Static compression of articular cartilage can reduce solute diffusivity and partitioning: implications for the chondrocyte biological response

pQCT study on diffusion and equilibrium distribution of iodinated anionic contrast agent in human articular cartilage--associations to matrix composition and integrity

OBJECTIVE

X-ray imaging of articular cartilage using anionic contrast agents has been introduced for quantification of tissue glycosaminoglycan (GAG) concentration. In this in vitro study we investigated diffusion and equilibrium distribution of an anionic contrast agent in human articular cartilage and related the results to tissue composition and integrity.

METHODS

Osteochondral cylinders (d=4.0mm, n=24) were prepared from femoral medial condyles (FMCs, cartilage thickness 2.13+/-0.54 mm, mean+/-standard deviation [SD]), and tibial medial plateaus ([TMPs]1.99+/-0.38 mm) of human cadaver knees. Samples were immersed for 24h at room temperature in 21 mM concentration of anionic contrast agent Hexabrix. The X-ray absorption maps and profiles were measured before immersion, and after every 2h of immersion using clinical peripheral quantitative computed tomography (pQCT).

RESULTS

An increase in X-ray attenuation along cartilage depth, indicating a characteristic density profile increasing from superficial to deep tissue, could be seen in pQCT images acquired without contrast agent. The complete diffusion of the contrast agent into cartilage took more than 12h. However, the uronic acid concentration correlated with the contrast agent concentration in femoral cartilage (r=-0.76, n=12, P=0.004) as early as after 2h of immersion, and the linear correlation was virtually unchanged during the remaining 22 h. Similarly, the histological tissue integrity (Mankin score) correlated positively with the contrast agent concentration in tibial cartilage (r=+0.75, P=0.005) after 2h of immersion. The X-ray absorption profiles before immersion, i.e., without the contrast agent, and after 24h of immersion were significantly correlated (r=-0.76+/-0.34, mean+/-SD).

CONCLUSIONS

Although the complete contrast agent diffusion into human articular cartilage in vitro took more than 12h, significant apparent correlations were revealed between the spatial proteoglycan (PG) and contrast agent distributions already after 2h of immersion. At the stage of incomplete penetration, however, the spatial contrast agent concentration distribution cannot directly reflect the true PG distribution as the Donnan equilibrium has not been reached. However, in degenerated cartilage the diffusion rate increases. Obviously, this can lead to the reported correlation between the bulk PG content and the bulk contrast agent concentration already at the early stages of diffusion.

Microscale diffusion properties of the cartilage pericellular matrix measured using 3D scanning microphotolysis

Chondrocytes, the cells in articular cartilage, are enclosed within a pericellular matrix (PCM) whose composition and structure differ from those of the extracellular matrix (ECM). Since the PCM surrounds each cell, molecules that interact with the chondrocyte must pass through the pericellular environment. A quantitative understanding of the diffusional properties of the PCM may help in elucidating the regulatory role of the PCM in controlling transport to and from the chondrocyte. The diffusivities of fluorescently labeled 70 kDa and 500 kDa dextrans were quantified within the PCM of porcine articular cartilage using a newly developed mathematical model of scanning microphotolysis (SCAMP). SCAMP is a rapid line photobleaching method that accounts for out-of-plane bleaching attributable to high magnification. Data were analyzed by a best-fit comparison to simulations generated using a discretization of the diffusion-reaction equation in conjunction with the microscope-specific three-dimensional excitation and detection profiles. The diffusivity of the larger molecule (500 kDa dextran) was significantly lower than that of the smaller molecule (70 kDa dextran), and values were consistent with those reported previously using standard techniques. Furthermore, for both dextran sizes, the diffusion coefficient was significantly lower in the PCM than in the ECM; however, this difference was not detected in early-stage arthritic tissue. We have successfully modified the SCAMP technique to measure diffusion coefficients within the small volume of the PCM using confocal laser scanning microscopy. Our results support the hypothesis that diffusivity within the PCM of healthy articular cartilage is lower than that within the ECM, presumably due to differences in proteoglycan content.

Effects of mechanical compression on metabolism and distribution of oxygen and lactate in intervertebral disc

The objective of this study was to examine the effects of mechanical compression on metabolism and distributions of oxygen and lactate in the intervertebral disc (IVD) using a new formulation of the triphasic theory. In this study, the cellular metabolic rates of oxygen and lactate were incorporated into the newly developed formulation of the mechano-electrochemical mixture model [Huang, C.-Y., Gu, W.Y., 2007. Effect of tension-compression nonlinearity on solute transport in charged hydrated fibrosus tissues under dynamic unconfined compression. Journal of Biomechanical Engineering 129, 423-429]. The model was used to numerically analyze metabolism and transport of oxygen and lactate in the IVD under static or dynamic compression. The theoretical analyses demonstrated that compressive loading could affect transport and metabolism of nutrients. Dynamic compression increased oxygen concentration, reduced lactate accumulation, and promoted oxygen consumption and lactate production (i.e., energy conversion) within the IVD. Such effects of dynamic loading were dependent on strain level and loading frequency, and more pronounced in the IVD with less permeable endplate. In contrast, static compression exhibited inverse effects on transport and metabolism of oxygen and lactate. The theoretical predictions in this study are in good agreement with those in the literature. This study established a new theoretical model for analyzing cellular metabolism of nutrients in hydrated, fibrous soft tissues under mechanical compression.

