## 3 Results
### Evolution of Pore Size and PAR during Electroporation  
The evolution of pore radius is simultaneously driven by TMP and pore density. Regardless, the size change mostly occurred in the polar and transition regions, and the radius of the pores in the equatorial regions is always approximately 0.8 nm, known as the minimum energy radius [51]. A distinguishing feature of pore radius is that the largest pores are induced in the transition region, not in the more electrically charged polar regions, where one might expect (see Figure 4a). The reason for this phenomenon is that the densest pores in the polar region exert a negative influence and suppress the further expansion of the pore size. The detailed mechanism is further interpreted through the local dynamic conductivity of the cell membrane (see Figure 4b) in the Discussion. Overall, under the combined effect of TMP and pore density, the SCE model predicts that large pores will be produced in the transition regions.  
Figure 3: Two boundaries of the transition region, X and Y, shift with (**a**) time and (**b**) electric field strength.  
Given that PAR integrates information on both pore number and size, we have selected PAR as the indicator to evaluate the dynamics of electroporation. The values of PAR around the circumference are shown in Figure 2d. It is noted that the value of PAR in the transition region is the largest. The reasons behind this are (1) although the pore number in the transition regions is less than that in the polar regions, their order of magnitude are the same, while the pore size in the transition region can be much larger than that in the polar regions; (2) the spherical shape dictates that the area weight of the transition region is larger than that of the polar region (for a spherical cell, the 0\(\sim\)30\({}^{\circ}\) region occupies 13.4% of the total area, the 30\(\sim\)60\({}^{\circ}\) region accounts for 36.6%, and the 60\(\sim\)90\({}^{\circ}\) region accounts for 50%). Overall, the primary source of PAR comes from the polar and transition regions at the beginning of pulse delivery, and the transition regions are the predominant contributor to PAR. As the pulsing protocol goes on (up to hundreds of microseconds), the percentage sourced from the transition region to the pore area constantly increases, and a small part of the membrane (38-47\({}^{\circ}\) and 132-139\({}^{\circ}\) region) provides more than 95% PAR, as shown in Figure 2e. The formation of large pores is responsible for the majority of the increase in PAR and comprises the majority of the pore area as the pulses continue. It should be noted that the appearance of the two peaks of PAR is different. This is thought to be due to the existence of the resting potential, which leads to subtle differences on two sides of the cell membrane, strengthening one side and weakening the other side [26,28].  
In conclusion, our simulation reveals some basic rules about pore evolution: (1) most pores are formed during the first applied electrical pulse, and these small pores occupy a majority of the pore area at the beginning; (2) with the delivery of pulses, large pores evolve in the transition region and comprise the majority of the pore area for pore formation in the long term. This same observation has been made in other simulations and experiments [28,52].