## 3 Results
### The Cumulative Effect of PAR  
As indicated before, PAR was considered a suitable index in the setting of IRE because a higher PAR corresponds to a higher likelihood of cell death. PAR contains information from both pore number and size. Pore density can be considered steady after the first pulse on most membrane regions; hence, PAR is deeply affected by pore size. In most cases, it was found that PAR will fluctuate along with the pore size fluctuation, such as in protocol 1-3-1 with 1000 V/cm, as the solid line shown in Figure 5a. Under specific protocols, PAR was found to constantly increase instead of fluctuating with a sigmoid pattern, as in the dashed line seen for the protocol 1-1-1 with 1000 V/cm shown in Figure 5a. This sigmoid pattern of PAR changing with respect to time duration is termed the cumulative effect. The cumulative effect of PAR is desirable in H-FIRE protocol design and considered  
Figure 4: The changes of (**a**) pore radius and (**b**) conductivity along the semi-circumference from 0\({}^{\circ}\)\(\sim\)180\({}^{\circ}\) at different moments using 1-1-1 protocol with 1000 V/cm. high-performance in the context of tumor ablation because it reflects a high probability of irrecoverable damage to cells. Therefore, this cumulative effect was investigated further in our study to provide guidance for high-performance H-FIRE protocol design. The key to achieving the cumulative effect requires certain combinations of pulse width and pulse delay. For instance, in all protocols with a pulse width of 1 \(\upmu\)s and electric field strength of 1000 V/cm, only a pulse delay of 2 \(\upmu\)s or less can trigger the cumulative effect, as shown in Figure 5b. On the other hand, electric field strength also plays a role in driving the cumulative effect. In Figure 5c, the occurrence of the cumulative effect requires a minimum electric field strength of 520 V/cm for 1-1-1 protocols. Figure 5: The change of PAR with respect to (**a**) time duration of protocols 1-1-1 and 1-3-1; the maximum of PAR with respect to (**b**) pulse delay when the pulse width is fixed at 1 \(\upmu\)s and the electric field strength is fixed at 1000 V/cm, and to (**c**) electric field strength when the pulse width is fixed at 1 \(\upmu\)s and the pulse delay is fixed at 1 \(\upmu\)s.  
The Effect of Electric Field Strength, Pulse Width, Pulse Delay, and Pulse Burst Duration on the Dynamics of Electroporation  
The parameters that describe a protocol, i.e., electric field strength, pulse width, pulse delay, and pulse burst duration, are of particular interest to researchers when designing H-FIRE protocols. Yet comprehensive guidelines for protocol design have not yet been elucidated due to the complex interactions between the pulse-setting parameters. To date, only a few qualitative recommendations have been made based on numerical studies [34,41] and experimental studies [53,54], e.g., a higher electric field strength and a longer pulse width will lead to a greater extent of electroporation. In this study, quantitative guidelines were given for H-FIRE protocol design based on our SCE model. As shown in Figure 6a, there is a plateau of the PAR, which reflects the occurrence of the cumulative effect described earlier. The range of the plateau serves as a recommendation for protocol selection. Specifically, for a pulse width of 1 us, the boundary of the pulse delay is around 2 us, and the margin of electric field strength is about 500 V/cm. This indicates that the 1-us pulse width should be preferentially matched with a pulse delay shorter than 2 us, and the electric field strength should be higher than 500 V/cm. Importantly, the influence of the pulse burst duration on the cumulative effect was also given in this study, which is rarely mentioned in other papers. As mentioned earlier, the value of PAR exhibits a sigmoid curve with pulse burst duration. That means the cumulative effect will be cut off before reaching the plateau if the pulse burst duration is not long enough.