A Mixture Theory for Charged-Hydrated Soft Tissues Containing Multi-electrolytes: Passive Transport and Swelling Behaviors

[+] Author and Article Information
W. Y. Gu

Department of Orthopædic Surgery, Columbia University, New York, NY 10032

W. M. Lai, V. C. Mow

Departments of Mechanical Engineering and Orthopædic Surgery, Columbia University, New York, NY 10032

J Biomech Eng 120(2), 169-180 (Apr 01, 1998) (12 pages) doi:10.1115/1.2798299 History: Received October 17, 1996; Revised April 09, 1997; Online October 30, 2007


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.

Copyright © 1998 by The American Society of Mechanical Engineers
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