Three-axial strain controlled testing applied to bone specimens from the proximal tibial epiphysis

Reproducibility of the determination of Young's modulus and energy absorption along the three axes of trabecular bone cubes was analysed by non-destructive compression to 0.5% strain using different testing protocols. These protocols included testing with and without pre-conditioning to a viscoelastic steady state, and different orders of test directions. Reproducibility of conditioned tests was generally better than that of non-conditioned tests. No major effect of changing the order of the test direction was found. Three-axial conditioned testing of cubes from the proximal tibial epiphysis of five humans revealed a global transverse isotrophy while most cubes showed orthotropy. The ratio between stiffness along the long axis of the tibia and the stiffness in the transverse plane was 3.7 +/- 0.4 (mean +/- 2 SE). The corresponding ratios for elastic energy storage and viscoelastic energy dissipation were 2.5 +/- 0.2. There was no difference between the relative energy loss during a testing cycle (loss tangent) in the three axes.     

X-ray quantitative computed tomography: the relations to physical properties of proximal tibial trabecular bone specimens

Cylindrical bone specimens from the proximal epiphysis of ten normal human proximal tibiae were randomly assigned to a destructive axial compression test-series (N = 94) or to a protocol of standardized mechanical conditioning followed by non-destructive repeated testing to 0.6% strain and a final destructive test (N = 121). Specimen X-ray quantitative computed tomography (QCT) obtained at different scanning energies (100, 120 and 140 kVp) yielded closely related results (r = 1.00). Accordingly, predictions of physically measured densities or mechanical properties were not improved by using more than one scanning energy. QCT and physically measured densities were intimately related (QCT at 140 kVp to apparent density using linear regression: r = 0.94, and to apparent ash density: r = 0.95) and did not differ significantly in their ability to predict the mechanical properties, thus favouring the more easily implemented QCT for routine work. Evaluation of the relation of apparent density to Young's modulus and ultimate strength suggested that a power law regression model is preferable to a linear model, although linear model prediction of mechanical properties does not have significantly worse accuracy within the narrow density range investigated. The effect of conditioning on the behaviour of bone specimens subjected to destructive compression tests was to increase the stiffness and strength by approximately 50 and 20% respectively.     

Mechanical properties of trabecular bone. Dependency on strain rate.

The effect of strain rate (epsilon) and apparent density (rho) on stiffness (E), strength (sigma u), and ultimate strain (epsilon u) was studied in 60 human trabecular bone specimens from the proximal tibia. Testing was performed by uniaxial compression to 5% specimen strain. Six different strain rates were used: 0.0001, 0.001, 0.01, 0.1, 1, and 10 s-1. Apparent density ranged between 0.23 and 0.59 g cm-3. Linear and non-linear regression analyses using strength, stiffness and ultimate strain as dependent variables (Y) and strain rate and apparent density as independent variables were performed using the following models: Y = a rho b epsilon c, Y = rho b(a + c epsilon; Y = (a + b rho)epsilon c, Y = a rho 2 epsilon c, E = a rho 3 epsilon c. The variations of strength and stiffness were explained equally well by the linear and the power function relationship to strain rate. The exponent was 0.07 in the power function relationship between strength and strain rate and 0.05 between stiffness and strain rate. The variation of ultimate strain was explained best using a power function relationship to strain rate (exponent = 0.03). The variation of strength and stiffness was explained equally well by the linear, power function and quadratic relationship to apparent density. The cubic relationship between stiffness and apparent density showed a less good fit. Ultimate strain varied independently of apparent density.     

The effect of constraint on the mechanical behaviour of trabecular bone specimens

The effect of the boundary conditions between trabecular bone specimens and the test columns of the testing machine was studied together with the effect of side-constraint on the mechanical behaviour of trabecular bone during axial compression. Cylindrical specimens taken from the upper tibial epiphysis of autopsy knees were tested non-destructively by cyclic compression to 0.8% strain under different conditions. Fixation of the specimens to the test columns by a thin layer of bone cement increased the stiffness by 40% and reduced the energy dissipation to 67% of those measured under unconstrained conditions (p less than 0.001). The thin cement layer alone increased the stiffness 19% and reduced energy dissipation to 86% (n.s.). When the machine was equipped with polished steel columns coated by a film of low-viscous oil, both the stiffness and the energy dissipation were reduced to 93% of those measured under standard conditions (p less than 0.005). Trabecular bone specimens tested side-constrained by the surrounding trabecular bone (in situ) showed a 19% larger stiffness than that measured during later testing of the corresponding machined specimens (p less than 0.005) whereas the energy dissipation was not altered significantly. The same specimens showed a 22% increase of stiffness and a 68% increase of energy dissipation when they were side-constrained by a closely fitting steel cylinder (p less than 0.005).     

