Validation of net joint loads calculated by inverse dynamics in case of complex movements: application to balance recovery movements

The joint forces and moments driving the motion of a human subject are classically computed by an inverse dynamic calculation. However, even if this process is theoretically simple, many sources of errors may lead to huge inaccuracies in the results. Moreover, a direct comparison with in vivo measured loads or with "gold standard" values from literature is only possible for very specific studies. Therefore, assessing the inaccuracy of inverse dynamic results is not a trivial problem and a simple method is still required. This paper presents a simple method to evaluate both: (1) the consistency of the results obtained by inverse dynamics; (2) the influence of possible modifications in the inverse dynamic hypotheses. This technique concerns recursive calculation performed on full kinematic chains, and consists in evaluating the loads obtained by two different recursive strategies. It has been applied to complex 3D whole body movements of balance recovery. A recursive Newton-Euler procedure was used to compute the net joint loads. Two models were used to represent the subject bodies, considering or not the upper body as a unique rigid segment. The inertial parameters of the body segments were estimated from two different sets of scaling equations [De Leva, P., 1996. Adjustments to Zatsiorsky-Suleyanov's segment inertia parameters. Journal of Biomechanics 29, 1223-1230; Dumas, R., Chèze, L., Verriest, J.-P., 2006b. Adjustments to McConville et al. and Young et al. Body Segment Inertial Parameters. Journal of Biomechanics, in press]. Using this comparison technique, it has been shown that, for the balance recovery motions investigated: (1) the use of the scaling equations proposed by Dumas et al., instead of those proposed by De Leva, improves the consistency of the results (average relative influence up to 30% for the transversal moment); (2) the arm motions dynamically influence the recovery motion in a non negligible way (average relative influence up to 15% and 30% for the longitudinal force and the transversal moment, respectively).     

An approach for hip joint center calculation for use in seated postures

In seated postures, such as those in office or automotive seats, locating the hip joint center (HJC) using three markers on the pelvis has been difficult if not impossible. A two-target approach by Bell et al. (J. Biomech. 23 (1990) 617) has been used, however, this method was shown to have inaccuracies when compared to the three-target method developed by Seidel et al. (J. Biomech. 28 (1995) 995). A new two-target method that is specific to the seated environment, has better accuracy than the Bell et al. approach, and is based on the Seidel et al. approach was developed and tested on 13 seated subjects. This new method used three targets and an initial reference file to estimate the HJC location. Once the HJC was located, assumptions were made that the magnitudes between the HJC and the respective anterior superior iliac spine, and the HJC and the respective lateral epicondyle remained constant. The primary concern when evaluating this new method was the affect of seated posture movement, in particular leg splay and spinal flexion on the assumptions. The results obtained with the new approach were compared to Seidel et al. and provided HJC locations with average differences of 3.8, 1.2 and 2.8mm for spinal flexion in the anterior/posterior, medial/lateral and superior/inferior directions, respectively, and 2.3, 1.0 and 1.4mm for knee splay. The proposed method provided better HJC estimation than the Bell et al. approach particularly in the superior/inferior dimensions.     

Pelvic function in anuran jumping: Interspecific differences in the kinematics and motor control of the iliosacral articulation during take‐off and landing

Although the anuran pelvis is thought to be adapted for jumping, the function of the iliosacral joint has seen little direct study. Previous work has contrasted the basal “ lateral‐bender ” pelvis from the “ rod‐like ” pelvis of crown taxa hypothesized to function as a sagittal hinge to align the trunk with take‐off forces. We compared iliosacral movements and pelvic motor patterns during jumping in the two pelvic types. Pelvic muscle activity patterns, iliosacral anteroposterior (AP) movements and sagittal bending of the pelvis during the take‐off and landing phases were quantified in lateral bender taxa Ascaphus (Leiopelmatidae) and Rhinella (Bufonidae) and the rod‐like Lithobates (Ranidae). All three species exhibit sagittal extension during take‐off, therefore, both pelvic types employ a sagittal hinge. However, trunk elevation occurs significantly earlier in the anuran rod‐like pelvis. Motor patterns confirm that the piriformis muscles depress the urostyle while the longissimus dorsi muscles elevate the trunk during take‐off. However, the coccygeoiliacus muscles also produce anterior translation of the sacrum on the ilia. A new model illustrates how AP translation facilitates trunk extension in the lateral‐bender anurans that have long been thought to have limited sagittal bending. During landing, AP translation patterns are similar because impact forces slide the sacrum from its posterior to anterior limits. Sagittal flexion during landing differs among the three taxa depending on the way the species land. AP translation during landing may dampen impact forces especially in Rhinella in which pelvic function is tuned to forelimb‐landing dynamics. The flexibility of the lateral‐bender pelvis to function in sagittal bending and AP translation helps to explain the retention of this basal configuration in many anurans. The novel function of the rod‐like pelvis may be to increase the rate of trunk elevation relative to faster rates of energy release from the hindlimbs enabling them to jump farther. J. Morphol. 277:1539–1558, 2016. © 2016 Wiley Periodicals, Inc.     

Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543–548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion–extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.     

Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543-548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion-extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.     

Model transformations to evaluate transient thermal responses at a tissue surface

For a spatially distributed model describing the transient temperature response of a thermistor-tissue system, Wei et al. [J. Biomech. Eng., 117:74-85, 1995] obtained an approximate transformation for fast analysis of the temperature response at the tissue surface. This approximate transformation reduces the model to a single ordinary differential equation. Here, we present an exact transformation that yields a single differential-integral equation. Numerical solutions from the approximate and exact transformations were compared to evaluate the differences with several sets of parameter values. The maximum difference between the exact and approximate solutions did not exceed 15 percent and occurred for only a short time interval. The root-mean-square error of the approximate solution was no more than 5 percent and within the level of experimental noise. Under the experimental conditions used by Wei et al., the approximate transformation is justified for estimating model parameters from transient thermal responses.     

Functional knee axis based on isokinetic dynamometry data: Comparison of two methods, MRI validation, and effect on knee joint kinematics

This paper compares geometry-based knee axes of rotation (transepicondylar axis and geometric center axis) and motion-based functional knee axes of rotation (fAoR). Two algorithms are evaluated to calculate fAoRs: Gamage and Lasenby's sphere fitting algorithm (GL) and Ehrig et al.'s axis transformation algorithm (SARA). Calculations are based on 3D motion data acquired during isokinetic dynamometry. AoRs are validated with the equivalent axis based on static MR-images. We quantified the difference in orientation between two knee axes of rotation as the angle between the projection of the axes in the transversal and frontal planes, and the difference in location as the distance between the intersection points of the axes with the sagittal plane. Maximum differences between fAoRs resulting from GL and SARA were 5.7° and 15.4mm, respectively. Maximum differences between fAoRs resulting from GL or SARA and the equivalent axis were 5.4°/11.5mm and 8.6°/12.8mm, respectively. Differences between geometry-based axes and EA are larger than differences between fAoR and EA both in orientation (maximum 10.6°).and location (maximum 20.8mm). Knee joint angle trajectories and the corresponding accelerations for the different knee axes of rotation were estimated using Kalman smoothing. For the joint angles, the maximum RMS difference with the MRI-based equivalent axis, which was used as a reference, was 3°. For the knee joint accelerations, the maximum RMS difference with the equivalent axis was 20°/s(2). Functional knee axes of rotation describe knee motion better than geometry-based axes. GL performs better than SARA for calculations based on experimental dynamometry.     

Adjustments to McConville et al. and Young et al. body segment inertial parameters

Body segment inertial parameters (BSIPs) are important data in biomechanics. They are usually estimated from predictive equations reported in the literature. However, most of the predictive equations are ambiguously applicable in the conventional 3D segment coordinate systems (SCSs). Also, the predictive equations reported in the literature all include two assumptions: the centre of mass and the proximal and distal endpoints are assumed to be aligned, and the inertia tensor is assumed to be principal in the segment axes. These predictive equations, restraining both position of the centre of mass and orientation of the principal axes of inertia, become restrictive when computing 3D inverse dynamics, when analyzing the influence of BSIP estimations on joint forces and moments and when evaluating personalized 3D BSIPs obtained from medical imaging. In the current study, the extensive data from McConville et al. (1980. Anthropometric relationships of body and body segment moments of inertia. AFAMRL-TR-80-119, Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio) and from Young et al. (1983. Anthropometric and mass distribution characteristics of the adults female. Technical Report AFAMRL-TR-80-119, FAA Civil Aeromedical Institute, Oklaoma City, Oklaoma) are adjusted in order to correspond to joint centres and to conventional segment axes. In this way, scaling equations are obtained for both males and females that provide BSIPs which are directly applicable in the conventional SCSs and do not restrain the position of the centre of mass and the orientation of the principal axes. These adjusted scaling equations may be useful for researchers who wish to use appropriate 3D BSIPs for posture and movement analysis.     

