Determination of Poisson's ratio of articular cartilage by indentation using different-sized indenters

Articular cartilage is often characterized as an isotropic elastic material with no interstitial fluid flow during instantaneous and equilibrium conditions, and indentation testing commonly used to deduce material properties of Young's modulus and Poisson's ratio. Since only one elastic parameter can be deduced from a single indentation test, some other test method is often used to allow separate measurement of both parameters. In this study, a new method is introduced by which the two material parameters can be obtained using indentation tests alone, without requiring a secondary different type of test. This feature makes the method more suitable for testing small samples in situ. The method takes advantages of the finite layer effect. By indenting the sample twice with different-sized indenters, a nonlinear equation with the Poisson's ratio as the only unknown can be formed and Poisson's ratio obtained by solving the nonlinear equation. The method was validated by comparing the predicted Poisson's ratio for urethane rubber with the manufacturer's supplied value, and comparing the predicted Young's modulus for urethane rubber and an elastic foam material with modulii measured by unconfined compression. Anisotropic and nonhomogeneous finite-element (FE) models of the indentation were developed to aid in data interpretation. Applying the method to bovine patellar cartilage, the tissue Young's modulus was found to be 1.79 +/- 0.59 MPa in instantaneous response and 0.45 +/- 0.26 MPa in equilibrium, and the Poisson's ratio 0.503 +/- 0.028 and 0.463 +/- 0.073 in instantaneous and equilibrium, respectively. The equilibrium Poisson's ratio obtained in our work was substantially higher than those derived from biphasic indentation theory and those optically measured in an unconfined compression test. The finite element model results and examination of viscoelastic-biphasic models suggest this could be due to viscoelastic, inhomogeneity, and anisotropy effects.     

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.     

Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy

Cartilage stiffness was measured ex vivo at the micrometer and nanometer scales to explore structure-mechanical property relationships at smaller scales than has been done previously. A method was developed to measure the dynamic elastic modulus, |E(*)|, in compression by indentation-type atomic force microscopy (IT AFM). Spherical indenter tips (radius = approximately 2.5 microm) and sharp pyramidal tips (radius = approximately 20 nm) were employed to probe micrometer-scale and nanometer-scale response, respectively. |E(*)| values were obtained at 3 Hz from 1024 unloading response curves recorded at a given location on subsurface cartilage from porcine femoral condyles. With the microsphere tips, the average modulus was approximately 2.6 MPa, in agreement with available millimeter-scale data, whereas with the sharp pyramidal tips, it was typically 100-fold lower. In contrast to cartilage, measurements made on agarose gels, a much more molecularly amorphous biomaterial, resulted in the same average modulus for both indentation tips. From results of AFM imaging of cartilage, the micrometer-scale spherical tips resolved no fine structure except some chondrocytes, whereas the nanometer-scale pyramidal tips resolved individual collagen fibers and their 67-nm axial repeat distance. These results suggest that the spherical AFM tip is large enough to measure the aggregate dynamic elastic modulus of cartilage, whereas the sharp AFM tip depicts the elastic properties of its fine structure. Additional measurements of cartilage stiffness following enzyme action revealed that elastase digestion of the collagen moiety lowered the modulus at the micrometer scale. In contrast, digestion of the proteoglycans moiety by cathepsin D had little effect on |E(*)| at the micrometer scale, but yielded a clear stiffening at the nanometer scale. Thus, cartilage compressive stiffness is different at the nanometer scale compared to the overall structural stiffness measured at the micrometer and larger scales because of the fine nanometer-scale structure, and enzyme-induced structural changes can affect this scale-dependent stiffness differently.     

