No abstract

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.

SUMMARYAn equivalent new expression of the triphasic mechano-electrochemical theory [9] is presented and a mixed "nite element formulation is developed using the standard Galerkin weighted residual method. Solid displacement u s , modi,ed electrochemical/chemical potentials , >and \ (with dimensions of concentration) for water, cation and anion are chosen as the four primary degrees of freedom (DOFs) and are independently interpolated. The modi"ed Newton}Raphson iterative procedure is employed to handle the non-linear terms. The resulting "rst-order Ordinary Di!erential Equations (ODEs) with respect to time are solved using the implicit Euler backward scheme which is unconditionally stable. One-dimensional (1-D) linear isoparametric element is developed. The "nal algebraic equations form a non-symmetric but sparse matrix system. With the current choice of primary DOFs, the formulation has the advantage of small amount of storage, and the jump conditions between elements and across the interface boundary are satis"ed automatically. The "nite element formulation has been used to investigate a 1-D triphasic stress relaxation problem in the con"ned compression con"guration and a 1-D triphasic free swelling problem. The formulation accuracy and convergence for 1-D cases are examined with independent "nite di!erence methods. The FEM results are in excellent agreement with those obtained from the other methods.

Study Design Simulate the progression of human disc degeneration. Objective The objective of this study was to quantitatively analyze and simulate the changes in cell density, nutrition level, proteoglycan content, water content, and volume change during human disc degeneration using a numerical method. Summary of Background Data Understanding the etiology and progression of intervertebral disc (IVD) degeneration is crucial for developing effective treatment strategies for IVD-degeneration related diseases. During tissue degeneration, the disc undergoes losses of cell viability and activities, changes in extracellular matrix composition and structure, and compromise of the tissue-level integrity and function, which is significantly influenced by the inter-coupled biological, chemical, electrical, and mechanical signals in the disc. Characterizing these signals in human discs in vivo is difficult. Methods A realistic 3D finite element model of the human IVD was developed based on biomechano-electrochemical continuum mixture theory. The theoretical framework and the constitutive relationships were all biophysics based. All the material properties were obtained from experimental results. The cell-mediated disc degeneration process caused by lowered nutrition levels at disc boundaries was simulated and validated by comparing with experimental results. Results Cell density reached equilibrium state in 30 days after reduced nutrition supply at the disc boundary, while the proteoglycan (PG) and water contents reached a new equilibrium state in 55 years. The simulated results for the distributions of PG and water contents within the disc were consistent with the results measured in the literature, except for the distribution of PG content in the sagittal direction. Conclusions Poor nutrition supply has a long-term effect on disc degeneration.

STEM CELLS 2007;25: 3155-3164 Disclosure of potential conflicts of interest is found at the end of this article.

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Research has shown that mechanical loading affects matrix biosynthesis of intervertebral disc (IVD) cells; however the pathway(s) to this effect is currently unknown. Cellular matrix biosynthesis is an energy demanding process. The objective of this study was to investigate the effects of static and dynamic compressive loading on energy metabolism of IVD cells. Porcine annulus fibrosus (AF) and nucleus pulposus (NP) cells seeded in 2% agarose were used in this experiment. Experimental groups included 15% static compression and 0.1 and 1 Hz dynamic compression at 15% strain magnitude for 4 hours. ATP, lactate, glucose and nitric oxide (NO) contents in culture media, and ATP content in cell-agarose construct were measured using biochemical assays. While the total ATP content of AF cells was promoted by static and dynamic loading, only 1 Hz dynamic loading increased total ATP content of NP cells. Increases in lactate production and glucose consumption of AF cells suggest that ATP production via glycolysis is promoted by dynamic compression. ATP release and NO production of AF and NP cells were significantly increased by dynamic loading. Thus, this study clearly illustrates that static and dynamic compressive loading affect IVD cell energy production while cellular responses to mechanical loading were both cell type and compression type dependent.

Intervertebral disc (IVD) degeneration is closely associated with low back pain (LBP), which is a major health concern in the U.S. Cellular biosynthesis of extracellular matrix (ECM), which is important for maintaining tissue integrity and preventing tissue degeneration, is an energy demanding process. Due to impaired nutrient support in avascular IVD, adenosine triphosphate (ATP) supply could be a limiting factor for maintaining normal ECM synthesis. Therefore, the objective of this study was to investigate the energy metabolism in the annulus fibrosus (AF) and nucleus pulposus (NP) of porcine IVD under static and dynamic compressions. Under compression, pH decreased and the contents of lactate and ATP increased significantly in both AF and NP regions, suggesting that compression can promote ATP production via glycolysis and reduce pH by increasing lactate accumulation. A high level of extracellular ATP content was detected in the NP region and regulated by compressive loading. Since ATP can serve not only as an intra-cellular energy currency, but also as a regulator of a variety of cellular activities extracellularly through the purinergic signaling pathway, our findings suggest that compression-mediated ATP metabolism could be a novel mechanobiological pathway for regulating IVD metabolism.