Poissons Ratio of Articular Cartilage

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DETERMINATION OF POISSON'S RATIO OF ARTICULAR CARTILAGE IN INDENTATION TEST USING DIFFERENT SIZED INDENTERS Hui Jin, Jack L. Lewis Department of Orthopaedic Surgery, University of Minnesota, Minneapolis, MN 55455 INTRODUCTION Indentation has been commonly used in testing the mechanical properties of articular cartilage, and its loading condition is considered more relevant to the physiological condition. Unlike in simple tension or compression tests, in indentation test, the material constants are coupled in the indentation load-deflection relations, and additional independent tests are needed to uncouple them. In previous studies, confined compression and torsion test[1], as well as directly measuring the lateral expansion in unconfined compression[2] have been used along with indentation test. There are two issues that may impede the application of such procedures. Firstly, the discrepancy between material constants obtained from different test geometry has been observed. As a result, a material constant measured or calculated in a certain test geometry may not be applicable to others[2]. Secondly, some samples, such as mouse patellar cartilage, could be too small to be handled and tested by means other than indentation. A method of determining all the material constants by a single indentation test had been achieved in the context of biphasic theory[3]. The method has been applied in many works to determine all the material parameters required by biphasic models. In general, the values of Poisson’s ratio reported in these works have been small, the mean value typically ranging from 0.0 to 0.28[3,4]. The small Poisson’s ratio values have been confirmed by the direct measurements in unconfined compression[2]. However, it has also been shown that applying the Poisson’s ratio directly measured in unconfined compression to the indentation will result in a higher Young’s modulus in comparison with that from the confined and unconfined compression[2]. In this study, we introduce a method for determining Poisson’s ratio and Young’s modulus of soft materials in indentation using different sized indenters, without requiring assistance from other test methods. The method was firstly validated on polyurethane rubber and a elastic foam with Young’s moduli known from unconfined compression. Then, it was applied to bovine cartilage, to obtain the Young’s modulus and Poisson’s ratio in instantaneous and equilibrium response, where the cartilage can be treated as a single-phase elastic media. A basic finding was that the Poisson’s ratio in indentation geometry obtained in this work was consistently higher than those directly measured in unconfined compression and those derived from biphasic indentation theory. Using finite element simulations, we were able to attribute this discovery to the inhomogeneity and anisotropy of the cartilage. METHODS AND MATERIALS The method is derived from the solution developed by Hayes et al[5], for a flat-ended cylindrical rigid punch with radius a indenting on the surface of a linear elastic layer with thickness h, shear modulus G and Poisson’s ratio ν . The layer is bonded onto a flat rigid substrate. The indentation stiffness that is defined as the ratio of the indenting load p to the indenting depth ω , in ideal linear elastic cases may be expressed as: p 4Ga = κ(a / h, ν ) ω 1− ν (1) where, κ(a / h, ν ) is a correction factor that accounts for the finite layer effect. Under the same condition, and following the same procedure, indenting the sample twice using two different sized indenters with radius a1 and a2 respectively, we have:  p    ω 1 a κ (a1 / h ,ν )  p   = 1 ω a  2 2 κ (a 2 / h,ν ) (2) In Eq. (2), Poisson’s ratio is the only unknown and it can be obtained by solving this nonlinear equation. Once the Poisson’s ratio is obtained, the shear modulus can be recovered using Eq. (1). Indentation tests on cartilage samples were performed by indenting with flat-ended cylindrical indenters to 0.15 mm at a nominal loading rate 1.5mm/sec, and holding for 1200 seconds. The actual loading rate for each test was checked to assure the uniformity of loading rate. Testing was done on an EnduraTec 3200 system. The stiffness during loading that obtained by linearly fitting the loading part of the loaddepth curve was designated the instantaneous stiffness, the stiffness at 1200 second the equilibrium stiffness, they are related by: 2003 Summer Bioengineering Conference, June 25-29, Sonesta Beach Resort in Key Biscayne, Florida Starting page #: 0565  p  p   =   H (t = ∞ )  ω ∞  ω  o (3) the subscripts o and ∞ represent the instantaneous and equilibrium entity, respectively. H (t ) is the load relaxation function obtained by normalizing the load relaxation history with its peak The instantaneous and equilibrium Poisson’s ratio can then be calculated using Eq.(2) and the indentation stiffness. Verification tests were performed on a polyurethane rubber and an elastic foam. The Young’s moduli of the two materials determined in indentation and unconfined compression in small deformation range (5% compressive strain for rubber, 3%for foam) are shown in Table 1. The relative error between the Young’s moduli determined from the two methods was 6.5% for the rubber and 3.3% for the foam. The Poisson’s ratios for the two materials are also shown in Table 1. For cartilage tests, 7 square shaped samples (20X20mm) were cut from the relatively flat part of 7 cow patellae. Each sample was indented three times using flat-ended cylindrical indenters with radius 2mm, 4mm and 6mm, respectively. Cartilage thickness was measured with a sharp tipped thickness detector, as described in reference[3]. The load and displacement history data were collected from each test. Material Elastic Foam Urethane Rubber Indenter Size (mm) Poisson’s ratio (Indent) 13.0/6.0 6.0 / 4.0 6.0 / 2.0 4.0 / 2.0 Average 0.347 0.489 0.489 0.490 0.489 Young’s Modulus (Mpa) Indent Compress 0.432 0.418 4.420 4.416 4.712 4.402 4.413 Table 1. Elastic Properties of Urethane Rubber and A Elastic Foam Obtained From Indentation and Unconfined Compression Tests In order to understand the effects of inhomogeneity and anisotropy, a finite element model was created to simulate the process of an elastic layer indented by different sized indenters. The anisotropy and inhomogeneity of the elastic layer was modeled respectively. In the transversely isotropic case, the equivalent Poisson’s ratio depends on the ratio of Young’s moduli, ratio of shear moduli and two Poisson’s ratios, namely, E p Et , G p Gt , ν p and ν tp [8], here p and t represent in-plane and out-plane entity, respectively. In inhomogeneous case, the elastic layer consisted of three homogeneous and isotropic sublayers with the thickness of 10%, 60% and 30% of the layer thickness, respectively, simulating the superficial, the middle and the deep layers of cartilage. Using the indentation stiffness data generated by the FE model, we were able to find the equivalent homogeneous and isotropic Poisson’s ratio, as well as the elastic moduli. RESULTS Table 2 shows the predicted Poisson’s ratio Young’s modulus from one cartilage sample. The values of Young’s modulus found in our tests were 1.79 ± 0.59 Mpa in instantaneous response, and 0.45 ± 0.26 Mpa in equilibrium. The values of Poisson’s ratio were 0.503 ± 0.028 in instantaneous response and 0.463 ± 0.073 in equilibrium. In the anisotropic FE model, we found that the equivalent Poisson’s ratio increased with the increase of E p Et , ν p and ν tp , and changed only slightly