Jd. Evans et al., TECHNIQUES FOR THE APPLICATION OF THE ANALYTICAL SOLUTION TO THE MULTICYLINDER SOMATIC SHUNT CABLE MODEL FOR PASSIVE NEURONS, Mathematical biosciences, 125(1), 1995, pp. 1-50
The general solution for the voltage response to a generic impulse cur
rent input in a multicylinder somatic shunt cable model for passive ne
urones has been developed in [1]. In this paper we consider the applic
ation of the multicylinder solution to examples previously considered
by other authors for the single cylinder case: long and short current
input and synaptic input modeled by an alpha-function and a multi-expo
nential function. Simple expansions appropriate for small and large ti
mes are found and efficient means of obtaining these expansions are cl
early demonstrated. The dependence of the small and large time solutio
ns upon the dimensionless parameters appearing in the conservation of
current condition at the soma is investigated. Relevant limits of thes
e dimensionless parameters which further simplify the small and large
time solutions are related back to equivalent dimensional problems of
interest to the practitioner. The well-posedness of the dimensionless
inverse problem is investigated and a method proposed for the solution
of the dimensional inverse problem for the somatic shunt.