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

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

A linearized formulation of triphasic mixture theory for articular cartilage,and its application to indentation analysis

The negative charges on proteoglycans significantly affect the mechanical behaviors of articular cartilage. Mixture theories, such as the triphasic theory, can describe quantitatively how this charged nature contributes to the mechano-electrochemical behaviors of such tissue. However, the mathematical complexity of the theory has hindered its application to complicated loading profiles, e.g., indentation or other multi-dimensional configurations. In this study, the governing equations of triphasic mixture theory for soft tissue were linearized and dramatically simplified by using a regular perturbation method and the use of two potential functions. We showed that this new formulation can be used for any axisymmetric problem, such as confined or unconfined compressions, hydraulic perfusion, and indentation. A finite difference numerical program was further developed to calculate the deformational, electrical, and flow behaviors inside the articular cartilage under indentation. The calculated tissue response was highly consistent with the data from indentation experiments (our own and those reported in the literature). It was found that the charged nature of proteoglycans can increase the apparent stiffness of the solid matrix and lessen the viscous effect introduced by fluid flow. The effects of geometric and physical properties of indenter tip, cartilage thickness, and that of the electro-chemical properties of cartilage on the resulting deformation and fluid pressure fields across the tissue were also investigated and presented. These results have implications for studying chondrocyte mechanotransduction in different cartilage zones and for tissue engineering designs or in vivo cartilage repair.     

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.     

Fixed Electrical Charges and Mobile Ions Affect the Measurable Mechano-Electrochemical Properties of Charged-Hydrated Biological Tissues: The Articular Cartilage Paradigm

The triphasic constitutive law [Lai, Hou and Mow (1991)] has been shown in some special 1D cases to successfully model the deformational and transport behaviors of charged-hydrated, porous-permeable, soft biological tissues, as typified by articular cartilage. Due to nonlinearities and other mathematical complexities of these equations, few problems for the deformation of such materials have ever been solved analytically. Using a perturbation procedure, we have linearized the triphasic equations with respect to a small imposed axial compressive strain, and obtained an equilibrium solution, as well as a short-time boundary layer solution for the mechano- electrochemical (MEC) fields for such a material under a 2D unconfined compression test. The present results show that the key physical parameter determining the deformational behaviors is the ratio of the perturbation of osmotic pressure to elastic stress, which leads to changes of the measurable elastic coefficients. From the short-time boundary layer solution, both the lateral expansion and the applied load are found to decrease with the square root of time. The predicted deformations, flow fields and stresses are consistent with the analysis of the short time and equilibrium biphasic (i.e., the solid matrix has no attached electric charges) [Armstrong, Lai and Mow (1984)]. These results provide a better understanding of the manner in which fixed electric charges and mobile ions within the tissue contribute to the observed material responses.     

In situ measurement of articular cartilage deformation in intact femoropatellar joints under static loading

The deformational behavior of articular cartilage has been investigated in confined and unconfined compression experiments and indentation tests, but to date there exist no reliable data on the in situ deformation of the cartilage during static loading. The objective of the current study was to perform a systematic study into cartilage compression of intact human femoro-patellar joints under short- and long-term static loading with MR imaging. A non-metallic pneumatic pressure device was used to apply loads of 150% body weight to six joints within the extremity coil of an MRI scanner. The cartilage was delineated during the compression experiment with previously validated 2D and 3D fat-suppressed gradient echo sequences. We observed a mean (maximal) in situ deformation of 44% (57%) in patellar cartilage after 32 h of loading (mean contact pressure 3.6 MPa), the femoral cartilage showing a smaller amount of deformation than the patella. However, only around 7% of the final deformation (3% absolute deformation) occurred during the first minute of loading. A 43% fluid loss from the interstitial patellar matrix was recorded, the initial fluid flux being 0.217 +/- 0.083 microm/s, and a high inter-individual variability of the deformational behavior (coefficients of variation 11-38%). In conjunction with finite-element analyses, these data may be used to compute the load partitioning between the solid matrix and fluid phase, and to elucidate the etiologic factors relevant in mechanically induced osteoarthritis. They can also provide direct estimates of the mechanical strain to be encountered by cartilage transplants.     

