We study a hierarchy of electrical conduction problems in biological tissues. These problems are set in a finely mixed periodic medium, and the unknown electric potentials solve standard elliptic equations set in dierent conductive regions (the intracellular and extracellular spaces), separated by an interface (the cell membranes), which exhibits a capacitive and a nonlinear conductive behavior, due to its biochemical structure. Dierent scalings in the interface condition correspond to dierent problems in the hierarchy. As the spatial period of the medium goes to zero, the problems approach a homogenization limit depending on the initial scaling. The macroscopic models are obtained by using the technique of two-scale convergence.

A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: The nonlinear case / Amar, Micol; Andreucci, Daniele; P., Bisegna; Gianni, Roberto. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - STAMPA. - 26:9-10(2013), pp. 885-912.

A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: The nonlinear case

AMAR, Micol;ANDREUCCI, Daniele;GIANNI, Roberto
2013

Abstract

We study a hierarchy of electrical conduction problems in biological tissues. These problems are set in a finely mixed periodic medium, and the unknown electric potentials solve standard elliptic equations set in dierent conductive regions (the intracellular and extracellular spaces), separated by an interface (the cell membranes), which exhibits a capacitive and a nonlinear conductive behavior, due to its biochemical structure. Dierent scalings in the interface condition correspond to dierent problems in the hierarchy. As the spatial period of the medium goes to zero, the problems approach a homogenization limit depending on the initial scaling. The macroscopic models are obtained by using the technique of two-scale convergence.
2013
asymptotics; nonlinear equations; homogenization; electrical conduction in biological tissues
01 Pubblicazione su rivista::01a Articolo in rivista
A hierarchy of models for the electrical conduction in biological tissues via two-scale convergence: The nonlinear case / Amar, Micol; Andreucci, Daniele; P., Bisegna; Gianni, Roberto. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - STAMPA. - 26:9-10(2013), pp. 885-912.
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/516201
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 27
  • ???jsp.display-item.citation.isi??? 26
social impact