Tensile strength of bovine trabecular bone

Data on the tensile and compressive properties of trabecular bone are needed to define input parameters and failure criteria for modeling total joint replacements. To help resolve differences in reports comparing tensile and compressive properties of trabecular bone, we have developed new methods, based on porous foam technology, for tensile testing of fresh/frozen trabecular bone specimens. Using bovine trabecular bone from an isotropic region from the proximal humerus as a model material, we measured ultimate strengths in tension and compression for two groups of 24 specimens each. The average ultimate strength in tension was 7.6 +/- 2.2 (95% C.I.) MPa and in compression was 12.4 +/- 3.2 MPa. This difference was statistically significant (p = 0.013) and was not related to density differences between the test groups (p = 0.28). Strength was related by a power-law function of the local apparent density, but, even accounting for density influences, isotropic bovine trabecular bone exhibits significantly lower strengths in tension than in compression.     

Viscoelastic properties of passive skeletal muscle in compression—Cyclic behaviour

Skeletal muscle relaxation behaviour in compression has been previously reported, but the anisotropic behaviour at higher loading rates remains poorly understood. In this paper, uniaxial unconfined cyclic compression tests were performed on fresh porcine muscle samples at various fibre orientations to determine muscle viscoelastic behaviour. Mean compression level of 25% was applied and cycles of 2% and 10% amplitude were performed at 0.2–80 Hz. Under cycles of low frequency and amplitude, linear viscoelastic cyclic relaxation was observed. Fibre/cross-fibre results were qualitatively similar, but the cross-fibre direction was stiffer (ratio of 1.2). In higher amplitude tests nonlinear viscoelastic behaviour with a frequency dependent increase in the stress cycles amplitude was found (factor of 4.1 from 0.2 to 80 Hz).The predictive capability of an anisotropic quasi-linear viscoelastic model previously fitted to stress-relaxation data from similar tissue samples was investigated. Good qualitative results were obtained for low amplitude cycles but differences were observed in the stress cycle amplitudes (errors of 7.5% and 31.8%, respectively, in the fibre/cross-fibre directions). At higher amplitudes significant qualitative and quantitative differences were evident. A nonlinear model formulation was therefore developed which provided a good fit and predictions to high amplitude low frequency cyclic tests performed in the fibre/cross-fibre directions. However, this model gave a poorer fit to high frequency cyclic tests and to relaxation tests. Neither model adequately predicts the stiffness increase observed at frequencies above 5 Hz.Together with data previously presented, the experimental data presented here provide a unique dataset for validation of future constitutive models for skeletal muscle in compression.     

HR-pQCT-based homogenised finite element models provide quantitative predictions of experimental vertebral body stiffness and strength with the same accuracy as μFE models

This study validated two different high-resolution peripheral quantitative computer tomography (HR-pQCT)-based finite element (FE) approaches, enhanced homogenised continuum-level (hFE) and micro-finite element (μFE) models, by comparing them with compression test results of vertebral body sections. Thirty-five vertebral body sections were prepared by removing endplates and posterior elements, scanned with HR-pQCT and tested in compression up to failure. Linear hFE and μFE models were created from segmented and grey-level CT images, and apparent model stiffness values were compared with experimental stiffness as well as strength results. Experimental and numerical apparent elastic properties based on grey-level/segmented CT images (N=35) correlated well for μFE (r2=0.748/0.842) and hFE models (r2=0.741/0.864). Vertebral section stiffness values from the linear μFE/hFE models estimated experimental ultimate apparent strength very well (r2=0.920/0.927). Calibrated hFE models were able to predict quantitatively apparent stiffness with the same accuracy as μFE models. However, hFE models needed no back-calculation of a tissue modulus or any kind of fitting and were computationally much cheaper.     

