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The accumulation of potassium in the narrow space outside nerve cells is aclassical subject of biophysics that has received much attention recently. Itmay be involved in potassium accumulation \textcolor{black}{including}spreading depression, perhaps migraine and some kinds of epilepsy, even(speculatively) learning. Quantitative analysis is likely to help evaluate therole of potassium clearance from the extracellular space after a train ofaction potentials. Clearance involves three structures that extend down thelength of the nerve: glia, extracellular space, and axon and so need to bedescribed as systems distributed in space in the tradition used for electricalpotential in the `cable equations' of nerve since the work of Hodgkin in 1937.A three-compartment model is proposed here for the optic nerve and is used tostudy the accumulation of potassium and its clearance. The model allows theconvection, diffusion, and electrical migration of water and ions. We depend onthe data of Orkand et al to ensure the relevance of our model and align itsparameters with the anatomy and properties of membranes, channels, andtransporters: our model fits their experimental data quite well. The alignedmodel shows that glia has an important role in buffering potassium, asexpected. The model shows that potassium is cleared mostly by convective flowthrough the syncytia of glia driven by osmotic pressure differences. Asimplified model might be possible, but it must involve flow down the length ofthe optic nerve. It is easy for compartment models to neglect this flow. Ourmodel can be used for structures quite different from the optic nerve thatmight have different distributions of channels and transporters in its threecompartments. It can be generalized to include a fourth (distributed)compartment representing blood vessels to deal with the glymphatic flow intothe circulatory system.

A Tridomain Model for Potassium Clearance in Optic Nerve of Necturus