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Published February 1985 | public
Journal Article

A simple algorithm for solving the cable equation in dendritic trees of arbitrary geometry

Abstract

We present an efficient algorithm for solving the one-dimensional cable equation in the Laplace (frequency) domain for an arbitrary linear membrane. This method, a reformulation and extension of the geometrical calculus developed by Butz and Cowan (1974), solves for the transfer impedance between any two points in a branched cable structure of arbitrary geometry (but without loops) by the repetitive application of four simple equations. Such an algorithm is used to analyze the electrical behaviour of nerve cells with highly branched dendritic trees. The algorithm can be implemented using a language such as C, PASCAL or LISP and runs on small machines.

Additional Information

Received 16 April 1984. Revised 16 August 1984. Accepted 1 October 1984. Available online 11 March 2003. Copyright © 1985 Published by Elsevier B.V. C.K. is supported by the Fritz Thyssen foundation. Support for T.P. is provided in part by the Sloan Foundation and the Whitaker College and by the Artificial Intelligence Laboratory, a research program supported in part by the Advanced Research Project Agency of the Department of Defense under Office of Naval Research contract N00014-80-C-0505.

Additional details

Created:
September 15, 2023
Modified:
October 23, 2023