The effects of damage and microcracking on the impact strength of bone

Microcracking has been shown to occur when bone is 'damaged' as shown by a loss of stiffness. The effect on bone's toughness of the types of damage produced at low losses of stiffness are not known. We loaded bovine bone specimens in bending and tension to stiffness losses of up to 27%, and examined the microcracking produced. The tensile specimens had diffuse arrays of microcracks of 2-20 microm in length, characteristic of tensile loading, on all surfaces. The bending specimens showed tensile microcracking on the tensile surface and characteristic long, straight, cross-hatched compression cracks on the compressive surface. Specimens were then broken in impact. Those that had been damaged in bending were divided into two groups, in one group the part of the specimen which had undergone compression damage was placed in tension, and in the other group the tensile damage was placed in tension. Tensile damage loaded in tension did not reduce the bone's energy-absorbing ability in impact until a modulus reduction of over 20%. However compression damage loaded in tension did severely reduce the bone's energy absorption capabilities (by an average of about 40%).     

The mechanical characteristics of cancellous bone at the upper femoral region

Mechanical behaviour of trabecular bone at the upper femoral region of human bones has been studied by compression tests on trabecular bone specimens removed from normal femora obtained at autopsy. Compression tests were performed along three different axes of loading on wet specimens and high loading rates. Femoral head specimens proved to be the strongest for any axis of loading.

Large variation in compressive strength and modulus of elasticity is seen within and between femoral bone samples. Anisotropy and differences in anisotropy for the different regions have been observed. A significant correlation between mechanical properties (σ max − E) and bone mineral content of the specimen was found.

Tests on whole bone structures demonstrate that removal of the central part of the trabecular bone at the proximal femur reduces the strength for impact loading considerably (± 50%).     

Ultrasonic measurement of depth-dependent transient behaviors of articular cartilage under compression

We previously reported an ultrasound method for measuring the depth-dependent equilibrium mechanical properties of articular cartilage using quasi-static compression. The objective of this paper was to introduce our recent development for nondestructively measuring the transient depth-dependent strains of full-thickness articular cartilage specimens prepared from bovine patellae. A 50 MHz focused ultrasound transducer was used to collect ultrasound echoes from articular cartilage specimens (n=8) and sponge phantoms with open pores (n=10) during tests of compression and subsequent stress-relaxation. The transient displacements of the tissues at different depths along the compression direction were calculated from the ultrasound echoes using a cross-correlation tracking technique. An LVDT sensor and a load cell were used to measure the overall deformation of the tissue and the applied force, respectively. Results showed that the tissues inside the cartilage layer continued to move during the stress-relaxation phase after the compression was completed. In the equilibrium state, the displacements of the cartilage tissues at the depths of 1/4, 1/2, and 3/4 of the full-thickness reduced by 51%+/-22%, 54%+/-17%, and 50+/-17%, respectively, in comparison with its peak value. However, no similar phenomenon was observed in the sponge phantoms. Our preliminary results demonstrated that this ultrasound method may provide a potential tool for the nondestructive measurement of the transient depth-dependent processes involved in biological and bioengineered soft tissues as well as soft biomaterials under dynamic loading.     

A patient-specific finite element methodology to predict damage accumulation in vertebral bodies under axial compression, sagittal flexion and combined loads

Due to the inherent limitations of DXA, assessment of the biomechanical properties of vertebral bodies relies increasingly on CT-based finite element (FE) models, but these often use simplistic material behaviour and/or single loading cases. In this study, we applied a novel constitutive law for bone elasticity, plasticity and damage to FE models created from coarsened pQCT images of human vertebrae, and compared vertebral stiffness, strength and damage accumulation for axial compression, anterior flexion and a combination of these two cases. FE axial stiffness and strength correlated with experiments and were linearly related to flexion properties. In all loading modes, damage localised preferentially in the trabecular compartment. Damage for the combined loading was higher than cumulated damage produced by individual compression and flexion. In conclusion, this FE method predicts stiffness and strength of vertebral bodies from CT images with clinical resolution and provides insight into damage accumulation in various loading modes.     

Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage ?1.16 %, tension damage 0.69 %, compression fracture ?2.91 % and tension fracture 1.98 %. Ultimate strength and post–ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile–brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post–ultimate strength softening.     

