We derive a macroscopic model of electrical conduction in biological tissues in the high radio-frequency range, which is relevant in applications like electric impedance tomography. This model is derived via a homogenization limit by a microscopic formulation, based on Maxwell's equations, taking into account the periodic geometry of the microstructure. We also study the asymptotic behavior of the solution for large times. Our results imply that periodic boundary data lead to an asymptotically periodic solution.
Homogenization limit and asymptotic decay for electrical conduction in biological tissues in the high radiofrequency range / Amar, Micol; Andreucci, Daniele; P., Bisegna; Gianni, Roberto. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 9:5(2010), pp. 1131-1160. (Intervento presentato al convegno 6th European Conference on Elliptic and Parabolic Problems tenutosi a Gaeta, ITALY nel MAY 25-29, 2009) [10.3934/cpaa.2010.9.1131].
Homogenization limit and asymptotic decay for electrical conduction in biological tissues in the high radiofrequency range
AMAR, Micol;ANDREUCCI, Daniele;GIANNI, Roberto
2010
Abstract
We derive a macroscopic model of electrical conduction in biological tissues in the high radio-frequency range, which is relevant in applications like electric impedance tomography. This model is derived via a homogenization limit by a microscopic formulation, based on Maxwell's equations, taking into account the periodic geometry of the microstructure. We also study the asymptotic behavior of the solution for large times. Our results imply that periodic boundary data lead to an asymptotically periodic solution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
