A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure

TL;DR

This paper presents a comprehensive mathematical model for ionic electrodiffusion and osmotic water flow in biological tissues, ensuring energy consistency and providing numerical methods for cell volume regulation.

Contribution

It introduces a novel PDE-based model that captures electrodiffusion, osmotic flow, and membrane deformation with an energy-dissipative structure, along with numerical schemes and applications.

Findings

Model satisfies a natural energy equality.

Limiting models derived for small parameters.

Numerical simulations demonstrate cell volume control.

Abstract

We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control.