Shape Minimization of Dendritic Attenuation

Antoine Henrot (1) , Yannick Privat (1)

1 CORIDA - Robust control of infinite dimensional systems and applications

What is the optimal shape of a dendrite? Of course, optimality refers to some particular criterion. In this paper, we look at the case of a dendrite sealed 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 dendrite 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.

Mots clés: optimal shape; cable equation; dendrite; eigenvalue problem

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Morphogenèse

Antoine Henrot, Yannick Privat. Shape Minimization of Dendritic Attenuation. Applied Mathematics and Optimization, 2008, 57 (1), pp.1-17. ⟨10.1007/s00245-007-9002-0⟩. ⟨hal-00128444v2⟩