with the variation of G p Gt . When the material exhibits strong anisotropy ( E p Et >5.0, for example), the equivalent Poisson’s ratio could be close to 0.50 even if ν p and νtp are as small as 0.10. Using the experimental data provided in reference[6] and assigning 0.49 to the instantaneous Poisson’s ratio for each sublayer, we were able to show that the equivalent isotropic and homogeneous Poisson’s ratio could exceed 0.50 in instantaneous response; and in equilibrium state, it was greater than 0.40, significantly higher than that of individual sublayers (0.08, 0.32 and 0.16 for superficial, middle and deep layers in equilibrium), it was also significantly higher than that obtained from unconfined compression FE simulation (0.23). The dependency of predictions on the indenter sizes was also observed in both inhomogeneous and anisotropic finite element simulations. Indenter Size (mm) 6.0 & 4.0 6.0 & 2.0 4.0 & 2.0 Average Poisson’s Ratio ν Young’s Modulus E (Mpa) t=0 t= ∞ t=0 0.482 0.466 0.447 0.465 0.333 0.326 0.320 0.326 1.913 2.111 2.207 2.077 t= ∞ 0.512 0.519 0.523 0.518 Table 2 A Bovine Cartilage Indentation Test Result, t=0 for instantaneous response, and t= ∞ the equilibrium SUMMARY AND DISCUSSION A method for determining the Poisson’s ratio and Young’s modulus of articular cartilage and other soft materials from indentation using different sized indenters has been introduced. The effectiveness of this method has been shown in rubber and elastic foam tests. Applying the method to bovine cartilage, we were able to determine the equivalent elastic properties of the tissue in both instantaneous and equilibrium states. The equilibrium Young’s modulus found in our tests was consistent with those in [7]. The Poisson’s ratio found in our tests may be compared with some previous works[5], however, it was significantly higher than those directly measured in unconfined compression. Out-of-range Poisson’s ratio values (>0.50) and indenter size dependency of the predictions were also observed for some samples. Using FE simulation, we were able to show that, for an anisotropic and inhomogeneous elastic layer, its equivalent Poisson’s ratio and Young’s modulus in indentation geometry are not comparable to any individual anisotropic Poisson’s ratio and Young’s modulus. We also discovered that the anisotropy and inhomogeneity could be responsible for the high values of Poisson’s ratio found in this work. Those findings suggest that, for the cartilage exhibiting relatively weak inhomogeneity and anisotropy, it could be properly modeled as homogeneous, isotropic and linear elastic material in instantaneous and equilibrium states, and the introduced method may be used to determine the associated Poisson’s ratio and elastic moduli; however, in order to adequately model those with strong inhomogeneity and strong anisotropy, more sophisticated material and structural models have to be employed. AKNOWLEDGEMENTS This work was supported by the IPRIME, and the MRSEC Program of the NSF under Award Number DMR-9809364. REFERENCES 1. Hayes, W.C. et al, J. Appl. Physiol., 1971, 31, pp562-568. 2. Jurvelin, J.S., et al, J. Biomech., 1997, 30, pp235-241. 3. Mow, V.C. et al, J. Biomech., 1989, 22, pp853-861 4. Setton, L.A. et al, J. Orthop. Res., 1994, 12, pp451-463. 5. Hayes, W.C. et al, J. Biomech., 1972, 5, pp541-551. 6. Rieppo, J. et al, private communication. 7. Jurvelin, J.S. et al, J. Biomech., 2002, 35, pp903-909. 8. Sakamoto, S. et al, JSME intl. J., 1991, Series I, 34,pp130-134. 2003 Summer Bioengineering Conference, June 25-29, Sonesta Beach Resort in Key Biscayne, Florida
MAC Corresponding Author: Lori A. First Name Setton Last Name Presenting Author: Dawn M. First Name Elliott Last Name ABSTRACT NO. 1303 PAPER NO. 0649 I prefer a Poster Presentation Please consider for New Investigator Recognition Awards Please consider for the American Geriatrics Society Award REQUIRED - Supply first keyword from one of these lists: Cartilage Mechanics Supply 4 remaining keywords from the list in the Instructions: None Anisotropy Articular Cartilage Material Properties Mechanical Testing DIRECT MEASUREMENT OF THE POISSON'S RATIO OF HUMAN ARTICULAR CARTILAGE IN TENSION *Elliott, D.M., **Kydd, S.R., Perry, C.H., +Setton, L.A. *+ Department of Biomedical Engineering, Duke University, Durham, NC 27708; (919) 660-5131, fax (919) 684-4488; setton@duke.edu INTRODUCTION The tensile modulus of articular cartilage has been widely measured as a function of depth, orientation, and degeneration (1-5). Collagen is believed to provide cartilage with its resistance to tensile loading, contributing to anisotropic effects which are observed as a dependence of tensile behavior on orientation with respect to the collagen ultrastructure (2,4,5). The Poisson’s ratio is also required to fully describe the tensile behavior of articular cartilage, but has not been previously measured. The Poisson's ratio for bovine cartilage in unconfined compression has been directly measured with evidence for material isotropy in compression (6). Given the nonuniform and highly oriented ultrastructure of collagen in articular cartilage, we may expect the Poisson’s ratio for cartilage to exhibit anisotropic effects in tension and to vary with spatial position. In this study, we directly measure the Poisson's ratio and tensile modulus of articular cartilage from the human patella and its variations with depth using a newly developed optical system. This is the first reported data for the Poisson's ratio of cartilage in tension, with evidence of significant anisotropy for the Poisson’s ratio throughout the tissue depth. This finding has important implications for predicting the stress-strain state within cartilage and suggests that volumetric changes, with associated fluid flow, may be a significant mechanical phenomenon in tensile loading of cartilage. METHODS Test samples were prepared from articular cartilage on the lateral facet of non-degenerate human patella (n=4, average age 51). Samples were prepared from the surface and mid-zone (~1.5 mm below the surface). Planar strips of uniform thickness (0.47 ± 0.13 mm, mean ± sd, n=8) and width (2.01 ± 0.26) were prepared with the length (9.65 ± 3.71) oriented parallel to the split-line direction (7). Samples were tested in uniaxial tension in a 0.15 M PBS bath using a custom-built material test system (8) with optical image analysis. A uniform distribution of enamel markers was applied to the sample surface with an airbrush. Samples were oriented with the length aligned with the axis of loading, and allowed to equilibrate under a tare load (0.1 MPa). A digital image was taken of the sample mid-substance (2 x 3.6 mm) at high resolution (3.6 µm/pixel) for calculation of the reference marker positions. Uniaxial displacements were applied to a prescribed strain of εy = 0.02 (grip-to-grip), and the axial force was recorded for 1800s to equilibrium. A digital image of the sample surface was taken at the equilibrium, deformed state. The protocol was repeated in 0.02 strain increments to εy = 0.16. The coordinates of the surface markers were recorded and the planar components of Lagrangian strain (Eij) were calculated at each strain increment for triads on the sample surface using a custom-written program (PV/Wave, Visual Numerics). The Poisson's ratio, νyx = −Exx/Eyy, was calculated for each triad and for each strain increment, where x-y is defined in the plane of the sample surface. Values for νyx were found to be relatively constant with spatial position and with strain increment, so that an average value was calculated for each sample for all