An electrochemical model of the transport of charged molecules through the capillary glycocalyx

An electrochemical theory of the glycocalyx surface layer on capillary endothelial cells is developed as a model to study the electrochemical dynamics of anionic molecular transport within capillaries. Combining a constitutive relationship for electrochemical transport, derived from Fick's and Ohm's laws, with the conservation of mass and Gauss's law from electrostatics, a system of three nonlinear, coupled, second-order, partial, integro-differential equations is obtained for the concentrations of the diffusing anionic molecules and the cations and anions in the blood. With the exception of small departures from electroneutrality that arise locally near the apical region of the glycocalyx, the model assumes that cations in the blood counterbalance the fixed negative charges bound to the macromolecular matrix of the glycocalyx in equilibrium. In the presence of anionic molecular tracers injected into the capillary lumen, the model predicts the size- and charge-dependent electrophoretic mobility of ions and tracers within the layer. In particular, the model predicts that anionic molecules are excluded from the glycocalyx at equilibrium and that the extent of this exclusion, which increases with increasing tracer and/or glycocalyx electronegativity, is a fundamental determinant of anionic molecular transport through the layer. The model equations were integrated numerically using a Crank-Nicolson finite-difference scheme and Newton-Raphson iteration. When the concentration of the anionic molecular tracer is small compared with the concentration of ions in the blood, a linearized version of the model can be obtained and solved as an eigenvalue problem. The results of the linear and nonlinear models were found to be in good agreement for this physiologically important case. Furthermore, if the fixed-charge density of the glycocalyx is of the order of the concentration of ions in the blood, or larger, or if the magnitude of the anionic molecular valence is large, a closed-form asymptotic solution for the diffusion time can be obtained from the eigenvalue problem that compares favorably with the numerical solution. In either case, if leakage of anionic molecules out of the capillary occurs, diffusion time is seen to vary exponentially with anionic valence and in inverse proportion to the steady-state anionic tracer concentration in the layer relative to the lumen. These findings suggest several methods for obtaining an estimate of the glycocalyx fixed-charge density in vivo.     

Modeling and simulation of deformation of hydrogels responding to electric stimulus

A model for simulation of pH-sensitive hydrogels is refined in this paper to extend its application to electric-sensitive hydrogels, termed the refined multi-effect-coupling electric-stimulus (rMECe) model. By reformulation of the fixed-charge density and consideration of finite deformation, the rMECe model is able to predict the responsive deformations of the hydrogels when they are immersed in a bath solution subject to externally applied electric field. The rMECe model consists of nonlinear partial differential governing equations with chemo-electro-mechanical coupling effects and the fixed-charge density with electric-field effect. By comparison between simulation and experiment extracted from literature, the model is verified to be accurate and stable. The rMECe model performs quantitatively for deformation analysis of the electric-sensitive hydrogels. The influences of several physical parameters, including the externally applied electric voltage, initial fixed-charge density, hydrogel strip thickness, ionic strength and valence of surrounding solution, are discussed in detail on the displacement and average curvature of the hydrogels.     

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.     

Measuring endothelial glycocalyx dimensions in humans: a potential novel tool to monitor vascular vulnerability.

The endothelial glycocalyx is increasingly considered as an intravascular compartment that protects the vessel wall against pathogenic insults. The purpose of this study was to translate an established experimental method of estimating capillary glycocalyx dimension into a clinically useful tool and to assess its reproducibility in humans. We first evaluated by intravital microscopy the relation between the distance between the endothelium and erythrocytes, as a measure of glycocalyx thickness, and the transient widening of the erythrocyte column on glycocalyx compression by passing leukocytes in hamster cremaster muscle capillaries. We subsequently assessed sublingual microvascular glycocalyx thickness in 24 healthy men using orthogonal polarization spectral imaging. In parallel, systemic glycocalyx volume (using a previously published tracer dilution technique) as well as cardiovascular risk profiles were assessed. Estimates of microvascular glycocalyx dimension from the transient erythrocyte widening correlated well with the size of the erythrocyte-endothelium gap (r = 0.63). Measurements in humans were reproducible (0.58 +/- 0.16 and 0.53 +/- 0.15 microm, coefficient of variance 15 +/- 5%). In univariate analysis, microvascular glycocalyx thickness significantly correlated with systemic glycocalyx volume (r = 0.45), fasting plasma glucose (r = 0.43), and high-density lipoprotein-cholesterol (r = 0.40) and correlated negatively with low-density lipoprotein-cholesterol (r = -0.41) as well as body mass index (r = -0.45) (all P < 0.05). In conclusion, the dimension of the endothelial glycocalyx can be measured reproducibly in humans and is related to cardiovascular risk factors. It remains to be tested whether glycocalyx dimension can be used as an early marker of vascular damage and whether therapies aimed at glycocalyx repair can protect the vasculature against pathogenic challenges.     

