## 1 Introduction  
Electroporation is the term that describes the creation of porous defects in the cell membrane when the cell is exposed to a pulsed electric field (PEF) [1; 2; 3]. Electroporation can be used in two ways: reversible and irreversible. For reversible electroporation (RE), the pores in nanometers induced in the cell membrane are transient and expected to recover after the removal of the PEF; this process has been used to introduce drugs or DNA into cells [4; 5; 6; 7; 8]. In the case of irreversible electroporation (IRE), however, larger pores are created, pores that are not able to recover and which will lead to permanent injuries and eventual cell death. IRE has been used for bacterial decontamination [9; 10] and tissue ablation [11; 12; 13; 14; 15; 16]. The generation of pores in the cell membrane has been thought to depend on the pulsing protocol of the PEF, described by a set of parameters such as pulse width, pulse strength, and the rate that pulses are delivered [17; 18]. There is a need to quantitatively describe the relationship between the pulsing protocol and pore evolution in the cell membrane, and this would allow further customization of this promising technique for different scenarios [19; 20; 21; 22]. Currently, several probing techniques have been applied to provide insights into electroporation, such as fluorescent dyes [23], cell impedance monitoring [24], and transmembrane potential visualization [25]. However, the information acquired from these methods is not enough to reflect an event in which the temporal and spatial resolution is at the micro- or nanoscale. On the other hand, the mathematical modelling of electroporation has yielded acceptable results in the prediction of pore evolution [26; 27; 28]. With the development of numerical techniques, mathematical modelling has become a powerful tool in providing a dynamic analysis for electroporation [29; 30] and has been widely acknowledged in relevant fields [31; 32]. State-of-the-art mathematical modelling of electroporation should suffice to describe the pore evolution, i.e., pore formation, pore expansion, and pore resealing [2; 33]. Because the size of a pore can be precisely characterized by the mathematical model of electroporation, increasing attention has been garnered in pore size monitoring [34], specifically, the termination of the pore (i.e., recoverable or irrecoverable) [35; 36]. However, currently, the relationship between the pulsing protocols and the pore evolution is yet to be explored. In this study, the ratio of the total area of all the pores on a cell to the surface area of the cell membrane (the pore area ratio, PAR) was adopted as an indicator of the overall pore evolution. The PAR integrates pore number and pore size to characterize the dynamics of electroporation in a single cell. The surface tension of the cell membrane has not been accounted for in pore evolution using PAR as an indicator [35; 37]. Furthermore, in prior reports, cells were considered in two dimensions in existing mathematical models of electroporation [34; 36; 28; 37], which inevitably sacrificed accuracy in the estimation of the PAR. To address this issue, an area weight (explained in Section 2.1) was proposed in this study to allow cells to be considered in a three-dimensional manner. The second generation of PEF, high-frequency irreversible electroporation (H-FIRE), has attracted great interest in the field of tissue ablation due to the fact that electric pulses can be administered without nerve activation or muscle contractions [38; 39; 40; 41; 42]. An H-FIRE protocol usually includes the selection of several pulse-setting parameters, such as positive pulse and negative pulse widths, inter-phase and inter-pulse delays, pulse burst duration, and pulse frequency. It is noteworthy that no study has yet delineated the relationship between the pulse-setting parameters of H-FIRE and the dynamics of electroporation (i.e., PAR).