Biophysical Journal 25: 323-339 (1979)
© 1979 the Biophysical Society

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A network thermodynamic two-port element to represent the coupled flow of salt and current. Improved alternative for the equivalent circuit.

ABSTRACT

A two-port for coupled salt and current flow is created by using the network thermodynamic approach in the same manner as that for coupled solute and volume flow (Mikulecky et al., 1977b; Mikulecky, 1977). This electrochemical two-port has distinct advantages over the equivalent circuit representation and overcomes difficulties pointed out by Finkelstein and Mauro (1963). The electrochemical two-port is used to produce a schematic diagram of the coupled flows through a tissue. The network is superimposable on the tissue morphology and preserves the physical qualities of the flows and forces in each part of an organized structure (e.g., an epithelium). The topological properties are manipulated independently from the constitutive (flow-force) relations. The constitutive relations are chosen from a number of alternatives depending on the detail and rigor desired. With the topology and constitutive parameters specified, the steady-state behavior is simulated with a network simulation program. By using capacitance to represent the filling and depletion of compartments, as well as the traditional electrical capacitances, time-dependent behavior is also simulated. Nonlinear effects arising from the integration of equations describing local behavior (e.g., the Nernst-Planck equations) are dealt with explicitly. The network thermodynamic approach provides a simple, straightforward method for representing a system diagrammatically and then simulating the system's behavior from the diagram with a minimum of mathematical manipulation.