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

Koch, Christof and Poggio, Tomaso (1985) A simple algorithm for solving the cable equation in dendritic trees of arbitrary geometry. Journal of Neuroscience Methods, 12 (4). pp. 303-315. ISSN 0165-0270. doi:10.1016/0165-0270(85)90015-9.

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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.

Item Type:Article
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Koch, Christof0000-0001-6482-8067
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.
Group:Koch Laboratory (KLAB)
Funding AgencyGrant Number
Fritz Thyssen FoundationUNSPECIFIED
Sloan FoundationUNSPECIFIED
Whitaker CollegeUNSPECIFIED
Artificial Intelligence LaboratoryUNSPECIFIED
U.S. Office of Naval Research. Advanced Research Projects AgencyN00014-80-C-0505
Subject Keywords: neuronal modeling; cable theory; algorithm; Laplace domain; Green function; dendritic tree; synaptic input; quasi-active membrane; retinal ganglion cells; dendritic spines
Issue or Number:4
Record Number:CaltechAUTHORS:20130816-103203408
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Official Citation:Christof Koch, Tomaso Poggio, A simple algorithm for solving the cable equation in dendritic trees of arbitrary geometry, Journal of Neuroscience Methods, Volume 12, Issue 4, February 1985, Pages 303-315, ISSN 0165-0270, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:40428
Deposited By: KLAB Import
Deposited On:26 Jan 2008 03:19
Last Modified:09 Nov 2021 23:48

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