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.     

A triphasic theory for the swelling and deformation behaviors of articular cartilage

Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single-salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by mu i = mu io + (RT/Mi)ln[gamma 2 +/- c(c + cF)] and mu w = mu wo + [p-RT phi (2c + cF) + Bwe]/pwT, where R, T, Mi, gamma +/-, phi, pwT and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is sigma = - pI-TcI + lambda s(trE)I + 2 musE, where E is the strain tensor and (lambda s, mu s) are the Lamé constants of the elastic solid matrix. The chemical-expansion stress (-Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the "pre-stress" in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.     

3D finite element analysis of nutrient distributions and cell viability in the intervertebral disc: effects of deformation and degeneration

The intervertebral disc (IVD) receives important nutrients, such as glucose, from surrounding blood vessels. Poor nutritional supply is believed to play a key role in disc degeneration. Several investigators have presented finite element models of the IVD to investigate disc nutrition; however, none has predicted nutrient levels and cell viability in the disc with a realistic 3D geometry and tissue properties coupled to mechanical deformation. Understanding how degeneration and loading affect nutrition and cell viability is necessary for elucidating the mechanisms of disc degeneration and low back pain. The objective of this study was to analyze the effects of disc degeneration and static deformation on glucose distributions and cell viability in the IVD using finite element analysis. A realistic 3D finite element model of the IVD was developed based on mechano-electrochemical mixture theory. In the model, the cellular metabolic activities and viability were related to nutrient concentrations, and transport properties of nutrients were dependent on tissue deformation. The effects of disc degeneration and mechanical compression on glucose concentrations and cell density distributions in the IVD were investigated. To examine effects of disc degeneration, tissue properties were altered to reflect those of degenerated tissue, including reduced water content, fixed charge density, height, and endplate permeability. Two mechanical loading conditions were also investigated: a reference (undeformed) case and a 10% static deformation case. In general, nutrient levels decreased moving away from the nutritional supply at the disc periphery. Minimum glucose levels were at the interface between the nucleus and annulus regions of the disc. Deformation caused a 6.2% decrease in the minimum glucose concentration in the normal IVD, while degeneration resulted in an 80% decrease. Although cell density was not affected in the undeformed normal disc, there was a decrease in cell viability in the degenerated case, in which averaged cell density fell 11% compared with the normal case. This effect was further exacerbated by deformation of the degenerated IVD. Both deformation and disc degeneration altered the glucose distribution in the IVD. For the degenerated case, glucose levels fell below levels necessary for maintaining cell viability, and cell density decreased. This study provides important insight into nutrition-related mechanisms of disc degeneration. Moreover, our model may serve as a powerful tool in the development of new treatments for low back pain.     

Physical signals and solute transport in human intervertebral disc during compressive stress relaxation: 3D finite element analysis

A 3D finite element model for charged hydrated soft tissues containing charged/uncharged solutes was developed based on the multi-phasic mechano-electrochemical mixture theory (Lai et al., J. Biomech. Eng. 113 (1991), 245-258; Gu et al., J. Biomech. Eng. 120 (1998), 169-180). This model was applied to analyze the mechanical, chemical and electrical signals within the human intervertebral disc during an unconfined compressive stress relaxation test. The effects of tissue composition [e.g., water content and fixed charge density (FCD)] on the physical signals and the transport rate of fluid, ions and nutrients were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization was more pronounced at the center (nucleus) region of the disc while the effective (von Mises) stress was higher at the outer (annulus) region. Parametric analyses revealed that the decrease in initial tissue water content (0.7-0.8) increased the peak stress and relaxation time due to the reduction of permeability, causing greater fluid pressurization effect. The electrical signals within the disc were more sensitive to FCD than tissue porosity, and mechanical loading affected the large solute (e.g., growth factor) transport significantly, but not for small solute (e.g., glucose). Moreover, this study confirmed that the interstitial fluid pressurization plays an important role in the load support mechanism of IVD by sharing more than 40% of the total load during disc compression. This study is important for understanding disc biomechanics, disc nutrition and disc mechanobiology.     