triads and for all strains from εy = 0.04 - 0.10 (i.e., the linear region). The equilibrium stress-strain response was modeled by an exponential law and the tangent modulus (E) was determined in the toe (zero strain) and linear (Eyy = 0.10) regions, as described previously (8). A paired ttest was used to test for an effect of depth on the Poisson's ratio and moduli. RESULTS Values for Exx and Eyy were measured at 20-30 triads per sample. This technique for local strain measurement is capable of detecting inhomogeneities due to stress Figure 1. Strain (Eij) for a concentrations, clamping effects and edge effects. For the samples typical surface zone sample in this study, the strains were 0.2 relatively uniform across the frame Eyy area and exhibited no detectable 0.1 pattern of inhomogeneity in either 0 0.04 0.06 0.08 0.10 x or y directions (e.g., at εy = 0.02 εy -0.1 average sd = 0.007 and 0.006 for Exx Eyy and Exx, respectively, n=8 samples). Average values for Exx -0.2 and Eyy were highly correlated -0.3 within each sample (0.96 < r2 < 0.999, n=8), providing further -0.4 0.2 0.2 0.1 evidence of a uniform value for νyx with amplitude of strain, Figure 1. The surface and mid-zone νyx were 2.2 ± 1.2 and 0.60 ± 0.22, respectively (Figure 2, mean ± sd, n=4). There was evidence of a difference in E and νyx with zone which was significant at p<0.05 for the tensile modulus only (Figure 2). DISCUSSION Values for the tensile modulus and Poisson’s ratio of patellar cartilage from the mid-zone were found to be 12% and 27% of their respective values at the surface. These findings are consistent with previous studies of human (1-3) and bovine cartilage (4,5) in which the tensile moduli of deeper zone cartilage was ~15% of values at the articular surface (1,2). This trend is believed to arise from a higher collagen density and preferential collagen fiber orientation at the surface as compared to the deeper layers. Further support of this hypothesis are findings of a higher tensile modulus for samples oriented parallel, compared to perpendicular, to the split-line direction (2,4,5), where split-lines correspond to collagen fiber orientation at the articular surface (7). It is likely that the trend for higher Poisson's ratio at the cartilage surface also arises from these zonal variations in the collagen ultrastructure. Values for Poisson’s ratio greater than 0.5 indicate that anisotropy is significant in governing the tensile behavior of cartilage at the surface and mid-zones, and suggest that an isotropic model for the cartilage solid matrix may be insufficient to describe the material behavior in tension. Previous studies have directly measured the Poisson’s ratio of bovine cartilage for unconfined compression in the axial plane (i.e., the x-z plane using the convention in our study) with values for ν of ~ 0.19, which are significantly lower than νyx measured in our study. These differences may partly arise from different tension-compression behaviors for cartilage (9), and also support the hypothesis that collagen fibers in the sample contribute to material anisotropy in tension but not compression. To fully assess the order of anisotropy for cartilage as suggested by the data in this study, additional material properties are required (e.g., Poisson’s ratio and moduli in the x-z and y-z planes). Finally, values for νyx greater than unity, where the transverse strain exceeds the axial strain, suggest that a negative dilatation may occur during uniaxial elongation. One mechanism for volumetric changes in articular cartilage could be through fluid exchange, as has been well-studied for cartilage in compression (9). Material models for anisotropy with explicit representations of the collagen fibers (10-12), in combination with models of fluid-solid interactions, are promising for describing the tensile behavior of cartilage and other collagen-reinforced soft tissues. ACKNOWLEDGMENTS Supported by a grant from The Whitaker Foundation and an NIH Pre-Doctoral Fellowship. REFERENCES 1. Akizuki S et al (1986) J Orthop Res 4:379-392. 2. Kempson GE et al (1973) Biochim Biophys 297:465-472. 3. Kempson GE (1982) Ann Rheum Dis 41:508-511. 4. Roth V, Mow VC (1980) J Bone Joint Surg 62A:1102-1117. 5. Woo SLY et al (1976) J Biomech 9:785-791. 6. Jurvelin JS et al (1997) J Biomech 30:235-241. 7. Meachim G et al (1974) J Anat 118:101-118. 8. Elliott DM et al (1996) ASME BED-33:247-248. 9. Mow et al (1995) in Osteoarthritic Disorders, pp. 147-171. 10. Elliott DM et al (1997) ASME BED-36:165-166. 11. Puso MA et al (1998) J Biomech Eng 120:62-70. 12. Soulhat J et al (1998) Trans Orthop Res Soc 23:226. ** Department of Mechanical Engineering, City College, CUNY One or more of the authors have received something of value from a commercial or other party related directly or indirectly to the subject of my presentation. The authors have not received anything of value from a commercial or other party related directly or indirectly to the subject of my presentation. 45th Annual Meeting, Orthopaedic Research Society, February 1-4, 1999, Anaheim, California 649
PII: ~21-92~(96~13~9 OPTICAL AND MECHANICAL DETERMINATION OF POISSON’S RATIO OF ADULT BOVINE HUMERAL ARTICULAR CARTILAGE J. S. Jurvelin,*t M. D. Buschmannf and E. B. Hunziker* * M. E. Miller Institute for Biomechanics, University of Bern, P.O. Box 30, CH-3010 Bern, Switzerland; i Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, Kuopio, Finland; and $ Biomedical Engineering Institute, Ecole Polytechnique and Faculty of Medicine, University of Montreal, Montreal, PQ, Canada Abstract-The equilibrium stiffness of articular cartilage is controlled by flow-independent elastic properties (Young’s modulus, Es, and Poisson’s ratio. us) of the hydrated tissue matrix. In the current study, an optical (microscopic) method has been developed for the visualization of the boundaries of cylindrical bovine humeral head articular cartilage disks (n = 9) immersed in physiological solution. and compressed in unconfined geometry. This method allowed a direct, model-independent estimation of Poisson’s ratio of the tissue at equilibrium, as well as characterization of the shape changes of the sample during the nonequilibrium dynamic phase. In addition to optical analyses, the equilibrium behavior of cartilage disks in unconfined and confined ramp-stress relaxation tests provided a direct estimation of the aggregate modulus, Ha, and Young’s modulus and, indirectly, Poisson’s ratio for the articular cartilage. The mean value for Poisson’s ratio obtained from the optical analysis was 0.185 f 0.065 (mean If: SD., n = 9). Values of elastic parameters obtained from the mechanical tests were 0.754 & 0.198 MPa, 0.677 k 0.223 MPa, and 0.174 f 0.106 for Ha, Es. and zis, respectively (mean k S.D., n = 7). The similar us-values obtained with optical and mechanical techniques imply that, at equilibrium, for these two tests, the isotropic model is acceptable for mechanical analysis. However, the microscopic technique revealed that the lateral expansion, especially during the initial phase of relaxation. was inhomogeneous through the tissue depth. The superficial cartilage zone expanded less than the radial zone. The zonal differences in expansion were attributed to the known zonal differences in the fibrillar collagen architecture and proteoglycan concentrati~~n. -i’ 1997 Elsevier Science Ltd. All rights reserved. k’eyn~ds: Articular cartilage: Cartilage mechanics: Cartiiage material properties; Mechanical testing: Video microscopy 5-10 times larger in tension than in compression (Mow et al., 1992). In mechanical studies, cartilage is