American Institute of Mathematical Sciences

September  2010, 9(5): 1131-1160. doi: 10.3934/cpaa.2010.9.1131

Homogenization limit and asymptotic decay for electrical conduction in biological tissues in the high radiofrequency range

 1 Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy, Italy 2 Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, Via del Politecnico 1, 00133 Roma, Italy 3 Dipartimento di Metodi e Modelli Matematici, Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy

Received  September 2009 Revised  November 2009 Published  May 2010

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.
Citation: Micol Amar, Daniele Andreucci, Paolo Bisegna, Roberto Gianni. Homogenization limit and asymptotic decay for electrical conduction in biological tissues in the high radiofrequency range. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1131-1160. doi: 10.3934/cpaa.2010.9.1131
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