Improving joint torque calculations: optimization-based inverse dynamics to reduce the effect of motion errors

The accuracy of joint torques calculated from inverse dynamics methods is strongly dependent upon errors in body segment motion profiles, which arise from two sources of noise: the motion capture system and movement artifacts of skin-mounted markers. The current study presents a method to increase the accuracy of estimated joint torques through the optimization of the angular position data used to describe these segment motions. To compute these angular data, we formulated a constrained nonlinear optimization problem with a cost function that minimizes the difference between the known ground reaction forces (GRFs) and the GRF calculated via a top-down inverse dynamics solution. To evaluate this approach, we constructed idealized error-free reference movements (of squatting and lifting) that produced a set of known “true” motions and associated true joint torques and GRF. To simulate real-world inaccuracies in motion data, these true motions were perturbed by artificial noise. We then applied our approach to these noise-induced data to determine optimized motions and related joint torques. To evaluate the efficacy of the optimization approach compared to traditional (bottom-up or top-down) inverse dynamics approaches, we computed the root mean square error (RMSE) values of joint torques derived from each approach relative to the expected true joint torques. Compared to traditional approaches, the optimization approach reduced the RMSE by 54% to 79%. Average reduction due to our method was 65%; previous methods only achieved an overall reduction of 30%. These results suggest that significant improvement in the accuracy of joint torque calculations can be achieved using this approach.     

Regional left ventricular myocardial contractility and stress in a finite element model of posterobasal myocardial infarction

Recently, a noninvasive method for determining regional myocardial contractility, using an animal-specific finite element (FE) model-based optimization, was developed to study a sheep with anteroapical infarction (Sun et al., 2009, "A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm," ASME J. Biomech. Eng., 131(11), p. 111001). Using the methodology developed in the previous study (Sun et al., 2009, "A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm," ASME J. Biomech. Eng., 131(11), p. 111001), which incorporates tagged magnetic resonance images, three-dimensional myocardial strains, left ventricular (LV) volumes, and LV cardiac catheterization pressures, the regional myocardial contractility and stress distribution of a sheep with posterobasal infarction were investigated. Active material parameters in the noninfarcted border zone (BZ) myocardium adjacent to the infarct (T(max_B)), in the myocardium remote from the infarct (T(max_R)), and in the infarct (T(max_I)) were estimated by minimizing the errors between FE model-predicted and experimentally measured systolic strains and LV volumes using the previously developed optimization scheme. The optimized T(max_B) was found to be significantly depressed relative to T(max_R), while T(max_I) was found to be zero. The myofiber stress in the BZ was found to be elevated, relative to the remote region. This could cause further damage to the contracting myocytes, leading to heart failure.     

Effects of tension-compression nonlinearity on solute transport in charged hydrated fibrous tissues under dynamic unconfined compression

Cartilage is a charged hydrated fibrous tissue exhibiting a high degree of tension-compression nonlinearity (i.e., tissue anisotropy). The effect of tension-compression nonlinearity on solute transport has not been investigated in cartilaginous tissue under dynamic loading conditions. In this study, a new model was developed based on the mechano-electrochemical mixture model [Yao and Gu, 2007, J. Biomech. Model Mechanobiol., 6, pp. 63-72, Lai et al., 1991, J. Biomech. Eng., 113, pp. 245-258], and conewise linear elasticity model [Soltz and Ateshian, 2000, J. Biomech. Eng., 122, pp. 576-586; Curnier et al., 1995, J. Elasticity, 37, pp. 1-38]. The solute desorption in cartilage under unconfined dynamic compression was investigated numerically using this new model. Analyses and results demonstrated that a high degree of tissue tension-compression nonlinearity could enhance the transport of large solutes considerably in the cartilage sample under dynamic unconfined compression, whereas it had little effect on the transport of small solutes (at 5% dynamic strain level). The loading-induced convection is an important mechanism for enhancing the transport of large solutes in the cartilage sample with tension-compression nonlinearity. The dynamic compression also promoted diffusion of large solutes in both tissues with and without tension-compression nonlinearity. These findings provide a new insight into the mechanisms of solute transport in hydrated, fibrous soft tissues.     

Inverse dynamic investigation of voluntary leg lateral movements in weightlessness: a new microgravity-specific strategy