typically modeled as homogeneous and isotropic tissue in order to reduce computational complexity. Elastic (Hayes er ul,, 1972), viscoelastic (Parsons and Black, 19773, and poroelastic (Biot, 1941) or biphasic (Mow et trf., 1980) models have been introduced for the theoretical analysis of dynamic cartilage mechanical behavior. The homogeneous isotropic biphasic model has been used successfully in the analysis of confined compression behavior of cartilage (Frank and Grodzinsky, 1987; Mow et al., 1980). In contrast, model predictions for dynamic tests in unconfined geometry were seen to be unsuccessful initially (Armstrong et al., 1984; Brown and Singermann, 1986). The source of disagreement has been ascribed to both experimental difficulties (Kim et L&, 1995; Spilker et at., 1990) as well as structural mechanisms, such as matrix viscoelasticity (Mak, 1987) or the tension~ompression nonlinearity (Cohen et ni., 1992) of the matrix. The lack of agreement between experiment and theory has limited the application of the unconfined test for the determination of Poisson’s ratio. The confined test, on the other hand, is inherently one-dimensional and, therefore, cannot be used alone for estimation of Poisson’s ratio. The biphasic indentation technique (Mak et al., 1987: Mow et al., 1989) has provided a means for the evaluation of Poisson’s ratio. Although the indentation problem of a homogeneous isotropic model of articular cartilage does not completely agree with the high experimental dynamic stiffness of articular cartilage (Cohen INTRODUCTION Adult articular cartilage is a structurally inhomogeneous and anisotropic tissue. The main constituents of the cartilage matrix, i.e. proteoglycans (PCs) and fibrillar collagens show zonal differences with respect to their concentration and structural arrangement. The concentration of PG (mainly aggrecan) is lowest in the superficial cartilage zone and increases in deeper zones of the cartilage (Jones et ul., 1977; Poole, 1993). Moreover, at any given depth from the articular surface, PG concentration can change as a function of the distance from the chondrocytes (Hunziker, 1992). The content of collagen (mainly type II) within mature articular cartilage may vary less (Lipschitz et al., 1975; Muir et al., 1970), but the three-dimensional architecture of collagen shows an arcade-like organization consisting of tangential/horizontal fibril network in the superficial zone, a more randomly arranged fibrillar organization within the transitional zone and larger diameter fibres running principally in a vertical direction within the radial zone, through the calcified cartilage to the subchondral bone (Benninghof, 1922; Speer and Dahners, 1979). Due to this complex structure, mature articular cartilage is inhomogeneous and mechanically anisotropic. A significant compression-tension nonlinearity is also well known where the equilibrium stiffness can be 235 ‘36 .I. S. Jurvelin LJ~111.; 1993) the technique has recently been applied extensively to determine, from a single indentation measurement, all three material parameters of the model, i.e. shear modulus, /cs, Poisson’s ratio, ls, and permeability, k, for in situ articular cartilage (Athanasiou et al., 199 1, 1994; Hale et al.. 1993; Schenck et ul., 1994: Setton ct LII., 1994). In general, the values of Poisson’s ratio derived from these analyses have been small and they vary with species, type of joint and the joint area analyzed. For example, the values of 0.098 & 0.069, 0.074 -t 0.084 and 0.00 + 0.00 (mean f S.D., II = 446) were determined for human knee articular cartilage of the lateral condyle, medial condyle and patellar groove of femur (Athanasiou et a/., 1991). Earlier, most values for Poisson’s ratio of articular cartilage were in the range 0.37-0.50, either experimentally determined or assumed for indentation analysis (Altman et al., 1984; Hayes and Mockros, 1971; Hori and Mockros, 1976; Hock et al., 1983; Jurvelin et al., 1987; Kempson et ul., 1971). In this study, we present an optical method for recording the shape changes of bovine humeral head articular cartilage disks loaded in unconfined geometry. By applying constant axial strain for loading, the quantification of lateral strain at equilibrium makes possible a direct and essentially model-independent calculation of Poisson’s ratio for the cartilage matrix. In addition, we measure the stress relaxation behavior of humeral cartilage in confined and unconfined compression. By assuming material isotropy, we indirectly calculate Poisson’s ratio for the cartilage matrix from the equilibrium compression data. Comparison of the values of Poisson’s ratio obtained from optical and mechanical analyses thereby allows us to test the validity of a basic assumption of most mechanical models, i.e. isotropy of the cartilage matrix in compression. The optical measurement may also offer new information concerning depth-dependent inhomogeneities of intrinsic material properties. MATERIALS AND METHODS Intact shoulder joints of l-2 yr old cows (n = 12) were obtained within 24 h of slaughter from a local abattoir. The joint was opened, and a cylindrical cartilage disk from the central area of the humeral head was cut perpendicularly to the articular surface using a dermal biopsy punch (diameter: 6 mm). Subsequently, the full-thickness disk was removed from the subchondral bone by slicing horizontally with a razor blade and then punched to either 3.7 mm (mechanical analysis) or 1.8 mm diameter (microscopic analysis). During these procedures the cartilage was kept moistened with phosphate-buffered saline (PBS). In total, 16 disks were prepared for immediate microscopic analyses (n = 9) or mechanical tests (n = 7). In addition, three 3.7 mm disks were frozen for the later microscopic analyses. The original thickness of the uncompressed disks was measured using a stereomicroscope (Jurvelin et al., 1987). Microscopic An image visualization disks which analysis analysis method was developed for the of the boundaries of the cylindrical cartilage were immersed in PBS and compressed in rt ~11 unconfined geometry. The compression device consisted of a nonrotating micrometer and a stainless-steel immersion chamber with two glass windows (Fig. 1). The device was fixed to the stage of a light microscope (Olympus Vanox-S AH-2, Olympus Optical Co. Ltd. Tokyo, Japan). The optical path of the microscope was adjusted through the immersion chamber and. using a 4 x objective (Olympus SPlanApo4, numerical aperture = 0.16). the projection of the cartilage disk between the smooth, impermeable compression platens was visualized. The cartilage-platen interfaces were lubricated with synovial fluid. The disk was first compressed to a 5% offset strain. after which a waiting period of 1 h was used to guarantee the mechanical equilibrium. For further compression, steps of 5% strain (manually controlled strain rate - 0.05 s- ‘) were applied up to a total offset of 20%. Using the imaging system, consisting of a microscope, videocamera (Sony DXC-930P, Sony Co., Tokyo, Japan). frame grabber (RasterOps 24XLTV. RasterOps Co., Santa Clara, CA, U.S.A.) and computer (Macintosh 11x), the shape of the sample projected perpendicular to the sample axis was recorded during a complete stress relaxation (< 30 min) by capturing a total number of 15--20 images over this period of time. Image capture and analysis were performed using commercial software (IP-Lab Spectrum, Signal Analytics Co., Vienna, Virginia, U.S.A.). The final magnification of the captured images was 80 x, with a corresponding pixel size of 4 llrn. Using automatic segmentation (thresholding) of the images, the edges of the disk were recognized and the program then calculated the projected area of the disk. With the projected area and the known thickness (obtained from the micrometer) the mean diameter of the disk was calculated and plotted as a function of time. This automatic procedure for area determination allowed an accurate detection of small dimensional changes of the mean disk diameter. By comparing the diameter of the disk before and after compression, we were able to determine quantitatively the average lateral strain as a function of time. At equilibrium the ratio of average-lateral to average-axial strain yields the value of Poisson’sratio of articular cartilage. The lateralto-axial strain ratios were calculated systematically at two time points, i.e. 3 s after the onset of the strain (first image) and after obtaining equilibrium (typically within 30 min), as judged by the constant lateral strain for 10 min. Fig. 1. Schematic presentation of the device used for optical determination of Poisson’s ratio of articular cartilage. The device is fixed to the stage of the light microscope and the lateral expansion of the sample under unconfined compression is recorded with the microscooevideocamera&computer system. See text for the operational details: (I) nonrotating micrometer; (2) immersion chamber with two glass windows: (3) compression platens: (4) seal; (5) cartilage sample. Optical and mechanical determination of Poisson’s ratio The microscopic imaging and analysis were carried out for each sample in two mutually perpendicular projections, each of which was also perpendicular to the axis of the cartilage disk. Since bovine humeral cartilage shows no or only a weak split line formation after puncturing the articular surface with a round needle, these two mutually perpendicular directions are not necessarily related to collagen fibril orientation in the superficial layer. We chose the first direction of projection randomly and the second at 90” from the first. The depth-averaged lateral strains for these two projections were quantified in the whole uncalcified cartilage, as well as separately in the superficial and radial zones. These zones were defined as the most superficial (super~cial zone) or the deepest (radial zone) cartilage layer with a thickness of 10% that of the entire uncalcified cartilage layer.* To investigate the possible dependence of our Poisson’s ratio results on the size (diameter) of the disk, three 3.7 mm disks were measured using the technique described above (2 x objective, Olympus Splan Fl-1, numerical aperture = 0.08). Subsequently, the disks were then punched to 1.X mm and measured again using a 4 x objective. In both cases, a 5% step after a 10% offset strain was utilized. Reduction of the diameter increased the thickness/radius aspect ratio of the disk typically by 2.1 x . In this way we wanted to test if the measured Poisson’s ratio is an intrinsic parameter of the tissue, independent of the sample dimensions and consequently not affected by the possible friction between sample and platen surfaces. The optical technique was calibrated by measuring the diameter of small cylindrical metal rods first with the mechanical micrometer (1 pm resolution) and then, after placing the rod between compression platens in the same measurement geometry as for cartilage samples, with the microscope. A custom-built material testing device (Buschmann et ni., 1995) was used to conduct confined and unconfined compression measurements on the same specimen. The confined compression measurement was performed initially. We used a confining stainless-steel chamber and a stainless-steel porous platen (5 flrn pores, 50% porosity). A series of stress relaxation tests (step 10 jirn, velocity 1 /m s - ” ) was executed up to a 20% offset under automatic computer control. When the slope of the load relaxation curve was less than 9.8 mN min- ’ (3.0 g min- ‘) the next step was automatically started. For each step the complete time-position-load data was collected using the sampling frequency of 1 Hz. During nleasurement the disk was kept immersed in PBS. After termination of the confined test the sample was allowed to reswell back to equilibrium. To minimize the friction between compression platens and cartilage surfaces in unconfined compression measurements, the interfaces were lubricated with synovial fluid, harvested from the same joint as the disk. The unconfined compression test * While we found no systematic differences between two perpendicular projections, tbe measured lateral strains were averaged over projections to yield one mean value for each sample. 231 followed the same testing protocol used for the confined test. Both confined and uncon~ned compression testing took a total time of 2.5-3 h, Aggregate modulus (Ha), and Young’s modulus (Es), were determined from confined and unconfined tests, respectively, using the equilibrium stress-strain data in the most linear range (typically 520% strain). Analysis of the rne~s~re~e~z~s At equilibrium, the predictions of biphasic model necessarily reduce to those of the elastic matrix alone. Using the equilibrium moduli obtained from the confined and unconfined measurements, the (isotropic) Poisson ratio, os, was determined. For an isotropic linearly elastic material H,, Es and L’~and are related through the following formula: 1 -I;, Ha = (1 + z&)(1 -2L$. The positive root of Equation (1) was used to yield us. RESULTS The test measurements with metal rods showed a high accuracy and good linearity (r = 0.99992, vl = 10) of the optical technique for the determination of the diameter of a small, cylindrical object (data not shown). The optical analyses of cartilage disks revealed that the maximal lateral strain of the disk occurred immediately after the 5% ramp. During the ensuing stress relaxation the expansion partially recoiled and stabilized to a constant value. A typical time-dependent change in the lateral strain of cartilage and the measured stress relaxation (5% offset, 5% strain) are presented in Fig. 2. For comparison, the lateral strain vs time behavior of a single-phase elastic material, rubber (cylindrical rod, thickness = 1.5 mm, diameter = 1.8 mm), is also shown in Fig. 2. The observed shape changes of the cartilage disk under compression systematically revealed that the superficial cartilage layer undergoes a smaller dimensional expansion than the deeper layers immediately after ramp straining (Figs 2 and 3; Table 1). The depthaveraged Poisson’s ratio for the complete hyaline articular cartilage layer (without the calcified zone), determined from the equilibrium response, was 0.185 -I- 0.065 (mean I S.D., n = 9). For the disks measured inigally at a diameter of 3.7 mm and then after coring to 1.8 mm diameter, Poisson ratio values were 0.131 4 0.062 and 0.135 &.0.064, respectively (mean i: SD,, n = 3). The mean difference of these paired measurements was 0.005 (3.76%). No significant changes in the values of Poisson’s ratio measured at different offset strains (5, 10 and 15%) were observed (Table 1, p > 0.05, Friedman two-way ANOVA). The mean lateral strain of uncalcified cartilage, measured in the beginning phase of the relaxation (3 s after 1 s ramp) and normalized to the axial strain (SOh), was 0.380 rf: 0.065. When the expansion results of the superficial and radial cartilage zones were analyzed separately, then the ‘short time’ and the equilibrium values for lateral strains were 0.129 4 0.057 and 0.068 4 0.040 for the superficial zone, and 0.593 & 0.129 J. S. Jurvelin er (I/. A . Uncalclfied carillage, -vSuperhcialzane A Radlalzane -.