Topographical variation of the elastic properties of articular cartilage in the canine knee

Equilibrium response of articular cartilage to indentation loading is controlled by the thickness (h) and elastic properties (shear modulus, mu, and Poisson's ratio, nu) of the tissue. In this study, we characterized topographical variation of Poisson's ratio of the articular cartilage in the canine knee joint (N=6). Poisson's ratio was measured using a microscopic technique. In this technique, the shape change of the cartilage disk was visualized while the cartilage was immersed in physiological solution and compressed in unconfined geometry. After a constant 5% axial strain, the lateral strain was measured during stress relaxation. At equilibrium, the lateral-to-axial strain ratio indicates the Poisson's ratio of the tissue. Indentation (equilibrium) data from our prior study (Arokoski et al., 1994. International Journal of Sports Medicine 15, 254-260) was re-analyzed using the Poisson's ratio results at the test site to derive values for shear and aggregate moduli. The lowest Poisson's ratio (0.070+/-0.016) located at the patellar surface of femur (FPI) and the highest (0.236+/-0.026) at the medial tibial plateau (TMI). The stiffest cartilage was found at the patellar groove of femur (micro=0.964+/-0.189MPa, H(a)=2.084+/-0. 409MPa) and the softest at the tibial plateaus (micro=0.385+/-0. 062MPa, H(a)=1.113+/-0.141MPa). Comparison of the mechanical results and the biochemical composition of the tissue (Jurvelin et al., 1988. Engineering in Medicine 17, 157-162) at the matched sites of the canine knee joint indicated a negative correlation between the Poisson's ratio and collagen-to-PG content ratio. This is in harmony with our previous findings which suggested that, in unconfined compression, the degree of lateral expansion in different tissue zones is related to collagen-to-PG ratio of the zone.     

Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study

Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.     

Effect of specimen thickness on fracture toughness of bovine patellar cartilage

Fracture toughness and crack tip opening angle were measured for bovine patellar cartilage using modified single-edged notch specimens of two thicknesses. There was no difference in fracture toughness between thin (0.7 mm) versus relatively thick (2.7 mm) specimens, but the crack tip opening angle at initiation of crack propagation was larger for the thin specimens (106 deg) than for the thick specimens (70 deg). Fracture toughness of the bovine patellar cartilage (1.03 kJ/m2) was not statistically different than that reported previously for canine patellar cartilage (1.07 kJ/m2) employing the same methods. Large variation in measurements for both bovine and canine cartilage are in part attributable to variation between individual animals, and are consistent with variation in other mechanical property measurements for articular cartilage. The observed reduction in crack tip opening angle with increased specimen thickness is consistent with behavior of some engineering materials, and demonstrates that specimen thickness influences fracture behavior for bovine patellar cartilage.     

Estimation of the Young's modulus of articular cartilage using an arthroscopic indentation instrument and ultrasonic measurement of tissue thickness

We evaluated whether the use of cartilage thickness measurement would improve the ability of the arthroscopic indentation technique to estimate the intrinsic stiffness of articular cartilage. First, cartilage thickness and ultrasound reflection from the surface of bovine humeral head were registered in situ using a high-frequency ultrasound probe. Subsequently, cartilage was indented in situ at the sites of the ultrasound measurements using arthroscopic instruments with plane-ended and spherical-ended indenters. Finally, full-thickness cartilage disks (n=30) were extracted from the indented sites (thickness=799-1654microm) and the equilibrium Young's modulus was determined with a material testing device in unconfined compression geometry. We applied analytical and numerical indentation models for the theoretical correction of experimental indentation measurements. An aspect-ratio (the ratio of indenter radius to cartilage thickness) correction improved the correlation of the indenter force with the equilibrium Young's modulus from r(2)=0.488 to r(2)=0.642-0.648 (n=30) for the plane-ended indenter (diameter=1.000mm, height=0.300mm) and from r(2)=0.654 to r(2)=0.684-0.692 (n=30) for the spherical-ended indenter (diameter=0.500mm, height=0.100mm), depending on the indentation model used for the correction. The linear correlation between the ultrasound reflection and the Young's modulus was r(2)=0.400 (n=30). These results suggest that with large indenters, knowledge of the cartilage thickness improves the reliability of the indentation measurements, especially in pathological situations where cartilage thickness may be significantly lower than normal. Ultrasound measurements also provide diagnostically important information about cartilage thickness as well as knowledge of the integrity of the superficial zone of cartilage.     