This study deals with the quantitative assessment of exchanged forces and torques at the restraint point during whole body posture perturbation movements in long-term microgravity. The work was based on the results of a previous study focused on trunk bending protocol, which suggested that the minimization of the torques exchanged at the restraint point could be a strategy for movement planning in microgravity (J. Biomech. 36(11) (2003) 1691). Torques minimization would lead to the optimization of muscles activity, to the minimization of energy expenditure and, ultimately, to higher movement control capabilities. Here, we focus on leg lateral abduction from anchored stance. The analysis was based on inverse dynamic modelling, leading to the estimation of the total angular momentum at the supporting ankle joint. Results agree with those obtained for trunk bending movements and point out a consistent minimization of the torques exchanged at the restraint point in weightlessness. Given the kinematic features of the examined motor task, this strategy was interpreted as a way to master the rotational dynamic effects on the frontal plane produced by leg lateral abduction. This postural stabilizing effects was the result of a multi-segmental compensation strategy, consisting of the counter rotation of the supporting limb and trunk accompanying the leg raising. The observed consistency of movement-posture co-ordination patterns among lateral leg raising and trunk bending is put forward as a novel interpretative issue of the adaptation mechanisms of the motor system to sustained microgravity, especially if one considers the completely different kinematics of the centre of mass, which was observed in weightlessness for these two motor tasks.     

A shell finite element model of the pelvic floor muscles

The pelvic floor gives support to the organs in the abdominal cavity. Using the dataset made public in (Janda et al. J. Biomech. (2003) 36(6), pp. 749-757), we have reconstructed the geometry of one of the most important parts of the pelvic floor, the levator ani, using NURB surfaces. Once the surface is triangulated, the corresponding mesh is used in a finite element analysis with shell elements.Based on the 3D behavior of the muscle we have constructed a shell that takes into account the direction of the muscle fibers and the incompressibility of the tissue. The constitutive model for the isotropic strain energy and the passive strain energy stored in the fibers is adapted from Humphrey's model for cardiac muscles. To this the active behavior of the skeletal muscle is added.We present preliminary results of a simulation of the levator ani muscle under pressure and with active contraction. This research aims at helping simulate the damages to the pelvic floor that can occur after childbirth.     

A full body musculoskeletal model based on flexible multibody simulation approach utilised in bone strain analysis during human locomotion

Load-induced strains applied to bone can stimulate its development and adaptation. In order to quantify the incident strains within the skeleton, in vivo implementation of strain gauges on the surfaces of bone is typically used. However, in vivo strain measurements require invasive methodology that is challenging and limited to certain regions of superficial bones only such as the anterior surface of the tibia. Based on our previous study [Al Nazer et al. (2008) J Biomech. 41:1036-1043], an alternative numerical approach to analyse in vivo strains based on the flexible multibody simulation approach was proposed. The purpose of this study was to extend the idea of using the flexible multibody approach in the analysis of bone strains during physical activity through integrating the magnetic resonance imaging (MRI) technique within the framework. In order to investigate the reliability and validity of the proposed approach, a three-dimensional full body musculoskeletal model with a flexible tibia was used as a demonstration example. The model was used in a forward dynamics simulation in order to predict the tibial strains during walking on a level exercise. The flexible tibial model was developed using the actual geometry of human tibia, which was obtained from three-dimensional reconstruction of MRI. Motion capture data obtained from walking at constant velocity were used to drive the model during the inverse dynamics simulation in order to teach the muscles to reproduce the motion in the forward dynamics simulation. Based on the agreement between the literature-based in vivo strain measurements and the simulated strain results, it can be concluded that the flexible multibody approach enables reasonable predictions of bone strain in response to dynamic loading. The information obtained from the present approach can be useful in clinical applications including devising exercises to prevent bone fragility or to accelerate fracture healing.     

Estimating the L5S1 flexion/extension moment in symmetrical lifting using a simplified ambulatory measurement system

Mechanical loading of the spine has been shown to be an important risk factor for the development of low-back pain. Inertial motion capture (IMC) systems might allow measuring lumbar moments in realistic working conditions, and thus support evaluation of measures to reduce mechanical loading. As the number of sensors limits applicability, the objective of this study was to investigate the effect of the number of sensors on estimates of L5S1 moments.Hand forces, ground reaction forces (GRF) and full-body kinematics were measured using a gold standard (GS) laboratory setup. In the ambulatory setup, hand forces were estimated based on the force plates measured GRF and body kinematics that were measured using (subsets of) an IMC system. Using top-down inverse dynamics, L5S1 flexion/extension moments were calculated.RMSerrors (Nm) were lowest (16.6) with the full set of 17 sensors and increased to 20.5, 22 and 30.6, for 8, 6 and 4 sensors. Absolute errors in peak moments (Nm) ranged from 17.7 to 16.4, 16.9 and 49.3 Nm, for IMC setup’s with 17, 8, 6 and 4 sensors, respectively. When horizontal GRF were neglected for 6 sensors, RMSerrors and peak moment errors decreased from 22 to 17.3 and from 16.9 to 13 Nm, respectively.In conclusion, while reasonable moment estimates can be obtained with 6 sensors, omitting the forearm sensors led to unacceptable errors. Furthermore, vertical GRF information is sufficient to estimate L5S1 moments in lifting.     

