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.

Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2003). Homogenization limit for electrical conduction in biological tissues in the radio-frequency range. COMPTES RENDUS MECANIQUE, 331(7), 503-508 [10.1016/S1631-0721(03)00107-4].

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

BISEGNA, PAOLO;
2003-01-01

Abstract

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.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ICAR/08 - Scienza delle Costruzioni
Settore ING-IND/34 - Bioingegneria Industriale
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
Biomathematics; continuum mechanics; electrical conduction; homogenization
Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2003). Homogenization limit for electrical conduction in biological tissues in the radio-frequency range. COMPTES RENDUS MECANIQUE, 331(7), 503-508 [10.1016/S1631-0721(03)00107-4].
Amar, M; Andreucci, D; Bisegna, P; Gianni, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/23549
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