A Finite Element Analysis Methodology for Representing the Articular Cartilage Functional Structure

Recognising that the unique biomechanical properties of articular cartilage are a consequence of its structure, this paper describes a finite element methodology which explicitly represents this structure using a modified overlay element model. The validity of this novel concept was then tested by using it to predict the axial curling forces generated by cartilage matrices subjected to saline solutions of known molality and concentration in a novel experimental protocol. Our results show that the finite element modelling methodology accurately represents the intrinsic biomechanical state of the cartilage matrix and can be used to predict its transient load-carriage behaviour. We conclude that this ability to represent the intrinsic swollen condition of a given cartilage matrix offers a viable avenue for numerical analysis of degenerate articular cartilage and also those matrices affected by disease.     

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.     

A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion

A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.     

Type III collagen is a key regulator of the collagen fibrillar structure and biomechanics of articular cartilage and meniscus

Despite the fact that type III collagen is the second most abundant collagen type in the body, its contribution to the physiologic maintenance and repair of skeletal tissues remains poorly understood. This study queried the role of type III collagen in the structure and biomechanical functions of two structurally distinctive tissues in the knee joint, type II collagen-rich articular cartilage and type I collagen-dominated meniscus. Integrating outcomes from atomic force microscopy-based nanomechanical tests, collagen fibril nanostructural analysis, collagen cross-link analysis and histology, we elucidated the impact of type III collagen haplodeficiency on the morphology, nanostructure and biomechanical properties of articular cartilage and meniscus in Col3a1^+/− mice. Reduction of type III collagen leads to increased heterogeneity and mean thickness of collagen fibril diameter, as well as reduced modulus in both tissues, and these effects became more pronounced with skeletal maturation. These data suggest a crucial role of type III collagen in mediating fibril assembly and biomechanical functions of both articular cartilage and meniscus during post-natal growth. In articular cartilage, type III collagen has a marked contribution to the micromechanics of the pericellular matrix, indicating a potential role in mediating the early stage of type II collagen fibrillogenesis and chondrocyte mechanotransduction. In both tissues, reduction of type III collagen leads to decrease in tissue modulus despite the increase in collagen cross-linking. This suggests that the disruption of matrix structure due to type III collagen deficiency outweighs the stiffening of collagen fibrils by increased cross-linking, leading to a net negative impact on tissue modulus. Collectively, this study is the first to highlight the crucial structural role of type III collagen in both articular cartilage and meniscus extracellular matrices. We expect these results to expand our understanding of type III collagen across various tissue types, and to uncover critical molecular components of the microniche for regenerative strategies targeting articular cartilage and meniscus repair.     

Transport phenomena in articular cartilage cryopreservation as predicted by the modified triphasic model and the effect of natural inhomogeneities

Knowledge of the spatial and temporal distribution of cryoprotective agent (CPA) is necessary for the cryopreservation of articular cartilage. Cartilage dehydration and shrinkage, as well as the change in extracellular osmolality, may have a significant impact on chondrocyte survival during and after CPA loading, freezing, and thawing, and during CPA unloading. In the literature, Fick's law of diffusion is commonly used to predict the spatial distribution and overall concentration of the CPA in the cartilage matrix, and the shrinkage and stress-strain in the cartilage matrix during CPA loading are neglected. In this study, we used a previously described biomechanical model to predict the spatial and temporal distributions of CPA during loading. We measured the intrinsic inhomogeneities in initial water and fixed charge densities in the cartilage using magnetic resonance imaging and introduced them into the model as initial conditions. We then compared the prediction results with the results obtained using uniform initial conditions. The simulation results in this study demonstrate the presence of a significant mechanical strain in the matrix of the cartilage, within all layers, during CPA loading. The osmotic response of the chondrocytes to the cartilage dehydration during CPA loading was also simulated. The results reveal that a transient shrinking occurs to different levels, and the chondrocytes experience a significant decrease in volume, particularly in the middle and deep zones of articular cartilage, during CPA loading.     

Load sharing between solid and fluid phases in articular cartilage: II--Comparison of experimental results and u-p finite element predictions.

