Pucihar Gorazd, Miklavcic Damijan, Kotnik Tadej
Faculty of Electrical Engineering, University of Ljubljana, Ljubljana SI-1000, Slovenia.
IEEE Trans Biomed Eng. 2009 May;56(5):1491-501. doi: 10.1109/TBME.2009.2014244. Epub 2009 Feb 6.
We describe a finite-element model of a realistic irregularly shaped biological cell in an external electric field that allows the calculation of time-dependent changes of the induced transmembrane voltage (Delta Psi) and simulation of cell membrane electroporation. The model was first tested by comparing its results to the time-dependent analytical solution for Delta Psi on a nonporated spherical cell, and a good agreement was obtained. To simulate electroporation, the model was extended by introducing a variable membrane conductivity. In the regions exposed to a sufficiently high Delta Psi, the membrane conductivity rapidly increased with time, leading to a modified spatial distribution of Delta Psi. We show that steady-state models are insufficient for accurate description of Delta Psi, as well as determination of electroporated regions of the membrane, and time-dependent models should be used instead. Our modeling approach also allows direct comparison of calculations and experiments. As an example, we show that calculated regions of electroporation correspond to the regions of molecular transport observed experimentally on the same cell from which the model was constructed. Both the time-dependent model of Delta Psi and the model of electroporation can be exploited further to study the behavior of more complicated cell systems, including those with cell-to-cell interactions.
我们描述了一个处于外部电场中的实际不规则形状生物细胞的有限元模型，该模型能够计算感应跨膜电压（ΔΨ）随时间的变化，并模拟细胞膜电穿孔。该模型首先通过将其结果与非穿孔球形细胞上ΔΨ的时间相关解析解进行比较来进行测试，结果获得了良好的一致性。为了模拟电穿孔，通过引入可变膜电导率对模型进行了扩展。在暴露于足够高ΔΨ的区域，膜电导率随时间迅速增加，导致ΔΨ的空间分布发生改变。我们表明，稳态模型不足以准确描述ΔΨ以及确定膜的电穿孔区域，而应使用时间相关模型。我们的建模方法还允许直接比较计算结果和实验结果。例如，我们表明计算出的电穿孔区域与在构建模型所使用的同一细胞上实验观察到的分子运输区域相对应。ΔΨ的时间相关模型和电穿孔模型都可以进一步用于研究更复杂的细胞系统的行为，包括那些具有细胞间相互作用的系统。
