Cartilage interstitial fluid load support in unconfined compression

Under physiological conditions of loading, articular cartilage is subjected to both compressive strains, normal to the articular surface, and tensile strains, tangential to the articular surface. Previous studies have shown that articular cartilage exhibits a much higher modulus in tension than in compression, and theoretical analyses have suggested that this tension–compression nonlinearity enhances the magnitude of interstitial fluid pressurization during loading in unconfined compression, above a theoretical threshold of 33% of the average applied stress. The first hypothesis of this experimental study is that the peak fluid load support in unconfined compression is significantly greater than the 33% theoretical limit predicted for porous permeable tissues modeled with equal moduli in tension and compression. The second hypothesis is that the peak fluid load support is higher at the articular surface side of the tissue samples than near the deep zone, because the disparity between the tensile and compressive moduli is greater at the surface zone. Ten human cartilage samples from six patellofemoral joints, and 10 bovine cartilage specimens from three calf patellofemoral joints were tested in unconfined compression. The peak fluid load support was measured at 79±11% and 69±15% at the articular surface and deep zone of human cartilage, respectively, and at 94±4% and 71±8% at the articular surface and deep zone of bovine calf cartilage, respectively. Statistical analyses confirmed both hypotheses of this study. These experimental results suggest that the tension–compression nonlinearity of cartilage is an essential functional property of the tissue which makes interstitial fluid pressurization the dominant mechanism of load support in articular cartilage.     

Modeling of neutral solute transport in a dynamically loaded porous permeable gel: implications for articular cartilage biosynthesis and tissue engineering

A primary mechanism of solute transport in articular cartilage is believed to occur through passive diffusion across the articular surface, but cyclical loading has been shown experimentally to enhance the transport of large solutes. The objective of this study is to examine the effect of dynamic loading within a theoretical context, and to investigate the circumstances under which convective transport induced by dynamic loading might supplement diffusive transport. The theory of incompressible mixtures was used to model the tissue (gel) as a mixture of a gel solid matrix (extracellular matrix/scaffold), and two fluid phases (interstitial fluid solvent and neutral solute), to solve the problem of solute transport through the lateral surface of a cylindrical sample loaded dynamically in unconfined compression with frictionless impermeable platens in a bathing solution containing an excess of solute. The resulting equations are governed by nondimensional parameters, the most significant of which are the ratio of the diffusive velocity of the interstitial fluid in the gel to the solute diffusivity in the gel (Rg), the ratio of actual to ideal solute diffusive velocities inside the gel (Rd), the ratio of loading frequency to the characteristic frequency of the gel (f), and the compressive strain amplitude (epsilon 0). Results show that when Rg > 1, Rd < 1, and f > 1, dynamic loading can significantly enhance solute transport into the gel, and that this effect is enhanced as epsilon 0 increases. Based on representative material properties of cartilage and agarose gels, and diffusivities of various solutes in these gels, it is found that the ranges Rg > 1, Rd < 1, correspond to large solutes, whereas f > 1 is in the range of physiological loading frequencies. These theoretical predictions are thus in agreement with the limited experimental data available in the literature. The results of this study apply to any porous hydrated tissue or material, and it is therefore plausible to hypothesize that dynamic loading may serve to enhance solute transport in a variety of physiological processes.     

Effect of dynamic loading on the frictional response of bovine articular cartilage

The objective of this study was to test the hypotheses that (1) the steady-state friction coefficient of articular cartilage is significantly smaller under cyclical compressive loading than the equilibrium friction coefficient under static loading, and decreases as a function of loading frequency; (2) the steady-state cartilage interstitial fluid load support remains significantly greater than zero under cyclical compressive loading and increases as a function of loading frequency. Unconfined compression tests with sliding of bovine shoulder cartilage against glass in saline were carried out on fresh cylindrical plugs (n=12), under three sinusoidal loading frequencies (0.05, 0.5 and 1 Hz) and under static loading; the time-dependent friction coefficient mu(eff) was measured. The interstitial fluid load support was also predicted theoretically. Under static loading mu(eff) increased from a minimum value (mu(min)=0.005+/-0.003) to an equilibrium value (mu(eq)=0.153+/-0.032). In cyclical compressive loading tests mu(eff) similarly rose from a minimum value (mu(min)=0.004+/-0.002, 0.003+/-0.001 and 0.003+/-0.001 at 0.05, 0.5 and 1 Hz) and reached a steady-state response oscillating between a lower-bound (mu(lb)=0.092+/-0.016, 0.083+/-0.019 and 0.084+/-0.020) and upper bound (mu(ub)=0.382+/-0.057, 0.358+/-0.059, and 0.298+/-0.061). For all frequencies it was found that mu(ub)>mu(eq) and mu(lb)相似文献   

