## 3 Results  
Figure 3 shows the 99 th percentiles of the electric field module obtained for two different distances (\(d_{1}\) and \(d_{2}\)) of the cell from the coil for the three different Au NP configurations considered, and, for a comparison, when no Au NP was used. As a first finding, a huge enhancement of the induced electric field was observed for both \(d_{1}\) and \(d_{2}\). For \(d_{1}\), the observed values of \(E^{99\text{th}}\)AllBOX were equal to 2580, 1955, and 1797 V/cm for the 24 spherical NPs, for the 24 cubic NPs, and for the 40 spherical NPs grouped in eight clusters, respectively, while when no Au NP was used, the 99 th percentile of the module of the electric field was equal to 12.22 V/cm. When considering the enhancement in the neighboring of each NPs, a great difference was observed between NPs placed in different positions: in the spherical NP configuration, the maximum value of the 99 th percentiles of the module of the electric field calculated around each NP, \(E^{99\text{th}}\)MAX, was equal to 2959.2 V/cm, while the minimum \(E^{99\text{th}}\)MIN was equal to 36.938 V/cm. A higher difference was observed for the cubic NP configuration, were \(E^{99\text{th}}\)MAX and \(E^{99\text{th}}\)MIN were found to be equal to 3553.8 V/cm and 34.3 V/cm. Finally, when considering clusters of NPs, \(E^{99\text{th}}\)MAX and \(E^{99\text{th}}\)MIN were found to be equal to 1796.6 V/cm and 58.95 V/cm. For \(d_{2}\), as expected, lower values were observed, but the presence of the Au NPs still caused a significant enhancement of the electric field: the observed values of \(E^{99\text{th}}\)AllBOX were equal  
to 924.26, 701.38, and 644.16V/cm for the 24 spherical NPs, for the 24 cubic NPs, and for the 40 spherical NPs grouped in eight clusters, respectively, while when no Au NP was used, \(E^{\text{99 th}}\)\({}_{\text{AllBox}}\) was equal to 4.38 V/cm. Moreover, for \(d_{2}\), a great difference was observed in the local enhancement of the electric field among NPs placed in different positions: \(E^{\text{99 th}}\)\({}_{\text{MAX}}\) and \(E^{\text{99 th}}\)\({}_{\text{MIN}}\) were found to be equal to 1059.9 and 13.786 V/cm for the spherical NP configuration, to 1276.5 and 12.25 V/cm for the cubic NP configuration, and to 811.4 and 42.5 V/cm for the 40 spherical NPs grouped in eight clusters. Figure 4 shows time evolution of the transmembrane voltage \(V_{m}\) and pore density \(N\) in three points of the cell membrane corresponding to \(\theta\) equal to \(0^{\circ}\), \(45^{\circ}\) and \(90^{\circ}\) (see Figure 1b), and the variation in the conductivity along the cell membrane for \(t\) equal to 15 \(\upmu\)s when considering the amplitude of the external applied electric field equal to \(E^{\text{99 th}}\)\({}_{\text{AllBox}}\), \(E^{\text{99 th}}\)\({}_{\text{MAX}}\) and \(E^{\text{99 th}}\)\({}_{\text{MIN}}\) for all the Au NP configurations when the distance between the cell and the coil was equal to \(d_{1}\). An enlarged detail of the time evolution of the transmembrane voltage \(V_{m}\) is reported in Figure 4d,g,j, to highlight the effect of the pore dynamics on \(V_{m}\). When no Au NP was considered, the transmembrane voltage \(V_{m}\) was not high enough to allow the pore opening in any point of the cell membrane (see Figure 4a-c). For the spherical Au NP configuration (Figure 4d-f), when the amplitude of the external applied electric field was set to \(E^{\text{99 th}}\)\({}_{\text{AllBox}}\) (red lines) and to \(E^{\text{99 th}}\)\({}_{\text{MAX}}\) (gray lines), the time evolution of \(V_{m}\) was almost identical--in both cases, higher than the critical threshold assumed to enable pore opening for \(\theta\) equal to \(45^{\circ}\) (dashed lines) and \(90^{\circ}\) (continuous lines). The corresponding time evolutions of the pore density \(N\) are shown in Figure 4e. As expected, the pore opening caused a sudden decrease in the time evolution of \(V_{m}\) (see the enlarged detail of Figure 4d).