Femoral stiffness and strength critically depend on loading angle: a parametric study in a mouse-inbred strain

Biomechanical tests of human femora have shown that small variations of the loading direction result in significant changes in measured bone mechanical properties. However, the heterogeneity in geometrical and bone tissue properties does not make human bones well suited to reproducibly assess the effects of loading direction on stiffness and strength. To precisely quantify the influence of loading direction on stiffness and strength of femora loaded at the femoral head, we tested femora from C57BL/6 inbred mice. We developed an image-based alignment protocol and investigated the loading direction influence on proximal femur stiffness and strength. An aluminum femoral phantom and C57BL/6 femora were tested under compression with different loading directions. Both tests, with the aluminum phantom and the murine bones, showed and quantified the linear dependence of stiffness on loading direction: a 5 degrees change in loading direction resulted in almost 30% change in stiffness. Murine bone testing also revealed and quantified the variation in strength due to loading direction: 5 degrees change in loading direction resulted in 8.5% change in strength. In conclusion, this study quantified, for the first time, the influence of misalignment on bone stiffness and strength for femoral head loading. We showed the extreme sensitivity of this site regarding loading direction.     

Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling

At autopsy, 13 nonstenotic human left anterior descending coronary arteries [71.5 +/- 7.3 (mean +/- SD) yr old] were harvested, and related anamnesis was documented. Preconditioned prepared strips (n = 78) of segments from the midregion of the left anterior descending coronary artery from the individual layers in axial and circumferential directions were subjected to cyclic quasi-static uniaxial tension tests, and ultimate tensile stresses and stretches were documented. The ratio of outer diameter to total wall thickness was 0.189 +/- 0.014; ratios of adventitia, media, and intima thickness to total wall thickness were 0.4 +/- 0.03, 0.36 +/- 0.03, and 0.27 +/- 0.02, respectively; axial in situ stretch of 1.044 +/- 0.06 decreased with age. Stress-stretch responses for the individual tissues showed pronounced mechanical heterogeneity. The intima is the stiffest layer over the whole deformation domain, whereas the media in the longitudinal direction is the softest. All specimens exhibited small hysteresis and anisotropic and strong nonlinear behavior in both loading directions. The media and intima showed similar ultimate tensile stresses, which are on average three times smaller than ultimate tensile stresses in the adventitia (1,430 +/- 604 kPa circumferential and 1,300 +/- 692 kPa longitudinal). The ultimate tensile stretches are similar for all tissue layers. A recently proposed constitutive model was extended and used to represent the deformation behavior for each tissue type over the entire loading range. The study showed the need to model nonstenotic human coronary arteries with nonatherosclerotic intimal thickening as a composite structure composed of three solid mechanically relevant layers with different mechanical properties. The intima showed significant thickness, load-bearing capacity, and mechanical strength compared with the media and adventitia.     

Material characterization of human medial collateral ligament.

The objectives of this study were to determine the longitudinal and transverse material properties of the human medial collateral ligament (MCL) and to evaluate the ability of three existing constitutive models to describe the material behavior of MCL. Uniaxial test specimens were punched from ten human cadaveric MCLs and tensile tested along and transverse to the collagen fiber direction. Using load and optical strain analysis information, the tangent modulus, tensile strength and ultimate strain were determined. The material coefficients for each constitutive model were determined using nonlinear regression. All specimens failed within the substance of the tissue. Specimens tested along the collagen fiber direction exhibited the typical nonlinear behavior reported for ligaments. This behavior was absent from the stress-strain curves of the transverse specimens. The average tensile strength, ultimate strain, and tangent modulus for the longitudinal specimens was 38.6 +/- 4.8 MPa, 17.1 +/- 1.5 percent, and 332.2 +/- 58.3 MPa, respectively. The average tensile strength, ultimate strain, and tangent modulus for the transverse specimens was 1.7 +/- 0.5 MPa, 11.7 +/- 0.9 percent, and 11.0 +/- 3.6 MPa, respectively. All three constitutive models described the longitudinal behavior of the ligament equally well. However, the ability of the models to describe the transverse behavior of the ligament varied.     

Kinetics of turnover of cefotaxime by the Enterobacter cloacae P99 and GCl beta-lactamases: two free enzyme forms of the P99 beta-lactamase detected by a combination of pre- and post-steady state kinetics

