A general approach to modeling conduction and concentration dynamics in excitable cells of concentric cylindrical geometry

This paper discusses mathematical approaches for modeling the propagation o f the action potential and ion concentration dynamics in a general class of excitable cells and cell assemblies of concentric cylindrical geometry. Ex amples include myelinated and unmyelinated axons, single strands of interco nnected cardiac cells and outer hair cells. A key feature in some of the ce lls is the presence of a small working volume such as the periaxonal space between the myelin sheath and the axon in the myelinated axon and the extra cisternal space between the plasma membrane and the subsurface cisterna of the outer hair cell. Proper treatment of these cell types requires a modeli ng approach which can readily address these anatomical properties and the n on-uniform biophysical properties of the concentric membranes and the ionic composition of the volumes between the membranes. An electrodiffusion appr oach is first developed in which the Nernst-Planck equation is used to char acterize axial ion fluxes. It is then demonstrated that this "full" model c an be stepwise reduced, eventually becoming equivalent to the standard cabl e equation formulation. This is done in a manner that permits direct compar isons between the full and simplified models by running simulations using a single parameter set. An intermediate approach where the contributions of the axial currents to ion concentration changes and the effect of varying i on concentrations on solution conductivities are ignored is derived and is found adequate in many cases. Two application examples are given: a "cardia c strand" model, for which the intermediate formulation is shown sufficient and a model of the myelinated axon, for which the full electrodiffusion fo rmulation is clearly necessary. The latter finding is due to spatial inhomo geneities in the anatomy and distribution of ion channels and transporters in the myelinated axon and the restricted periaxonal space between the myel in sheath and the axon. (C) 1999 Academic Press.