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

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.

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