synthesized aggrecan monomers within the tissue.     

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.     

Effects of shear stress on articular chondrocyte metabolism

The articular cartilage of diarthrodial joints experiences a variety of stresses, strains and pressures that result from normal activities of daily living. In normal cartilage, the extracellular matrix exists as a highly organized composite of specialized macromolecules that distributes loads at the bony ends. The chondrocyte response to mechanical loading is recognized as an integral component in the maintenance of articular cartilage matrix homeostasis. With inappropriate mechanical loading of the joint, as occurs with traumatic injury, ligament instability, bony malalignment or excessive weight bearing, the cartilage exhibits manifestations characteristic of osteoarthritis. Breakdown of cartilage in osteoarthritis involves degradation of the extracellular matrix macromolecules and decreased expression of chondrocyte proteins necessary for normal joint function. Osteoarthritic cartilage often exhibits increased amounts of type I collagen and synthesis of proteoglycans characteristic of immature cartilage. The shift in cartilage phenotype in response to altered load yields a matrix that fails to support normal joint function. Mathematical modeling and experimental studies in animal models confirm an association between altered loading of diarthrotic joints and arthritic changes. Both types of studies implicate shear forces as a critical component in the destructive profile. The severity of cartilage destruction in response to altered loads appears linked to expression of biological factors influencing matrix integrity and cellular metabolism. Determining how shear stress alters chondrocyte metabolism is fundamental to understanding how to limit matrix destruction and stimulate cartilage repair and regeneration. At present, the precise biochemical and molecular mechanisms by which shear forces alter chondrocyte metabolism from a normal to a degenerative phenotype remain unclear. The results presented here address the hypothesis that articular chondrocyte metabolism is modulated by direct effects of shear forces that act on the cell through mechanotransduction processes. The purpose of this work is to develop critical knowledge regarding the basic mechanisms by which mechanical loading modulates cartilage metabolism in health and disease. This presentation will describe the effects of using fluid induced shear stress as a model system for stimulation of articular chondrocytes in vitro. The fluid induced shear stress was applied using a cone viscometer system to stimulate all the cells uniformly under conditions of minimal turbulence. The experiments were carried using high-density primary monolayer cultures of normal and osteoarthritic human and normal bovine articular chondrocytes. The analysis of the cellular response included quantification of cytokine release, matrix metalloproteinase expression and activation of intracellular signaling pathways. The data presented here show that articular chondrocytes exhibit a dose- and time-dependent response to shear stress that results in the release of soluble mediators and extracellular matrix macromolecules. The data suggest that the chondrocyte response to mechanical stimulation contributes to the maintenance of articular cartilage homeostasis in vivo.     

Role of pericellular matrix in development of a mechanically functional neocartilage

The role of the chondrocyte pericellular matrix (PCM) was examined in a three-dimensional chondrocyte culture system to determine whether retention of the native pericellular matrix could stimulate collagen and proteoglycan accumulation and also promote the formation of a mechanically functional hyaline-like neocartilage. Porcine chondrocytes and chondrons, consisting of the chondrocyte with its intact pericellular matrix, were maintained in pellet culture for up to 12 weeks. Sulfated glycosaminoclycans and type II collagen were measured biochemically. Immunocytochemistry was used to examine collagen localization as well as cell distribution within the pellets. In addition, the equilibrium compressive moduli of developing pellets were measured to determine whether matrix deposition contributed to the mechanical stiffness of the cartilage constructs. Pellets increased in size and weight over a 6-week period without apparent cell proliferation. Although chondrocytes quickly rebuilt a PCM rich in type VI collagen, chondron pellets accumulated significantly more proteoglycan and type II collagen than did chondrocyte pellets, indicating a greater positive effect of the native PCM. After 5 weeks in chondron pellets, matrix remodeling was evident by microscopy. Cells that had been uniformly distributed throughout the pellets began to cluster between large areas of interterritorial matrix rich in type II collagen. After 12 weeks, clusters were stacked in columns. A rapid increase in compressive strength was observed between 1 and 3 weeks in culture for both chondron and chondrocyte pellets and, by 6 weeks, both had achieved 25% of the equilibrium compressive stiffness of cartilage explants. Retention of the in vivo PCM during chondrocyte isolation promotes the formation of a mechanically functional neocartilage construct, suitable for modeling the responses of articular cartilage to chemical stimuli or mechanical compression.     

Differing in vitro biology of equine,ovine, porcine and human articular chondrocytes derived from the knee joint: an immunomorphological study

For lack of sufficient human cartilage donors, chondrocytes isolated from various animal species are used for cartilage tissue engineering. The present study was undertaken to compare key features of cultured large animal and human articular chondrocytes of the knee joint. Primary chondrocytes were isolated from human, porcine, ovine and equine full thickness knee joint cartilage and investigated flow cytometrically for their proliferation rate. Synthesis of extracellular matrix proteins collagen type II, cartilage proteoglycans, collagen type I, fibronectin and cytoskeletal organization were studied in freshly isolated or passaged chondrocytes using immunohistochemistry and western blotting. Chondrocytes morphology, proliferation, extracellular matrix synthesis and cytoskeleton assembly differed substantially between these species. Proliferation was higher in animal derived compared with human chondrocytes. All chondrocytes expressed a cartilage-specific extracellular matrix. However, after monolayer expansion, cartilage proteoglycan expression was barely detectable in equine chondrocytes whereby fibronectin and collagen type I deposition increased compared with porcine and human chondrocytes. Animal-derived chondrocytes developed more F-actin fibers during culturing than human chondrocytes. With respect to proliferation and extracellular matrix synthesis, human chondrocytes shared more similarity with porcine than with ovine or equine chondrocytes. These interspecies differences in chondrocytes in vitro biology should be considered when using animal models.     

