A triphasic analysis of negative osmotic flows through charged hydrated soft tissues

Department of Orthopaedic Surgery, Columbia University, New York, NY 10032, USA.
Journal of Biomechanics (Impact Factor: 2.5). 02/1997; 30(1):71-8. DOI: 10.1016/S0021-9290(96)00099-1
Source: PubMed

ABSTRACT Osmotic flow and ion transport in a one-dimensional steady diffusion process through charged hydrated soft tissues such as articular cartilage were analysed using the triphasic theory (Lai et al., 1991, J. biomech. Engng 113, 245-258). It was found that solvent would flow from the high NaCl concentration side to the low concentration side (i.e. negative osmosis) when the fixed charge density within the tissue (or membrane) separating the two electrolyte (NaCl) solutions was lower than a critical value. The condition for negative osmosis was derived based on a linear version of the triphasic theory. Distributions of ion concentration and strain field within the tissue were calculated numerically. Quantitative results of osmotic flow rates (ordinary and negative osmosis), ion flux and electric potential across the tissue during this diffusion process suggest that the negative osmosis phenomenon is due to the friction between ions and water since they could flow through the tissues at different rates and different directions.

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    • "So far, the triphasic mechano-electrochemical theory has been applied to model the mechanics of the articular cartilage [27] [28] [29] [30]. However the theory can be applied to any charged hydrated soft tissue made of an intrinsically incompressible, porous-permeable, charged solid phase; an intrinsically incompressible, interstitial fluid phase; and an ion phase with two monovalent ion species anion (-) and cation (+). "
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    ABSTRACT: In recent years, the fields of brain biomechanics and neural engineering have started to play an increasingly important role to modern neuroscience. Although the object of study of these two research areas is the brain, the two fields have developed independently of each other, neglecting any possible linkage between the electric brain and the mechanical brain. The aim of the present paper is to formulate the first neuro-mechanical model of the brain that will couple the electro-chemical and mechanical properties of the brain. We assume that the brain tissue is a charged hydrated soft tissue made of a solid phase, an interstitial fluid phase and an ion phase with two monovalent ion species. To investigate the mechano-electrochemical coupling phenomena of the brain tissue, we study the onset of normal pressure hydrocephalus due to a change in the ionic concentrations of the ventricular cerebrospinal fluid in the absence of an elevated intracranial pressure.
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    • "A particular emphasis has been placed on the transport of ions in a charged, deformable solid matrix, as embodied in the triphasic theory of Lai et al. [8], the quadriphasic theory of Huyghe and Janssen [9], and the multielectrolyte theory of Gu et al. [10]. These investigations have often focused on mechanoelectrochemical phenomena arising from the transport of charged species within a charged matrix, such as streaming and diffusion potentials and currents [11] [12], Donnan osmotic swelling [8] [9] [10] [13], and phenomena such as reverse osmosis [14]. Finite element implementations of charged porous media have been presented by several authors, which are applicable to infinitesimal deformations [15] [16] [17] [18] [19] [20] and finite deformations [21]. "
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    ABSTRACT: Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http:∕∕∕software).
    Journal of Biomechanical Engineering 08/2011; 133(8):081005. DOI:10.1115/1.4004810 · 1.75 Impact Factor
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    • "Lai et al (1991) proposed a triphasic model of articular cartilage as an extension of the biphasic model, where negatively charged proteoglycans are modelled to be fixed to the solid matrix, and monovalent ions in the interstitial fluid are modelled as additional fluid phases. This model was later extended to incorporate multiple polyvalent ions by Gu et al. (1997,1999). Similar modification of the biphasic model to include thermo-chemo-electro-mechanical interactions in saturated charged porous solids was made by Huyghe and Janssen (1999), van Meerveld et al. (2003) and Zhang and Szeri (2007). "
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    ABSTRACT: A nonlinear, macroscopic multi-phasic model for describing the interactions between solid, fluid, and ionic species in porous materials is presented. Governing equations are derived based on the nonlinear theories of solid mechanics, linear flow theory of Newtonian fluids, and theory of irreversible thermodynamics for the transport of ions and ionic solutions. The model shows that the transport coupling between ions and ionic solution exists only when the porous material has a membrane-like feature, which could be inside the material or on the material boundaries. Otherwise, the coupling occurs only between the solid and fluid phases and the transport of ionic species will have no effect on the macroscopic stresses, strains and displacements of the porous material. As an application of the present multi-phasic model, a numerical example of the human cornea under the shock of NaCl hypertonic solution applied to its endothelial surface is presented. This is a typical example of how ionic transport induces swelling in biological tissues. The results obtained from the present multi-phasic model demonstrate that the mechanical properties of the tissue have an important influence on the swelling of the cornea. Without taking into account this influence, the predicted swelling may be exaggerated.
    Philosophical Magazine A 01/2011; 91(2):300-314. DOI:10.1080/14786435.2010.519353
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