Experimental measurements in conjunction with theoretical predictions were used to determine the extent of load supported by the fluid phase of cartilage at the articular surface. The u-p finite element model was used to simulate the loading of six separate porcine knee joints and to predict surface deformations of the cartilage layer on the lateral femoral condyle. Representative geometry for the condyle, contact pressures, and intrinsic material properties of the cartilage layer were supplied from experimental measures (see Part I). The u-p finite element predictions for surface deformations of the cartilage layer were obtained for several load partitioning states between the solid and fluid phases of cartilage at the articular surface. These were then compared to actual surface deformations obtained experimentally. It appeared from the comparison that approximately 75 percent of the applied load was borne by the fluid phase at the articular surface under this loading regime. This was qualitatively in agreement with the hypothesis that an applied load to articular joints is partitioned at the surface to the two phases according to the surface area ratios of the solid and fluid phases. It appeared that the solid phase was shielded from the total applied stress on the articular surface by the fluid and could be a reason for the excellent durability of the tissue under the demanding conditions in a diarthrodial joint.     

Functional tissue engineering of chondral and osteochondral constructs

Due to the prevalence of osteoarthritis (OA) and damage to articular cartilage, coupled with the poor intrinsic healing capacity of this avascular connective tissue, there is a great demand for an articular cartilage substitute. As the bearing material of diarthrodial joints, articular cartilage has remarkable functional properties that have been difficult to reproduce in tissue-engineered constructs. We have previously demonstrated that by using a functional tissue engineering approach that incorporates mechanical loading into the long-term culture environment, one can enhance the development of mechanical properties in chondrocyte-seeded agarose constructs. As these gel constructs begin to achieve material properties similar to that of the native tissue, however, new challenges arise, including integration of the construct with the underlying native bone. To address this issue, we have developed a technique for producing gel constructs integrated into an underlying bony substrate. These osteochondral constructs develop cartilage-like extracellular matrix and material properties over time in free swelling culture. In this study, as a preliminary to loading such osteochondral constructs, finite element modeling (FEM) was used to predict the spatial and temporal stress, strain, and fluid flow fields within constructs subjected to dynamic deformational loading. The results of these models suggest that while chondral ("gel alone") constructs see a largely homogenous field of mechanical signals, osteochondral ("gel bone") constructs see a largely inhomogeneous distribution of mechanical signals. Such inhomogeneity in the mechanical environment may aid in the development of inhomogeneity in the engineered osteochondral constructs. Together with experimental observations, we anticipate that such modeling efforts will provide direction for our efforts aimed at the optimization of applied physical forces for the functional tissue engineering of an osteochondral articular cartilage substitute.     

Changes in articular cartilage mechanics with meniscectomy: A novel image-based modeling approach and comparison to patterns of OA

Meniscectomy is a significant risk factor for osteoarthritis, involving altered cell synthesis, central fibrillation, and peripheral osteophyte formation. Though changes in articular cartilage contact pressure are known, changes in tissue-level mechanical parameters within articular cartilage are not well understood. Recent imaging research has revealed the effects of meniscectomy on the time-dependent deformation of physiologically loaded articular cartilage. To determine tissue-level cartilage mechanics that underlie observed deformation, a novel finite element modeling approach using imaging data and a contacting indenter boundary condition was developed. The indenter method reproduces observed articular surface deformation and avoids assumptions about tangential stretching. Comparison of results from an indenter model with a traditional femur-tibia model verified the method, giving errors in displacement, solid and fluid stress, and strain below 1% (RMS) and 7% (max.) of the absolute maximum of the parameters of interest. Indenter finite element models using real joint image data showed increased fluid pressure, fluid exudation, loss of fluid load support, and increased tensile strains centrally on the tibial condyle after meniscectomy-patterns corresponding to clinical observations of cartilage matrix damage and fibrillation. Peripherally there was decreased consolidation, which corresponds to reduced contact and fluid pressure in this analysis. Clinically, these areas have exhibited advance of the subchondral growth front, biological destruction of the cartilage matrix, cartilage thinning, and eventual replacement of the cartilage via endochondral ossification. Characterizing the changes in cartilage mechanics with meniscectomy and correspondence with observed tissue-level effects may help elucidate the etiology of joint-level degradation seen in osteoarthritis.     

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.     

