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

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

Cartilage interstitial fluid load support in unconfined compression

Under physiological conditions of loading, articular cartilage is subjected to both compressive strains, normal to the articular surface, and tensile strains, tangential to the articular surface. Previous studies have shown that articular cartilage exhibits a much higher modulus in tension than in compression, and theoretical analyses have suggested that this tension–compression nonlinearity enhances the magnitude of interstitial fluid pressurization during loading in unconfined compression, above a theoretical threshold of 33% of the average applied stress. The first hypothesis of this experimental study is that the peak fluid load support in unconfined compression is significantly greater than the 33% theoretical limit predicted for porous permeable tissues modeled with equal moduli in tension and compression. The second hypothesis is that the peak fluid load support is higher at the articular surface side of the tissue samples than near the deep zone, because the disparity between the tensile and compressive moduli is greater at the surface zone. Ten human cartilage samples from six patellofemoral joints, and 10 bovine cartilage specimens from three calf patellofemoral joints were tested in unconfined compression. The peak fluid load support was measured at 79±11% and 69±15% at the articular surface and deep zone of human cartilage, respectively, and at 94±4% and 71±8% at the articular surface and deep zone of bovine calf cartilage, respectively. Statistical analyses confirmed both hypotheses of this study. These experimental results suggest that the tension–compression nonlinearity of cartilage is an essential functional property of the tissue which makes interstitial fluid pressurization the dominant mechanism of load support in articular cartilage.     

A Conewise Linear Elasticity mixture model for the analysis of tension-compression nonlinearity in articular cartilage

A biphasic mixture model is developed that can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J. Elasticity, 37, 1-38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H-A = 0.64 +/- 0.22 MPa, k2 = 3.62 +/- 0.97 x 10(-16) m4/N.s, r2 = 0.95 +/- 0.03), the tensile modulus, compressive Poisson ratio, and radial permeability were obtained from unconfined compression (E+Y = 12.75 +/- 1.56 MPa, v- = 0.03 +/- 0.01, kr = 6.06 +/- 2.10 x 10(-16) m4/N.s, r2 = 0.99 +/- 0.00), and the shear modulus was obtained from torsional shear (mu = 0.17 +/- 0.06 MPa). The model was also employed to predict the interstitial fluid pressure successfully at the center of the cartilage plug in unconfined compression (r2 = 0.98 +/- 0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage that can successfully curve-fit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.     

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.     

The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension-compression stress-strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng., 102, pp. 73-84] to incorporate tension-compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng., 122, pp. 576-586] and based on the bimodular stress-strain constitutive law introduced by Curnier et al. [1995, J. Elasticity, 37, pp. 1-38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108, pp. 123-130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension-compression nonlinearity.     

Modeling the stability of the human glenohumeral joint during external rotation

An analytical model of the human glenohumeral joint was developed to predict glenohumeral kinematics and investigate how the glenohumeral capsule and articular contact between the humeral head and the glenoid stabilize the joint. This was performed during a simulation of an apprehension clinical exam or the cocked phase of throwing, when the humerus is susceptible to anterior instability or dislocation. Contact between the joint surfaces was modeled using a deformable articular contact method and the capsule was modeled as five elements with the ability to wrap around the surface of the humeral head. Experimental measurements (Novotny et al., Journal of Shoulder and Elbow surgery, 1998, 7, 629-639) provided geometric data from four in vitro specimens and kinematic results to validate model predictions. Material properties were taken from the literature. An equilibrium approach was used with the forces and moments produced by the ligaments and surface contact balanced against those applied externally to the humerus during external rotation of the abducted and extended humerus. The six equilibrium equations were solved for the position and orientation of the humerus. The center of the humeral head translated posteriorly and superiorly with external rotation. Model predictions for translational and rotational ranges of motion were not significantly different from experimental findings; however, at individual moment increments, the model underestimated the external rotation and overestimated the superior-inferior position of the humerus relative to the glenoid. The anterior band of the inferior glenohumeral ligament increased in tension with external rotation, while the axillary pouch and posterior band decreased in tension. Contact area, stress and force increased with external rotation and the contact area moved posteriorly and inferiorly around the rim of the glenoid. The model results provide information on how the relationship between the ligament element tensions and contact forces may act to avoid glenohumeral instability.     

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.     

Glenohumeral joint cartilage contact in the healthy adult during scapular plane elevation depression with external humeral rotation

The shoulder (glenohumeral) joint has the greatest range of motion of all human joints; as a result, it is particularly vulnerable to dislocation and injury. The ability to non-invasively quantify in-vivo articular cartilage contact patterns of joints has been and remains a difficult biomechanics problem. As a result, little is known about normal in-vivo glenohumeral joint contact patterns or the consequences that surgery has on altering them. In addition, the effect of quantifying glenohumeral joint contact patterns by means of proximity mapping, both with and without cartilage data, is unknown. Therefore, the objectives of this study are to (1) describe a technique for quantifying in-vivo glenohumeral joint contact patterns during dynamic shoulder motion, (2) quantify normal glenohumeral joint contact patterns in the young healthy adult during scapular plane elevation depression with external humeral rotation, and (3) compare glenohumeral joint contact patterns determined both with and without articular cartilage data. Our results show that the inclusion of articular cartilage data when quantifying in-vivo glenohumeral joint contact patterns has significant effects on the anterior–posterior contact centroid location, the superior–inferior contact centroid range of travel, and the total contact path length. As a result, our technique offers an advantage over glenohumeral joint contact pattern measurement techniques that neglect articular cartilage data. Likewise, this technique may be more sensitive than traditional 6-Degree-of-Freedom (6-DOF) joint kinematics for the assessment of overall glenohumeral joint health. Lastly, for the shoulder motion tested, we found that glenohumeral joint contact was located on the anterior–inferior glenoid surface.     