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.     

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

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

Influence of fixed charge density magnitude and distribution on the intervertebral disc: applications of a poroelastic and chemical electric (PEACE) model

A 3-dimensional formulation for a poroelastic and chemical electric (PEACE) model is presented and applied to an intervertebral disc slice in a 1-dimensional validation problem and a 2-dimensional plane stress problem. The model was used to investigate the influence of fixed charge density magnitude and distribution on this slice of disc material. Results indicated that the mechanical, chemical, and electrical behaviors were all strongly influenced by the amount as well as the distribution of fixed charges in the matrix. Without any other changes in material properties, alterations in the fixed charge density (proteoglycan content) from a healthy to a degenerated distribution will cause an increase in solid matrix stresses and can affect whether the tissue imbibes or exudes fluid under different loading conditions. Disc tissue with a degenerated fixed charge density distribution exhibited greater solid matrix stresses and decreased streaming potential, all of which have implications for disc nutrition, disc biomechanics, and tissue remodeling. It was also seen that application of an electrical potential across the disc can induce fluid transport.     

The functional environment of chondrocytes within cartilage subjected to compressive loading: a theoretical and experimental approach

A non-invasive methodology (based on video microscopy, optimized digital image correlation and thin plate spline smoothing technique) has been developed to determine the intrinsic tissue stiffness (H(a)) and the intrinsic fixed charge density (c(0)(F)) distribution for hydrated soft tissues such as articular cartilage. Using this technique, the depth-dependent inhomogeneous parameters H(a)(z) and c(0)(F)(z) were determined for young bovine cartilage and incorporated into a triphasic mixture model. This model was then used to predict the mechanical and electrochemical events (stress, strain, fluid/osmotic pressure, and electrical potentials) inside the tissue specimen under a confined compression stress relaxation test. The integration of experimental measurements with theoretical analyses can help to understand the unique material behaviors of articular cartilage. Coupled with biological assays of cell-scale biosynthesis, there is also a great potential in the future to study chondrocyte mechanotransduction in situ with a new level of specificity.     

Measuring fixed charge density of goat articular cartilage using indentation methods and biochemical analysis

An important indicator of osteoarthritis (OA) progression is the loss of proteoglycan (PG) aggregates from the cartilage tissue. Using the indentation creep test, two analytical methods, as previously developed by Lu et al. [Lu, X. L., Miller, C., Chen, F. H., Guo, X. E., Mow, V. C., 2007. The generalized triphasic correspondence principle for simultaneous determination of the mechanical properties and proteoglycan content of articular cartilage by indentation. Journal of Biomechanics 40, 2434-2441 (EPub).], for predicting the fixed charge density (FCD) of goat knee articular cartilage in the normal (control) and degenerated states were compared: (1) a "dual-stage" method to calculate FCD from the mechanical properties of the tissue when tested in isotonic and hypertonic solutions; and (2) a "single-stage" method to predict FCD (as in (1)) assuming an intrinsic Poisson's ratio of 0.05 in the hypertonic state. A biochemical analysis using 1,9-dimethylmethylene blue (DMMB) assay was conducted to directly measure PG content, and hence FCD. The association between the FCD and the aggregate modulus of the tissue was also explored. The mean (+/-S.D.) FCD values measured using the dual-stage method were the closest (control: 0.129+/-0.039, degenerated: 0.046+/-029) to the DMMB results (control: 0.125+/-0.034, degenerated: 0.057+/-0.024) as compared to those of the single-stage method (control: 0.147+/-0.035, degenerated: 0.063+/-0.026). The single-stage method was more reliable (r(2)=0.81) when compared to the dual-stage method (r(2)=0.79). A prediction of FCD from the aggregate modulus generated the least reliable FCD prediction (r(2)=0.68). Because both the dual- and single-stage methods provided reliable FCD estimates for normal and degenerated tissue, the less time-consuming single-stage method was concluded to be the ideal technique for predicting FCD and hence PG content of the tissue.     