Osteoarthritic changes in the biphasic mechanical properties of the chondrocyte pericellular matrix in articular cartilage

The pericellular matrix (PCM) is a narrow region of cartilaginous tissue that surrounds chondrocytes in articular cartilage. Previous modeling studies indicate that the mechanical properties of the PCM relative to those of the extracellular matrix (ECM) can significantly affect the stress-strain, fluid flow, and physicochemical environments of the chondrocyte, suggesting that the PCM plays a biomechanical role in articular cartilage. The goals of this study were to measure the mechanical properties of the PCM using micropipette aspiration coupled with a linear biphasic finite element model, and to determine the alterations in the mechanical properties of the PCM with osteoarthritis (OA). Using a recently developed isolation technique, chondrons (the chondrocyte and its PCM) were mechanically extracted from non-degenerate and osteoarthritic human cartilage. The transient mechanical behavior of the PCM was well-described by a biphasic model, suggesting that the viscoelastic response of the PCM is attributable to flow-dependent effects, similar to that of the ECM. With OA, the mean Young's modulus of the PCM was significantly decreased (38.7+/-16.2 kPa vs. 23.5+/-12.9 kPa, p < 0.001), and the permeability was significantly elevated (4.19+/-3.78 x10(-17) m(4)/Ns vs. 10.2+/-9.38 x 10(-17) m(4)/Ns, p < 0.01). The Poisson's ratio was similar for both non-degenerate and OA PCM (0.044+/-0.063 vs. 0.030+/-0.068, p > 0.6). These findings suggest that the PCM may undergo degenerative processes with OA, similar to those occurring in the ECM. In combination with previous theoretical models of cell-matrix interactions in cartilage, our findings suggest that changes in the properties of the PCM with OA may have an important influence on the biomechanical environment of the chondrocyte.     

The influence of the fixed negative charges on mechanical and electrical behaviors of articular cartilage under unconfined compression

Unconfined compression test has been frequently used to study the mechanical behaviors of articular cartilage, both theoretically and experimentally. It has also been used in explant and gel-cell-complex studies in tissue engineering. In biphasic and poroelastic theories, the effect of charges fixed on the proteoglycan macromolecules in articular cartilage is embodied in the apparent compressive Young's modulus and the apparent Poisson's ratio of the tissue, and the fluid pressure is considered to be the portion above the osmotic pressure. In order to understand how proteoglycan fixed charges might affect the mechanical behaviors of articular cartilage, and in order to predict the osmotic pressure and electric fields inside the tissue in this experimental configuration, it is necessary to use a model that explicitly takes into account the charged nature of the tissue and the flow of ions within its porous interstices. In this paper, we used a finite element model based on the triphasic theory to study how fixed charges in the porous-permeable soft tissue can modulate its mechanical and electrochemical responses under a step displacement in unconfined compression. The results from finite element calculations showed that: 1) A charged tissue always supports a larger load than an uncharged tissue of the same intrinsic elastic moduli. 2) The apparent Young's modulus (the ratio of the equilibrium axial stress to the axial strain) is always greater than the intrinsic Young's modulus of an uncharged tissue. 3) The apparent Poisson's ratio (the negative ratio of the lateral strain to the axial strain) is always larger than the intrinsic Poisson's ratio of an uncharged tissue. 4) Load support derives from three sources: intrinsic matrix stiffness, hydraulic pressure and osmotic pressure. Under the unconfined compression, the Donnan osmotic pressure can constitute between 13%-22% of the total load support at equilibrium. 5) During the stress-relaxation process following the initial instant of loading, the diffusion potential (due to the gradient of the fixed charge density and the associated gradient of ion concentrations) and the streaming potential (due to fluid convection) compete against each other. Within the physiological range of material parameters, the polarity of the electric potential depends on both the mechanical properties and the fixed charge density (FCD) of the tissue. For softer tissues, the diffusion effects dominate the electromechanical response, while for stiffer tissues, the streaming potential dominates this response. 6) Fixed charges do not affect the instantaneous strain field relative to the initial equilibrium state. However, there is a sudden increase in the fluid pressure above the initial equilibrium osmotic pressure. These new findings are relevant and necessary for the understanding of cartilage mechanics, cartilage biosynthesis, electromechanical signal transduction by chondrocytes, and tissue engineering.     

The influence of repair tissue maturation on the response to oscillatory compression in a cartilage defect repair model

This study examined the effects of mechanical compression on engineered cartilage in a novel hybrid culture system. Cylindrical holes were cut in discs of bovine articular cartilage and filled with agarose gels containing chondrocytes. These constructs were compressed in radiolabeled medium under static or oscillatory unconfined compression. Oscillatory compression at 1 Hz significantly stimulated synthesis above static control levels. Control experiments indicate that oscillatory compression does not stimulate freshly cast gels (without annuli), but does so after several weeks. This may be because physiologic fluid flow levels do not occur until sufficient extracellular matrix has accumulated. Finite element models predict minimal fluid flow in the gel core, and minimal differences in flow patterns between free and constrained gels. However, the models predict fluid pressures in constrained gels to be substantially higher than those in free gels. Our results suggest that pressure variations may influence synthesis of engineered cartilage matrices, with implications for construct development and post-implantation survival.     

