On a hierarchy of models for electrical conduction in biological tissues

Abstract

Abstract In this paper we derive a hierarchy of models for electrical conduction in a biological tissue, which is represented by a periodic array of period ε of conducting phases surrounded by dielectric shells of thickness εη included in a conductive matrix. Such a hierarchy will be obtained from the Maxwell equations by means of a concentration process η → 0, followed by a homogenization limit with respect to ε . These models are then compared with regard to their physical meaning and mathematical issues. Copyright © 2005 John Wiley & Sons, Ltd.