## 2 Materials and Methods  
### Mathematical Modelling of electroporation  
In this study, a spherical cell with a radius of 10 \(\upmu\)m was immersed in conductive media and exposed to an equivalent PEF generated by two parallel plates, as shown in Figure 1a. The electric potential distribution in this model was governed by Equation (1). \[-\
abla(\lambda\
abla\psi)-\varepsilon_{0}\varepsilon_{r}\
abla\bigg{(}\frac{ \partial}{\partial t}(\
abla\psi)\bigg{)}=0, \tag{1}\]  
where \(\psi\) represents the electric potential, \(\lambda\) denotes the conductivity, \(\varepsilon_{0}\) is the permittivity of free space, and \(\varepsilon_{r}\) is the relative dielectric constant. The transmembrane potential (TMP) is defined as the difference between the potential at the inner side of the membrane \(\psi_{i}(t)\) and the outer side of the membrane \(\psi_{o}(t)\),  
\[\Delta\psi=\psi_{i}(t)-\psi_{o}(t). \tag{2}\]  
When a pore is formed, there will be an extra conductive pathway for current density besides the conduction current density and the induction current density, as follows:  
\[J(t)=\frac{\lambda_{m0}\Delta\psi}{d}+\frac{\varepsilon_{0}\varepsilon_{mem}} {d}\frac{\partial(\Delta\psi)}{\partial t}+J_{EP}(t), \tag{3}\]  
where the first item means the conduction current density, \(\lambda_{m0}\) is the initial conductivity of the plasm membrane, and \(d\) is the thickness of the plasm membrane; the second item represents the induction current density, and \(\varepsilon_{mem}\) is the relative dielectric constant; the third item denotes the current density induced by electroporation, and it is further determined by Equation (4). \[J_{EP}(t)=i_{EP}(t)N(t), \tag{4}\]  
where \(i_{EP}(t)\) represents the current density passing through an individual pore, and \(N(t)\) represents the pore density. Figure 1: The schematic diagram of (**a**) the simulation space and three regions classified by different patterns of pore evolution, (**b**) the area weight of a differential of arc \(dl\) regarding the position \(\theta\), (**c**) the mesh construction of the SCE model and the close-up view of the mapped mesh of the cell membrane, (**d**) the symmetric bipolar H-FIRE protocol used in this study. The current-voltage relationship of an individual pore, \(i_{EP}(t)\), can be described as:  
\[i_{EP}(t)=\frac{\Delta\psi}{R_{p}+R_{i}}=\Delta\psi\bigg{/}\bigg{(}\frac{d}{ \lambda_{p}\pi r^{2}}+\frac{1}{2\lambda_{p}r}\bigg{)}\,, \tag{5}\]  
where \(R_{p}\) represents pore resistance and \(R_{i}\) represents input resistance, which are in series [46; 47], \(\lambda_{p}\) means the conductivity of the solution filling the pore, and \(r\) is the radius of the pore. Equation (5) provides a nonlinear relationship between the pore radius and its conductance, contrary to the assumption that conductance is irrelevant to the pore size [30; 37]. To simplify the calculation, the dynamic conductivity of the plasm membrane, \(\lambda_{m}(t)\), was introduced to merge the \(J_{EP}(t)\) into the conduction current density:  
\[\lambda_{m}(t)=\lambda_{m0}+N(t)\frac{d}{R_{p}+R_{i}}, \tag{6}\]  
\[J(t)=\lambda_{m}(t)\frac{\Delta\psi}{d}+\frac{\varepsilon_{0}\varepsilon_{mem} }{d}\frac{\partial(\Delta\psi)}{\partial t}. \tag{7}\]  
To reduce the calculation cost, this study ignores the hydrophobic stage in the pore evolution process and assumes that all nanopores appear with an initial radius \(r^{*}\). The rate of pore production is determined by an ordinary differential equation,  
\[\frac{dN(t)}{dt}=\alpha e^{(\frac{\Delta\psi(t)}{V_{EP}})^{2}}\bigg{(}1-\frac{ N(t)}{N0}e^{-q(\frac{\Delta\psi(t)}{V_{EP}})^{2}}\bigg{)}, \tag{8}\]  
where \(V_{EP}\) is the characteristic voltage of electroporation, \(N0\) is the equilibrium pore density for \(\Delta\psi=0\), \(\alpha\) is the creation rate coefficient, and \(q\) is the constant for pore creation rate. Equation (8) is solved with an initial condition \(N(t)=0\) (no pores) and can describe not only pore creation but also pore resealing [48].