Glycosaminoglycan network geometry may contribute to anisotropic hydraulic permeability in cartilage under compression.

Resistance to fluid flow within cartilage extracellular matrix is provided primarily by a dense network of rod-like glycosaminoglycans (GAGs). If the geometrical organization of this network is random, the hydraulic permeability tensor of cartilage is expected to be isotropic. However, experimental data have suggested that hydraulic permeability may become anisotropic when the matrix is mechanically compressed, contributing to cartilage biomechanical functions such as lubrication. We hypothesized that this may be due to preferred GAG rod orientations and directionally-dependent reduction of inter-GAG spacings which reflect molecular responses to tissue deformations. To examine this hypothesis, we developed a model for effects of compression which allows the GAG rod network to deform consistently with tissue-scale deformations but while still respecting limitations imposed by molecular structure. This network deformation model was combined with a perturbation analysis of a classical analytical model for hydraulic permeability based on molecular structure. Finite element analyses were undertaken to ensure that this approach exhibited results similar to those emerging from more exact calculations. Model predictions for effects of uniaxial confined compression on the hydraulic permeability tensor were consistent with previous experimental results. Permeability decreased more rapidly in the direction perpendicular to compression than in the parallel direction, for matrix solid volume fractions associated with fluid transport in articular cartilage. GAG network deformations may therefore introduce anisotropy to the permeability (and other GAG-associated matrix properties) as physiological compression is applied, and play an important role in cartilage lubrication and other biomechanical functions.     

Anisotropic hydraulic permeability in compressed articular cartilage

The extent to which articular cartilage hydraulic permeability is anisotropic is largely unknown, despite its importance for understanding mechanisms of joint lubrication, load bearing, transport phenomena, and mechanotransduction. We developed and applied new techniques for the direct measurement of hydraulic permeability within statically compressed adult bovine cartilage explant disks, dissected such that disk axes were perpendicular to the articular surface. Applied pressure gradients were kept small to minimize flow-induced matrix compaction, and fluid outflows were measured by observation of a meniscus in a glass capillary under a microscope. Explant disk geometry under radially unconfined axial compression was measured by direct microscopic observation. Pressure, flow, and geometry data were input to a finite element model where hydraulic permeabilities in the disk axial and radial directions were determined. At less than 10% static compression, near free-swelling conditions, hydraulic permeability was nearly isotropic, with values corresponding to those of previous studies. With increasing static compression, hydraulic permeability decreased, but the radially directed permeability decreased more dramatically than the axially directed permeability such that strong anisotropy (a 10-fold difference between axial and radial directions) in the hydraulic permeability tensor was evident for static compression of 20-40%. Results correspond well with predictions of a previous microstructurally-based model for effects of tissue mechanical deformations on glycosaminoglycan architecture and cartilage hydraulic permeability. Findings inform understanding of structure-function relationships in cartilage matrix, and suggest several biomechanical roles for compression-induced anisotropic hydraulic permeability in articular cartilage.     

Quantitative ultrasonic assessment for detecting microscopic cartilage damage in osteoarthritis

Osteoarthritis (OA) is one of the most prevalent chronic conditions. The histological cartilage changes in OA include surface erosion and irregularities, deep fissures, and alterations in the staining of the matrix. The reversibility of these chondral alterations is still under debate. It is expected that clinical and basic science studies will provide the clinician with new scientific information about the natural history and optimal treatment of OA at an early stage. However, a reliable method for detecting microscopic changes in early OA has not yet been established. We have developed a novel system for evaluating articular cartilage, in which the acoustic properties of the articular cartilage are measured by introducing an ultrasonic probe into the knee joint under arthroscopy. The purpose of this study was to assess microscopic cartilage damage in OA by using this cartilage evaluation system on collagenase-treated articular cartilage in vivo and in vitro. Ultrasonic echoes from articular cartilage were converted into a wavelet map by wavelet transformation. On the wavelet map, the maximum magnitude and echo duration were selected as quantitative indices. Using these indices, the articular cartilage was examined to elucidate the relationships of the ultrasonic analysis with biochemical, biomechanical and histological analyses. In the in vitro study, the maximum magnitude decreased as the duration of collagenase digestion increased. Correlations were observed between the maximum magnitude and the proteoglycan content from biochemical findings, and the maximum magnitude and the aggregate modulus from biomechanical findings. From the histological findings, matrix staining of the surface layer to a depth of 500 mum was closely related to the maximum magnitude. In the in vivo study, the maximum magnitude decreased with increasing duration of the collagenase injection. There was a significant correlation between the maximum magnitude and the aggregate modulus. The evaluation system therefore successfully detected microscopic changes in degenerated cartilage with the use of collagen-induced OA.     