Thermodynamics of polyelectrolyte solutions. An empirical extension of the manning theory to finite salt concentrations

The range of application of the Manning theory of polyelectrolyte solutions (J. Chem. Phys., 51 , 924 (1969)) is extended to finite concentrations of simple electrolyte by the empirical superposition of excess free energies arising from (i) interactions between mobile ions and polyions and (ii) mutual interactions between mobile ions. A comparison of published results with the modified theory shows excellent agreement over a wide range of concentrations. Results for a polyelectrolyte of low charge density suggest that the effective inter-charge spacing may be less than that of the fully extended polyion.     

Poromechanics of compressible charged porous media using the theory of mixtures

Osmotic, electrostatic, and/or hydrational swellings are essential mechanisms in the deformation behavior of porous media, such as biological tissues, synthetic hydrogels, and clay-rich rocks. Present theories are restricted to incompressible constituents. This assumption typically fails for bone, in which electrokinetic effects are closely coupled to deformation. An electrochemomechanical formulation of quasistatic finite deformation of compressible charged porous media is derived from the theory of mixtures. The model consists of a compressible charged porous solid saturated with a compressible ionic solution. Four constituents following different kinematic paths are identified: a charged solid and three streaming constituents carrying either a positive, negative, or no electrical charge, which are the cations, anions, and fluid, respectively. The finite deformation model is reduced to infinitesimal theory. In the limiting case without ionic effects, the presented model is consistent with Blot's theory. Viscous drag compression is computed under closed circuit and open circuit conditions. Viscous drag compression is shown to be independent of the storage modulus. A compressible version of the electrochemomechanical theory is formulated. Using material parameter values for bone, the theory predicts a substantial influence of density changes on a viscous drag compression simulation. In the context of quasistatic deformations, conflicts between poromechanics and mixture theory are only semantic in nature.     

Effects of initial-fixed charge density on pH-sensitive hydrogels subjected to coupled pH and electric field stimuli: a meshless analysis

In this paper, we study the effects of initial fixed-charge density on the response behavior of pH-sensitive hydrogels subjected to coupled stimuli, namely, solution pH and externally applied electric field. This is the first instance in which a coupled stimuli numerical analysis has been carried out for these polymer gels, which are used as active sensing/actuating elements in advanced biomicroelectromechanical systems devices. In this work, a chemo-electro-mechanical formulation, termed the multi-effect-coupling pH-stimulus (MECpH) model, is first presented. This mathematical model takes into account the ionic species diffusion, electric potential coupling, and large mechanical deformation. In addition, a correlation between the diffusive hydrogen ions and fixed-charge groups on the hydrogel polymeric chains is established based on the Langmuir absorption isotherm, and incorporated accordingly into the MECpH model. To solve the resulting highly nonlinear and highly coupled partial differential equations of this mathematical model, the Hermite-Cloud method, a novel true meshless technique, is employed. To demonstrate the accuracy and robustness the MECpH model, computed numerical results are compared with experimental data available from literature. Following this validation, several numerical studies are carried out to investigate the effects of initial fixed-charge density on the volumetric variations of these pH-stimulus-responsive hydrogels when immersed in buffered solutions.     

Increasing strain and strain rate strengthen transient stiffness but weaken the response to subsequent compression for articular cartilage in unconfined compression

