What is the optimal shape of an axon?

Antoine Henrot; Yannick Privat

hal-00128444, version 1

What is the optimal shape of an axon?

Antoine Henrot ( Author to contact preferably ) ^1, 2, Yannick Privat () ^1, 2

Abstract: What is the optimal shape of an axon? Of course, optimality refers to some particular criterion. In this paper, we look at the case of an axon tapered at one end and connected at the other end to a soma. The electrical potential in the fiber follows the classical cable equations as established by W. Rall. We are interested in the shape of the axon which minimizes either the attenuation in time of the potential or the attenuation in space. In both cases, we prove that the cylindrical shape is optimal.

1: Institut Elie Cartan Nancy (IECN)
CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2: CORIDA (INRIA Nancy - Grand Est / IECN / LMAM)
INRIA – CNRS : UMR7502 – Université de Lorraine

hal-00128444, version 1
http://hal.archives-ouvertes.fr/hal-00128444
oai:hal.archives-ouvertes.fr:hal-00128444
From: Antoine Henrot <>
Submitted on: Thursday, 1 February 2007 11:49:58
Updated on: Thursday, 1 February 2007 12:01:00

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arXiv: math.AP/0702017

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