Cell scale modeling of electropermeabilization by periodic pulses

Michael Leguèbe

doi:10.3934/mbe.2015.12.537

Article Contents

2015, Volume 12, Issue 3: 537-554. Doi: 10.3934/mbe.2015.12.537

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Cell scale modeling of electropermeabilization by periodic pulses

Michael Leguèbe^1,

1.
Inria Bordeaux Sud-Ouest, 200, Rue de la Veille Tour, 33405 Talence

Received: November 2013

Revised: January 2015

Published: January 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we focus on the behaviour of periodic solutions to a cell-scale electropermeabilization model previously proposed by Kavian et al. [6]. Since clinical permeabilization protocols mostly submit cancer cells to trains of periodic pulses, we investigate on parameters that modify significantly the resulting permeabilization. Theoretical results of existence and uniqueness of periodic solutions are presented, for two different models of membrane electric conductivity. Numerical simulations were performed to corroborate these results and illustrate the asymptotic convergence to periodic solutions, as well as the dependency on biological parameters such as the cell size and the extracellular conductivity.

Keywords:

Cell modeling,
electropermeabilization,
non-linear partial differential equations.

Mathematics Subject Classification: Primary: 35Q92, 35Q60; Secondary: 92B05, 92C05.

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