On the analytic solution of electrotonic spread in branched passive dendritic trees

Journal of Computational Neuroscience
I Z Steinberg

Abstract

From the classical work of Rall it is known that the spread of electric potential in a passive dendritic tree may be obtained by expressing the initial conditions as a linear combination of a set of trigonometric eigenfunctions, each decaying with the associated time constant. It is shown here that in order to evaluate the permissible parameters in these eigenfunctions one may formulate the boundary conditions at all the junctions and endings of the dendritic tree as a set of homogeneous linear equations in which the parameters in the eigenfunctions are the unknowns. These equations have a nontrivial solution if the relevant determinant vanishes, a condition that permits the evaluation of the various parameters, thus providing an analytic approach to the expression of the eigenfunctions as well as the decay time constants. The above approach is illustrated by application to a dendritic tree that has a parent segments and two generations of offspring segments, without any restrictions as to the relative diameters or lengths of the various segments in the tree. General properties of the tree may be readily derived, like the variation of the eigenvalues on scaling of the lengths or diameters of all the segments. A few special case...Continue Reading

References

Feb 1, 1978·Scientific American·G M Shepherd
Aug 1, 1992·Neuron·B LambolezJ Rossier
Sep 1, 1989·Computer Methods and Programs in Biomedicine·W R Seitz
Jan 1, 1966·Experimental Neurology·W RallM W Brightman
Jan 1, 1981·Neuroscience·D H PerkelR W Budelli
Sep 6, 1957·Science·W RALL
Nov 1, 1959·Experimental Neurology·W RALL

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Citations

Oct 25, 2001·Neural Computation·K A LindsayJ R Rosenberg
Oct 23, 1997·Proceedings of the National Academy of Sciences of the United States of America·E Y SnyderJ D Macklis

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