title: A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree.
abstract: A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree extending Rall's equivalent cylinder model is presented. It is obtained from a combination of cable theory with the continuum approach. Replacing the fine structure of the branching dendrites by an equivalent, conductive medium characterized by averaged electrical parameters, the one-dimensional cable equations with spatially varying parameters are derived. While these equations can be solved in general only numerically, we were able to formulate a general branching condition (comprising Rall's 3/2 power relationship as a special case) under which analytical solutions can be deduced from those of the equivalent cylinder model. This model allows dendritic trees with a greater variety of branching patterns than before to be analytically treated.
authors.affiliation: Karl Marx University, Carl Ludwig Institute for Physiology, Leipzig.
authors.forename: A K
authors.initials: AK
authors.lastname: Schierwagen
mesh_terms: D000818:Animals; D002462:Cell Membrane / Q000502:physiology*; D003712:Dendrites / Q000502:physiology*; D008433:Mathematics; D008564:Membrane Potentials; D008959:Models, Neurological