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Cartilage Biomechanics Group, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Correspondence: Address reprint requests to Thomas M. Quinn, PhD, Cartilage Biomechanics Group, AI 1234 EPFL Station 15, CH-1015 Lausanne, Switzerland. Tel.: 41-21-693-83-50; Fax: 41-21-693-86-60; E-mail: thomas.quinn{at}epfl.ch.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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–7.5 µL/As in the range of 0–20% compression to –6.0 µL/As in the 35–50% range) consistent with predictions of microstructure-based models of cartilage material properties. However, no significant dependence on direction of the electrokinetic coupling coefficient was detected, even for conditions where the hydraulic permeability tensor is known to be anisotropic. This contrast may also be interpreted using microstructure-based models, and provides insights into structure-function relationships in cartilage extracellular matrix and physical mediators of cell responses to tissue compression. Findings support the use of relatively simple isotropic modeling approaches for electrokinetic phenomena in cartilage and related materials, and indicate that measurement of electrokinetic properties may provide particularly robust means for clinical evaluation of cartilage matrix integrity. |
INTRODUCTION |
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,2). Tissue deformations induce relative motion between matrix fluid and solid, giving rise to electrokinetic phenomena including electric streaming potentials that accompany pressure-driven fluid flows (3,4), and electroosmotic fluid flows driven by electric current (5). These phenomena reflect coupling between fluid-solid relative motion and electric charge transport, which occurs in many contexts (6,7). Electrokinetic phenomena contribute to functions of many biological tissues (2) and have practical applications including microfluidics (8) and control of molecular filtration (9–11).
In cartilage, electrokinetic phenomena depend upon the concentration of glycosaminoglycans immobilized in the matrix (12,13). Changes in this matrix component are among the earliest events in osteoarthritic cartilage degradation (14). In situ measurements of electromechanical coupling (15–17) and electric conductivity (18,19) therefore carry promise for early detection of focal cartilage lesions. Accurate theoretical modeling of cartilage electromechanics (20–22) can be important for interpretation of such measurements. Characterization of electrokinetic properties of compressed cartilage therefore supports accurate application of electrically based measurements of cartilage integrity.
Electrokinetic transport phenomena may also mediate cell biological responses to tissue compression (23). The extracellular matrix of adult articular cartilage is avascular, and chondrocytes rely upon interstitial solute transport for acquisition of nutrients, rejection of wastes, intercellular signaling, and matrix remodeling (1). Solute transport is influenced by changes in matrix composition (24) and structure (25,26), fluid flows (27), and associated electrokinetic phenomena (5). Fields, forces, and flows around individual chondrocytes may therefore influence their responses to cartilage compression (23,28) by modulation of solute transport. Elucidation of relationships between cartilage matrix deformations and electrokinetic phenomena therefore improves understanding of cartilage physiology and may lead to improved tissue repair methods.
During compression, cartilage glycosaminoglycans are thought to change their orientations and relative positions such that matrix molecular architecture can acquire direction-dependent features though none exist in unloaded tissue (29). Such changes appear to underlie the emergence of anisotropy (direction-dependence) in the hydraulic permeability tensor of cartilage with increasing compression (30). Because electrokinetic transport phenomena are also governed by matrix glycosaminoglycans (2,31), it is reasonable to hypothesize that these properties may also become anisotropic with cartilage compression. Such changes could mediate cell responses to cartilage compression, including direction-dependent pericellular matrix deposition (28). Furthermore, though the inhomogeneities of cartilage electrokinetic properties have been explored somewhat (4), relatively little is known regarding their anisotropies (32).
The direction-dependent tensorial character of cartilage electrokinetic transport properties is therefore important to understanding tissue physiology and for clinical evaluation of matrix integrity. Our goals were to examine this direction-dependence by performing electroosmosis experiments on compressed cartilage explant disks. Experiments were designed such that electrokinetic properties could be measured in multiple directions within individual statically compressed explants, to highlight compression-dependent, anisotropic behavior despite variations in composition and structure.
