## 4 Discussion  
Due to the low dielectric constant of the cell membrane, traditional microsecond-level pulse electric fields face difficulties in penetrating the \"capacitance\" of the cell membrane due to the dominance of low-frequency components. As a result, the primary target of pulse electric fields above the microsecond level is the cell membrane itself. By reducing the pulse width, it becomes possible to target the intracellular biomembranes, thereby enabling the regulation of subcellular structures. Investigating the mechanism behind the force-electric response of subcellular structures under high-frequency and high-voltage pulse electric fields can contribute to the advancement of pulse power technology in clinical and biomedical engineering fields. This research has the potential to address the current limitations of mainstream thermal tumor therapy, such as heat loss and poor prognosis [38]. Based on the finite element simulation results of the progressive electric perforation model, this study demonstrates that nsPEFs induce the electroporation of the nuclear membrane faster and at a significantly higher pore density compared to the cell membrane. This finding suggests a conversion of the pulsed electric field target from the cell membrane to the nuclear membrane. Previous simulation studies by [PERSON] et al. [34] have shown that a pulse width of 60 ns is more likely to cause the perforation of the inner and outer mitochondrial membranes compared to a 600 ns pulse width. Additionally, [PERSON] et al. [39] applied pulsed electric fields with pulse widths ranging from 30 ns to 100 us to normal and cancerous skin cell models and found that nsPEFs with rich high-frequency components generate higher transmembrane voltages on the nuclear membrane. Equivalent circuit model analysis reveals that biological membranes can be considered as high-pass filters for pulsed electric fields due to their small dielectric constant and large equivalent capacitance. Consistent with the results of this study, nsPEFs contain rich high-frequency components  
Figure 10: Fluorescence intensity corresponding to three subcellular structures exposed to different electric field intensities and pulse numbers. (**a**) Fluorescence intensity corresponding to nucleus exposed to different electric field intensities and pulse numbers. (**b**) Fluorescence intensity corresponding to mitochondria exposed to different electric field intensities and pulse numbers. (**c**) Fluorescence intensity corresponding to endoplasmic reticulum exposed to different electric field intensities and pulse numbers. that can penetrate the cell interior based on the cell membrane's low permeability at high frequencies, in addition to inducing the electroporation of the cell membrane through high amplitude. In a study by [PERSON] et al. [40], a pulsed electric field with an amplitude of 80 kV/cm and a pulse width of 5 ns was applied to a chromaffin cell model, which resulted in the electroporation of not only the cell membrane but also the endoplasmic reticulum membrane, secretory granule membrane, and outer mitochondrial membrane. However, [PERSON] et al. hold the belief that the electroporation threshold of subcellular biomembranes is higher than that of the cell membrane, which contradicts the findings of this study and previous studies [41; 42; 43]. In addition to elucidating the mechanism of nsPEFs-induced subcellular structural damage through pore density, this study also calculated the Maxwell stress exerted on the cell membrane and nuclear membrane. The results indicate that the electric field force acting on the nuclear membrane is significantly greater than that on the cell membrane. From an energy perspective, the higher the transmembrane voltage across the cytoplasmic membrane, the greater the electric field force it experiences.