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.