The internal mechanical functioning of intervertebral discs and articular cartilage,and its relevance to matrix biology

Degeneration of intervertebral discs and articular cartilage can cause pain and disability. Risk factors include genetic inheritance and age, but mechanical loading also is important. Its influence has been investigated using miniature pressure transducers to measure the distribution of compressive stress (force per unit area) within loaded tissue. The technique quantifies stress concentrations, and detects regions that behave in a fluid-like manner.Intervertebral discs demonstrate a central fluid-like region which normally extends beyond the anatomical nucleus pulposus so that the whole disc functions like a “water bed”. With increasing age, the fluid region shrinks and pressure within it falls. Stress concentrations appear in the surrounding anulus fibrosus, with location depending on posture. Stress concentrations become large in degenerated discs, and are intensified by sustained loading or injury. Articular cartilage never exhibits an internal fluid pressure: stress gradients and concentrations normally occur within it, and are intensified by sustained loading.Excessive matrix stresses can cause pain and progressive damage. They also inhibit matrix synthesis and stimulate production of matrix-degrading enzymes. In this way, injury to chondroid tissues can initiate a ‘vicious circle’ of abnormal matrix stresses, abnormal metabolism, weakened matrix, and further injury, which explains many features of their degeneration.     

Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes

The collagen network and proteoglycan matrix of articular cartilage are thought to play an important role in controlling the stresses and strains in and around chondrocytes, in regulating the biosynthesis of the solid matrix, and consequently in maintaining the health of diarthrodial joints. Understanding the detailed effects of the mechanical environment of chondrocytes on cell behavior is therefore essential for the study of the development, adaptation, and degeneration of articular cartilage. Recent progress in macroscopic models has improved our understanding of depth-dependent properties of cartilage. However, none of the previous works considered the effect of realistic collagen orientation or depth-dependent negative charges in microscopic models of chondrocyte mechanics. The aim of this study was to investigate the effects of the collagen network and fixed charge densities of cartilage on the mechanical environment of the chondrocytes in a depth-dependent manner. We developed an anisotropic, inhomogeneous, microstructural fibril-reinforced finite element model of articular cartilage for application in unconfined compression. The model consisted of the extracellular matrix and chondrocytes located in the superficial, middle, and deep zones. Chondrocytes were surrounded by a pericellular matrix and were assumed spherical prior to tissue swelling and load application. Material properties of the chondrocytes, pericellular matrix, and extracellular matrix were obtained from the literature. The loading protocol included a free swelling step followed by a stress-relaxation step. Results from traditional isotropic and transversely isotropic biphasic models were used for comparison with predictions from the current model. In the superficial zone, cell shapes changed from rounded to elliptic after free swelling. The stresses and strains as well as fluid flow in cells were greatly affected by the modulus of the collagen network. The fixed charge density of the chondrocytes, pericellular matrix, and extracellular matrix primarily affected the aspect ratios (height/width) and the solid matrix stresses of cells. The mechanical responses of the cells were strongly location and time dependent. The current model highlights that the collagen orientation and the depth-dependent negative fixed charge densities of articular cartilage have a great effect in modulating the mechanical environment in the vicinity of chondrocytes, and it provides an important improvement over earlier models in describing the possible pathways from loading of articular cartilage to the mechanical and biological responses of chondrocytes.     

Analysis of the dynamic permeation experiment with implication to cartilaginous tissue engineering

In the present study, a I-D dynamic permeation of a monovalent electrolyte solution through a negatively charged-hydrated cartilaginous tissue is analyzed using the mechano-electrochemical theory developed by Lai et al. (1991) as the constitutive model for the tissue. The spatial distributions of stress, strain, fluid pressure, ion concentrations, electrical potential, ion and fluid fluxes within and across the tissue have been calculated. The dependencies of these mechanical, electrical and physicochemical responses on the tissue fixed charge density, with specified modulus, permeability, diffusion coefficients, and frequency and magnitude of pressure differential are determined. The results demonstrate that these mechanical, electrical and physicochemical fields within the tissue are intrinsically and nonlinearly coupled, and they all vary with time and depth within the tissue.     

