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Copyright © 2006 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 91, Issue 6, 2349-2355, 15 September 2006

doi:10.1529/biophysj.106.082263

Electrophysiology

Tensorial Electrokinetics in Articular Cartilage

Boris Reynaud and Thomas M. Quinn^,  

Cartilage Biomechanics Group, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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.

The biomechanically functional extracellular matrix of articular cartilage is a hydrated polyelectrolyte gel containing fixed negative charges on proteoglycans enmeshed within a collagen network, with corresponding positive charges in the matrix fluid 1,2. 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 9,10,11.

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 15,16,17 and electric conductivity 18,19 therefore carry promise for early detection of focal cartilage lesions. Accurate theoretical modeling of cartilage electromechanics 20,21,22 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.

Refrigerated humeri of 18-month-old cows were obtained within 24h of slaughter. Osteochondral cores of 4mm diameter were taken from the proximal articular surface using a biopsy drill and bone saw (Stratec, Oberdorf, Switzerland) under irrigation with phosphate buffered saline ((PBS); without Ca²⁺ or Mg²⁺). Using a microtome (Leica RM 2135, Wetzlar, Germany), a superficial layer ∼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 2h 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, 2.35mm diameter×2mm 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 4mm diameter×100μm 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 10cm and inner diameter 3.2mm (MasterFlex, Cole-Parmer Instrument, Vernon Hills, IL) leading to a 50-μm×5 mm×20mm 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 200mL 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 (Figure 1 and Figure 2) of 340-μm inner diameter (Drummond Scientific, Broomall, PA) leading to atmospheric conditions.

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Figure 1

Exploded view of apparatus used to measure electrokinetic fluid transport in statically compressed cartilage explants. Cylindrical explant disks were sandwiched between precision-machined plexiglass blocks. Dotted lines indicate conduits for currents and fluid flows through the apparatus. Above and below explants, 2.35-mm diameter porous ceramic disks were centered on the explant axis.

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Figure 2

Schematic sketch of experimental apparatus.

The plexiglass blocks were held together by aluminum plates with central openings allowing observation of cartilage explants. Screws between the plates were tightened uniformly to statically compress explants. After mounting in the apparatus under a relatively small compression (≤25%), explant geometry was measured using a microscope (Zeiss LSM 410, Jena, Germany) with 20× 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 100×100 and MultiControl 2000, ITK Kassen GmbH, Lahnau, Germany; interfaced with LabVIEW, National Instruments) of another microscope (Zeiss Axiovert 100) and left for 4–12h 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 −150μA<I<150μA 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 (±0.1μA) was delivered by a high-voltage supply (Keithley model 248, Keithley Instruments, Cleveland, OH) in series with a 10-MΩ resistance. Positive currents induced positive fluid outflows (Fig. 2). Each time changed, current was held constant for 15min or more while outflows were monitored using a charge-coupled device camera (Sony XC-75CE, Tokyo, Japan) and 10× 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; Figure 3a) providing axial and radial outflows versus applied current within individual compressed cartilage disks (Figure 3b). Static compression was then increased (to ∼25–50%) and measurements repeated. Explants were used for at most 2 days.

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Figure 3

(a) Applied electric current and radial flow meniscus position versus time for a cartilage disk under 29% static compression. Dotted lines indicate regimes with constant currents and fluid flow rates. (b) Axial (○) 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.

A total of 11 explants were used from three different dissections. All explants contributed data at two static compression levels. Differences between electrokinetic coupling coefficients (defined below) in radial and axial directions were examined using t-tests for paired samples. Linear correlation analysis (Pearson’s r) was used to quantify significance of trends versus static compression 33. Findings were considered significant for p<0.05. Data are reported as mean±SE (n).

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 (ϕ):

(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 K_ij may be written

(2)

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)

(4)

Integrating both sides of Eq. (4) over a surface through which current and fluid pass perpendicularly during 1-D electroosmosis provides

(5)

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)

These intuitive arguments may be formalized somewhat by using Eqs. (1) 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)

When electric current was changed from 0 to 150μA to the radial electrode (Fig. 2), radial fluid outflow reached a steady value after several minutes (Figure 3a). This transitional period was consistently shorter for negative than positive currents, and appeared to be the time required to attain adequate pressures to drive fluid flow through the capillary, where the asymmetric delay reflected nonlinear (tension versus compression) deformations in the PMA gel salt bridges. As previously described 20, unlike pressure-induced fluid flow, pure electroosmotic fluid flow does not intrinsically involve cartilage matrix deformations. Therefore, the observed delay (Figure 3a) 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 (Figure 3a) after ∼20min 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 (Figure 3b). For both axial and radial outflows, the relationship between Q and I appeared to be linear with similar slopes in the range −150μA<I<150μA. Slight departures from zero flow rate at zero current (Figure 3b) 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 (Figure 3b) provided and (Eq. (5)). The range of values (from −4.8 to −11.2μL/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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Figure 4

Electrokinetic coupling coefficients in the axial (, ○) and radial (, ■) directions of cartilage disks under varying levels of radially unconfined static axial compression. Lines connect data acquired from a single explant disk at one compression level. Dotted line indicates predicted derived from results of an isotropic model of cartilage matrix electrokinetics 38.

Anisotropy of 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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Figure 5

The ratio between axial and radial electrokinetic coupling coefficients () of cartilage disks under varying levels of radially unconfined static axial compression. Lines connect data acquired from a single explant disk.

Cartilage explant disks compressed axially up to 50% exhibited k_e with a weak dependence upon compression, but no detectable direction dependence (). 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 k_e 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 k_e 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 (Figure 3b), 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 (Figure 3b). When current was switched between axial and radial directions, fluid outflow also switched without detectable changes in magnitude, indicating that k_e was isotropic. Had k_e 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 k_e was indeed isotropic.

Isotropy of k_e 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 α filled with saline of viscosity η, 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 ζ at the pore wall, these results may be written

(10)

Results for the relatively weak dependence of k_e 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 k_e 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 k_e 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 k_e 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 k_e also justify relatively simple isotropic modeling of cartilage electrokinetic behavior 20,21,22, which may help improve clinical diagnosis of cartilage disease 15,16,17,18,19.