-Rubber.v=0500 v=O 165 8. Cartilage, ES = 0.55 MPa ically showed a higher stiffness (Fig. 5). The aggregate modulus, H,, obtained from the confined compression tests was 0.754 + 0.198 MPa (mean f S.D., rr = 7) while Es = 0.677 -t 0.223 MPa (mean + S.D.. II = 7) was derived for Young’s modulus from the unconfined compression measurements. Using the mathematical relation of H,, Es and us [Equation (I)], the value for the isotropic Poisson’s ratio was found to be 0.174 Ifl 0.106 (Table 2). Values of Poisson’s ratio obtained from the optical and mechanical analyses showed no statistical difference (p > 0.05, Mann-Whitney [j-test). DISCUSSION In the present study we measured Poisson’s ratio of bovine humeral head articular cartilage by microscopic visualization and quantification of the lateral expansion of cylindrical cartilage disks in unconfined compression d 160 260 360 ” 12bOldOO (Table 1). We also investigated the stress relaxation reTIME (set) sponse of humeral articular cartilage in confined and Fig. 2. Typical lateral strain (top; normalized with the axial strain) and unconfined compression in order to evaluate the elastic the stress relaxation (below; strain .5%, load normalized with the properties (E,, us)of the tissue(Table 2). Dynamic visualequilibrium load) of bovine humeral head cartilage disk (diameter ization revealed a very fundamental difference between 1.8 mm). Lateral strain of superficial zone (defined as the most superfisingle-phase elastic material (rubber, c - 0.50) and bicial cartilage layer with the thickness of l/10 of the total uncalcified phasic cartilage (Fig. 2): the former displays a constant, cartilage), radial zone (defined as the deepest cartilage layer with the time-independent, lateral expansion during the stressrethickness of l/l0 of the toal uncalcified cartilage) and whole uncalcified cartilage are plotted separately. Equilibrium lateral strain for uncalcilaxation while the maximal lateral strain of the latter is fied cartilage indicates the value of Poisson’s ratio. The lateral strain found immediately after the ramp displacement and is data of a single-phase elastic material, rubber, is also shown. followed by a subsequent partial recoil and stabilization to a constant value, as expected according to biphasic theory (Armstrong et al., 1984).The biphasic model interprets the recoil as entirely due to water flow out of the ORIGINAL tissue. Due to the time needed for manual compression n 10% COMPRESSED and to additional time for the computer to capture the first image we were not able to record the lateral displacement during the very first seconds after the onset of compression. Relatively high values of 0.380 + 0.065 (mean f SD., n = 9) were obtained for normalized lateral strain of cartilage at 3 s after the compression. It is thus possible that, under an ideal step input, cartilage tissue behaves like an incompressible (r = 0.50) elastic material (Armstrong et al., 1984). The value of 0.380 is also in harmony with the experimental values for apparent Poisson’s ratio, v = 0.42, determined previously from short-term mechanical tests (Hayes and Mockros, 1971). The values obtained for Poisson’s ratio from mechanFig. 3. Shape change of the cylindrical cartilage sample 3 s after a 10% ical (0.174 IfI 0.106) or microscopic (0.185 2 0.065) compression. The lateral expansion is nonuniform. The superficial zone analyseswere comparable and thus suggestthat, ut equiis expanded less than the deeper zones. librium, for these two test geometries, the isotropy of the matrix is a reasonable assumption for compression studand 0.225 f 0.099 for the radial zone (Table l), respec- ies. However, due to the relatively high standard devitively. In statistical comparison, the superficial zone ex- ations in Poisson’s ratio values it is not possible to panded instantaneously and at equilibrium lessthan the precisely distinguish between anisotropic and isotropic radial zone (p < 0.01, Wilcoxon matched-pairs, Signed- behavior. We are not aware of any previous studies describing the equilibrium modulus or Poisson’sratio for ranks test). For mechanical tests, a typical load-time responsefor mature bovine humeral head cartilage with which we both unconfined and confined measurementsis presented could compare our results. Based on biphasic indentain Fig. 4. For both tests and any given samplethe equilib- tion analysesaggregate modulus values of 0.472 ir 0.147, rium responseswere typically similar during the first 5% 0.899 + 0.427, 0.894 + 0.293 MPa (mean + S.D., n = 10) applied strain. Upon increasing the strain (5-20%), the and Poisson’s ratio values of 0.245 k 0.065, 0.383 -f equilibrium stress-strain behavior was highly linear and 0.047, 0.396 + 0.023 (mean + S.D., n = 10) have been the samples tested in (complete) confinement systemat- derived in situ for the cartilage of bovine patellar groove Optical and mechanical determination of Poisson’s ratio 239 Table 1. Lateral strain vatues (normalized with axial strain, 5%) of the bovine humeral articular cartilage determined with increasing offset strains (5,lO and 15%) using the microscopic analysis. Values (mean & SD.) were derived for the (total) uncalcified cartilage and separately for the superficial and radial zones Lateral strain 5-100/u IO-15% 1520% Mean 0.386 + 0.074 0.186 ‘i 0.086 0.382 k 0.062 0.190 & 0.061 0.373 + 0.064 0.180 i. 0.051 0.380 & 0.065 0.185 & 0.065t Short term Equilibrium 0.153 & 0.085 0.087 * 0.050 0.118 * 0.051 0.067 + 0.041 0.138 f 0.049 0.054 + 0.042 0.129 f 0.057 0.068 + 0.040 Rudiul .xm?$ (n = 9) Short term Equilibrium 0.547 * 0.157 0.177 + 0.095 0.579 * 0.112 0.218 4 0.104 0.622 $- 0.167 0.23 1 + 0.098 0.593 + 0.129 0.225 -f 0.099 L~ncu/c$d cartilap (n = 9) Short term* Equilibrium S~~~~~~i~~ mze$ (n = 9) *Determined 3 s after the strain application. ’ Indicates the value of Poisson’s ratio. t Defined as the most superficial cartilage layer with the thickness of l/l0 of the total uncalcified cartilage *Defined as the deepest cartilage layer with the thickness of l/10 of the total uncalcified cartilage. 0 TIME (see) Fig. 4. A series of confined and unconfined ramp stress relaxation test (step 10 iun, velocity 1 pm s-l) up to a 20% offset strain for cartilage disk (thickness 0.90 mm, diameter 3.7 mm). When the slope of the load relaxation curve was less than 9.8 mNmin-’ (1.0 gmin-‘) the next step was automatically started. 0 Confined ff,=O.521 MPa 0 Unconfined Es=0.479 MPa b 5 EQUILIBRIUM 1’0 13 STRAIN 20 (x) Fig. 5. An example of the equilibrium Ioad-compression behavior of bovine humeral head cartilage in confined and unconfined compression. The aggregate and Young’s moduli were determined using the confined and unconfined compression data, respectively, in the linear strain range (lines). as well as for the medial and lateral condyles (Athanasion et al., 1991). Our value for the aggregate modulus, H, = 0.754 + 0.198 MPa, is comparable, but the value of Poisson’s ratio, rs = 0.185 + 0.065, is slightly lower than those obtained for the bovme knee joint articular cartilage. However, our value of Poisson’s ratio is within the range of values found for human or canine articular cartilage in situ using biphasic indentation measurements (Athanasiou et al., 1991, 1994; Hale et al., X993; Setton et al., 1994). Therefore, our results indicate that Poisson’s ratio of the articular cartilage, when measured using excised cartilage cylinders, is relatively small and comparable to that derived for intact articular cartilage. Microscopic visualization of adult bovine humeral cartilage under compression showed a highly depth-dependent