Structural biomechanics modulate intramuscular distribution of locally delivered drugs

As local drug delivery continues to emerge as a clinical force, so does understanding of its potentially narrow therapeutic window. Classic molecular transport studies are of value but do not typically account for the local nature of drug transport or the effects of regional dynamic function in target tissues like muscle that may undergo cyclical and variable mechanical motion and loading. We examined the impact of dynamic architecture on intramuscular drug distribution. We designed a tissue mounting technique and mechanical loading system that uniquely enables pharmacokinetics investigations in association with control of muscle biomechanics while preserving physiologic tissue architecture. The system was validated and used to elucidate the influence of architecture and controlled cyclic strain on intramuscular drug distribution. Rat soleus muscles underwent controlled deformations within a drug delivery chamber that preserved in vivo physiology. Penetration of 1mM 20 kDa FITC-dextran at planar surfaces of the soleus axial cross-section increased significantly from 0.52+/-0.09 mm under 80 min of static (0%) strain to 0.81+/-0.09 mm under cyclic (3 Hz, 0-20% peak-to-peak) strain, demonstrating the driving effect of cyclic loading on transport. Penetration at curved margins was 1.57- and 2.53-fold greater than at planar surfaces under static and cyclic strain, respectively, and was enhanced 1.6-fold more by cyclic strain, revealing architecturally dictated spatial heterogeneity in transport and modulation of motion dynamics. Architectural geometry and dynamics modulate the impact of mechanical loading on local drug penetration and intramuscular distribution. Future work will use the biomechanical test system to investigate mechanisms underlying transport effects of specific loading regimens. It is hoped that this work will initiate a broader understanding of intramuscular pharmacokinetics and guide local drug delivery strategies.

Solute transport in the deep and calcified zones of articular cartilage

OBJECTIVES

(1) To establish whether the tidemark and calcified cartilage are permeable to low molecular weight solutes, thereby providing a potential pathway for nutrition of cells in the deep cartilage. (2) To investigate transport from the subchondral microcirculation into calcified cartilage in an intact perfused joint and the effects on transport of static loading.

METHODS

The permeability of the tidemark and calcified cartilage was investigated in plugs of cartilage and subchondral bone which formed the membrane of a diffusion cell. Transport from the subchondral microcirculation and the effects of load were studied in an intact perfused joint. Both preparations used the metacarpophalangeal joints of mature horses and fluorescein and rhodamine (m.w. approximately 400 Da) were employed as tracers, assayed by quantitative fluorescence microscopy on histological sections.

RESULTS

Calcified cartilage was permeable to both solutes, both from the superficial and the subchondral sides. The effective diffusivity of both solutes was of the order of 9 x 10(-9) cm(2) s(-1), fivefold less than in the uncalcified cartilage. The calcified zone was heterogeneous, with high uptake of both tracers in the vicinity of the tidemark. The distribution volume of rhodamine B was higher than for fluorescein, consistent with a significant anionic charge in the calcified matrix. Static loading of the intact joint did not affect the transport of rhodamine B but caused a significant decrease in concentration of fluorescein both in the surface and deep zones of the tissue.

CONCLUSIONS

Calcified cartilage is permeable to small solutes and the subchondral circulation may make a significant contribution to the nutrition of deep cartilage in the mature horse. Static loading reduces the uptake of small anionic solutes in the intact joint.

Biofunctional polymer nanoparticles for intra-articular targeting and retention in cartilage

The extracellular matrix of dense, avascular tissues presents a barrier to entry for polymer-based therapeutics, such as drugs encapsulated within polymeric particles. Here, we present an approach by which polymer nanoparticles, sufficiently small to enter the matrix of the targeted tissue, here articular cartilage, are further modified with a biomolecular ligand for matrix binding. This combination of ultrasmall size and biomolecular binding converts the matrix from a barrier into a reservoir, resisting rapid release of the nanoparticles and clearance from the tissue site. Phage display of a peptide library was used to discover appropriate targeting ligands by biopanning on denuded cartilage. The ligand WYRGRL was selected in 94 of 96 clones sequenced after five rounds of biopanning and was demonstrated to bind to collagen II alpha1. Peptide-functionalized nanoparticles targeted articular cartilage up to 72-fold more than nanoparticles displaying a scrambled peptide sequence following intra-articular injection in the mouse.