Temporal changes of mechanical signals and extracellular composition in human intervertebral disc during degenerative progression

In this study, a three-dimensional finite element model was used to investigate the changes in tissue composition and mechanical signals within human lumbar intervertebral disc during the degenerative progression. This model was developed based on the cell-activity coupled mechano-electrochemical mixture theory. The disc degeneration was simulated by lowering nutrition levels at disc boundaries, and the temporal and spatial distributions of the fixed charge density, water content, fluid pressure, Von Mises stress, and disc deformation were analyzed. Results showed that fixed charge density, fluid pressure, and water content decreased significantly in the nucleus pulposus (NP) and the inner to middle annulus fibrosus (AF) regions of the degenerative disc. It was found that, with degenerative progression, the Von Mises stress (relative to that at healthy state) increased within the disc, with a larger increase in the outer AF region. Both the disc volume and height decreased with the degenerative progression. The predicted results of fluid pressure change in the NP were consistent with experimental findings in the literature. The knowledge of the variations of temporal and spatial distributions of composition and mechanical signals within the human IVDs provide a better understanding of the progression of disc degeneration.     

The functional environment of chondrocytes within cartilage subjected to compressive loading: a theoretical and experimental approach

A non-invasive methodology (based on video microscopy, optimized digital image correlation and thin plate spline smoothing technique) has been developed to determine the intrinsic tissue stiffness (H(a)) and the intrinsic fixed charge density (c(0)(F)) distribution for hydrated soft tissues such as articular cartilage. Using this technique, the depth-dependent inhomogeneous parameters H(a)(z) and c(0)(F)(z) were determined for young bovine cartilage and incorporated into a triphasic mixture model. This model was then used to predict the mechanical and electrochemical events (stress, strain, fluid/osmotic pressure, and electrical potentials) inside the tissue specimen under a confined compression stress relaxation test. The integration of experimental measurements with theoretical analyses can help to understand the unique material behaviors of articular cartilage. Coupled with biological assays of cell-scale biosynthesis, there is also a great potential in the future to study chondrocyte mechanotransduction in situ with a new level of specificity.     

Osmotic loading to determine the intrinsic material properties of guinea pig knee cartilage

Few methods exist to study cartilage mechanics in small animal joints due to the difficulties associated with handling small tissue samples. In this study, we apply an osmotic loading method to quantify the intrinsic material properties of articular cartilage in small animal joints. Cartilage samples were studied from the femoral condyle and tibial plateau of two-month old guinea pigs. Swelling strains were measured using confocal fluorescence scanning microscopy in samples subjected to osmotic loading. A histochemical staining method was developed and calibrated for quantification of negative fixed charge density in guinea pig cartilage. Site-matched swelling strain data and fixed charge density values were then used with a triphasic theoretical model for cartilage swelling to determine the uniaxial modulus of the cartilage solid matrix. Moduli obtained in this study (7.2 MPa femoral condyle; 10.8 MPa, tibial plateau) compare well with previously reported values for the tensile moduli of human and other animal cartilages determined from uniaxial tension experiments. This study provides the first available data for material properties and fixed charge density in cartilage from the guinea pig knee and suggests a promising method for tracking changes in cartilage mechanics in small animal models of degeneration.     

The generalized triphasic correspondence principle for simultaneous determination of the mechanical properties and proteoglycan content of articular cartilage by indentation

The triphasic mixture theory has been used to describe the mechanical and physicochemical behaviors of articular cartilage under some specialized loading conditions. However, the mathematical complexities of this theory have limited its applications for theoretical analyses of experimental studies and models for predicting cartilage and other biological tissues' deformational behaviors. A generalized correspondence principle has been established in the present study, and this principle shows that the equilibrium deformational behavior of a charged-hydrated material under loading is identical to that of an elastic medium without charge. A set of explicit formulas has been derived to correlate the mechanical properties of an equivalent material with the intrinsic elastic moduli, fixed charge density and free-ion concentration within the cartilage tissue. The validity of these formulas is independent of the deformation state of the elastic solid matrix under an infinitesimal strain. Therefore they can be employed for any loading conditions, such as confined or unconfined compression, tension, and indentation tests, etc. In the current study, the fixed charge density of bovine cartilage is determined from the indentation creep data using this generalized correspondence principle. The proteoglycan content results were then compared with those from biochemical assay, yielding a linear regression slope of 1.034. Additionally a correspondence principle within a framework of cubic symmetry and a bilinear response in tension-compression (the conewise linear elasticity model) has also been developed to demonstrate the potential application of current methodology for inhomogeneous, anisotropic and nonlinear situations.     

