Modeling the electrical behavior of anatomically complex neurons using a network analysis program: passive membrane

Abstract

We describe the application of a popular and widely available electrical circuit simulation program called SPICE to modeling the electrical behavior of neurons with passive membrane properties and arbitrarily complex dendritic trees. Transient responses may be calculated at any location in the cell model following current, voltage or conductance perturbations at any point. A numbering method is described for binary trees which is helpful in transforming complex dendritic structures into a coded list of short cylindrical dendritic segments suitable for input to SPICE. Individual segments are modeled as isopotential compartments comprised of a parallel resistor and capacitor, representing the transmembrane impedance, in series with one or two core resistors. Synaptic current is modeled by a current source controlled by the local membrane potential and an "alpha-shaped" voltage, thus simulating a conductance change in series with a driving potential. Extensively branched test cell circuits were constructed which satisfied the equivalent cylinder constraints (Rall 1959). These model neurons were perturbed by independent current sources and by synaptic currents. Responses calculated by SPICE are compared with analytical results. With appropriately chosen model parameters, extremely accurate transient calculations may be obtained. Details of the SPICE circuit elements are presented, along with illustrative examples sufficient to allow implementation of passive nerve cell models on a number of common computers. Methods for modeling excitable membrane are presented in the companion paper (Bunow et al. 1985).