Effect of compression and anisotropy on the diffusion of glucose in annulus fibrosus

STUDY DESIGN

Investigation of the effect of static compression and anisotropy on the apparent diffusivity of glucose in bovine annulus fibrosus (AF). OBJECTIVE. To determine the apparent glucose diffusivity in 2 directions (axial and radial) of bovine AF under 3 levels of compressive strain (0%, 10%, and 20%).

SUMMARY OF BACKGROUND DATA

Knowledge of diffusivity of small molecules is important for understanding nutritional supply in intervertebral discs and the mechanisms of disc degeneration. However, little is known regarding the strain-dependent and anisotropic behavior of glucose diffusivity in intervertebral discs.

METHODS

Apparent glucose diffusivity measurements were performed on 10 axial and 10 radial AF specimens from bovine coccygeal discs. The dependence of diffusivity on compression was determined using 3 levels of strain (0%, 10%, and 20%).

RESULTS

The apparent glucose diffusivity (mean +/- standard deviation) of the bovine AF in the axial direction was 1.38 +/- 0.015 x 10 cm/s (n = 10) at 0%, 1.00 +/- 0.070 x 10 cm/s (n = 10) at 10%, and 7.65 +/- 0.552 x 10 cm/s (n = 10) at 20% compression. For radial specimens, the apparent glucose diffusivity was determined to be 9.17 +/- 1.12 x 10 cm/s (n = 10), 7.29 +/- 0.863 x 10 cm/s (n = 10), and 5.43 +/- 1.16 x 10 cm/s (n = 10) for 0%, 10%, and 20% compressions, respectively. A significant decrease in diffusivity with increasing strain was found for both axial and radial specimens [analysis of variance (ANOVA), P < 0.05]. Diffusion in the radial direction was determined to be significantly less than that in the axial direction (ANOVA, P < 0.05). A significant interaction was found between the level of strain and the direction of diffusion (ANOVA, P < 0.05).

CONCLUSION

Diffusion of glucose in bovine AF is dependent on strain and the direction of diffusion.

Anti-inflammatory and chondroprotective effects of nutraceuticals from Sasha's Blend in a cartilage explant model of inflammation

New Zealand green lipped mussel (NZGLM), abalone (AB), and shark cartilage (SC) are extensively used for treatment of and/or as preventatives for arthritis, despite a relative paucity of scientific evidence for efficacy. This research integrated a simulated digestion protocol with ultrafiltration and cartilage explants to generate new information on the anti-inflammatory and chondroprotective properties of NZGLM, SC, and AB. Each nutraceutical was artificially digested using simulated gastric and intestinal fluids, and the crude digest was ultrafiltered (50 kDa). Each filtrate was applied individually to cartilage explants before the explants were stimulated with IL-1 to induce an acute inflammatory response. Media were collected daily for 48 h and analyzed for prostaglandin E(2) (PGE(2)), glycosaminoglycan (GAG), and nitric oxide (NO), and cartilage tissue was differentially stained to determine the relative proportion of live and dead cells. SC and NZGLM significantly inhibited IL-1-induced PGE(2) synthesis and IL-1-induced GAG release, and AB was an effective inhibitor of IL-1-induced NO production. The three test nutraceuticals affect at least three major pathways involved in the catabolic cycle of arthritis and may prove important treatments and/or preventatives for the pain and degradation associated with this condition. The methodology and results describe a useful model for evaluating dietary nutraceuticals in vitro.

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.

Solute transport in growth plate cartilage: in vitro and in vivo

Bone elongation originates from cartilaginous discs (growth plates) at both ends of a growing bone. Here chondrocytes proliferate and subsequently enlarge (hypertrophy), laying down a matrix that serves as the scaffolding for subsequent bone matrix deposition. Because cartilage is generally avascular, all nutrients, oxygen, signaling molecules, and waste must be transported relatively long distances through the tissue for it to survive and function. Here we examine the transport properties of growth plate cartilage. Ex vivo, fluorescence photobleaching recovery methods are used in tissue explants. In vivo, multiphoton microscopy is used to image through an intact perichondrium and into the cartilage of anesthetized mice. Systemically introduced fluorescent tracers are monitored directly as they move from the vasculature into the cartilage. We demonstrate the existence of a relatively permissive region at the midplane of the growth plate, where chondrocytes transition from late proliferative to early hypertrophic stages and where paracrine communication is known to occur between chondrocytes and cells in the surrounding perichondrium. Transport in the living mouse is also significantly affected by fluid flow from the two chondro-osseus junctions, presumably resulting from a pressure difference between the bone vasculature and the cartilage.

Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression

A 3D inhomogeneous finite-element model for charged hydrated soft tissues containing charged/uncharged solutes was developed and applied to analyze the mechanical, chemical, and electrical signals within the human intervertebral disc during an axial unconfined compression. The effects of tissue properties and boundary conditions on the physical signals and the transport of fluid and solute were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization and the effective (von Misses) solid stress were more pronounced in the annulus fibrosus (AF) region near the interface between AF and nucleus pulposus (NP). In NP, the distributions of the fluid pressure, effective stress, and electrical potential were more uniform than those in AF. The electrical signals were very sensitive to fixed charge density. Changes in material properties of NP (water content, fixed charge density, and modulus) affected fluid pressure, electrical potential, effective stress, and solute transport in the disc. This study is important for understanding disc biomechanics, disc nutrition, and disc mechanobiology.

An in vitro organ culturing system for intervertebral disc explants with vertebral endplates: a feasibility study with ovine caudal discs

STUDY DESIGN

Whole ovine caudal intervertebral discs with vertebral endplates were cultured under uniaxial diurnal loading for 7 days.

OBJECTIVES

To establish and characterize an organ culture system for intervertebral discs, in which disc cells may be "maintained" in their native three-dimensional environment under load.

SUMMARY OF BACKGROUND DATA

In vitro culturing of entire discs with preserved biologic and structural integrity would be a useful model to study the effects of nutrition and mechanical loading.

METHODS

To maintain endplate permeability, sheep were systemically anticoagulated before death and their caudal vasculature was evacuated with saline postmortem. The first 4 caudal discs were explanted with their adjacent endplates and cultured in bioreactors under uniaxial diurnal loading (0.2 MPa for 8 hours and 0.8 MPa for 16 hours) for 4 or 7 days. Solute transport into the center of the disc was measured after 4 days of culture using a low molecular weight fluorescent marker. Cell viability, glycosaminoglycan synthesis rate, and gene expression profile were measured after 7 days of culture and compared with fresh tissue.

RESULTS

Fluorescent images showed that solutes could diffuse into the disc under both static and diurnal loading, but penetration through the endplate increased with diurnal loading. Cell viability and glycosaminoglycan synthesis rates remained unchanged after 7 days of culture. Expression of catabolic genes was significantly up-regulated, whereas anabolic genes tended to be down-regulated after 7 days.

CONCLUSIONS

With this novel preparation and culturing technique, endplate permeability could be maintained, which allowed culturing of intact disc explants with endplates for up to 7 days.

Convection and diffusion in charged hydrated soft tissues: a mixture theory approach

The extracellular matrix of cartilage is a charged porous fibrous material. Transport phenomena in such a medium are very complex. In this study, solute diffusive flux and convective flux in porous fibrous media were investigated using a continuum mixture theory approach. The intrinsic diffusion coefficient of solute in the mixture was defined and its relation to drag coefficients was presented. The effect of mechanical loading on solute diffusion in cartilage under unconfined compression with a frictionless boundary condition was analyzed numerically using the model developed. Both strain-dependent hydraulic permeability and diffusivity were considered. Analyses and results show that (1) In porous media, the convective velocity for each solute phase is different. (2) The solute convection in tissue is governed by the relative convective velocity (i.e., relative to solid velocity). (3) Under the assumption that all the frictional interactions among solutes are negligible, the relative convective velocity for alpha-solute phase is equal to the relative solvent velocity multiplied by its convective coefficient (H (alpha)) which is also known as the hindrance factor in the literature. The relationship between the convective coefficient and the relative diffusivity of solute is presented. (4) Solute concentration profile within the cartilage sample depends on the phase of dynamic compression.

Microstructural Modeling of Collagen Network Mechanics and Interactions with the Proteoglycan Gel in Articular Cartilage

Cartilage matrix mechanical function is largely determined by interactions between the collagen fibrillar network and the proteoglycan gel. Although the molecular physics of these matrix constituents have been characterized and modern imaging methods are capable of localized measurement of molecular densities and orientation distributions, theoretical tools for using this information for prediction of cartilage mechanical behavior are lacking. We introduce a means to model collagen network contributions to cartilage mechanics based upon accessible microstructural information (fibril density and orientation distributions) and which self-consistently follows changes in microstructural geometry with matrix deformations. The interplay between the molecular physics of the collagen network and the proteoglycan gel is scaled up to determine matrix material properties, with features such as collagen fibril pre-stress in free-swelling cartilage emerging naturally and without introduction of ad hoc parameters. Methods are developed for theoretical treatment of the collagen network as a continuum-like distribution of fibrils, such that mechanical analysis of the network may be simplified by consideration of the spherical harmonic components of functions of the fibril orientation, strain, and stress distributions. Expressions for the collagen network contributions to matrix stress and stiffness tensors are derived, illustrating that only spherical harmonic components of orders 0 and 2 contribute to the stress, while orders 0, 2, and 4 contribute to the stiffness. Depth- and compression-dependent equilibrium mechanical properties of cartilage matrix are modeled, and advantages of the approach are illustrated by exploration of orientation and strain distributions of collagen fibrils in compressed cartilage. Results highlight collagen-proteoglycan interactions, especially for very small physiological strains where experimental data are relatively sparse. These methods for determining matrix mechanical properties from measurable quantities at the microscale (composition, structure, and molecular physics) may be useful for investigating cartilage structure-function relationships relevant to load-bearing, injury, and repair.

