We collect some results concerning electrical conduction problems in biological tissues. These problems are set in a finely mixed periodic medium and the unknown electric potentials solve standard elliptic equations set in different conductive regions (the intracellular and extracellular spaces), separated by an interface (the cell membrane), which exhibits both a capacitive and a conductive behavior. As the spatial period of the medium goes to zero, the problems approach a homogenization limit. The macroscopic models are obtained by using the technique of asymptotic expansions, in the case where the conductive behavior of the cell membrane is linear, and by means of two-scale convergence, in the case where, due to its biochemical structure, the cell membrane performs a strongly nonlinear conductive behavior. The asymptotic behavior of the macroscopic potential for large times is investigated, too.
Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2013). Electrical conduction in biological tissues: Homogenization techniques and asymptotic decay for linear and nonlinear problems. In SIMULTECH 2013 - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (pp.696-703). Reykjavik.
Electrical conduction in biological tissues: Homogenization techniques and asymptotic decay for linear and nonlinear problems
Bisegna P.
;
2013-01-01
Abstract
We collect some results concerning electrical conduction problems in biological tissues. These problems are set in a finely mixed periodic medium and the unknown electric potentials solve standard elliptic equations set in different conductive regions (the intracellular and extracellular spaces), separated by an interface (the cell membrane), which exhibits both a capacitive and a conductive behavior. As the spatial period of the medium goes to zero, the problems approach a homogenization limit. The macroscopic models are obtained by using the technique of asymptotic expansions, in the case where the conductive behavior of the cell membrane is linear, and by means of two-scale convergence, in the case where, due to its biochemical structure, the cell membrane performs a strongly nonlinear conductive behavior. The asymptotic behavior of the macroscopic potential for large times is investigated, too.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
