Cell scale modeling of electropermeabilization by periodic pulses

  • Received: 01 November 2013 Accepted: 29 June 2018 Published: 01 January 2015
  • MSC : Primary: 35Q92, 35Q60; Secondary: 92B05, 92C05.

  • 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.

    Citation: Michael Leguèbe. Cell scale modeling of electropermeabilization by periodic pulses[J]. Mathematical Biosciences and Engineering, 2015, 12(3): 537-554. doi: 10.3934/mbe.2015.12.537

    Related Papers:

  • 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.


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    [1] Technology in Cancer Research and Treatment, 11 (2012), 561-570.
    [2] Communications in Computational Physics, 12 (2012), 1562-1587.
    [3] Biophysical Journal, 77 (1999), 1213-1224.
    [4] Cancer Treatment Reviews, 29 (2003), 371-387.
    [5] Dielectrics and Electrical Insulation, IEEE Transactions on, 10 (2003), 778-787.
    [6] Journal of Mathematical Biology, 68 (2014), 235-265.
    [7] PhD thesis, Université de Bordeaux, 2014.
    [8] Technical Report RR-8302, Inria, 2013.
    [9] Journal of Theoretical Biology, 360 (2014), 83-94.
    [10] Biomicrofluidics, 4 (2010), 13206.
    [11] Wiley-VCH Verlag GmbH & Co. KGaA, (2006), 219-226.
    [12] Biochimica et Biophysica Acta - Biomembranes, 1808 (2011), 792-801.
    [13] Physical Review E, 53 (1999), 3471-3482.
    [14] PhD thesis, Université Rennes 1, 2009.
    [15] Biochemical Pharmacology, 42 (1991), S67-S75.
    [16] Mathematical Methods in the Applied Sciences, 32 (2009), 435-453.
    [17] IEEE Trans Biomed Eng, 58 (2011), 3279-3288.
    [18] Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2002.
    [19] Human Gene Therapy, 16 (2005), 1194-1201.
    [20] in Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP), (2011), 3164-3167.
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  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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