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METHODS |
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100-µm thick was removed then a disk 1000-µm thick was cut consisting primarily of intermediate zone cartilage. The disk axial direction corresponded to that perpendicular to the articular surface, whereas the radial direction corresponded to the parallel direction. Explants were stored at –20°C in PBS containing protease inhibitors (complete tablets, Boehringer Mannheim, Basel, Switzerland) and 0.1 mg/ml sodium azide (Sigma, St. Louis, MO), then defrosted for 2 h in PBS before experiments. Free-swelling explant thicknesses were measured under a dissection microscope and used as references for compressive strain. Explant disks were sandwiched between two precision-machined plexiglass blocks. Along the explant axis, 2.35 mm diameter x 2 mm thick rigid porous cylinders (laser machined from Al2O3 0.5-µm pore size cut-off filters; Kerafol GmbH, Eschenbach, Germany) were mounted flush inside the plexiglass blocks, providing conduits to PBS reservoirs (Fig. 1). Both plexiglass blocks also contained 4 mm diameter x 100 µm deep recesses to keep explants centered during mounting and compression. An O-ring around explants functioned as a gasket. Between the explant radial boundary and O-ring, another porous ceramic cylinder was mounted in the lower plexiglass block, leading to another PBS reservoir. Care was taken during assembly to avoid air bubbles inside the apparatus. The explant represented the only source for electroosmotic fluid flow. Each of the three PBS reservoirs branched into paths for electric current and fluid flow (Fig. 2). Electric current paths consisted of a 10% polymethacrylate (PMA) gel cast within a silicone rubber tube of length 10 cm and inner diameter 3.2 mm (MasterFlex, Cole-Parmer Instrument, Vernon Hills, IL) leading to a 50-µm x 5 mm x 20 mm platinum sheet electrode (Johnson-Matthey, London, UK) partially immersed in a 200-mL PBS bath. PMA gels served as salt bridges to inhibit transport of electrode reaction products to the cartilage disk, and as high flow-resistance elements to force fluid flows into separate paths. Above the cartilage explant, the fluid flow path consisted of a silicone rubber tube leading to a fourth 200 mL PBS bath. Fluid flow through the explant lower axial surface (axial outflow) and through the explant radial edge (radial outflow) were directed into glass capillaries (Figs. 1 and 2) of 340-µm inner diameter (Drummond Scientific, Broomall, PA) leading to atmospheric conditions.
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25%), explant geometry was measured using a microscope (Zeiss LSM 410, Jena, Germany) with 20x objective and motorized stage. Disk diameter was quantified by stage displacements whereas thickness was determined by changes in focal depth between plexiglass surfaces bounding the explant (accounting for the indices of refraction of air and PBS). The apparatus was then placed on the motorized stage (Scan IM 100 x 100 and MultiControl 2000, ITK Kassen GmbH, Lahnau, Germany; interfaced with LabVIEW, National Instruments) of another microscope (Zeiss Axiovert 100) and left for 4–12 h without applied electric currents. To minimize temperature fluctuations the apparatus was surrounded by a styrofoam freezer box lined with plastic tubing through which water at 18.5°C flowed in series with a fixed-temperature recirculator (model 18205, Fischer Bioblock Scientific, Illkirch, France).
When PBS-air menisci in axial and radial outflow capillaries were stable for a few hours, an electric current (I) in the range –150 µA < I < 150 µA was passed through the explant disk in either the axial or radial outflow direction (Fig. 2); current densities were similar to previous studies (5). Steady current (±0.1 µA) was delivered by a high-voltage supply (Keithley model 248, Keithley Instruments, Cleveland, OH) in series with a 10-M
resistance. Positive currents induced positive fluid outflows (Fig. 2). Each time changed, current was held constant for 15 min or more while outflows were monitored using a charge-coupled device camera (Sony XC-75CE, Tokyo, Japan) and 10x objective. Menisci velocities and capillary cross-sectional areas provided volumetric outflow rates (Q). This procedure was repeated for four to six different applied currents (including zero; Fig. 3 a) providing axial and radial outflows versus applied current within individual compressed cartilage disks (Fig. 3 b). Static compression was then increased (to 25–50%) and measurements repeated. Explants were used for at most 2 days.