Kinematic measurement of the lumbar spine and pelvis in the normal population

Spinal and pelvis motion has been studied by a variety of different methods, the majority of which have a number of limitations. The present study investigated motion characteristics of the lumbar spine and pelvis using a three-dimensional optoelectronic system. The aim of our study was to determine kinematic parameters of spine and pelvis during trunk flexion, extension and lateral bending in normal, healthy subjects. Kinematic motion analysis was performed on 63 asymptomatic volunteers for four different trunk motions. This study has shown that the pelvis range of motion is affected by the gender Contribution of pelvic movement to trunk flexion was 50%, while pelvic angle was significantly higher in women. During lateral bending female subjects had statistically significant higher values of vertebral arc with respect to male subjects. During extension the contribution of pelvic movement was 45%. There was no significant difference found in total angle, pelvic angle and vertebral arc.     

Gluteus maximus muscle function and the origin of hominid bipedality

Bipedality not only frees the hands for tool use but also enhances tool use by allowing use of the trunk for leverage in applying force and thus imparting greater final velocity to tools. Since the weight and acceleration of the trunk and forelimbs on the hindlimbs must be counteracted by muscles such as m. gluteus maximus that control pelvic and trunk movements, it is suggested that the large size of the cranial portion of the human gluteus maximus muscle and its unique attachment to the dorsal ilium (which is apparent in the Makapan australopithecine ilium) may have contributed to the effectiveness with which trunk movement was exploited in early hominid foraging activities. To test this hypothesis, the cranial portions of both right and left muscles were investigated in six human subjects with electromyography during throwing, clubbing, digging, and lifting. The muscles were found to be significantly recruited when the trunk is used in throwing and clubbing, initiating rotation of the pelvis and braking it as trunk rotation ceases and the forelimb accelerates. They stabilize the pelvis during digging and exhibit marked and prolonged activity when the trunk is maintained in partial flexion during lifting of heavy objects.     

A model for the modulation of microvessel permeability by junction strands

To investigate the effect of junction strands on microvessel permeability, we extend the previous analytical model developed by Fu et al. (1994, J. Biomech. Eng., 116, pp. 502-513), for the interendothelial cleft to include multiple junction strands in the cleft and an interface between the surface glycocalyx layer and the cleft entrance. Based on the electron microscopic observations by Adamson et al. (1998, Am. J. Physiol., 274(43), pp. H1885-H1894), that elevation of intracellular cAMP levels would increase number of tight junction strands, this two-junction-strand and two-pore model can successfully account for the experimental data for the decreased permeability to water, small and intermediate-sized solutes by cAMP.     

Reconstructed bone end loads on the canine forelimb during gait

The objective of this work was to determine bone loading conditions that, when applied to a finite element model, would best reproduce the in vivo strain field as measured by surface-mounted strain rosettes. The present study adopts the basic mathematical approach to load reconstruction introduced by Weinans and Blankevoort (J. Biomech. 28 (1995) 739) who determined the relationship between applied loads and bone strain distribution using ex vivo calibration testing. Our method eliminates the need for subsequent ex vivo calibration tests by instead substituting a computational calibration procedure. This first application of the method is with in vivo strains on the canine forelimb during gait (Coleman et al., J. Biomech. 35 (2002) 1677), but with further refinements the method could be used to reconstruct the in vivo loading conditions in living subjects.     

The correspondence between equilibrium biphasic and triphasic material properties in mixture models of articular cartilage

Mixture models have been successfully used to describe the response of articular cartilage to various loading conditions. Mow et al. (J. Biomech. Eng. 102 (1980) 73) formulated a biphasic mixture model of articular cartilage where the collagen-proteoglycan matrix is modeled as an intrinsically incompressible porous-permeable solid matrix, and the interstitial fluid is modeled as an incompressible fluid. Lai et al. (J. Biomech. Eng. 113 (1991) 245) proposed a triphasic model of articular cartilage as an extension of their biphasic theory, where negatively charged proteoglycans are modeled to be fixed to the solid matrix, and monovalent ions in the interstitial fluid are modeled as additional fluid phases. Since both models co-exist in the cartilage literature, it is useful to show how the measured properties of articular cartilage (the confined and unconfined compressive and tensile moduli, the compressive and tensile Poisson's ratios, and the shear modulus) relate to both theories. In this study, closed-form expressions are presented that relate biphasic and triphasic material properties in tension, compression and shear. These expressions are then compared to experimental findings in the literature to provide greater insight into the measured properties of articular cartilage as a function of bathing solutions salt concentrations and proteoglycan fixed-charge density.