A multidomain model for ionic electrodiffusion and osmosis with an application to cortical spreading depression

•We develop a PDE model for ionic electrodiffusion and osmosis in biological tissue.•An important feature of the model is the presence of a free energy identity.•Relations to other electrophysiology models including the cardiac bidomain and cable models are discussed.•The model is applied to the study of cortical spreading depression (SD).•The model allows for successful computation of the extracellular DC shift in SD.

Ionic electrodiffusion and osmotic water flow are central processes in many physiological systems. We formulate a system of partial differential equations that governs ion movement and water flow in biological tissue. A salient feature of this model is that it satisfies a free energy identity, ensuring the thermodynamic consistency of the model. A numerical scheme is developed for the model in one spatial dimension and is applied to a model of cortical spreading depression, a propagating breakdown of ionic and cell volume homeostasis in the brain.