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). Findings were considered significant for p < 0.05. Data are reported as mean ± SE (n).
Theoretical methods
Extending previous work (20,34,35), a tensorial description of electrokinetic phenomena in homogeneous porous materials may be summarized by a matrix relating area-averaged fluid velocity (U) and electric current density (J) vectors to gradients of fluid hydrostatic pressure (p) and electric potential (
):
 | (1) |
Tensor components of this matrix include the "short-circuit" hydraulic permeability (K11), electric conductivity (K22), and the electromechanical coupling tensors (K12 and K21). The "open circuit" (Darcy) hydraulic permeability, relating U to 
p in the common case where 
, can be direction-dependent in compressed cartilage, with up to 10-fold greater permeability in the direction of compression (perpendicular to the articular surface) (30). Consistent with microstructure-based models of cartilage anisotropic material properties (29), principal axes of the "open circuit" hydraulic permeability appear to correspond to dominant directions defining tissue structure and function. Because all phenomenological tensor components arise from the same microstructure, we assume that all Kij may be written
 | (2) |
values are constant scalars (i, j, and x being dummy variables).
For one-dimensional (1-D) electroosmosis along a principal axis (denoted by x), fluid flows may be driven solely by electric potential gradients (
) and the ratio between U and J defines the electrokinetic coupling coefficient (20) of magnitude
 | (3) |
The vector components of U and J are then simply related by
 | (4) |
Integrating both sides of Eq. 4 over a surface through which current and fluid pass perpendicularly during 1-D electroosmosis provides
 | (5) |
may therefore be determined from macroscale measurements of Qx and Ix, for a purely 1-D experiment.
For two-dimensional (2-D) electric currents and fluid flows as in this study, conservation of fluid volume and electric charge at steady-state imply
 | (6) |
For the case of radial outflow (Fig. 2), current and volumetric fluid flow entering the explant through its upper axial surface must therefore equal those leaving through the radial surface. If ke (a tensor with form as in Eq. 2 and components 
and 
) is isotropic, then pure electroosmotic flows ( everywhere) can be maintained because Eq. 5 may be consistently applied at both the inflow and the outflow surfaces. (The imposed current induces the same volumetric fluid flow into and out of the explant.) In contrast, if ke is anisotropic similarly to the "open circuit" hydraulic permeability such that 
(for example), then constant electric current that changes from the axial to the radial direction will induce greater electroosmotic fluid flows in the axial versus the radial direction. To satisfy Eq. 6, pressure gradients would then arise to diminish axial fluid inflow and augment radial outflow, for this hypothetical case. Direction-dependence of ke is therefore expected to manifest itself by differences in fluid outflow when constant electric current is switched between axial and radial cases (Fig. 2). If constant electric current is switched and fluid outflow remains unchanged, this indicates 
.
These intuitive arguments may be formalized somewhat by using Eqs. 1–3 to write, as in previous work (20),
 | (7) |
 | (8) |
Taking the divergence of both sides of Eq. 7, integrating the result over the explant volume for a radial outflow experiment, and applying Gauss' divergence theorem together with Eq. 6 then provides
 | (9) |
represents the mean value of the outward-directed component of p over the inflow or outflow surface Sx. Equation 9 therefore illustrates that pressure gradients will arise if 
, driving fluid flows that compensate for the difference between electroosmotically driven flows into and out of the explant. In contrast, an axial outflow experiment is expected to be nearly 1-D in nature, with identical electrokinetic coupling coefficients at the inflow and outflow surfaces; therefore fluid flows in that case are nearly purely electroosmotic, and expected to differ from those of the radial flow case if . |
RESULTS |
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), unlike pressure-induced fluid flow, pure electroosmotic fluid flow does not intrinsically involve cartilage matrix deformations. Therefore, the observed delay (Fig. 3 a) was not necessarily related to mechanical relaxation within the cartilage explant itself. Furthermore, direct observation of explants during this transitional period did not reveal noticeable deformations.
