Homogenization limit for electrical conduction in biological tissues in the radio-frequency range

被引：17

作者：

Amar, M

Andreucci, D

Bisegna, P

Gianni, R

机构：

[1] Univ Roma La Sapienza, Dipartimento Metodi & Modelli Matematici, I-00161 Rome, Italy

[2] Univ Roma Tor Vergata, Dipartimento Ingn Civile, I-00133 Rome, Italy

来源：

COMPTES RENDUS MECANIQUE | 2003年 / 331卷 / 07期

关键词：

continuum mechanics; electrical conduction; homogenization; biomathematics;

D O I：

10.1016/S1631-0721(03)00107-4

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We study an evolutive model for electrical conduction in biological tissues, where the conductive intra-cellular and extracellular spaces are separated by insulating cell membranes. The mathematical scheme is an elliptic problem, with dynamical boundary conditions on the cell membranes. The problem is set in a finely mixed periodic medium. We show that the homogenization limit u(0) of the electric potential, obtained as the period of the microscopic structure approaches zero, solves the equation -div(sigma(0)del(x)u(0) + A(0)del(x)u(0) + integral(0)(t) A(1)(t - tau)del(x)u(0)(x, tau)dtau - F(x, t)) = 0 where sigma(0) > 0 and the matrices A(0), A(1) depend on geometric and material properties, while the vector function F keeps trace of the initial data of the original problem. Memory effects explicitly appear here, making this elliptic equation of non standard type.

引用

页码：503 / 508

页数：6