Neandertal scapular glenoid morphology

Analysis of Neandertal and recent human scapular glenoid fossae reveals that the former had long, narrow, and flat glenoid articular surfaces relative to those of modern humans. Comparison of glenoid length, breadth, and curvature to humeral articular dimensions demonstrates that Neandertal glenoid length and curvature scale to proximal and distal humeral articular dimensions in the same manner as those of modern humans. The remaining contrast is in the relatively greater glenoid fossa width seen in modern humans. This difference in morphology implies differences in the habitual degree of dorsoventral glenohumeral movement between Neandertals and modern humans. This in turn may be related to contrasts in tool use, especially with respect to throwing and projectile use.     

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

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

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.     

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.     

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

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

Tensile and compressive properties of healthy and osteoarthritic human articular cartilage

Osteoarthritis (OA) is a disease affecting articular cartilage and the underlying bone, resulting from many biological and mechanical interacting factors which change the extracellular matrix (ECM) and cells and lead to increasing levels of cartilage degeneration, like softening, fibrillation, ulceration and cartilage loss. The early diagnosis of the disease is fundamental to prevent pain, further tissue degeneration and reduce hospital costs. Although morphological modifications can be detected by modern non-invasive diagnostic techniques, they may not be evident in the early stages of OA. The mechanical properties of articular cartilage are related to its composition and structure and are sensitive to even small changes in the ECM that could occur in early OA. The aim of the present study was to compare the mechanical properties of healthy and OA cartilage using a combined experimental-numerical approach. Experimental assessments consisted of step wise confined and unconfined compression and tension stress relaxation tests on disks (for compression) or strips (for tension) of cartilage obtained from human femoral heads discarded from the operating room after total hip replacement. The numerical model was based on the biphasic theory and included the tension-compression non-linearity. Considering OA samples vs normal samples, the static compressive modulus was 55-68% lower, the permeability was 60-80% higher, the dynamic compressive modulus was 59-64% lower, the static tension modulus was 72-83% lower. The model successfully simulated the experimental tests performed on healthy and OA cartilage and was used in combination with the experimental tests to evaluate the role of different ECM components in the mechanical response of normal and OA cartilage.     

Inducing articular cartilage phenotype in costochondral cells

Introduction

Costochondral cells may be isolated with minimal donor site morbidity and are unaffected by pathologies of the diarthrodial joints. Identification of optimal exogenous stimuli will allow abundant and robust hyaline articular cartilage to be formed from this cell source.

Methods

In a three factor, two level full factorial design, the effects of hydrostatic pressure (HP), transforming growth factor β1 (TGF-β1), and chondroitinase ABC (C-ABC), and all resulting combinations, were assessed in third passage expanded, redifferentiated costochondral cells. After 4 wks, the new cartilage was assessed for matrix content, superficial zone protein (SZP), and mechanical properties.

Results

Hyaline articular cartilage was generated, demonstrating the presence of type II collagen and SZP, and the absence of type I collagen. TGF-β1 upregulated collagen synthesis by 175% and glycosaminoglycan synthesis by 75%, resulting in a nearly 200% increase in tensile and compressive moduli. C-ABC significantly increased collagen content, and fibril density and diameter, leading to a 125% increase in tensile modulus. Hydrostatic pressure increased fibril diameter by 30% and tensile modulus by 45%. Combining TGF-β1 with C-ABC synergistically increased collagen content by 300% and tensile strength by 320%, over control. No significant differences were observed between C-ABC/TGF-β1 dual treatment and HP/C-ABC/TGF-β1.

Conclusions

Employing biochemical, biophysical, and mechanical stimuli generated robust hyaline articular cartilage with a tensile modulus of 2 MPa and a compressive instantaneous modulus of 650 kPa. Using expanded, redifferentiated costochondral cells in the self-assembling process allows for recapitulation of robust mechanical properties, and induced SZP expression, key characteristics of functional articular cartilage.     