The PTHrP-Ihh feedback loop in the embryonic growth plate allows PTHrP to control hypertrophy and Ihh to regulate proliferation

Growth plate and long bone development is governed by biochemical signaling pathways of which the PTHrP-Ihh system is the best known. Other factors, such as BMPs, FGFs and mechanical loading, may interact with this system. This study aims at elucidating the relative importance of PTHrP and Ihh for controlling proliferation, and hypertrophy in fetal growth plate cartilage. We assessed the question why reduced Ihh expression leads to more pronounced effects on the number of non-hypertrophic cells and total bone formation, compared to PTHrP down-regulation. Using few basic equations, constituted from literature data, this paper shows how the PTHrP-Ihh feedback system can control different aspects of tissue differentiation at distinct locations. In particular, it is shown that (mechanical or biochemical) perturbations will affect proliferation via Ihh-related parameters, whereas changes in PTHrP-related parameters selectively interact with hypertrophy. This is contra-intuitive, since PTHrP acts to keep cells proliferating. In this context, the critical PTHrP level for keeping cells proliferating has been reconsidered. In addition, an explanation is provided for the aforementioned difference in effect between reduced Ihh and PTHrP expression.

Dynamic compression augments interstitial transport of a glucose-like solute in articular cartilage

Solute transport through the extracellular matrix is essential for cellular activities in articular cartilage. Increased solute transport via fluid convection may be a mechanism by which dynamic compression stimulates chondrocyte metabolism. However, loading conditions that optimally augment transport likely vary for different solutes. To investigate effects of dynamic loading on transport of a bioactive solute, triangular mechanical loading waveforms were applied to cartilage explants disks while interstitial transport of a fluorescent glucose analog was monitored. Peak-to-peak compression amplitudes varied from 5-50% and frequencies varied from 0.0006-0.1 Hz to alter the spatial distribution and magnitude of oscillatory fluid flow. Solute transport was quantified by monitoring accumulation of fluorescence in a saline bath circulated around the explant. Individual explants were subjected to a series of compression protocols, so that effects of loading on solute desorption could be observed directly. Maximum increases in solute transport were obtained with 10-20% compression amplitudes at 0.1 Hz; similar loading protocols were previously found to stimulate chondrocyte metabolism in vitro. Results therefore support hypotheses relating to increased solute transport as a mediator of the cartilage biological response to dynamic compression, and may have application in mechanical conditioning of cartilage constructs for tissue engineering.

Composition and transport properties of human ankle and knee cartilage

The incidence of osteoarthritis is significantly higher in the knee as compared to the ankle, suggesting that differences in the properties of cartilage from these joints may contribute to the development of osteoarthritis. As an avascular tissue, articular cartilage depends primarily upon diffusion for molecular transport. The goal of this study was to determine if differences in the structure and composition between ankle and knee cartilage were also reflected as differences in solute transport properties. The diffusion coefficient and partition coefficient of a 70-kDa dextran molecule were measured in human ankle and knee articular cartilage using fluorescence recovery after photobleaching (FRAP) and were compared to the proteoglycan, collagen, water, and DNA contents within each zone. The mean partition coefficient was significantly lower in the ankle compared to the knee (0.010+/-0.002 vs. 0.022+/-0.003, p<0.01), but no differences in the diffusion coefficients were observed (34.6 +/- 0.9 microm(2)s(-1) vs. 35.4+/-2.4 microm(2)s(-1), p=0.70). Ankle cartilage exhibited higher proteoglycan content as well as a trend toward lower water content, suggesting that ankle cartilage has a smaller effective pore size than knee cartilage. These findings suggest that differences in the composition of ankle and knee cartilage contribute to a difference in the partition coefficient. The results of this study provide further support for the hypothesis that the transport properties of cartilage may play a role in the differences in the incidence of osteoarthritis in these joints by altering the effective concentration of growth factors and cytokines to which chondrocytes are exposed.

