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IMA Journal of Mathematical Control and Information 2000 17(4):347-377; doi:10.1093/imamci/17.4.347
© 2000 by Institute of Mathematics and its Applications
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Analysis of a multiple equivalent cylinder model with generalized taper

J. D. EVANS{ddagger}

Department of Mathematical Sciences, University of Bath Bath BA2 7AY. UK

{dagger}Email: msjde{at}maths.bath.ac.uk

A multiple equivalent cylinder somatic shunt cable model for passive neurones is considered in which one or more tapering equivalent cylinders emanate from a uniformly polarized soma. Each tapering equivalent cylinder approximates the loss of dendritic trunk parameter in the one or more dendritic trees that it represents, relaxing certain symmetry conditions necessary for the Rall equivalent cylinder reduction and in particular allowing terminal branches to end at different electrotonic distances from the soma. The types of taper belong to a class of six specific forms which can account for strict taper, strict flare as well as tapering and flaring combinations. As such they can account for a wide variety of taper forms that arise in practice upon collapse of a dendritic tree to an appropriate equivalent cylinder involving taper. The uniform (i.e. non-taper) and exponential taper forms are two of the six taper types.

Keywords: non-uniform equivalent cable; tapering dendritic profiles; multi-cylinder; voltage transients; neuronal modelling.


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