Steady-state radial outflows attained (Fig. 3 a) after 20 min could be maintained for several hours. Concomitantly, fluid flow through the axial outflow capillary was negligible while no current flowed to that electrode. When electric current was switched to the axial electrode (Fig. 2), axial outflow became nonzero whereas radial outflow was negligible. Steady-state flow regimes provided electroosmotic flow rates versus applied current (Fig. 3 b). For both axial and radial outflows, the relationship between Q and I appeared to be linear with similar slopes in the range –150 µA < I < 150 µA. Slight departures from zero flow rate at zero current (Fig. 3 b) reflected background noise, likely due to thermal effects. Control studies using 10% PMA gel in place of cartilage disks resulted in negligible fluid flow regardless of applied current, confirming that cartilage was the sole source for electroosmotic flow.
The slopes of Q versus I plots (Fig. 3 b) provided and (Eq. 5). The range of values (from –4.8 to –11.2 µL/As; Fig. 4) was consistent with previous 1-D measurements in uncompressed calf cartilage (5). Paired sample analysis detected no significant differences (p > 0.05) between and over the full range of data (Fig. 4), nor within the compression ranges 0–20%, 20–35%, and 35–50%. Both and exhibited significant linear correlations as decreasing functions of compression (p 0.01). However, these decreases were not very dramatic over the range of compression applied (Fig. 4). Mean values of 
(with and pooled together) measured within the compression ranges 0–20%, 20–35%, and 35–50% were –7.5 ± 0.5 (n = 12), –6.6 ± 0.2 (n = 14), and –6.0 ± 0.2 (n = 18) µL/As, respectively.
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was also examined via the normalization 
versus compression (Fig. 5). No significant differences between this quantity and 1 were evident for the full range of data nor within the compression ranges 0–20%, 20–35%, and 35–50%. Furthermore, no significant linear correlation was detected between and compression (Fig. 5).
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DISCUSSION |
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). The material properties governing electroosmotic flows therefore appear to be isotropic even when cartilage is highly compressed and other transport properties such as hydraulic permeability are markedly anisotropic (30). Measurements did not include superficial zone cartilage that bears a relatively high concentration of preferentially oriented collagen fibrils and therefore may exhibit more anisotropic properties. However, electrokinetic phenomena arise primarily within the proteoglycan gel, and it remains unclear to what extent collagen fibrils affect the anisotropies of the matrix electromechanical coupling tensor K12 and conductivity K22 differentially, such that ke becomes significantly anisotropic. Therefore, these findings support relatively simple isotropic modeling approaches for electrokinetic phenomena, and provide important insights into structure-function relationships in cartilage matrix.
Several observations consistently supported the accuracy of our methods, and the conclusion that ke was isotropic. The electrokinetic coupling coefficients obtained in this study (Fig. 4) correspond well with previous measurements using different techniques and cartilage sources (5,20,36). No systematic deviation from linearity of Q versus I was evident (Fig. 3 b), indicating that neither ohmic heating (which might introduce current-dependent behavior) nor explant degradation (which might introduce time-dependence of measured properties) significantly affected results. The main technical problems encountered during apparatus development were associated with temperature fluctuations, but this seemed well controlled as indicated by negligible fluid flow at zero current (Fig. 3 b). When current was switched between axial and radial directions, fluid outflow also switched without detectable changes in magnitude, indicating that ke was isotropic. Had ke been significantly anisotropic, fluid pressure fields within explants would have changed when current was changed, as pressure-driven flows would have been required to compensate for differences between electroosmotic inflows and outflows. However, no evidence for this was observed. Fluid outflow was always restricted to the direction of current flow, which would not be expected for pressure-driven flows. Furthermore, since fluid flows associated with these changing currents were easily large enough to induce significant matrix deformations had they been pressure-driven (30), the absence of visible explant deformations provided further evidence that pressure gradients did not in fact arise, and that ke was indeed isotropic.