Diffusivity of ions in agarose gels and intervertebral disc: effect of porosity

The effect of tissue porosity on ion (sodium, potassium, and chloride) diffusivity in agarose gels and porcine intervertebral disc tissues was investigated using an electrical conductivity method. An empirical, constitutive model for diffusivity (D) of solutes in porous fibrous media was proposed: D/Do = exp[-alpha(r(s)/k(1/2))beta] where r(s) is the Stokes radius of a solute, kappa is the Darcy permeability of the porous medium, Do is the diffusivity in free solution, alpha and beta are two positive parameters whose values depend on material structure. It is found that alpha = 1.25 +/- 0.138, beta = 0.681 +/- 0.059 (95% confidence interval, R2 = 0.92, n = 72) for agarose gels and alpha = 1.29 +/- 0.171 and beta = 0.372 +/- 0.088 (95% confidence interval, R2 = 0.88, n = 86) for porcine annulus fibrosus. The functional relationship between solute diffusivity and tissue deformation was derived. Comparisons of our model prediction with experimental data on diffusion coefficients of macromolecules (proteins, dextrans, polymer beads) in agarose gels in the literature were made. Our results were also compared to the data on ion diffusivity in charged gels and in cartilaginous tissues reported in the literature. There was a good agreement between our model prediction and the data in the literature. The present study provides additional information on solute diffusivity in uncharged gels and charged tissues, and is important for understanding nutritional transport in avascular cartilaginous tissues under different mechanical loading conditions.

Solute diffusivity correlates with mechanical properties and matrix density of compressed articular cartilage

The biomechanical functions of articular cartilage are governed largely by the composition and density of its specialized extracellular matrix. Relationships between matrix density and functional indices such as mechanical properties or interstitial solute diffusivities have been previously explored. However, direct correlations between mechanical properties and solute transport parameters have received less attention, despite potential application of this information for cartilage functional assessment both in vivo and in vitro. The objective of this study was therefore to examine relationships among solute diffusivities, mechanical properties, and matrix density of compressed articular cartilage. Matrix density varied due to natural variation among explants and due to applied static compression. Matrix density of statically compressed cartilage explants was characterized by glycoaminoglycan (GAG) weight fraction and fluid volume fraction, while diffusion coefficients of a wide range of solutes were measured to characterize the transport environment. Explant mechanical properties were characterized by a non-linear Young's modulus (axial stress-strain ratio) and a non-linear Poisson's ratio (radial-to-axial strain ratio). Solute diffusivities were consistently correlated with Young's modulus, as well as with explant GAG weight and fluid volume fractions. Therefore, in vitro mechanical tests may provide a means of assessing transport environments in cartilage-like materials, while in vivo measurements of solute transport (for example with magnetic resonance imaging) may be a useful complement in identifying localized differences in matrix density and mechanical properties.

The influence of oxygen tension on the induction of nitric oxide and prostaglandin E2 by mechanical stress in articular cartilage

OBJECTIVES

Articular cartilage is an avascular tissue that exists at low oxygen tension. Oxygen tension can influence the production of the pro-inflammatory mediators nitric oxide (NO) and prostaglandin E2 (PGE(2)) in cartilage, which are increased in osteoarthritis (OA). The synthesis of these molecules can be stimulated by mechanical stress, which is an important risk factor for OA. The objective of this study was to determine the influence of oxygen tension on the induction of NO and PGE(2) production in articular cartilage in response to mechanical stress.

DESIGN

Intermittent mechanical compression (0.05MPa, 0.5Hz for 24h) was applied to full thickness skeletally mature porcine articular cartilage explants at either 20%, 5%, or 1% O(2). NO, PGE(2) and peroxynitrite formation were measured, and the effect of the selective nitric oxide synthase 2 inhibitor 1400W was tested.

RESULTS

Incubating articular cartilage at 5% O(2) significantly increased (P<0.001) baseline NO production, as compared with 1% or 20% O(2). Peroxynitrite formation was lower at reduced oxygen tension. Mechanical compression significantly increased (P<0.001) NO production at 20% O(2) but not at 5% or 1% O(2), and significantly increased (P<0.001) PGE(2) production at 20% O(2) (50 fold) and 5% O(2) (4 fold) but not at 1% O(2). 1400W blocked mechanically induced NO production and further increased PGE(2) production at 5% O(2) (P<0.05).

CONCLUSIONS

Oxygen tension influences the endogenous production of NO and PGE(2) in cartilage and can have a significant effect on the induction of these inflammatory mediators in response to mechanical compression.

Transport of neutral solute in articular cartilage: effects of loading and particle size

We investigate the influence that matrix structure, size of diffusing molecules and type and intensity of mechanical loading have on the transport of neutral solutes in articular cartilage. Although this type of investigation has been performed in the past, earlier researchers assumed a constant diffusion coefficient. By contrast, our diffusion coefficient depends on the local deformation of the matrix, and thus varies both in space and in time during an experiment.

