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The intervertebral disk (IVD) is the largest avascular structure in the human body. Transport of small molecules in IVD is mainly through diffusion from the endplates and the peripheral blood vessels surrounding IVD. Studies have investigated the structure, chemical components, and water content in IVD, but to our knowledge no study has investigated the effect of mechanical loading on oxygen transport in IVD. The objective of this study was to determine the strain-dependent behavior of oxygen diffusivity in IVD tissue. A one-dimensional steady-state diffusion experiment was designed and performed to determine the oxygen diffusivity in bovine annulus fibrosus (AF). The oxygen diffusivity was calculated using equation derived from Fick's law. A total of 20 AF specimens (d =6 mm, h~0.5 mm) from bovine coccygeal IVD were used to determine oxygen diffusivity at three levels of compressive strain. The average oxygen diffusivity (mean [+ or -] SD) of bovine AF in the axial direction was 1.43 [+ or -] 0.242 x [10.sup.-5] [cm.sup.2]/s (n=20) at 4.68 [+ or -] 1.67% compressive strain level, 1.05 [+ or -] 0.282 x [10.sup.-5] [cm.sup.2]/s (n=20) at 14.2 [+ or -] 1.50% strain level and 7.71 [+ or -] 1.63 x [10.sup.-6] [cm.sup.2]/s (n = 20) at 23.7 [+ or -] 1.34% strain level. There was a significant decrease in oxygen diffusivity with increasing level of compressive strain (ANOVA, p [DOI: 10.1115/1.3127254] Keywords: compression, nutrition, transport, intervertebral disk, diffusion coefficient, spine

In the present study a 1-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.

This paper describes a new apparatus and method for measuring swelling dependent electrical conductivity of charged hydrated soft tissues. The apparatus was calibrated using a conductivity standard. Swelling dependent specific conductivity of porcine annulus fibrosis (AF) samples was determined. The conductivity values for porcine AF were similar to those for human and bovine articular cartilage found in the literature. Results revealed a significant linear correlation between specific conductivity and water content for porcine AF tissues tested in phosphate buffered saline (PBS). [DOI: 10.1115/1.1516571]

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.sup.+] and [Ca.sup.++] through the tissue. These numerical results support our hypothesis that tissue fixed charge density ([c.sup.F]) plays a significant role in modulating kinetics of ions and solvent transport through charged-hydrated soft tissues.