Strain amplitude and strain rate dependent nonlinear behavior and load-induced mechanical property alterations of full-thickness bovine articular cartilage attached to bone were investigated in unconfined compression. A sequence of test compressions of finite deformation (ranging from 0.9% to 34.5% nominal strain) was performed at strain rates ranging from approximately 0.053%/s to 5.8%/s. Peak and equilibrium loads were analyzed to determine strain amplitude and strain rate dependence of linear versus nonlinear responses. The test protocol was designed to reveal changes in mechanical properties due to these finite deformations by interspersing small-amplitude witness ramps of approximately 1.1% deformation and approximately 0.44%/s strain rate between the test ramps ("witness" meaning to assess any mechanical property changes). We found that peak loads displayed high nonlinearity, stiffening with both increasing compression amplitude and more so with increasing strain rate. The response to witness ramps suggested that mechanical weakening occurred when compression amplitude reached 1.9-2.9% strain and beyond, and that weakening was much more significant at higher strain rate. These findings delineate regimes of linear versus nonlinear behavior of cartilage, and indicate the types of loads which can cause mechanical property alterations. Biological implications of this study are that strain amplitude and strain rate dependent stiffening may be essential to bear physiological loads and to protect cells and matrix from mechanical damage. Structural changes reflected by mechanical weakening at small compression could also initiate remodeling or disease processes.     

An electrodiffusion model for effects of surface glycocalyx layer on microvessel permeability

To investigate the charge effect of the endothelial surface glycocalyx on microvessel permeability, we extended the three-dimensional model developed by Fu et al. (J Biomech Eng 116: 502-513, 1994) for the interendothelial cleft to include a negatively charged glycocalyx layer at the entrance of the cleft. Both electrostatic and steric exclusions on charged solutes were considered within the glycocalyx layer and at the interfaces. Four charge-density profiles were assumed for the glycocalyx layer. Our model indicates that the overall solute permeability across the microvessel wall including the surface glycocalyx layer and the cleft region is independent of the charge-density profiles as long as they have the same maximum value and the same total charge. On the basis of experimental data, this model predicts that the charge density would be 25-35 meq/l in the glycolcalyx of frog mesenteric capillaries. An intriguing prediction of this model is that when the concentrations of cations and anions are unequal in the lumen due to the presence of negatively charged proteins, the negatively charged glycocalyx would provide more resistance to positively charged solutes than to negatively charged ones.     

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.     

Theory of the electrokinetic behavior of human erythrocytes

We develop a theory of electrophoresis of human erythrocytes that predicts mobilities significantly smaller than those based on the classical Smoluchowski relation. In the classical treatment the charge is assumed to be spread uniformly on the hydrodynamic surface. The present model takes into account that most of the charge, due mainly to sialic acid, is contained in the glycocalyx. The glycocalyx is modeled as a permeable layer of polyelectrolyte molecules anchored to the cell membrane. The charge is assumed to be uniformly distributed throughout this layer. The fluid flow in the layer is treated as being dominated by Stokes friction arising from idealized polymer segments. The Navier-Stokes equations are solved to give the dependence of electroosomotic velocity with distance from the cell surface. An expression for the electrophoretic mobility is obtained which contains two parameters (a) the thickness of the glycocalyx and (b) the mean polymer segment radius. The best fit to experimental data is obtained if these are given the values 75 A and 7 A, respectively. Deviation from experimental data at low ionic strength (less than 0.05 M) occurs. However, this deviation is in the direction one would expect if at low ionic strength the polyelectrolyte layer expands slightly due to decreased charge shielding.     

A comparison between mechano-electrochemical and biphasic swelling theories for soft hydrated tissues

Biological tissues like intervertebral discs and articular cartilage primarily consist of interstitial fluid, collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans, the total ion concentration inside the tissue is higher than in the surrounding synovial fluid (cation concentration is higher and the anion concentration is lower). This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. In the last decade several mechano-electrochemical models, which include this mechanism, have been developed. As these models are complex and computationally expensive, it is only possible to analyze geometrically relatively small problems. Furthermore, there is still no commercial finite element tool that includes such a mechano-electrochemical theory. Lanir (Biorheology, 24, pp. 173-187, 1987) hypothesized that electrolyte flux in articular cartilage can be neglected in mechanical studies. Lanir's hypothesis implies that the swelling behavior of cartilage is only determined by deformation of the solid and by fluid flow. Hence, the response could be described by adding a deformation-dependent pressure term to the standard biphasic equations. Based on this theory we developed a biphasic swelling model. The goal of the study was to test Lanir's hypothesis for a range of material properties. We compared the deformation behavior predicted by the biphasic swelling model and a full mechano-electrochemical model for confined compression and 1D swelling. It was shown that, depending on the material properties, the biphasic swelling model behaves largely the same as the mechano-electrochemical model, with regard to stresses and strains in the tissue following either mechanical or chemical perturbations. Hence, the biphasic swelling model could be an alternative for the more complex mechano-electrochemical model, in those cases where the ion flux itself is not the subject of the study. We propose thumbrules to estimate the correlation between the two models for specific problems.     

