A New Model for Current Flow in Dendrites of Arbitrary Geometry

Current flow within dendrites or axons of nerve cells has usually been represented in the framework of the core conductor concept /2/. Starting with its standard assumptions, a new model of current flow in branching dendrites is derived. The method is a variant of the continuum approach employed in many different fields of research /1/. In the present case, the fine structure of the branching dendrites is replaced by an equivalent, locally homogeneous electrical medium described by averaged electrical quantities. For the mean potential and the mean current density in this medium partial differential equations of parabolic type are derived which represent natural generalizations of the simple case of a leaky cable.