Analysis of the permeation of cryoprotectants in cartilage

Some tissues, such as cartilage and cornea, carry an internal fixed negative charge, leading to a swelling pressure that is balanced by tensile stress in the tissue matrix. During the addition and removal of cryoprotectants the changes in osmotic pressure will cause the tissue to deform. Because of the fixed charge and osmotic deformation, the permeation process in such tissues differs from ordinary diffusion processes. In this paper a biomechanical multi-solute theory is introduced to describe this process in cartilage tissue. Typical values for the physiological and biomechanical properties are used in the simulation. Several parameters - the aggregate modulus, the fixed charge density and the frictional parameter - are analyzed to show their impact on the process. It is shown that friction between water and cryoprotectant has the greatest influence but the fixed charge density is also important. The aggregate modulus and the frictional parameter between the cryoprotectant and the solid matrix have the least influence. Both the new biomechanical model and the conventional diffusion model were fitted to published experimental data concerning the time course of mean tissue cryoprotectant concentration when cartilage is immersed in solutions of dimethyl sulphoxide or propylene glycol: in all cases and with both models a good fit was obtained only when a substantial amount of non-solvent water was assumed.     

The influence of the fixed negative charges on mechanical and electrical behaviors of articular cartilage under unconfined compression

Unconfined compression test has been frequently used to study the mechanical behaviors of articular cartilage, both theoretically and experimentally. It has also been used in explant and gel-cell-complex studies in tissue engineering. In biphasic and poroelastic theories, the effect of charges fixed on the proteoglycan macromolecules in articular cartilage is embodied in the apparent compressive Young's modulus and the apparent Poisson's ratio of the tissue, and the fluid pressure is considered to be the portion above the osmotic pressure. In order to understand how proteoglycan fixed charges might affect the mechanical behaviors of articular cartilage, and in order to predict the osmotic pressure and electric fields inside the tissue in this experimental configuration, it is necessary to use a model that explicitly takes into account the charged nature of the tissue and the flow of ions within its porous interstices. In this paper, we used a finite element model based on the triphasic theory to study how fixed charges in the porous-permeable soft tissue can modulate its mechanical and electrochemical responses under a step displacement in unconfined compression. The results from finite element calculations showed that: 1) A charged tissue always supports a larger load than an uncharged tissue of the same intrinsic elastic moduli. 2) The apparent Young's modulus (the ratio of the equilibrium axial stress to the axial strain) is always greater than the intrinsic Young's modulus of an uncharged tissue. 3) The apparent Poisson's ratio (the negative ratio of the lateral strain to the axial strain) is always larger than the intrinsic Poisson's ratio of an uncharged tissue. 4) Load support derives from three sources: intrinsic matrix stiffness, hydraulic pressure and osmotic pressure. Under the unconfined compression, the Donnan osmotic pressure can constitute between 13%-22% of the total load support at equilibrium. 5) During the stress-relaxation process following the initial instant of loading, the diffusion potential (due to the gradient of the fixed charge density and the associated gradient of ion concentrations) and the streaming potential (due to fluid convection) compete against each other. Within the physiological range of material parameters, the polarity of the electric potential depends on both the mechanical properties and the fixed charge density (FCD) of the tissue. For softer tissues, the diffusion effects dominate the electromechanical response, while for stiffer tissues, the streaming potential dominates this response. 6) Fixed charges do not affect the instantaneous strain field relative to the initial equilibrium state. However, there is a sudden increase in the fluid pressure above the initial equilibrium osmotic pressure. These new findings are relevant and necessary for the understanding of cartilage mechanics, cartilage biosynthesis, electromechanical signal transduction by chondrocytes, and tissue engineering.     