inhomogeneous lateral expansion. The observed expansion 3 s after the application of a fast ramp strain was less in the superficial zone than in the radial cartilage zone. This differential response in the degree of lateral expansion was most pronounced during the short time period just after the onset of the stress relaxation. The similar values of Poisson’s ratio obtained for 1.8 and 3.7 mm disks, as well as the transient shape change of the disk (Fig. 4), indicating free relative motion of the cartilage surface along the platen surface, proposes that the friction between these two interfaces may not significantly restrict the lateral expansion of the cartilage disk. A major factor generating differences in the recorded lateral expansion of the cartilage zones may be related to patterns of collagen arrangement and proteoglycan density in the different zones. Since the collagen fibrils of the superficial zone are arranged parallel to the articular surface, this structural organization may produce the highest resistance to lateral expansion, a hypothesis supported by a high lateral tensile stiffness measured in this zone of human weight-bearing patellar groove cartilage, 6.22 i- 1.64 MPa (Akizuki et al., 1986). In the transitional zone collagen fibrils are organized more randomly in relation to both vertical and parallel planes to the 740 J. S. Jurvelin et al. Table 2. Thickness, h, and the elastic parameters (confined compression aggregate modulus. H,; Young’s modulus, Es; Poisson’s ratio, us) for the bovine humeral cartilage derived from the equilibrium response of the mechanical measurements (confined and unconfined compression. IT = 7) or from the microscopic analyses (n = 9) Mechanical Microscopic analysis analysis h (mm) H, (MPa) Es(MPa) 0.95 * 0.33* 1.20 +- 0.23 0.754 * 0.198 0.677 i 0.223 surface, whereas in the radial zone, the collagen fibrils are organized perpendicularly to the subchondral bonecartilage interface, adhering the matrix to subchondral bone (Meachim and Stockwell 1979). The axial arrangement of the fibrils in the radial zone may create a relatively low resistance to lateral shape change, consistent with a relatively low lateral tensile stiffness measured in this zone 0.93 + 0.42 MPa (Akizuki et al., 1986). In the normal, functioning joint, bonding of the cartilage layer to subchondral bone provides a mechanism, which effectively restricts the lateral expansion. Therefore, the degree of lateral expansion in different zones seems to be inversely related to tensile stiffness of the layer. As suggested earlier (Kim et al., 1995; McCutchen, 1987; Mizrahi et al., 1986), the role of collagen as a restrictor of shape change may be enhanced when high loading rates are used and cartilage starts to behave like an incompressible (u = 0.50) elastic material. Another important depth-dependent structural inhomogeneity is the concentration of proteoglycan. An approximately monotonic increase of PG concentration from the articular surface to the radial zone has been described for mature articular cartilage (Jones et al., 1977; Kiviranta et al., 1985). While the concentration and orientation of collagen fibrils may primarily dominate (lateral) tensile stiffness, PG concentration can strongly influence both the hydraulic premeability, and the (axial) compressive stiffness through the generation of repulsive electrostatic swelling forces between glycosaminoglycan chains (Maroudas and Bannon, 1981; Buschmann and Grodzinsky, 1995). Hence, under fast loads, the high, essentially volume conserving lateral expansion of the cartilage zones may be a consequence of both axial compressive stiffness, controlled by the PGs, and lateral tensile stiffness, controlled by the collagen in that region. In summary, our novel optical measurement of Poisson’s ratio for mature bovine humeral articular cartilage has provided a model-independent estimation of this important material parameter. The resulting values agree well with those found indirectly by comparing equilibrium confined and unconfined compression responses of the same disk. The optical method provides new information for the characterization of tissue mechanical behavior. It can provide a quantitative measure of the expansion and recoil of this biphasic material as well as precise information regarding the depth dependence of this response. Our experimental results on early time response highlight a significant role of depth-dependent structure and composition in this mature tissue in controlling its mechanical behavior and potentially influencing the distribution of intratissue deformation and stress under physiological dynamic loading conditions. ‘5 0.174 i 0.106 0.185 i- 0.065 Acknowledgements-The skillful technical assistance of Mr Urs Rohrer. Mr Erland Miihlheim and Mr Oliver Kaupp is acknowledged. This work was supported by grants from the Swiss National Science Foundation, the M. E. Miiller Foundation. Switzerland. The Medical Research Council of Canada, and the Finnish Research Council for Physical Education and Sports, Ministry of Education. Finland. REFERENCES Akizuki, S., Mow, V. C.. Miiller, F.. Pita, J. C., Howell, D. S. and Manicourt D. H. (1986) Tensile properties of human knee joint cartilage: I. Influence of ionic conditions, weight bearing, and fibrillation on the tensile modulus. J. orrhop. Res. 4, 379-392. Altman, R. D., Tenenbaum, J., Latta, L., Riskin, W., Blanco, L. N. and Howell, D. S. (1984) Biomechanical and biochemical properties of dog cartilage in experimentally induced osteoarthritis. Ann. Rheum. Dis. 43, 83-90. Armstrong, C. G.. Lai, W. M. and Mow, V. C. (1984) An analysis of the unconfined compression of articular cartilage. J. biomech. Engng 106, 165-173. Athanasiou, K. A.. Rosenwasser, M. P.. Buckwalter. J. A., Malinin, T. I. and Mow, V. C. (1991) Interspecies comparisons of in situ intrinsic mechanical properties of distal femoral cartilage. J. orthop. Rex 9, 330-340. Athanasiou, K. A., Agarawal, A. and Dzida, F. J. (1994) Comparative study of the intrinsic mechanical properties of the human acetabular and femoral head cartilage. J. orthop. Rex 12, 340-349. Benninghof, A. (1922) Uber den funktionellen Bau des Knorpels. Vrrh. Anat. Gesellsch. 55, 250-267. Biot, M. A. (1941) General theory of three-dimensional consolidation. J. Appl. Phys. 12, 155.-164. Brown, T. D. and Singermann, R. J. (1986) Experimentai determination of the linear biphasic constitutive coefficients of human fetal proximal femoral chondroepiphysis. J. Biomechanics 19, 597-605. Buschmann, M. D. and Grodzinsky. A. J. (1995) A molecular model of proteoglycan-associated electrostatic forces in cartilage mechanics. J. biomech. Engng 117, 1799192. Buschmann, M. D., Jurvelin, J. S. and Hunziker. E. B. (1995) Comparison of sinusoidal and stress relaxation measurements of cartilage in confined compression: The biphasic poroelastic model and the role of the porous compressing platen. Trans. orthop. Rex Sot. 20, 521. Cohen, B., Gardner, T. R. and Ateshian, G. (1993) The influence of transverse isotropy on cartilage indentation behavior. A study of the human humeral head. Trans. orthop. Res. Sot. 18, 185. Cohen, B., Lai, W. M., Chorney, G. S., Dick, H. M. and Mow, V. C. (1992) Unconfined compression of transversely isotropic biphasic tissues. Ado. Bioengng ASME 22, 187-190. Ebara, S., Kellar, R., Bigliani, L. U., Pollock, R. G., Pawluk, R. J., Flatow, E. L., Ratcliffe, A. and Mow, V. C. (1994) Bovine glenoid cartilage is less stiff than humeral head cartilage in tension. Trans. orthop. Res. Sot. 40, 146. Frank, E. H. and Grodzinsky, A. J. (1987) Cartilage electromechanics-II. A continuum model of cartilage electrokinetics and correlation with experiments. J. Biomechanics 20. 