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.
Tipologia: | Articolo su rivista |
Citazione: | 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. |
IF: | Con Impact Factor ISI |
Lingua: | English |
Settore Scientifico Disciplinare: | Settore ICAR/08 - Scienza delle Costruzioni Settore ING-IND/34 - Bioingegneria Industriale Settore MAT/05 - Analisi Matematica |
Revisione (peer review): | Sì, ma tipo non specificato |
Tipo: | Articolo |
Rilevanza: | Rilevanza internazionale |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/S1631-0721(03)00107-4 |
Stato di pubblicazione: | Pubblicato |
Data di pubblicazione: | 2003 |
Titolo: | Homogenization limit for electrical conduction in biological tissues in the radio-frequency range |
Autori: | |
Autori: | Amar, M; Andreucci, D; Bisegna, P; Gianni, R |
Appare nelle tipologie: | 01 - Articolo su rivista |
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