On the electric potentials inside a charged soft hydrated biological tissue: streaming potential versus diffusion potential

The main objective of this study is to determine the nature of electric fields inside articular cartilage while accounting for the effects of both streaming potential and diffusion potential. Specifically, we solve two tissue mechano-electrochemical problems using the triphasic theories developed by Lai et al. (1991, ASME J. Biomech Eng., 113, pp. 245-258) and Gu et al. (1998, ASME J. Biomech. Eng., 120, pp. 169-180) (1) the steady one-dimensional permeation problem; and (2) the transient one-dimensional ramped-displacement, confined-compression, stress-relaxation problem (both in an open circuit condition) so as to be able to calculate the compressive strain, the electric potential, and the fixed charged density (FCD) inside cartilage. Our calculations show that in these two technically important problems, the diffusion potential effects compete against the flow-induced kinetic effects (streaming potential) for dominance of the electric potential inside the tissue. For softer tissues of similar FCD (i.e., lower aggregate modulus), the diffusion potential effects are enhanced when the tissue is being compressed (i.e., increasing its FCD in a nonuniform manner) either by direct compression or by drag-induced compaction; indeed, the diffusion potential effect may dominate over the streaming potential effect. The polarity of the electric potential field is in the same direction of interstitial fluid flow when streaming potential dominates, and in the opposite direction of fluid flow when diffusion potential dominates. For physiologically realistic articular cartilage material parameters, the polarity of electric potential across the tissue on the outside (surface to surface) may be opposite to the polarity across the tissue on the inside (surface to surface). Since the electromechanical signals that chondrocytes perceive in situ are the stresses, strains, pressures and the electric field generated inside the extracellular matrix when the tissue is deformed, the results from this study offer new challenges for the understanding of possible mechanisms that control chondrocyte biosyntheses.     

A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors.

A new mixture theory was developed to model the mechano-electrochemical behaviors of charged-hydrated soft tissues containing multi-electrolytes. The mixture is composed of n + 2 constituents (1 charged solid phase, 1 noncharged solvent phase, and n ion species). Results from this theory show that three types of force are involved in the transport of ions and solvent through such materials: (1) a mechanochemical force (including hydraulic and osmotic pressures); (2) an electrochemical force; and (3) an electrical force. Our results also show that three types of material coefficients are required to characterize the transport rates of these ions and solvent: (1) a hydraulic permeability; (2) mechano-electrochemical coupling coefficients; and (3) an ionic conductance matrix. Specifically, we derived the fundamental governing relationships between these forces and material coefficients to describe such mechano-electrochemical transduction effects as streaming potential, streaming current, diffusion (membrane) potential, electro-osmosis, and anomalous (negative) osmosis. As an example, we showed that the well-known formula for the resting cell membrane potential (Hodgkin and Huxley, 1952a, b) could be derived using our new n + 2 mixture model (a generalized triphasic theory). In general, the n + 2 mixture theory is consistent with and subsumes all previous theories pertaining to specific aspects of charged-hydrated tissues. In addition, our results provided the stress, strain, and fluid velocity fields within a tissue of finite thickness during a one-dimensional steady diffusion process. Numerical results were provided for the exchange of Na+ and Ca++ through the tissue. These numerical results support our hypothesis that tissue fixed charge density (CF) plays a significant role in modulating kinetics of ions and solvent transport through charged-hydrated soft tissues.     

Matrix-assisted cell transfer for intervertebral disc cell therapy

Cell therapy seems to be a promising way to reconstitute degenerated discs. We elucidate the basic aspects of intervertebral disc (IVD) cell therapy to estimate its potential in disc regeneration. Cell transfer efficiency and survival was quantified by luciferase expression after injection of recombinant cells into healthy, nucleotomized or mechanically degenerated rabbit IVDs in vitro, in situ or in vivo. A two-component fibrin matrix was adapted to allow injection of a fluid cell suspension that quickly polymerizes in IVDs. Thirty-five to fifty percent of matrix injected cells remained in the nucleus and transition zone in contrast to a rapid loss of medium-injected cells. Nucleotomy, which reduces intradiscal pressure, was crucial to the survival of the transferred cells over 3 days and nutritional enrichment of the fibrin matrix with potent biomolecules from serum significantly enhanced cell viability. In conclusion, advanced matrix substitutes are needed for efficient transfer and improved cell survival in the low-nutrient intradiscal environment to further improve disc cell therapy.     