629-639. Hale, J. E., Rudert, M. J. and Brown, T. D. (1993) Indentation assessment of biphasic mechanical property deficits in size-dependent osteochondral defect repair. J. Biomechanics 26, 1319-l 325. Hayes, W. C., Keer, L. M., Herrman, G. and Mockros, L. F. (1972) A mathematical analysis for indentation tests of articular cartilage. J. Biomechanics 5, 541-551. Hayes. W. C. and Mockros. L. F. (1971) Viscoelastic properties of human articular cartilage. J. “ppl. Physiol. 31, 562 -56X. Optical and mechanical determination of Poisson’s ratio Hoch, D. II., Grodzinsky, A. J.,Koob, T. J., Albert, M. L. and Eyre, D. R. (1983) Early changes in the material properties of rabbit articular cartilage after meniscectomy. J. orthop. Res. 1, 4-12. Hori, R. and Mockros, L. F. (1976) Indentation tests of human articular cartilage. J. ~jo~ec~un~c~ 9, 259-268. Hunziker, E. B. (1992) Articular cartilage structure in humans and experimental animals. In Artier&r C~~~~~~ge and Osteourf~~~fi~ (Edited by Kuettner, K. E.. Schleyerbach, R., Peyron, 3. G. and Hascall, V. C.), pp. 183-199. Raven Press, New York. Jones, 1. L., Larsson. S. -E. and Lemperg, R. (1977) The glycosaminoglycans of human articular cartilage: concentration and distribution in different layers in the adult individuals. C/in. Orthop. rel Res. 127, 251- 264. Jurvelin, J.. Kiviranta, I., Arokoski, J., Tammi, M. and Helminen, H. J. (1987) Indentation study of the biomechanical properties of articular cartilage in the canine knee. Enyny Med. 16, 15-22. Kempson, G. E. (1971) The determination of a creep modulus for articular cartilage from indentation tests on the human femoral head. J. Biotnechanics 4, 239-250. Kim, Y. -J., Bonassar. J. and Grodzinsky, A. J. (1995) The role of cartilage streaming potential, fluid flow and pressure in the stimulation of chondrocyte biosynthesis during dynamic compression. J. Biornechrics 28, 1055-1066. Kiviranta, I., Jurvelin. J.,Tammi, M., Saamanen, A. -M. and Helminen, H. J. (1985) M~crospectrophotometric quantitation ofglycosaminogiycans in articular cartilage sections stained with Safranin 0. Histo~~e~istr~ 82, 2499255. Lipshitz, H., Etheredge, R. and Gilmcher: M. J. (1975) fn r&o wear in articular cartilage. I. Hydrox~roline, hexosamine and amino acid composition of bovine articular cartilage as a function of depth from the surface; hydroxyproline content of the lubricant and the wear debris as a measure of wear. 1. Bme Jt Sury. 57A, 527-534. McCutchen, C. W. (1987) Comment on “Experimental determination of the linear biphasic constitutive coefficients of human fetal proximal femoral chondroepiphysis”. J. Biomechanics 20, 691. Mak, A. F. (1987) The apparent viscoelastic behavior of articular cartilage: the contributions from the intrinsic matrix viscoelasticity and interstitial Auid flows. J. biomech Engng 108, 123-130. Mak. A. F., Lai. W. M. and Mow, V. C. (1987) Biphasic indentation of articular cartilage--I. Theoretical analysis. J. Biomechanics 20, 703%714. 241 Maroudas, A. and Bannon C. (1981) Measurement of swelling pressure in cartilage and comparison with the osmotic pressure of constituent proteoglycans. Biorheology 18, 6199632. Meachim, G. and Stockwelt, R. A. (19793 The chondrocytes. In Adult Arricufur Cartilage (Edited by Freeman, M. A. R.) pp. t-50. Pitman Medical, Kenth. Mizrahi, J., Maroudas, A., Lanir, Y., Ziv, I. and Webber, T. J. ( 1986) The ~‘instantaneous” deformation of cartilage: effects of collagen fiber orientation and osmotic stress. Bjur~eo~o~~ 23, 31 l-330. Mow. V. C., Gibbs, M. C., Lai, W. M., Zhu, W. B. and Athanasiou, K. A. (1989) Biphasic indentation of articular cartilage-II. A numerical algorithm and an experimental study. J. Biomechanics 22, 853-861. Mow. V. C.. Kuei. S. C., Lai. W. M. and Armstrons. C. G. (1980) Biphasic creep and stress relaxation of articular cartil&e in compres: sion: theory and experiments. J. biomech. Engnq 102, 73- 84. Mow, V. C., Ratcliffe, A. and Poole, A. R. (1992) Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures. Biornateria~s 13, 67-97. Muir, H., Bullough, P. and Maroudas, A. (1970) The distribution of collagen in human articular cartilage with some of its physiological implications. J. Bone Jt Surg. 52B, 554-563. Parsons, J. R. and Black, J. (1977) The viscoelastic shear behavior of normal rabbit articular cartilage. J. Biomechanics 10, 21-29. Poole, C. A. (1993) The structure and function of articular cartilage matrices. In Joint Cartilage ~~gr~du~jon. Basic and Clinictrl Aspects. (Edited by Woessner, J. F. J. and Howell, D. S.). pp. l--35. Marcel Dekker, New York. Schenk, R. C., Athanasiou. K. A., Constantinides, G. and Gomez, E. (1994) A biomechanical analysis of articular cartilage of the human elbow and a potential relationship to osteochondritis dissecans. Clin. Orthop. rei. Res. 299, 305-312. Setton. L. A., Mow, V. C., Miiller, F. J.. Pita, J. C. and Howell, D. S. (1994) Mechanical properties of canine articular cartilage are significantly altered following transection of the anterior cruciate ligament. J. orthop. Rex 12, 451-463. Speer, D. P. and Dahners, L. (1979) The collagcneous architecture of articular cartilage. Correlation of scanning electron microscopy and polarized light microscopy observations. C/in. Orrhop. rd. Res. 139, 261-275. Spilker, R. L., Suh, J. -K. and Mow, V. C. (1990) Effects of friction on the unconfined compressive response of articular cartilage: a finite element analysis. J. biomech. Engng 112, 138- 146.

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Poisson’s ratio of articular cartilage:
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POISSON’S RATIO OF ARTICULAR CARTILAGE

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Introduction.
Cartilage is a layered tissue which is softer and a little more flexible than bone. It is non-uniform
and takes the direction or shape of the bone. For mathematical research, collagen is usually modelled as a
similar tissue to ease the computational process. Indentation has used in a test the matrix, and its malleable
nature makes it be considered as more relevant to the physiological condition. Collagen supply's tissue with
resistance to malleable loading, contributing to anisotropic effects which are evident as a contingency of
soft behavior on positioning concerning the structure of collagen. The biphasic theory has been used once
and again in the analysis of confined compression behavior of collagen (Frank, & Grodzinsky,1987; Mow
et al., 1980).
However, the unconfined configuration method was not successful. The differences were due to
the challenges that are associated with experimenting. Some of these challenges included, the material used
for one test configuration could not be useful for other tests, and also some of the samples were too small
to be tested by any other methods other than indentation. The biphasic technique has been utilized to extort
all the real variables of the model, through a one indenture measurement. The small Poisson's ratio values
have been verified by using direct analysis in a free compression that will result in a higher young modulus
when compared to that of the unfree compression.
In this research, we introduce a technique of establishing the Poisson’s ratio derived from visual
and automated analyses of soft materials using indentation. This is achieved by recording the visual changes
of the collagen in free geometry and also measuring the stress relaxation in unfree and free compression.
Thro...

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