Third-generation cephalosporins bearing oximino side chains are resistant to hydrolysis by class C beta-lactamases such as that from Enterobacter cloacae P99. For example, steady state parameters for hydrolysis of cefotaxime by this enzyme are as follows: k(cat) = 0.41 s(-1), K(m) = 17.2 microM, and k(cat)/K(m) = 2.3 x 10(4) s(-1) M(-1). On the other hand, however, the K(i) value for cefotaxime as an inhibitor of cephalothin hydrolysis is 27 nM. The discrepancy between K(m) and K(i) indicated that a real steady state had not been achieved in at least one of these experiments. Analysis indicated that only two to three cefotaxime turnovers occurred during the K(i) determination. This suggested that the first few turnovers of cefotaxime by the P99 beta-lactamase may be different from those in the subsequent steady state. A direct pre-steady state experiment confirmed this hypothesis. The simplest reaction scheme that fitted the data involved replacement of the initial enzyme form, E, which bound cefotaxime tightly, with a second more weakly binding form, E', by partitioning of the acyl-enzyme intermediate during the first few turnovers. Steady state turnover of cefotaxime then largely involved E' as the free enzyme form. E' slowly reverted to E in the post-steady state regime. Further evidence for this scheme included quantitative analysis of the post-steady state and observation of a difference in the catalytic activity of E and E' in 2 M ammonium sulfate. The kinetics of P99 beta-lactamase-catalyzed hydrolysis of an acyclic depsipeptide substrate bearing a third-generation cephalosporin side chain showed that the side chain is necessary but not sufficient for production of resistance to beta-lactamase; a combination of the side chain and the dihydrothiazine ring of a cephalosporin is required. The beta-lactamase of E. cloacae GC1, an extended spectrum mutant of the P99 enzyme, rapidly hydrolyzes third-generation cephalosporins, without the structural transition described above. The flexibility of the extended Omega loop of the GC1 enzyme probably leads to this situation. Conformational restriction of the loop in the P99 enzyme is probably responsible for the long-lived acyl-enzyme intermediate and the transition to E' induced by cefotaxime.     

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

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

Biomechanical properties of sterilized human auditory ossicles.

Bone allograft material is treated with sterilization methods to prevent the transmission of diseases from the donor to the recipient. The effect of some of these treatments on the integrity of the bone is unknown. This study was performed to evaluate the effect of several sterilization methods on the mechanical behaviour of human middle ear bones. Due to the size and composition of the bones (approximately 1.5 mm diameter by 4 mm long), mechanical testing options were limited to the traditional platens compression test. Experiments were first performed with synthetic bone to evaluate the precision of this test applied to small specimens. Following this, fresh frozen human ossicles were thawed and sterilized with (i) 1 N NaOH (n = 12); (ii) 0.9% LpH, a phenolic solution (n = 12); or (iii) steam at 134 degrees C (n = 18). A group of 26 control specimens did not receive any sterilization treatment. Material and structural properties were determined from axial compression testing. Results from the synthetic bone showed that the test was reproducible, with standard deviations less than 20% of the means. Significant differences occurred in stiffness and ultimate force values between NaOH-treated and autoclaved bones when compared to normals (p<0.05), but not for LpH-treated bones. LpH is not approved for medical use, so NaOH is the most appropriate of the treatments studied for the sterilization of ossicle allografts.     

The mechanical behavior of PMMA/bone specimens extracted from augmented vertebrae: a numerical study of interface properties, PMMA shrinkage and trabecular bone damage

Recently published compression tests on PMMA/bone specimens extracted after vertebral bone augmentation indicated that PMMA/bone composites were not reinforced by the trabecular bone at all. In this study, the reasons for this unexpected behavior should be investigated by using non-linear micro-FE models. Six human vertebral bodies were augmented with either standard or low-modulus PMMA cement and scanned with a HR-pQCT system before and after augmentation. Six cylindrical PMMA/bone specimens were extracted from the augmented region, scanned with a micro-CT system and tested in compression. Four different micro-FE models were generated from these images which showed different bone tissue material behavior (with/without damage), interface behavior (perfect bonding, frictionless contact) and PMMA shrinkage due to polymerization. The non-linear stress-strain curves were compared between the different micro-FE models as well as to the compression tests of the PMMA/bone specimens. Micro-FE models with contact between bone and cement were 20% more compliant compared to those with perfect bonding. PMMA shrinkage damaged the trabecular bone already before mechanical loading, which further reduced the initial stiffness by 24%. Progressing bone damage during compression dominated the non-linear part of the stress-strain curves. The micro-FE models including bone damage and PMMA shrinkage were in good agreement with the compression tests. The results were similar with both cements. In conclusion, the PMMA/bone interface properties as well as the initial bone damage due to PMMA polymerization shrinkage clearly affected the stress-strain behavior of the composite and explained why trabecular bone did not contribute to the stiffness and strength of augmented bone.     

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

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