Microscale frictional response of bovine articular cartilage from atomic force microscopy

The objective of this study was to compare micro- and macroscale friction coefficients of bovine articular cartilage. Microscale measurements were performed using standard atomic force microscopy (AFM) techniques, using a 5 microm spherical probe tip. Twenty-four cylindrical osteochondral plugs were harvested in pairs from adjacent positions in six fresh bovine humeral heads (4-6 months old), and divided into two groups for AFM and macroscopic friction measurements. AFM measurements of friction were observed to be time-independent, whereas macroscale measurements demonstrated the well-documented time-dependent increase from a minimum to an equilibrium value. The microscale AFM friction coefficient (mu(AFM), 0.152+/-0.079) and macroscale equilibrium friction coefficient (mu(eq), 0.138+/-0.036) exhibited no statistical differences (p=0.50), while the macroscale minimum friction coefficient (mu(min), 0.004+/-0.001) was significantly smaller than mu(eq) and mu(AFM) (p<0.0001). Variations in articular surface roughness (Rq= 462+/-216 nm) did not correlate significantly with mu(AFM), mu(eq) or mu(min). The effective compressive modulus determined from AFM indentation tests using a Hertz contact analysis was E*=45.8+/-18.8 kPa. The main finding of this study is that mu(AFM) is more representative of the macroscale equilibrium friction coefficient, which represents the frictional response in the absence of cartilage interstitial fluid pressurization. These results suggest that AFM measurements may be highly suited for exploring the role of boundary lubricants in diarthrodial joint lubrication independently of the confounding effect of fluid pressurization to provide greater insight into articular cartilage lubrication.     

Ultrasound indentation of bovine knee articular cartilage in situ

We have earlier developed a handheld ultrasound indentation instrument for the diagnosis of articular cartilage degeneration. In ultrasound indentation, cartilage is compressed with the ultrasound transducer. Tissue thickness and deformation are calculated from the A-mode ultrasound signal and the stress applied is registered with the strain gauges. In this study, the applicability of the ultrasound indentation instrument to quantify site-dependent variation in the mechano-acoustic properties of bovine knee cartilage was investigated. Osteochondral blocks (n=6 per site) were prepared from the femoral medial condyle (FMC), the lateral facet of the patello-femoral groove (LPG) and the medial tibial plateau (MTP). Cartilage stiffness (dynamic modulus, E(dyn)), as obtained with the ultrasound indentation instrument in situ, correlated highly linearly (r=0.913, p<0.01) with the values obtained using the reference material-testing device in vitro. Reproducibility (standardized coefficient of variation) of the ultrasound indentation measurements was 5.2%, 1.7% and 3.1% for E(dyn), ultrasound reflection coefficient of articular surface (R) and thickness, respectively. E(dyn) and R were site dependent (p<0.05, Kruskall-Wallis H test). E(dyn) was significantly higher (p<0.05, Kruskall-Wallis Post Hoc test) in LPG (mean+/-SD: 10.1+/-3.1MPa) than in MTP (2.9+/-1.4MPa). In FMC, E(dyn) was 4.6+/-1.3MPa. R was significantly (p<0.05) lower at MTP (2.0+/-0.7%) than at other sites (FMC: 4.2+/-0.9%; LPG: 4.4+/-0.8%). Cartilage glycosaminoglycan concentration, as quantified with the digital densitometry, correlated positively with E(dyn) (r=0.678, p<0.01) and especially with the equilibrium Young's modulus (reference device, r=0.874, p<0.01) but it was not associated with R (r=0.294, p=0.24). We conclude that manual measurements are reproducible and the instrument may be used for detection of cartilage quality in situ. Especially, combined measurement of thickness, E(dyn) and R provides valuable diagnostic information on cartilage status.     

