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.
Department of Orthopaedic Surgery, Columbia University, New York, NY 10032, USA.
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D001692:Biological Transport / Q000502:physiology; D002118:Calcium / Q000378:metabolism; D002463:Cell Membrane Permeability / Q000502:physiology; D055598:Chemical Phenomena; D002627:Chemistry, Physical; D004058:Diffusion; D004563:Electrochemistry; D004573:Electrolytes / Q000378:metabolism*; D004594:Electrophysiology; D006801:Humans; D017136:Ion Transport; D008564:Membrane Potentials / Q000502:physiology; D008954:Models, Biological; D008956:Models, Chemical; D009997:Osmotic Pressure; D010539:Permeability; D011312:Pressure; D012212:Rheology; D012964:Sodium / Q000378:metabolism; D012997:Solvents / Q000378:metabolism; D014867:Water / Q000378:metabolism
D004573:Electrolytes; D012997:Solvents; D014867:Water; D012964:Sodium; D002118:Calcium