Finite element study of a tissue-engineered cartilage transplant in human tibiofemoral joint

Most tissue-engineered cartilage constructs are more compliant than native articular cartilage (AC) and are poorly integrated to the surrounding tissue. To investigate the effect of an implanted tissue-engineered construct (TEC) with these inferior properties on the mechanical environment of both the engineered and adjacent native tissues, a finite element study was conducted. Biphasic swelling was used to model tibial cartilage and an implanted TEC with the material properties of either native tissue or a decreased elastic modulus and fixed charged density. Creep loading was applied with a rigid impermeable indenter that represented the femur. In comparison with an intact joint, compressive strains in the transplant, surface contact stress in the adjacent native AC and load partitioning between different phases of cartilage were affected by inferior properties of TEC. Results of this study may lead to a better understanding of the complex mechanical environment of an implanted TEC.     

Finite element study of a tissue-engineered cartilage transplant in human tibiofemoral joint

Most tissue-engineered cartilage constructs are more compliant than native articular cartilage (AC) and are poorly integrated to the surrounding tissue. To investigate the effect of an implanted tissue-engineered construct (TEC) with these inferior properties on the mechanical environment of both the engineered and adjacent native tissues, a finite element study was conducted. Biphasic swelling was used to model tibial cartilage and an implanted TEC with the material properties of either native tissue or a decreased elastic modulus and fixed charged density. Creep loading was applied with a rigid impermeable indenter that represented the femur. In comparison with an intact joint, compressive strains in the transplant, surface contact stress in the adjacent native AC and load partitioning between different phases of cartilage were affected by inferior properties of TEC. Results of this study may lead to a better understanding of the complex mechanical environment of an implanted TEC.     

A triphasic theory for the swelling and deformation behaviors of articular cartilage

Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single-salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by mu i = mu io + (RT/Mi)ln[gamma 2 +/- c(c + cF)] and mu w = mu wo + [p-RT phi (2c + cF) + Bwe]/pwT, where R, T, Mi, gamma +/-, phi, pwT and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is sigma = - pI-TcI + lambda s(trE)I + 2 musE, where E is the strain tensor and (lambda s, mu s) are the Lamé constants of the elastic solid matrix. The chemical-expansion stress (-Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the "pre-stress" in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.     

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

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

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.     

Physiologic deformational loading does not counteract the catabolic effects of interleukin-1 in long-term culture of chondrocyte-seeded agarose constructs

An interplay of mechanical and chemical factors is integral to cartilage maintenance and/or degeneration. Interleukin-1 (IL-1) is a pro-inflammatory cytokine that is present at elevated concentrations in osteoarthritic joints and initiates the rapid degradation of cartilage when cultured in vitro. Several short-term studies have suggested that applied dynamic deformational loading may have a protective effect against the catabolic actions of IL-1. In the current study, we examine whether the long-term (42 days) application of dynamic deformational loading on chondrocyte-seeded agarose constructs can mitigate these catabolic effects. Three studies were carried out using two IL-1 isoforms (IL-1alpha and IL-1beta) in chemically defined medium supplemented with a broad range of cytokine concentrations and durations. Physiologic loading was unable to counteract the long-term catabolic effects of IL-1 under any of the conditions tested, and in some cases led to further degeneration over unloaded controls.     

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.     

Quasi-linear viscoelastic properties of costal cartilage using atomic force microscopy

Costal cartilage (CC) is one of the load-bearing tissues of the rib cage. Literature on material characterisation of the CC is limited. Atomic force microscopy (AFM) has been extremely successful in characterising the elastic properties of soft biomaterials such as articular cartilage and hydrogels, which are often the material of choice for cartilage models. But AFM data on CC are absent in the literature. In this study, AFM indentations using spherical beaded tips were performed on human CC to isolate the mechanical properties. A novel method was developed for modelling the relaxation indentation experiments based on Fung's quasi-linear viscoelasticity and a continuous relaxation spectrum. This particular model has been popular for uniaxial compression test data analysis. Using the model, the mean Young's modulus of CC was found to be about 2.17, 4.11 and 5.49?MPa for three specimens. A large variation of modulus was observed over the tissue. Also, the modulus values decreased with distance from the costochondral junction.     

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.