Comparison of single-phase isotropic elastic and fibril-reinforced poroelastic models for indentation of rabbit articular cartilage

Classically, single-phase isotropic elastic (IE) model has been used for in situ or in vivo indentation analysis of articular cartilage. The model significantly simplifies cartilage structure and properties. In this study, we apply a fibril-reinforced poroelastic (FRPE) model for indentation to extract more detailed information on cartilage properties. Specifically, we compare the information from short-term (instantaneous) and long-term (equilibrium) indentations, as described here by IE and FRPE models. Femoral and tibial cartilage from rabbit (age 0–18 months) knees (n=14) were tested using a plane-ended indenter (diameter=0.544 mm). Stepwise creep tests were conducted to equilibrium. Single-phase IE solution for indentation was used to derive instantaneous modulus and equilibrium (Young's) modulus for the samples. The classical and modified Hayes’ solutions were used to derive values for the indentation moduli. In the FRPE model, the indentation behavior was sample-specifically described with three material parameters, i.e. fibril network modulus, non-fibrillar matrix modulus and permeability. The instantaneous and fibril network modulus, and the equilibrium Young's modulus and non-fibrillar matrix modulus showed significant (p<0.01) linear correlations of R²=0.516 and 0.940, respectively (Hayes’ solution) and R²=0.531 and 0.960, respectively (the modified Hayes’ solution). No significant correlations were found between the non-fibrillar matrix modulus and instantaneous moduli or between the fibril network modulus and the equilibrium moduli. These results indicate that the instantaneous indentation modulus (IE model) provides information on tensile stiffness of collagen fibrils in cartilage while the equilibrium modulus (IE model) is a significant measure for stiffness of PG matrix. Thereby, this study highlights the feasibility of a simple indentation analysis.     

Intrinsic mechanical properties of trabecular calcaneus determined by finite-element models using 3D synchrotron microtomography

To determine intrinsic mechanical properties (elastic and failure) of trabecular calcaneus bone, chosen as a good predictor of hip fracture, we looked for the influence of image's size on a numerical simulation. One cubic sample of cancellous bone (9 x 9 x 9 mm(3)) was removed from the body of the calcaneus (6 females, 6 males, 79+/-9 yr). These samples were tested under compressive loading. Before compressive testing, these samples were imaged at 10.13 microm resolution using a 3D microcomputed tomography (muCT) (ESRF, France). The muCT images were converted to finite-element models. Depending on the bone density values (BV/TV), we compared two different finite element models: a linear hexahedral and a linear beam finite element models. Apparent experimental Young's modulus (E(app)(exp)) and maximum apparent experimental compressive stress (sigma(max)(exp)) were significantly correlated with bone density obtained by Archimedes's test (E(app)(exp)=236+/-231 MPa [19-742 MPa], sigma(max)(exp)=2.61+/-1.97 MPa [0.28-5.81 MPa], r>0.80, p<0.001). Under threshold at 40 microm, the size of the numerical samples (5.18(3) and 6.68(3)mm(3)) seems to be an important parameter on the accuracy of the results. The numerical trabecular Young's modulus was widely higher (E(trabecular)(num)=34,182+/-22,830 MPa [9700-87,211 MPa]) for the larger numerical samples and high BV/TV than those found classically by other techniques (4700-15,000 MPa). For rod-like bone samples (BV/TV<12%, n=7), Young's modulus, using linear beam element (E(trabecular)(num-skeleton): 10,305+/-5500 MPa), were closer to the Young's modulus found by other techniques. Those results show the limitation of hexahedral finite elements at 40 microm, mostly used, for thin trabecular structures.     