Effects of friction on the unconfined compressive response of articular cartilage: a finite element analysis

A finite element analysis is used to study a previously unresolved issue of the effects of platen-specimen friction on the response of the unconfined compression test; effects of platen permeability are also determined. The finite element formulation is based on the linear KLM biphasic model for articular cartilage and other hydrated soft tissues. A Galerkin weighted residual method is applied to both the solid phase and the fluid phase, and the continuity equation for the intrinsically incompressible binary mixture is introduced via a penalty method. The solid phase displacements and fluid phase velocities are interpolated for each element in terms of unknown nodal values, producing a system of first order differential equations which are solved using a standard numerical finite difference technique. An axisymmetric element of quadrilateral cross-section is developed and applied to the mechanical test problem of a cylindrical specimen of soft tissue in unconfined compression. These studies show that interfacial friction plays a major role in the unconfined compression response of articular cartilage specimens with small thickness to diameter ratios.     

Strain-rate dependent stiffness of articular cartilage in unconfined compression

The stiffness of articular cartilage is a nonlinear function of the strain amplitude and strain rate as well as the loading history, as a consequence of the flow of interstitial water and the stiffening of the collagen fibril network. This paper presents a full investigation of the interplay between the fluid kinetics and fibril stiffening of unconfined cartilage disks by analyzing over 200 cases with diverse material properties. The lower and upper elastic limits of the stress (under a given strain) are uniquely established by the instantaneous and equilibrium stiffness (obtained numerically for finite deformations and analytically for small deformations). These limits could be used to determine safe loading protocols in order that the stress in each solid constituent remains within its own elastic limit. For a given compressive strain applied at a low rate, the loading is close to the lower limit and is mostly borne directly by the solid constituents (with little contribution from the fluid). In contrast, however in case of faster compression, the extra loading is predominantly transported to the fibrillar matrix via rising fluid pressure with little increase of stress in the nonfibrillar matrix. The fibrillar matrix absorbs the loading increment by self-stiffening: the quicker the loading the faster the fibril stiffening until the upper elastic loading limit is reached. This self-protective mechanism prevents cartilage from damage since the fibrils are strong in tension. The present work demonstrates the ability of the fibril reinfored poroelastic models to describe the strain rate dependent behavior of articular cartilage in unconfined compression using a mechanism of fibril stiffening mainly induced by the fluid flow.     

Biorheology and fluid flux in swelling tissues, II. Analysis of unconfined compressive response of transversely isotropic cartilage disc

The response of a cartilage disc to unconfined compressive loading under small deformations is analyzed. The cartilage is considered as a transversely isotropic bicomponent (solid-fluid) tissue. Concentration effects (commonly termed osmotic pressure) are accounted for. The tissue's permeability is taken to be isotropic. Its concentration force is assumed to vary linearly with volume. The analysis shows that if the tissue's fibrous structure is taken into consideration, then the instantaneous response to a step loading depends on the tissue's elasticity and on its concentration force. The subsequent creep response, under commonly used experimental conditions, has a time constant which depends on the concentration force and permeability, but independent of its elastic response. The equilibrium volume is predicted to depend only on the concentration force. Where data is available it confirms the model's predictions. It is concluded from the present analysis that inclusion of concentration effects and the tissue's fibrous structure has significant consequences in terms of the relative roles of the collagen fibers (solid) vs. the ground substance (fluid) in the response of the cartilage to compressive loading.     

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.     

Cartilage interstitial fluid load support in unconfined compression following enzymatic digestion

Interstitial fluid pressurization plays an important role in cartilage biomechanics and is believed to be a primary mechanism of load support in synovial joints. The objective of this study was to investigate the effects of enzymatic degradation on the interstitial fluid load support mechanism of articular cartilage in unconfined compression. Thirty-seven immature bovine cartilage plugs were tested in unconfined compression before and after enzymatic digestion. The peak fluid load support decreased significantly (p < 0.0001) from 84 +/- 10% to 53 +/- 19% and from 80 +/- 10% to 46 +/- 21% after 18-hours digestion with 1.0 u/mg-wet-weight and 0.7 u/mg-wet-weight of collagenase, respectively. Treatment with 0.1 u/ml of chondroitinase ABC for 24 hours also significantly reduced the peak fluid load support from 83 +/- 12% to 48 +/- 16% (p < 0.0001). The drop in interstitial fluid load support following enzymatic treatment is believed to result from a decrease in the ratio of tensile to compressive moduli of the solid matrix.     

