## 4 Discussion
Finally, when the cell was placed in \(d_{2}\), even if cell permeabilization was not achieved in all the considered NP configurations and not in all points of the membrane, Au NPs played a fundamental role in enabling pore opening in conditions in which, without them, it would be completely impossible to reach permeabilization. Our findings--although not directly comparable with previously reported literature, as to our knowledge, no previous modeling study focused on the use of NPs when considering time-varying magnetic fields for cell permeabilization--were roughly in line with observations reported in studies about the use of Au NPs in electroporation protocols [20; 21; 22; 23; 24]. Moreover, our findings confirmed experimental findings reported in [18], in which authors found that conductive gold nanoparticles can significantly potentiate the permeabilizing effect of time-varying magnetic fields, with an increase in permeabilization from 1.57% with no NPs, to 10.99% using 20 nm Au NPs. In conclusion, our study showed that the combined use of Au NPs and time-varying magnetic fields can significantly improve the permeabilization of cell membranes. As the electric field induced in the cell suspension is not uniform, also due to the presence of nanoparticles in proximity of the membrane, the approach of applying an almost uniform electric field distribution to assess the pore dynamics used in this study could represent an important simplification of the phenomenon. However, this approach,well established and already used in previous studies dealing with computational evaluation of pore dynamics influenced by electric fields distributions with [25] or without (see, e.g., [27]) the presence of nanoparticles near the cell membrane, allowed reducing the computational effort due to the presence of both nano-scale and millimeter-scale structures, while preserving the representativeness of the results. The preliminary findings obtained in this study were encouraging and showed that the variability of NP geometries and configurations in proximity of the cell membrane had a strong influence on pore opening mechanisms. Future investigations should address all these aspects, and, due to the intrinsic variability and uncertainty characterizing a real in vitro experimental set, a stochastic dosimetry [30] approach, i.e., an innovative approach combining computational bioelectromagnetic and stochastic methods, could be used to obtain a realistic representation of the phenomena under study. Moreover, in future studies, it would be interesting to investigate how different types of NPs, such as magnetic ones, could influence the permeabilization of the cell membrane, and to take into account not only the enhancement of the electric field, but also the role that different types of NPs could play in terms of the mechanical stress on the cell membrane locally induced by the magnetic and electric fields, which are hypothesized to play an important role in the permeabilization mechanism [19]. Conceptualization, methodology, formal analysis, E.C., S.F. and M.P. ; writing--original draft preparation, E.C., S.F. and M.P. ; writing--review and editing, M.B. ([PERSON]), S.G. and M.B. ([PERSON]). All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are available on request from the corresponding author. The authors declare no conflict of interest. * [PERSON] et al. (2016) [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON] Pulsed Electromagnetic Field Assisted in vitro Electroporation: A Pilot Study. _Sci. Rep._**2016**, \(6\), 33537. [CrossRef]
* [PERSON] et al. (2017) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON];[PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON] Reversible Permeabilization of Cancer Cells by High Sub-Microsecond Magnetic Field. _IEEE Trans. Magn._**2017**, _53_, 1-4.