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A new computational method for cable theory problems Bulin J. Cao and L. F. Abbott

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.
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


Source: Abbott, Laurence - Center for Neurobiology and Behavior & Department of Physiology and Cellular Biophysics, Columbia University


Collections: Biology and Medicine