Osmosis and viscoelasticity both contribute to time-dependent behaviour of the intervertebral disc under compressive load: A caprine in vitro study

The mechanical behaviour of the intervertebral disc highly depends on the content and transport of interstitial fluid. It is unknown, however, to what extent the time-dependent behaviour can be attributed to osmosis. Here we investigate the effect of both mechanical and osmotic loading on water content, nucleus pressure and disc height. Eight goat intervertebral discs, immersed in physiological saline, were subjected to a compressive force with a pressure needle inserted in the nucleus. The loading protocol was: 10 N (6 h); 150 N (42 h); 10 N (24 h). Half-way the 150 N-phase (24 h), we eliminated the osmotic gradient by adding 26% poly-ethylene glycol to the surrounding fluid. For 62 additional discs, we determined the water content of both nucleus and annulus after 6, 24, 48, or 72 h. The compressive load was initially counterbalanced by the hydrostatic pressure in the nucleus. The load forced 4.3% of the water out of the nucleus, which reduced nucleus pressure by 44(±6)%. Reduction of the osmotic gradient disturbed the equilibrium disc height, and a significant loss of annulus water content was found. Remarkably, pressure and water content of the nucleus pulposus remained unchanged. This shows that annulus water content is important in the response to axial loading. After unloading, in the absence of an osmotic gradient, there was substantial viscoelastic recovery of 53(±11)% of the disc height, without a change in water content. However, for restoration of the nucleus pressure and for full restoration of disc height, restoration of the osmotic gradient was needed.     

Evidence for increased de novo synthesis of NAD in immune-activated RAW264.7 macrophages: a self-protective mechanism?

Chondrogenesis in cartilage development and repair and cartilage degeneration in arthritis can be regulated by mechanical-load-induced physical factors such as tissue deformation, interstitial fluid flow and pressure, and electrical fields or streaming potentials. Previous animal and tissue explant studies have shown that time-varying dynamic tissue loading can increase the synthesis and deposition of matrix molecules in an amplitude-, frequency-, and spatially dependent manner. To provide information on the cell-level physical factors which may stimulate chondrocytes to increase production and export of aggrecan, the main proteoglycan component of the cartilage matrix, we characterized local changes in aggrecan synthesis within cyclically loaded tissue explant disks and compared those changes to values of predicted local physical factors. Aggrecan synthesis following a 23-h compression/radiolabel protocol was measured with a spatial resolution of approximately 0.1 mm across the 1.5-mm radius of explanted disks using a quantitative autoradiography method. A uniform stimulation of aggrecan synthesis was observed at an intermediate frequency of 0.01 Hz, while, at a higher frequency of 0.1 Hz, stimulation was only seen at peripheral radial positions. Profiles of radial solid matrix deformation and interstitial fluid pressure and velocity predicted to be occurring across the radius of the disk during sinusoidal loading were estimated using a composite poroelastic model. Tissue regions experiencing high interstitial fluid velocities corresponded to those displaying increased aggrecan synthesis. These results reinforce the role of load-induced flow of interstitial fluid in the stimulation of aggrecan production during dynamic loading of cartilage.     

Cartilage responses to a novel triaxial mechanostimulatory culture system

We have developed a novel mechanically active cartilage culture device capable of modulating the interplay between compression and shear, at physiologic stress levels (2-5 MPa). This triaxial compression culture system subjects cylindrical cartilage explants to pulsatile axial compression from platen contact, plus pulsatile radially transverse compression from external fluid compression. These compressive loads can be independently modulated to impose stress states that resemble normal physiologic loading, and to investigate perturbations of individual components of the multi-axial stress state, such as increased shear stress. Based on the observation that joint incongruity predisposes cartilage to premature degeneration, we hypothesized that cartilage extracellular matrix (ECM) synthesis would be inhibited under conditions of low transverse buttressing (high shear stress). To test this hypothesis, we compared ECM synthesis in human cartilage explants exposed to axial compression without transverse compression (high shear stress), versus explants exposed to axial compression plus an equal level of transverse compression (low shear stress). Both total (35)SO(4) incorporation and aggrecan-specific (35)SO(4) incorporation were significantly inhibited by axial compression, relative to axial plus transverse compression.     