Glycocalyx electrostatic potential profile analysis: ion, pH, steric, and charge effects

The Poisson-Boltzmann equation is modified to consider charge ionogenicity, steric exclusion, and charge distribution in order to describe the perimembranous electrostatic potential profile in a manner consistent with the known morphology and biochemical composition of the cell's glycocalyx. Exact numerical and approximate analytical solutions are given for various charge distributions and for an extended form of the Donnan potential model. The interrelated effects of ionic conditions, bulk pH, ion binding, local dielectric, steric volume exclusion, and charge distribution on the local potential, pH, and charge density within the glycocalyx are examined. Local charge-induced, potential-mediated pH reductions cause glycocalyx charge neutralization. Under certain conditions, local potentials may be insensitive to ionic strength or may decrease in spite of increasing charge density. The volume exclusion of the glycocalyx reduces the local ion concentration, thereby increasing the local potential. With neutral lipid membranes, the Donnan and surface potential agree if the glycocalyx charge distribution is both uniform and several times thicker than the Debye length (approximately 20 A in thickness under physiological conditions). Model limitations in terms of application to microdomains or protein endo- and ectodomains are discussed.     

Effect of glycocalyx on shear-dependent albumin uptake in endothelial cells

The glycocalyx layer on the surface of an endothelial cell is an interface barrier for uptake of macromolecules, such as low-density lipoprotein and albumin, in the cell. The shear-dependent uptake of macromolecules thus might govern the function of the glycocalyx layer. We therefore studied the effect of glycocalyx on the shear-dependent uptake of macromolecules into endothelial cells. Bovine aorta endothelial cells were exposed to shear stress stimulus ranging from 0.5 to 3.0 Pa for 48 h. The albumin uptake into the cells was then measured using confocal laser scanning microscopy, and the microstructure of glycocalyx was observed using electron microscopy. Compared with the uptake into endothelial cells under static conditions (no shear stress stimulus), the albumin uptake at a shear stress of 1.0 Pa increased by 16% and at 3.0 Pa decreased by 27%. Compared with static conditions, the thickness of the glycocalyx layer increased by 70% and the glycocalyx charge increased by 80% at a shear stress of 3.0 Pa. The albumin uptake at a shear stress of 3.0 Pa for cells with a neutralized (no charge) glycocalyx layer was almost twice that of cells with charged layer. These findings indicate that glycocalyx influences the albumin uptake at higher shear stress and that glycocalyx properties (thickness and charge level) are involved with the shear-dependent albumin uptake process.     

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.     

A model for the nonlinear elastic response of large arteries

The nonlinear elastic response of large arteries subjected to finite deformations due to action of biaxial principal stresses, is described by simple constitutive equations. Generalized measures of strain and stress are introduced to account for material nonlinearity. This also ensures the existence of a strain energy density function. The orthotropic elastic response is described via quasi-linear relations between strains and stresses. One nonlinear parameter which defines the measures of strain and stress, and three elastic moduli are assumed to be constants. The lateral strain parameters (equivalent to Poisson's ratios in infinitesimal deformations) are deformation dependent. This dependence is defined by empirical relations developed via the incompressibility condition, and by the introduction of a fifth material parameter. The resulting constitutive model compares well with biaxial experimental data of canine carotid arteries.     

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.     

A bimodular polyconvex anisotropic strain energy function for articular cartilage

A strain energy function for finite deformations is developed that has the capability to describe the nonlinear, anisotropic, and asymmetric mechanical response that is typical of articular cartilage. In particular, the bimodular feature is employed by including strain energy terms that are only mechanically active when the corresponding fiber directions are in tension. Furthermore, the strain energy function is a polyconvex function of the deformation gradient tensor so that it meets material stability criteria. A novel feature of the model is the use of bimodular and polyconvex "strong interaction terms" for the strain invariants of orthotropic materials. Several regression analyses are performed using a hypothetical experimental dataset that captures the anisotropic and asymmetric behavior of articular cartilage. The results suggest that the main advantage of a model employing the strong interaction terms is to provide the capability for modeling anisotropic and asymmetric Poisson's ratios, as well as axial stress-axial strain responses, in tension and compression for finite deformations.     

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.