Direct measurement of the Poisson's ratio of human patella cartilage in tension

Articular cartilage has been shown to exhibit large transverse contractions when loaded in tension, suggesting the existence of large values for the Poisson's ratio. Previous studies have suggested that this effect is dependent on amplitude of applied strain, so that a single Poisson's ratio may not be sufficient to describe cartilage behavior. In this study, the Poisson's ratio (v), toe region modulus (Eo), and linear region modulus (E) of human patellar articular cartilage were calculated in simple tension tests from optical analysis of the two-dimensional strain fields at equilibrium. The Poisson's ratio was found to be independent of strain due to the absence of viscoelastic effects during testing. The Poisson's ratio was found to be significantly higher in the surface zone (1.87 +/- 1.11, p<0.01) than in the middle zone (0.62 +/- 0.23), with no significant correlation of v with age of the cartilage. In general, values for Poisson's ratio were greater than 0.5, suggesting cartilage behavior in tension deviates from isotropy. Reported values for the Poisson's ratio of cartilage in compression have been much lower than values measured here in tension, reflecting a mechanical contribution of the collagen fibers to anisotropy in tension but not compression. The toe-region modulus (Eo) was significantly higher in the surface zone (4.51 +/- 2.78 MPa, n=8) compared to the middle zone (2.51 +/- 1.93 MPa, n=10). In addition, the linear-region modulus (E) in the surface zone, but not middle zone (3.42 +/- 2.17 MPa, n=10), was found to correlate with age (R=0.97, p<0.02) with values of surface zone E equal to 23.92 +/- 12.29 MPa (n=5) for subjects under 70 yr of age, and 4.27 +/- 2.89 MPa (n=3) for subjects over 70 yr. Moduli values and trends with depth were consistent with previous studies of human and animal cartilage. From direct measures of two independent material properties, v and E, we calculated a shear modulus, G, which had not been previously reported for cartilage from tensile testing. Calculated values for surface zone G were 3.64 +/- 1.80 MPa for subjects under 70 yr old and 0.96 +/- 0.69 MPa for subjects over 70 yr old, and were significantly higher in the surface zone than in the middle zone (1.10 +/- 0.78 MPa). This study provides an intrinsic measure for the Poisson's ratio of articular cartilage and its dependence on depth which will be important in understanding the nonlinear tension-compression and anisotropic behaviors of articular cartilage.     

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.     

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.     

Indentation stiffness of young canine knee articular cartilage—Influence of strenuous joint loading

The indentation stiffness of knee articular cartilage subjected to strenuous physical training (SPT: treadmill running 20 km day⁻¹ for 15 weeks, n = 6) of young Beagles was tested and compared to that obtained from age-matched (55 weeks, n = 9) controls. The mathematical solution for the shear modulus, as determined from indentation of an elastic layer bonded to a rigid half space, was extended to small Poisson's ratios and applied to the analysis of cartilage response after a step stress (0.39 MPa) application. In these measurements with an impervious, plane-ended indenter, the equilibrium deformation was systematically greater than values predicted from the instant response by the linear biphasic theory. Therefore, the accurate determination of Poisson's ratio from the creep curves was not possible. The mean shear modulus (calculated by using the deformation at 900 s after load application and assuming a constant Poisson's ratio of 0.40 for the matrix) of canine knee articular cartilage was 0.37 MPa. While the cartilage thickness was not affected by SPT, the cartilage of the lateral tibial plateau was stiffer (13.3%, p<0.05) than that in controls. However, in the femoral condyles, the stiffness was at the control level or even below. Our results on cartilage structure and properties suggest that SPT, in contrast to our previous findings with moderate training, does not necessarily improve the biological properties of articular cartilage in young animals.     

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

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

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.     

Effect of length of the engineered tendon construct on its structure-function relationships in culture