The effect of matrix tension-compression nonlinearity and fixed negative charges on chondrocyte responses in cartilage

Thorough analyses of the mechano-electrochemical interaction between articular cartilage matrix and the chondrocytes are crucial to understanding of the signal transduction mechanisms that modulate the cell metabolic activities and biosynthesis. Attempts have been made to model the chondrocytes embedded in the collagen-proteoglycan extracellular matrix to determine the distribution of local stress-strain field, fluid pressure and the time-dependent deformation of the cell. To date, these models still have not taken into account a remarkable characteristic of the cartilage extracellular matrix given rise from organization of the collagen fiber architecture, now known as the tension-compression nonlinearity (TCN) of the tissue, as well as the effect of negative charges attached to the proteoglycan molecules, and the cell cytoskeleton that interacts with mobile ions in the interstitial fluid to create osmotic and electro-kinetic events in and around the cells. In this study, we proposed a triphasic, multi-scale, finite element model incorporating the Conewise Linear Elasticity that can describe the various known coupled mechanical, electrical and chemical events, while at the same time representing the TCN of the extracellular matrix. The model was employed to perform a detailed analysis of the chondrocytes' deformational and volume responses, and to quantitatively describe the mechano-electrochemical environment of these cells. Such a model describes contributions of the known detailed micro-structural and composition of articular cartilage. Expectedly, results from model simulations showed substantial effects of the matrix TCN on the cell deformational and volume change response. A low compressive Poisson's ratio of the cartilage matrix exhibiting TCN resulted in dramatic recoiling behavior of the tissue under unconfined compression and induced significant volume change in the cell. The fixed charge density of the chondrocyte and the pericellular matrix were also found to play an important role in both the time-dependent and equilibrium deformation of the cell. The pericellular matrix tended to create a uniform osmolarity around the cell and overall amplified the cell volume change. It is concluded that the proposed model can be a useful tool that allows detailed analysis of the mechano-electrochemical interactions between the chondrocytes and its surrounding extracellular matrix, which leads to more quantitative insights in the cell mechano-transduction.     

Cartilage electromechanics--I. Electrokinetic transduction and the effects of electrolyte pH and ionic strength

Articular cartilage contains a high fixed charge density under physiological conditions associated primarily with the ionized proteoglycan molecules of the extracellular matrix. Oscillatory compression of cartilage using physiological loads produces electrical potentials that have been shown previously to be the result of an electrokinetic (streaming) transduction mechanism. We have now observed two additional electromechanical phenomena not previously seen in cartilage or other soft tissues: 'streaming current' and 'current-generated stress'. Sinusoidal mechanical compression induced a sinusoidal streaming current density through cartilage disks when the Ag/AgCl electrodes that were used to compress the cartilage were shorted together externally. Conversely, a sinusoidal current density applied to the tissue generated a sinusoidal mechanical stress within the tissue. Both these phenomena were found to be consistent with the same electrokinetic transduction mechanism responsible for the streaming potential. Changes in the measured streaming potential response that resulted from modification of bath ionic strength and pH have provided additional insights into the molecular origins of these transduction processes. Finally, we have now observed streaming potentials in living cartilage maintained in organ culture, as well as in previously frozen tissue.     

Hyperpolarization of the Membrane Potential in Cardiomyocyte Tissue Slices by the Synchronization Modulation Electric Field

Our previous studies have shown that a specially designed, so-called synchronization modulation electric field can entrain active transporter Na/K pumps in the cell membrane. This approach was previously developed in a study of single cells using a voltage clamp to monitor the pump currents. We are now expanding our study from isolated single cells to aggregated cells in a 3-dimensional cell matrix, through the use of a tissue slice from the rat heart. The slice is about 150 μm in thickness, meaning the slices contain many cell layers, resulting in a simplified 3-dimensional system. A fluorescent probe was used to identify the membrane potential and the ionic concentration gradients across the cell membrane. In spite of intrinsic cell-to-cell interactions and the difficulty in stimulating cell aggregation in the tissue slice, the oscillating electric field increased the intracellular fluorescent intensity, indicating elevation of the cell ionic concentration and hyperpolarization of the cell membrane. Blockage of these changes by ouabain confirmed that the results are directly related to Na/K pumps. These results along with the backward modulation indicate that the synchronization modulation electric field can influence the Na/K pumps in tissue cells of a 3-dimensional matrix and therefore hyperpolarize the cell membrane.