Osteopontin promotes pathologic mineralization in articular cartilage.

Calcium pyrophosphate dihydrate (CPPD) crystals are commonly found in osteoarthritic joint tissues, where they predict severe disease. Unlike other types of calcium phosphate crystals, CPPD crystals form almost exclusively in the pericellular matrix of damaged articular cartilage, suggesting a key role for the extracellular matrix milieu in their development. Osteopontin is a matricellular protein found in increased quantities in the pericellular matrix of osteoarthritic cartilage. Osteopontin modulates the formation of calcium-containing crystals in many settings. We show here that osteopontin stimulates ATP-induced CPPD crystal formation by chondrocytes in vitro. This effect is augmented by osteopontin's incorporation into extracellular matrix by transglutaminase enzymes, is only modestly affected by its phosphorylation state, and is inhibited by integrin blockers. Surprisingly, osteopontin stimulates transglutaminase activity in cultured chondrocytes in a dose-responsive manner. As elevated levels of transglutaminase activity promote extracellular matrix changes that permit CPPD crystal formation, this is one possible mechanism of action. We demonstrate the presence of osteopontin in the pericellular matrix of chondrocytes adjacent to CPPD deposits and near active transglutaminases. Thus, osteopontin may play an important role in facilitating CPPD crystal formation in articular cartilage.     

Interrelationship of cartilage composition and chondrocyte mechanics after a partial meniscectomy in the rabbit knee joint – Experimental and numerical analysis

Site-specific and depth-dependent properties of cartilage were implemented within a finite element (FE) model to determine if compositional or structural changes in the tissue could explain site-specific alterations of chondrocyte deformations due to cartilage loading in rabbit knee joints 3 days after a partial meniscectomy (PM). Depth-dependent proteoglycan (PG) content, collagen content and collagen orientation in the cartilage extracellular matrix (ECM), and PG content in the pericellular matrix (PCM) were assessed with microscopic and spectroscopic methods. Patellar, femoral groove and samples from both the lateral and medial compartments of the femoral condyle and tibial plateau were extracted from healthy controls and from the partial meniscectomy group. For both groups and each knee joint site, axisymmetric FE models with measured properties were generated. Experimental cartilage loading was applied in the simulations and chondrocyte volumes were compared to the experimental values. ECM and PCM PG loss occurred within the superficial cartilage layer in the PM group at all locations, except in the lateral tibial plateau. Collagen content and orientation were not significantly altered due to the PM. The FE simulations predicted similar chondrocyte volume changes and group differences as obtained experimentally. Loss of PCM fixed charge density (FCD) decreased cell volume loss, as observed in the medial femur and medial tibia, whereas loss of ECM FCD increased cell volume loss, as seen in the patella, femoral groove and lateral femur. The model outcome, cell volume change, was also sensitive to applied tissue geometry, collagen fibril orientation and loading conditions.     

A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage

Articular cartilage is a multi-phasic, composite, fibre-reinforced material. Therefore, its mechanical properties are determined by the tissue microstructure. The presence of cells (chondrocytes) and collagen fibres within the proteoglycan matrix influences, at a local and a global level, the material symmetries. The volumetric concentration and shape of chondrocytes, and the volumetric concentration and spatial arrangement of collagen fibres have been observed to change as a function of depth in articular cartilage. In particular, collagen fibres are perpendicular to the bone-cartilage interface in the deep zone, their orientation is almost random in the middle zone, and they are parallel to the surface in the superficial zone. The aim of this work is to develop a model of elastic properties of articular cartilage based on its microstructure. In previous work, we addressed this problem based on Piola's notation for fourth-order tensors. Here, mathematical tools initially developed for transversely isotropic composite materials comprised of a statistical orientation of spheroidal inclusions are extended to articular cartilage, while taking into account the dependence of the elastic properties on cartilage depth. The resulting model is transversely isotropic and transversely homogeneous (TITH), the transverse plane being parallel to the bone-cartilage interface and the articular surface. Our results demonstrate that the axial elastic modulus decreases from the deep zone to the articular surface, a result that is in good agreement with experimental findings. Finite element simulations were carried out, in order to explore the TITH model's behaviour in articular cartilage compression tests. The force response, fluid flow and displacement fields obtained with the TITH model were compared with the classical linear elastic, isotropic, homogeneous (IH) model, showing that the IH model is unable to predict the non-uniform behaviour of the tissue. Based on considerations that the mechanical stability of the tissue depends on its topological and microstructural properties, our long-term goal is to clearly understand the stability conditions in topological terms, and the relationship with the growth and remodelling mechanisms in the healthy and diseased tissue.