Constructs containing autogenous mesenchymal stem cells (MSCs) seeded in collagen gels have been used by our group to repair rabbit central patellar tendon defect injuries. Although these cell-gel composites exhibit improved repair biomechanics compared to natural healing, they can be difficult to handle at surgery and lack the necessary stiffness to resist peak in vivo forces early thereafter. MSCs are typically suspended in collagen gels around two posts in the base of a well in a specially designed silicone dish. The distance between posts is approximately the length of the tendon wound site. MSCs contract the gel around the posts prior to removal of the construct for implantation at surgery. We hypothesized that in vitro construct alignment and stiffness might be enhanced in the midregion of the longer construct where the end effects of the posts on the bulk material (St. Venant effects) could be minimized. Rabbit MSCs were seeded in purified bovine collagen gel at 0.04 M cells/mg collagen. The cell-gel mixture was pipetted into silicone dishes having two post-to-post lengths (short: 11 mm and long: 51 mm) but equivalent well widths and depths and post diameters. After 14 days of incubation, tensile stiffness and modulus of the constructs were measured using equivalent grip-to-grip lengths. Collagen fiber orientation index or OI (which measures angular dispersion of fibers) was quantified using small angle light scattering (SALS). Long constructs showed significantly lower angular dispersion vs. short constructs (OI of 41.24 degrees +/-1.57 degrees vs. 48.43 degrees +/-1.27 degrees , mean+/-SEM, p<0.001) with significantly higher linear modulus (0.064+/-0.009 MPa vs. 0.024+/-0.004 MPa, p=0.0022) and linear stiffness (0.031+/-0.005 MPa vs. 0.018+/-0.004 N/mm, mean+/-SEM, respectively, p=0.0404). We now plan to use principles of functional tissue engineering to determine if repairs containing central regions of longer MSC-collagen constructs improve defect repair biomechanics after implantation at surgery.     

Nonlinear tensile properties of bovine articular cartilage and their variation with age and depth

Tensile stiffness of articular cartilage is much greater than its compressive stiffness and plays an essential role even in compressive properties by increasing transient fluid pressures during physiological loading. Recent studies of nonlinear properties of articular cartilage in compression revealed several physiologically pertinent nonlinear behaviors, all of which required that cartilage tensile stiffness increase significantly with stretch. We therefore performed sequences of uniaxial tension tests on fresh bovine articular cartilage slices using a protocol that allowed several hours to attain equilibrium and measured longitudinal and transverse tissue strain. By testing bovine cartilage from different ages (6 months to 6 years) we found that equilibrium and transient tensile modulus increased significantly with maturation and age, from 0 to 15 MPa at equilibrium and from 10 to 28 MPa transiently. Our results indicate that cartilage stiffens with age in a manner similar to other highly hydrated connective tissues, possibly due to age-dependent content of enzymatic and nonenzymatic collagen cross links. The long relaxation period used in our tests (5-10 hours) was necessary in order to attain equilibrium and avoid a very significant overestimation of equilibrium modulus that occurs when much shorter times are used (15-30 minutes). We also found that equilibrium and transient tensile modulus increased nonlinearly when cartilage is stretched from 0 to 10% strain without any previous tare load. Although our results estimate a nonlinear increase in tensile stiffness with stretch that is an order of magnitude lower than that required to predict nonlinear properties in compression, they are in agreement with previous results from other uniaxial tension tests of collagenous materials. We therefore speculate that biaxial tensile moduli may be much higher and thereby more compatible with observed nonlinear compressive properties.     

In situ friction measurement on murine cartilage by atomic force microscopy

Articular cartilage provides a low-friction, wear-resistant surface for the motion of diarthrodial joints. The objective of this study was to develop a method for in situ friction measurement of murine cartilage using a colloidal probe attached to the cantilever of an atomic force microscope. Sliding friction was measured between a chemically functionalized microsphere and the cartilage of the murine femoral head. Friction was measured at normal loads ranging incrementally from 20 to 100 nN with a sliding speed of 40 microm/s and sliding distance of 64 microm. Under these test conditions, hydrostatic pressurization and biphasic load support in the cartilage were minimized, providing frictional measurements that predominantly reflect boundary lubrication properties. Friction coefficients measured on murine tissue (0.25+/-0.11) were similar to those measured on porcine tissue (0.23+/-0.09) and were in general agreement with measurements of boundary friction on cartilage by other researchers. Using the colloidal probe as an indenter, the elastic mechanical properties and surface roughness were measured in the same configuration. Interfacial shear was found to be the principal mechanism of friction generation, with little to no friction resulting from plowing forces, collision forces, or energy losses due to normal deformation. This measurement technique can be applied to future studies of cartilage friction and mechanical properties on genetically altered mice or other small animals.