We derive a three-dimensional formulation of the problem based on mixture theory and utilize the commercial finite-element code ABAQUS to study it numerically. We also make use of the Cohen–Turnbull–Yasuda model to correlate the decrease of the diffusion coefficient with the increase in tortuosity, owing to the presence of the matrix. Under appropriate circumstances, the equations derived here reduce to the classical convection/diffusion equation and the equations of the biphasic cartilage model. Even though we chose axisymmetric sample geometry for the present calculations, the model can easily be applied to irregular three-dimensional samples.

Our results reinforce and refine previously published studies. The neutral solute's rate of diffusion is reduced under static compression, due to the strain dependence of the diffusion coefficient; an increase in static compression leads to a decrease in the rate of transport of solutes of all sizes. Dynamic loading, on the other hand, augments solute transport due to convection, depending on particle size. The transport of small molecular size solute is moderately enhanced, but only within the surface layer; however, the rate of transport of large molecule solute is greatly increased, even in the deep layer of the cartilage.

Determining diffusion coefficients in inhomogeneous tissues using fluorescence recovery after photobleaching

Diffusion plays an important role in the transport of nutrients and signaling molecules in cartilaginous tissues. Diffusion coefficients can be measured by fluorescence recovery after photobleaching (FRAP). Available methods to analyze FRAP data, however, assume homogeneity in the environment of the bleached area and neglect geometrical restrictions to diffusion. Hence, diffusion coefficients in inhomogeneous materials, such as most biological tissues, cannot be assessed accurately. In this study, a new method for analyzing data from FRAP measurements has been developed, which is applicable to inhomogeneous tissues. It is based on a fitting procedure of the intensity recovery after photobleaching with a two-dimensional finite element analysis, which includes Fick's law for diffusion. The finite element analysis can account for distinctive diffusivity in predefined zones, which allows determining diffusion coefficients in inhomogeneous samples. The method is validated theoretically and experimentally in both homogeneous and inhomogeneous tissues and subsequently applied to the proliferation zone of the growth plate. Finally, the importance of accounting for inhomogeneities, for appropriate assessment of diffusivity in inhomogeneous tissues, is illustrated.

Solute convection in dynamically compressed cartilage

Chondrocytes depend upon solute transport within the avascular extracellular matrix of articular cartilage for many of their biological activities. Alterations to solute transport parameters may therefore mediate the cell response to tissue compression. While interstitial solute transport may be supplemented by convection during dynamic tissue compression, matrix compression is also associated with decreased diffusivities. Such trade-offs between increased convection and decreased diffusivities of solutes in dynamically compressed cartilage remain largely unexplored. We measured diffusion and convection coefficients of a wide range of solutes in mature bovine cartilage explant disks subjected to radially unconfined axial ramp compression and release. Solutes included approximately 500 Da fluorophores bearing positive and negative charges, and 10 kDa dextrans bearing positive, neutral, and negative charges. Significantly positive values of convection coefficients were measured for several different solutes. Findings therefore support a role for solute convection in mediating the cartilage biological response to dynamic compression.

An integrated finite-element approach to mechanics, transport and biosynthesis in tissue engineering

A finite-element approach was formulated, aimed at enabling an integrated study of mechanical and biochemical factors that control the functional development of tissue engineered constructs. A nonlinear biphasic displacement-velocity-pressure description was combined with adjective and diffusive solute transport, uptake and biosynthesis. To illustrate the approach we focused on the synthesis and transport of macromolecules under influence of fluid flow induced by cyclic compression. In order to produce net transport the effect of dispersion was investigated. An abstract representation of biosynthesis was employed, three cases were distinguished: Synthesis dependent on a limited small solute, synthesis dependent on a limited large solute and synthesis independent of solute transport. Results show that a dispersion model can account for augmented solute transport by cyclic compression and indicate the different sensitivity to loading that can be expected depending on the size of the limiting solute.

Dynamic depth-dependent osmotic swelling and solute diffusion in articular cartilage monitored using real-time ultrasound