Isotropy of ke contrasts with anisotropy of hydraulic permeability in compressed cartilage (30), but has an intuitive basis when considered in light of molecular-scale physics. Modeling of cartilage matrix microstructural deformations indicates that effective pore sizes can become direction-dependent with compression (29), contributing to the emergence of anisotropic hydraulic permeability. In a 1-D description of electrokinetic transport through membranes containing perpendicular cylindrical pores of radius r at volume fraction 
filled with saline of viscosity 
, previous investigators have obtained analytical expressions for electrokinetic coupling matrices analogous to that of Eq. 1 (37). For the approximation of a "Helmholtz double layer" (arising from fixed surface charge density within pores) characterized by thickness d << r and electrostatic potential 
at the pore wall, these results may be written
 | (10) |
and 
represent dielectric permittivity and electric conductivity of saline. As indicated by its dependence upon r2, the hydraulic permeability (term in Eq. 10 corresponding to K11 in Eq. 1) is sensitive to the pore geometry. In contrast, K12 and K21 exhibit no r-dependence whereas K22 has relatively weak r-dependence (Eq. 10), suggesting that these properties are less affected by changes in pore structure. Similar insights also emerge from more geometrically complex modeling of electrokinetic transport in cartilage, where fluid flow and electric current through the interstices of a random array of charged solid cylinders (representing gylcosaminoglycans) was considered (31,38). This work indicates that changing matrix density will have relatively greater effects on hydraulic permeability than on electrokinetic transport coefficients (31,38). It is therefore reasonable that direction-dependent changes in matrix structure that underlie the emergence of anisotropic hydraulic permeability (K11) in compressed cartilage may not measurably affect the isotropy of K12, K21, or K22. Similarly, tissues bearing significant structural anisotropy even when undeformed, such as the cartilage superficial zone, might reasonably be expected to exhibit anisotropic K11, but isotropic K12, K21, and K22.
Results for the relatively weak dependence of ke on compression (Fig. 4) also followed predictions of microstructure-based models. Increased matrix density due to cartilage compression is expected to induce modest decreases in the magnitude of 
and increases in 
(31,38). Consistent with these predictions, the magnitudes of and (Eq. 3) were found to decrease somewhat with increasing compression (Fig. 4).
Findings of isotropic ke may provide insights into mediators of chondrocyte biological responses to cartilage compression, and help refine application of electrically based assessment of cartilage integrity. The extracellular matrix of articular cartilage may be expected to acquire anisotropic transport properties during tissue compression, due to direction-dependent changes in molecular architecture (29). This emergent anisotropy (30) may mediate direction-dependent pericellular matrix deposition in compressed cartilage (28). The isotropy exhibited by ke in compressed cartilage would therefore argue against contributions from matrix electrokinetic properties as microphysical mediators of direction-dependent chondrocyte behavior (28). Immobilized glycosaminoglycans provide most of the fixed charge density, which gives rise to electrokinetic phenomena in cartilage. Since ke is isotropic and relatively insensitive to matrix deformations, it may provide an indicator of immobolized glycosaminoglycan content that is more robust to different tissue loading conditions and measurement configurations than other cartilage material properties such as hydraulic permeability (30). These findings of directional invariance of ke also justify relatively simple isotropic modeling of cartilage electrokinetic behavior (20–22), which may help improve clinical diagnosis of cartilage disease (15–19).
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ACKNOWLEDGEMENTS |
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Submitted on January 30, 2006; accepted for publication June 12, 2006.
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REFERENCES |
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) and radial (
) fluid flow rates versus electric current for the same explant. Linearity of electrokinetic coupling is indicated by the solid line (linear fit) for radial flow and the dotted line for axial flow.
