## 4 Discussion  
In the present study, the dynamics of pore evolution caused by symmetric bipolar H-FIRE protocols were investigated using a proposed SCE model, which integrates electric field theory and pore mechanics to provide a principle-based modeling approach. The SCE model demonstrated the process of pore evolution within a pulse burst, showing most pores occur in the transition and polar regions during the administration of the first pulse in a small size (i.e., \(<\)5 nm), and the pores located in the transition region are found to expand to tens to hundreds of nm in diameter with the delivery of pulses (see Figure 4a). In the early phase of a pulse burst (e.g., the first 8 microseconds), the polar region and transition region contributed to PAR at the same magnitude, but in the later phase of the pulse burst (e.g., after 100 microseconds), large pores started to evolve in the transition regions and composed the majority of PAR (more than 95%) due to the cumulative effect of ongoing exposure to H-FIRE protocols. The cumulative effect was found to be critical in the electroporation dynamics, and this should guide the design of protocols to have a high probability of cell death. In this study, four pulse-setting parameters (pulse width, pulse delay, pulse burst duration, and electric field strength) for each of the two H-FIRE protocols (1-D-1 and 2-D-2) were investigated. The results indicated that, for 1-\(\upmu\)s pulses, the pulse delay should not exceed 2 \(\upmu\)s, and the pulse delay for 2-\(\upmu\)s pulses should not be longer than 4 \(\upmu\)s. Additionally, a minimum limit for the electric field strength leading to the cumulative effect was identified, which increases with an increase in the pulse width. The electric field strength should be at least 500 V/cm and 400 V/cm for 1-\(\upmu\)s and 2-\(\upmu\)s pulses, respectively. Additionally, the pulse burst duration was recommended to be longer than 300 \(\upmu\)s.  
The relationship between the cumulative effect of PAR and pulse-setting parameters can be illustrated by taking the cell membrane as a capacitor in the study. At first, the essence of the cumulative effect is the continuous expansion of the pore size in the transition regions, as discussed in Section 3.1. Based on the results shown in Figure 2c, the size of pores will expand when the pulses are on but will also shrink when the pulses are off. Based on this phenomenon, it can be concluded that the leading cause of the cumulative effect is that the increment in pore size when the pulse is on is larger than the decrement in pore size when the pulse is off. This explains why there is a minimum limit in the pulse delay that changes with the pulse width. Figure 6: The joint effect of the pulse delay and the electric field strength on (**a**) PAR and (**b**) the time required to reach plateau when the pulse width is 1 \(\upmu\)s; The joint effect of the pulse delay and the electric field strength on (**c**) PAR and (**d**) the time required to reach plateau when the pulse width is 2 \(\upmu\)s.  
Furthermore, to gain a deeper understanding of the cumulative effect from a quantitative perspective, the influences of the pulse-setting parameters on the rate of pore size change were illustrated here. Based on Equation (9), the rate of pore size change depended on two external factors, TMP and the effective membrane surface tension. The TMP can be affected significantly by the application or removal of PEFs, leading to the fluctuation of TMP as a process of charging and discharging a capacitor. Because the TMP does not reduce to zero instantly even if the pulse is off, the residual TMP is found to be able to mitigate the shrinkage of pores. Thus, the discharging time also exerts an influence on pore evolution. A long discharging time can hinder pores from shrinking during the pulse delay and be positive for the occurrence of the cumulative effect. The discharging time is determined by the local conductivity of the cell membrane, which depends on the local dynamics of electroporation.