A finite element formulation and program to study transient swelling and load-carriage in healthy and degenerate articular cartilage

The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u-pi-c program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.     

Quantitative ultrasonic assessment for detecting microscopic cartilage damage in osteoarthritis

Osteoarthritis (OA) is one of the most prevalent chronic conditions. The histological cartilage changes in OA include surface erosion and irregularities, deep fissures, and alterations in the staining of the matrix. The reversibility of these chondral alterations is still under debate. It is expected that clinical and basic science studies will provide the clinician with new scientific information about the natural history and optimal treatment of OA at an early stage. However, a reliable method for detecting microscopic changes in early OA has not yet been established. We have developed a novel system for evaluating articular cartilage, in which the acoustic properties of the articular cartilage are measured by introducing an ultrasonic probe into the knee joint under arthroscopy. The purpose of this study was to assess microscopic cartilage damage in OA by using this cartilage evaluation system on collagenase-treated articular cartilage in vivo and in vitro. Ultrasonic echoes from articular cartilage were converted into a wavelet map by wavelet transformation. On the wavelet map, the maximum magnitude and echo duration were selected as quantitative indices. Using these indices, the articular cartilage was examined to elucidate the relationships of the ultrasonic analysis with biochemical, biomechanical and histological analyses. In the in vitro study, the maximum magnitude decreased as the duration of collagenase digestion increased. Correlations were observed between the maximum magnitude and the proteoglycan content from biochemical findings, and the maximum magnitude and the aggregate modulus from biomechanical findings. From the histological findings, matrix staining of the surface layer to a depth of 500 μm was closely related to the maximum magnitude. In the in vivo study, the maximum magnitude decreased with increasing duration of the collagenase injection. There was a significant correlation between the maximum magnitude and the aggregate modulus. The evaluation system therefore successfully detected microscopic changes in degenerated cartilage with the use of collagen-induced OA.     

The deformation behavior and viscoelastic properties of chondrocytes in articular cartilage

Chondrocytes in articular cartilage utilize mechanical signals in conjunction with other environmental factors to regulate their metabolic activity. However, the sequence of biomechanical and biochemical events involved in the process of mechanical signal transduction has not been fully deciphered. A fundamental step in determining the role of various factors in regulating chondrocyte activity is to characterize accurately the biophysical environment within the tissue under physiological conditions of mechanical loading. Microscopic imaging studies have revealed that chondrocytes as well as their nuclei undergo shape and volume changes in a coordinated manner with deformation of the tissue matrix. Through micromechanical experiments, it has been shown that the chondrocyte behaves as a viscoelastic solid material with a mechanical stiffness that is several orders of magnitude lower than that of the cartilage extracellular matrix. These properties seem to be due to the structure of the chondrocyte cytoskeleton, and in part, the viscoelastic properties of the cell nucleus. The mechanical properties of the pericellular matrix that immediately surrounds the chondrocyte significantly differ from those of the chondrocyte and the extracellular matrix, suggesting that the pericellular matrix plays an important role in defining the mechanical environment of the chondrocyte. These experimentally measured values for chondrocyte and cartilage mechanical properties have been used in combination with theoretical constitutive modeling of the chondrocyte within articular cartilage to predict the non-uniform and time-varying stress-strain and fluid flow environment of the cell. The ultimate goal of these studies has been to elucidate the sequence of biomechanical and biochemical events through which mechanical stress influences chondrocyte activity in both health and in disease.     

A Finite Element Formulation and Program to Study Transient Swelling and Load-carriage in Healthy and Degenerate Articular Cartilage

The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u–π–c fortran program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.