Electroporation of concentric compound spherical and confocal spheroidal as well as eccentric compound spherical vesicles, considered to be good models for corresponding nucleate cells, are investigated with an emphasis on their response to nanosecond pulse electric field (nsPEF). Analytical models are developed for the estimation of the trans membrane potential (TMP) across the bilayers of the inner and the outer vesicles and finite element simulations are also carried out for the eccentric case. Our calculations show that with an increase in the aspect ratio, while the TMP decreases when nsPEF is used, it increases for confocal spheroids when the pulse width is greater than the membrane charging time, leading to fully charged vesicles. Bipolar pulses are shown to effectively control the TMP for a desired time period in the nsPEF regime, and a fast decay of the TMP to zero can be achieved by judicious use of pulse polarity. The external conductivity is found to significantly influence the TMP in nsPEF, unlike millisecond pulses where its effect is insignificant. Additionally the critical electric field required to induce a TMP of 1V at the inner vesicle is presented for different pulse widths, rise time as well as membrane capacitance, and the TMP of the outer vesicle is found to be within limits of reversible poration. It is found that the maximum TMP has a roughly linear dependence on the outer aspect ratio of the vesicle. We also introduce a new method to obtain the particular solution to the Laplace equation for bispherical system, and it is validated with finite element simulations. Our study on nsPEF electroporation of bispherical vesicles shows that the north pole TMP is typically greater than the south pole, thereby suggesting the typical pathway a charged species might take inside an eccentric nucleate cell under electroporation. [Keywords] nsPEF, TMP, Confocal Spheroids, Bipolar Pulse, Eccentric Cell, Bispherical Coordinates …

中文翻译：

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纳秒脉冲电场作用下同心球形，共聚焦球形和双球形囊泡中跨膜电位的发展

研究了同心复合球形和共聚焦球形以及偏心复合球形囊泡的电穿孔，认为它们是相应有核细胞的良好模型，并重点研究了它们对纳秒脉冲电场（nsPEF）的响应。建立了分析模型以估计跨内和外囊双层的跨膜电位（TMP），并且还针对偏心情况进行了有限元模拟。我们的计算表明，随着长宽比的增加，当使用nsPEF时TMP会降低，而当脉冲宽度大于膜的充电时间时，共焦球体的TMP会增加，从而导致囊泡完全充电。在nsPEF方案中，双极性脉冲可在所需时间段内有效控制TMP，明智地使用脉冲极性可以使TMP快速衰减到零。发现外部电导率显着影响nsPEF中的TMP，这与毫秒级脉冲的影响无关紧要。另外，对于不同的脉冲宽度，上升时间以及膜电容，还提出了在内部囊泡处引发1V TMP所需的临界电场，并且发现外部囊泡的TMP在可逆渗透的范围内。发现最大TMP对囊泡的外部长宽比具有大致线性的依赖性。我们还介绍了一种新方法来获得双球系统Laplace方程的特殊解，并已通过有限元模拟对其进行了验证。我们对双球囊泡nsPEF电穿孔的研究表明，北极TMP通常大于南极，从而表明带电物质在电穿孔下可能会进入偏心核细胞内的典型途径。[关键词] nsPEF，TMP，共聚焦球体，双极脉冲，偏心细胞，双球坐标…