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

Pages: 1131 - 1160, Volume 9, Issue 5, September 2010

doi:10.3934/cpaa.2010.9.1131       Abstract        Full Text (443.3K)       Related Articles

Micol Amar - Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy (email)
Daniele Andreucci - Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy (email)
Paolo Bisegna - Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, Via del Politecnico 1, 00133 Roma, Italy (email)
Roberto Gianni - Dipartimento di Metodi e Modelli Matematici, Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy (email)

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.

Keywords:  Homogenization, electrical conduction in biological tissues, dynamical boundary conditions, oscillating test-function method.
Mathematics Subject Classification:  35B27, 78A70, 45K05.

Received: September 2009;      Revised: November 2009;      Published: May 2010.