基于电穿孔和孔径变化方程的球形细胞微孔特性研究

Simulation Analysis of Microporous Characteristics of Spherical Cells Based on Electroporation and Pore Radii Change Equation

为进一步探究电穿孔理论机制,通过COMSOL建立单细胞电穿孔二维轴对称模型,该模型同时纳入表征微孔密度的电穿孔渐进方程和表征微孔动态演变过程的孔径变化方程,且模型的轴对称性使穿孔面积的计算更为准确,从而得到微孔的时空分布特性,并在此基础上探讨场强和脉宽对该特性的影响。结果表明:脉宽100μs、场强2 k V/cm的脉冲作用下,产生微孔7862个,穿孔面积达细胞表面积的6.3%,电穿孔各参量的时空分布规律与文献结果一致,从而可验证所建模型的有效性;在1~5 k V/cm范围内增大脉冲场强,微孔数与场强成正比,孔径则与场强成反比,孔面积与细胞面积之比从1.3%增至12.9%;对两组能量相同的纳秒脉冲和微秒脉冲进行比较,发现脉冲结束时前者产生的微孔数是后者的353.1倍,而在细胞膜上最靠近电极的点,后者的孔径是前者的19.3倍,说明纳秒脉冲有利于微孔数增加,而微秒脉冲有利于孔径扩大。仿真结果表明,微孔特性决定电穿孔的发生和发展过程,微孔特性的精确计算是阐释电穿孔效应的关键所在。

In order to explore the theoretical mechanism of electroporation(EP),a 2 D-axisymmetric model of single cell EP was established in this paper.The asymptotic electroporation equation and the pore radii evolution equation were included in the model to express the pore density and radii of EP.The perforation area was calculated more accurate by the axisymmetry of the model.Thus the temporal and spatial distribution characteristics of the micropores can be obtained,and the influence of the field strength and pulse width on EP was discussed.The results showed that 7862 micropores were produced under the microsecond pulse electric field(μs PEF)of 100μs and 2 k V/cm,and the perforation area accounted for 6.3%of the cell surface;the temporal and spatial distribution of the parameters of EP were consistent with the results of literature,which verified the correctness of the constructed model;in the range of 1 to 5 k V/cm,the number of pores was directly proportional to the field strength,the pore radius at P1 was in inverse proportion to the field strength,while the ratio of pore area to cell area increased from 1.3%to 12.9%;two groups of nsPEF andμs PEF with the same energy were selected for comparative study,it was found that at the end of the pulse,the number of pores generated by the former was 353.1 times of the latter one,and the pore radius at P1 of the latter was 19.3 times of the former one,indicated that nsPEF was conducive to the growth of the number of pores,while theμs PEF was conducive to the expansion of the pore radii.The simulation results showed that microporous characteristics determined the occurrence and development of EP,and the accurate calculation of microporosity was the key to explain the effect of EP.