Comparison of the equilibrium response of articular cartilage in unconfined compression,confined compression and indentation

At mechanical equilibrium, articular cartilage is usually characterized as an isotropic elastic material with no interstitial fluid flow. In this study, the equilibrium properties (Young's modulus, aggregate modulus and Poisson's ratio) of bovine humeral, patellar and femoral cartilage specimens (n=26) were investigated using unconfined compression, confined compression, and indentation tests. Optical measurements of the Poisson's ratio of cartilage were also carried out. Mean values of the Young's modulus (assessed from the unconfined compression test) were 0.80+/-0.33, 0.57+/-0.17 and 0.31+/-0.18MPa and of the Poisson's ratio (assessed from the optical test) 0.15+/-0.06, 0.16+/-0.05 and 0.21+/-0.05 for humeral, patellar, and femoral cartilages, respectively. The indentation tests showed 30-79% (p<0.01) higher Young's modulus values than the unconfined compression tests. In indentation, values of the Young's modulus were independent of the indenter diameter only in the humeral cartilage. The mean values of the Poisson's ratio, obtained indirectly using the mathematical relation between the Young's modulus and the aggregate modulus in isotropic material, were 0.16+/-0.06, 0.21+/-0.05, and 0.26+/-0.08 for humeral, patellar, and femoral cartilages, respectively. We conclude that the values of the elastic parameters of the cartilage are dependent on the measurement technique in use. Based on the similar values of Poisson's ratios, as determined directly or indirectly, the equilibrium response of articular cartilage under unconfined and confined compression is satisfactorily described by the isotropic elastic model. However, values of the isotropic Young's modulus obtained from the in situ indentation tests are higher than those obtained from the in vitro unconfined or confined compression tests and may depend on the indenter size in use.     

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.     

Optical determination of anisotropic material properties of bovine articular cartilage in compression

The precise nature of the material symmetry of articular cartilage in compression remains to be elucidated. The primary objective of this study was to determine the equilibrium compressive Young's moduli and Poisson's ratios of bovine cartilage along multiple directions (parallel and perpendicular to the split line direction, and normal to the articular surface) by loading small cubic specimens (0.9 x 0.9 x 0.8 mm, n =15) in unconfined compression, with the expectation that the material symmetry of cartilage could be determined more accurately with the help of a more complete set of material properties. The second objective was to investigate how the tension-compression nonlinearity of cartilage might alter the interpretation of material symmetry. Optimized digital image correlation was used to accurately determine the resultant strain fields within the specimens under loading. Experimental results demonstrated that neither the Young's moduli nor the Poisson's ratios exhibit the same values when measured along the three loading directions. The main findings of this study are that the framework of linear orthotropic elasticity (as well as higher symmetries of linear elasticity) is not suitable to describe the equilibrium response of articular cartilage nor characterize its material symmetry; a framework which accounts for the distinctly different responses of cartilage in tension and compression is more suitable for describing the equilibrium response of cartilage; within this framework, cartilage exhibits no lower than orthotropic symmetry.     

Osmotic loading to determine the intrinsic material properties of guinea pig knee cartilage

Few methods exist to study cartilage mechanics in small animal joints due to the difficulties associated with handling small tissue samples. In this study, we apply an osmotic loading method to quantify the intrinsic material properties of articular cartilage in small animal joints. Cartilage samples were studied from the femoral condyle and tibial plateau of two-month old guinea pigs. Swelling strains were measured using confocal fluorescence scanning microscopy in samples subjected to osmotic loading. A histochemical staining method was developed and calibrated for quantification of negative fixed charge density in guinea pig cartilage. Site-matched swelling strain data and fixed charge density values were then used with a triphasic theoretical model for cartilage swelling to determine the uniaxial modulus of the cartilage solid matrix. Moduli obtained in this study (7.2 MPa femoral condyle; 10.8 MPa, tibial plateau) compare well with previously reported values for the tensile moduli of human and other animal cartilages determined from uniaxial tension experiments. This study provides the first available data for material properties and fixed charge density in cartilage from the guinea pig knee and suggests a promising method for tracking changes in cartilage mechanics in small animal models of degeneration.     

Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus

Nonlinear, linear and failure properties of articular cartilage and meniscus in opposing contact surfaces are poorly known in tension. Relationships between the tensile properties of articular cartilage and meniscus in contact with each other within knee joints are also not known. In the present study, rectangular samples were prepared from the superficial lateral femoral condyle cartilage and lateral meniscus of bovine knee joints. Tensile tests were carried out with a loading rate of 5 mm/min until the tissue rupture. Nonlinear properties of the toe region, linear properties in larger strains, and failure properties of both tissues were analysed. The strain-dependent tensile modulus of the toe region, Young's modulus of the linear region, ultimate tensile stress and toughness were on average 98.2, 8.3, 4.0 and 1.9 times greater (p<0.05) for meniscus than for articular cartilage. In contrast, the toe region strain, yield strain and failure strain were on average 9.4, 3.1 and 2.3 times greater (p<0.05) for cartilage than for meniscus. There was a significant negative correlation between the strain-dependent tensile moduli of meniscus and articular cartilage samples within the same joints (r=−0.690, p=0.014). In conclusion, the meniscus possesses higher nonlinear and linear elastic stiffness and energy absorption capability before rupture than contacting articular cartilage, while cartilage has longer nonlinear region and can withstand greater strains before failure. These findings point out different load carrying demands that both articular cartilage and meniscus have to fulfil during normal physiological loading activities of knee joints.