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Summary: A new computational method for cable theory problems
Bulin J. Cao and L. F. Abbott
Physics Department and Center for Complex Systems, Brandeis University, Waltham, MA 02254 USA
ABSTRACT We discuss a new computational procedure for solving the linear cable equation on a tree of arbitrary geometry. The method
is based on a simple set of diagrammatic rules implemented using an efficient computer algorithm. Unlike most other methods, this
technique is particularly useful for determining the short-time behavior of the membrane potential. Examples are presented and the
convergence and accuracy of the method are discussed.
1. INTRODUCTION
Cable theory is the primary tool used to relate the geo-
metric form ofa neuron to its electrical function ( 1-3).
The basic problem of cable theory is to compute the
membrane potential everywhere on a complex neuron
as a function ofthe external and synaptic currents enter-
ing the cell. Much work has been done for neurons with
restricted dendritic structures (4-7) satisfying, for exam-
ple, Rall's 3/2 power rule (8). In addition, several power-
ful and practical techniques have been developed to
solve the cable equation for neurons with dendritic trees
ofarbitrary geometry (9-17). Because dendritictrees are
typically so elaborate, it is essential that any general
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