The objective of this study was to investigate the feasibility of ultrasonic monitoring for the transient depth-dependent osmotic swelling and solute diffusion in normal and degenerated articular cartilage (artC) tissues. Full-thickness artC specimens were collected from fresh bovine patellae. The artC specimens were continuously monitored using a focused beam of 50 MHz ultrasound (US) during sequential changes of the bathing solution from 0.15 mol/L to 2 mol/L saline, 0.15 mol/L saline, 1 mg/mL trypsin solution, 0.15 mol/L saline, 2 mol/L saline and back to 0.15 mol/L saline. The transient displacements of US echoes from the artC tissues at different depths were used to represent the tissue deformation and the NaCl diffusion. The trypsin solution was used selectively to digest the proteoglycans in artC. It was demonstrated that high-frequency US was feasible for monitoring the transient osmotic swelling, solute transport and progressive degeneration of artC in real-time. Preliminary results showed that the normal bovine patellar artC shrank during the first several minutes and then recovered to its original state in approximately 1 h when the solution was changed from 0.15 mol/L to 2 mol/L saline. Degenerated artC showed neither shrinkage nor recovery during the same process. In addition, a dehydrated-hydrated artC specimen showed much stronger shrinkage and it resumed the original state when the solution was changed from 2 mol/L back to 0.15 mol/L saline. The diffusion of NaCl and the digestion process of proteoglycans induced by trypsin were also successfully monitored in real-time.

Fluid flow and convective transport of solutes within the intervertebral disc

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport of larger molecules. The goal of the study was to predict the influence of load-induced interstitial fluid flow on mass transport in the intervertebral disc. An iterative procedure was used to predict the convective transport of physiologically relevant molecules within the disc. An axisymmetric, poroelastic finite-element structural model of the disc was developed. The diurnal loading was divided into discrete time steps. At each time step, the fluid flow within the disc due to compression or swelling was calculated. A sequentially coupled diffusion/convection model was then employed to calculate solute transport, with a constant concentration of solute being provided at the vascularised endplates and outer annulus. Loading was simulated for a complete diurnal cycle, and the relative convective and diffusive transport was compared for solutes with molecular weights ranging from 400 Da to 40 kDa. Consistent with previous studies, fluid flow did not enhance the transport of low-weight solutes. During swelling, interstitial fluid flow increased the unidirectional penetration of large solutes by approximately 100%. Due to the bi-directional temporal nature of disc loading, however, the net effect of convective transport over a full diurnal cycle was more limited (30% increase). Further study is required to determine the significance of large solutes and the timing of their delivery for disc physiology.

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.

Spatial assessment of articular cartilage proteoglycans with Gd-DTPA-enhanced T1 imaging

In Gd-DTPA-enhanced T(1) imaging of articular cartilage, the MRI contrast agent with two negative charges is understood to accumulate in tissue inversely to the negative charge of cartilage glycosaminoglycans (GAGs) of proteoglycans (PGs), and this leads to a decrease in the T(1) relaxation time of tissue relative to the charge in tissue. By assuming a constant relaxivity for Gd-DTPA in cartilage, it has further been hypothesized that the contrast agent concentration in tissue could be estimated from consecutive T(1) measurements in the absence or presence of the contrast agent. The spatial sensitivity of the technique was examined at 9.4 T in normal and PG-depleted bovine patellar cartilage samples. As a reference, spatial PG concentration was assessed with digital densitometry from safranin O-stained cartilage sections. An excellent linear correlation between spatial optical density (OD) of stained GAGs and T(1) with Gd-DTPA was observed in the control and chondroitinase ABC-treated cartilage specimens, and the MR parameter accounted for approximately 80% of the variations in GAG concentration within samples. Further, the MR-resolved Gd-DTPA concentration proved to be an even better estimate for PGs, with an improved correlation. However, the linear relation between MR parameters and PG concentration did not apply in the deep tissue, where MR measurements overestimated the PG content. While the absolute [Gd-DTPA] determination may be prone to error due to uncertainty of relaxivity in cartilage, or to other contributing factors such as variations in tissue permeability, the experimental evidence highlights the sensitivity of this technique to reflect spatial changes in cartilage PG concentration in normal and degenerated tissue.

Preservation and analysis of nonequilibrium solute concentration distributions within mechanically compressed cartilage explants

Solute transport within articular cartilage is of central importance to tissue physiology, and may mediate effects of mechanical compression on cell metabolism. We therefore developed and applied a freeze-substitution method for fixation of cartilage explant disks which had been compressed axially during radial solute desorption. Dextrans were used as model solutes. Explant morphology was well preserved and nonequilibrium solute concentration distributions were stable for several hours at room temperature. For desorption from explants compressed statically to 0-46% strain, analysis of laser confocal images and comparison to a theoretical model permitted measurement of effective diffusivities. Results were consistent with previous studies suggesting a role for transport limitations in mediating the decreases of chondrocyte metabolic rates associated with static compression. In explants compressed dynamically (23+/-5% strain at 0.001 Hz), evidence was obtained for the augmentation of effective transport rate of 3 kDa dextrans by oscillatory interstitial fluid flows. This suggests that augmented solute transport may play a role in mediating the increases of chondrocyte metabolic rates associated with dynamic compression. Methods appear suitable for quantitative studies of transport within mechanically compressed cartilage-like tissues, and may be valuable for identification of loading environments which optimize solute transport in tissue engineering applications.