ANALYTICAL SOLUTIONS TO THE MULTICYLINDER SOMATIC SHUNT CABLE MODEL FOR PASSIVE NEURONS WITH DIFFERING DENDRITIC ELECTRICAL PARAMETERS

The multicylinder somatic shunt cable model for passive neurones with differing time constants in each cylinder is considered in this paper. The solution to the model with general inputs is developed, and the p arametric dependence of the voltage response is investigated. The meth od of analysis is straightforward and follows that laid out in Evans e t al. (1992, 1994): (i) The dimensional problem is stated with general boundary and initial conditions. (ii) The model is fully non-dimensio nalised, and a dimensionless parameter family which uniquely governs t he behaviour of the dimensionless voltage response is obtained. (iii) The fundamental unit impulse problem is solved, and the solutions to p roblems involving general inputs are written in terms of the unit impu lse solution. (iv) The large and small time behaviour of the unit impu lse solution is examined. (v) The parametric dependence of the unit im pulse upon the dimensionless parameter family is explored for two limi ts of practical interest. A simple expression for the principle relati onship between the dimensionless parameter family is derived and provi des insight into the interaction between soma and cylinders. A well-po sed method for the solution of the dimensional inverse problem is pres ented.