Leguebe Michael
Inria Bordeaux Sud-Ouest, 200, Rue de la Veille Tour, 33405 Talence, France.
Math Biosci Eng. 2015 Jun;12(3):537-54. doi: 10.3934/mbe.2015.12.537.
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.
在本文中，我们关注Kavian等人[6]先前提出的细胞尺度电穿孔模型的周期解行为。由于临床渗透方案大多使癌细胞接受周期性脉冲序列，我们研究了显著改变最终渗透率的参数。针对两种不同的膜电导率模型，给出了周期解存在性和唯一性的理论结果。进行了数值模拟以证实这些结果，并说明向周期解的渐近收敛以及对诸如细胞大小和细胞外电导率等生物学参数的依赖性。