Inhomogeneous cartilage properties enhance superficial interstitial fluid support and frictional properties, but do not provide a homogeneous state of stress

It has been well established that articular cartilage is compositionally and mechanically inhomogenous through its depth. To what extent this structural inhomogeneity is a prerequisite for appropriate cartilage function and integrity is not well understood. The first hypothesis to be tested in this study was that the depth-dependent inhomogeneity of the cartilage acts to maximize the interstitial fluid load support at the articular surface, to provide efficient frictional and wear properties. The second hypothesis was that the inhomogeneity produces a more homogeneous state of elastic stress in the matrix than would be achieved with uniform properties. We have, for the first time, simultaneously determined depth-dependent tensile and compressive properties of human patellofemoral cartilage from unconfined compression stress relaxation tests. The results show that the tensile modulus increases significantly from 4.1 +/- 1.9 MPa in the deep zone to 8.3 +/- 3.7 MPa at the superficial zone, while the compressive modulus decreases from 0.73 +/- 0.26 MPa to 0.28 +/- 0.16 MPa. The experimental measurements were then implemented with the finite-element method to compute the response of an inhomogeneous and homogeneous cartilage layer to loading. The finite-element models demonstrate that structural inhomogeneity acts to increase the interstitial fluid load support at the articular surface. However, the state of stress, strain, or strain energy density in the solid matrix remained inhomogeneous through the depth of the articular layer, whether or not inhomogeneous material properties were employed. We suggest that increased fluid load support at the articular surface enhances the frictional and wear properties of articular cartilage, but that the tissue is not functionally adapted to produce homogeneous stress, strain, or strain energy density distributions. Interstitial fluid pressurization, but not a homogeneous elastic stress distribution, appears thus to be a prerequisite for the functional and morphological integrity of the cartilage.     

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.     

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.     

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

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

The role of fibril reinforcement in the mechanical behavior of cartilage

Collagen fibril reinforcement was incorporated into a nonlinear poroelastic model for articular cartilage in unconfined compression. It was found that the radial fibrils play a predominant role in the transient mechanical behavior but a less important role in the equilibrium response of cartilage. The radial fibrils are in tension and can be highly stressed during compression, in contrast to low compressive stresses in all directions for the proteoglycan matrix after a small initial compression. The strain dependent fibril stiffening produces strong nonlinear transient response; the fibrils provide extra stiffness to balance a rising fluid pressure and to restrain stress increase in the proteoglycans. The fibril reinforcement, induced by the fluid pressure and flow, also accounts for a complex pattern of strain-magnitude and strain-rate dependence of cartilage stiffness.     

Tissue engineering of cartilage using a mechanobioreactor exerting simultaneous mechanical shear and compression to simulate the rolling action of articular joints

The effect of dynamic mechanical shear and compression on the synthesis of human tissue‐engineered cartilage was investigated using a mechanobioreactor capable of simulating the rolling action of articular joints in a mixed fluid environment. Human chondrocytes seeded into polyglycolic acid (PGA) mesh or PGA–alginate scaffolds were precultured in shaking T‐flasks or recirculation perfusion bioreactors for 2.5 or 4 weeks prior to mechanical stimulation in the mechanobioreactor. Constructs were subjected to intermittent unconfined shear and compressive loading at a frequency of 0.05 Hz using a peak‐to‐peak compressive strain amplitude of 2.2% superimposed on a static axial compressive strain of 6.5%. The mechanical treatment was carried out for up to 2.5 weeks using a loading regime of 10 min duration each day with the direction of the shear forces reversed after 5 min and release of all loading at the end of the daily treatment period. Compared with shaking T‐flasks and mechanobioreactor control cultures without loading, mechanical treatment improved the amount and quality of cartilage produced. On a per cell basis, synthesis of both major structural components of cartilage, glycosaminoglycan (GAG) and collagen type II, was enhanced substantially by up to 5.3‐ and 10‐fold, respectively, depending on the scaffold type and seeding cell density. Levels of collagen type II as a percentage of total collagen were also increased after mechanical treatment by up to 3.4‐fold in PGA constructs. Mechanical treatment had a less pronounced effect on the composition of constructs precultured in perfusion bioreactors compared with perfusion culture controls. This work demonstrates that the quality of tissue‐engineered cartilage can be enhanced significantly by application of simultaneous dynamic mechanical shear and compression, with the greatest benefits evident for synthesis of collagen type II. Biotechnol. Bioeng. 2012; 109:1060–1073. © 2011 Wiley Periodicals, Inc.