## 2 Materials and Methods
### Evaluation of the Induced Electric Field  
The 3D geometry consisting of the coil, the cell, and the Au NPs in different positions was simulated. The induced electric field was calculated by solving the electromagnetic problem under the Frequency Dependent Study application mode under the \"Magnetic and Electric Field\" solver of the AC/DC module in COMSOL. The module of the electric field was evaluated in a cube with dimensions \(25\times 25\times 25\)\(\upmu\)m centered around the cell, containing the extracellular medium and the nanoparticles. The 99 th percentile of the module of the electric field was calculated on different volumes: on the whole cube under analysis, and, to consider the localized enhancement in proximity of each NP, in a 100 nm spherical neighborhood around each Au NP. In the case of the cluster of Au NPs, a 100 nm spherical neighborhood was considered around each NP, and the 99 th percentile of the electric field was calculated on the union of the five spherical neighborhoods built around each NP. Thus, for the 24 spherical and the 24 cubic Au NPs conditions, we calculated 25 values of electric field (99 th percentiles calculated in each NP spherical neighborhood plus the one calculated on the whole box); for the clusters of Au NPs, we calculated 9 values of electric field (99 th percentiles calculated in each cluster neighborhood plus the one calculated on the whole box); and for the \"no NPs\" condition, only the 99 th percentile of the electric field on the whole box was calculated. Among all these values, three parameters were considered for each simulation: \(E^{\text{99 th}}_{\text{A\"{I\"{B\"{O\"{O\"{O\"{O\"{O\"{O\"{O\"{O\"{O\"{O\"{O\"{O\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"  
three simulations were carried out, by applying as external electric potential to the high side of the square, modelled as positive anode electrode (Electrode 1 in Figure 1b), a cosine stimulus with frequency 33 kHz and amplitude equal to \(V_{max}=E_{max}\times d\), where \(E_{max}\) was set equal to \(E^{99\text{th}}\)ALLBOX, \(E^{99\text{th}}\)MAX, and \(E^{99\text{th}}\)MIN, calculated as described in Section 2.2, and \(d\) was the distance between the electrodes, equal to 40 \(\upmu\)m. The electric potential on the low side of the square (Electrode 2 in Figure 1b) was set equal to zero in all the simulations, while the remaining sides of the square were modeled as insulating, thus obtaining an almost uniform electric field distribution, as shown in Figure 1c. The time evolution and spatial distribution of the electric potential, \(V(P,t)\), and of the pore density, \(N(P,t)\), due to time-varying applied \(E(t)\), are obtained by solving the following system of equations:  
\[\left\{ \begin{array}{l}\
abla\cdot\left(-\frac{\partial\
abla V}{\partial t}- \sigma\
abla V-Ni_{ep}\right)=0\\ \frac{\partial N}{\partial t}=\alpha e^{\frac{V_{m}}{V_{op}}^{2}}\left(1-\frac {N}{N_{0}}e^{-q\frac{V_{m}}{V_{op}}^{2}}\right)\\ N(P,t)=0\ if\ P\
otin\text{cell membrane}\end{array} \right.\]  
where \(i_{op}\) is the current in an aqueous pore [26], and \(V_{m}=V_{m}\) (P*, \(t\)) is the transmembrane potential in a generic point \(P\)* on the external surface of the membrane, defined as the difference of electric potential in \(P\)* and the electric potential in its geometric projection on the internal cell membrane boundary. The second equation of the system is the asymptotic version of the Smoluchowski equation and describes the rate of creation and destruction of hydrophilic membrane pores per local membrane area \(N\) as a function of the \(V_{m}\). Constant values \(V_{op}=258\) mV, \(q=2.46\), \(\alpha=109\), and \(N_{0}=1.5\times 10^{9}\) m\({}^{-2}\) were adopted as in [26; 27], being \(N_{0}\) the \"equilibrium value\" of pore density when \(V_{m}=0\). The phenomenon of pore creation is assumed to be activated at a fixed time instant \(t\)* in a point \(P\)*, when \(V_{m}\) reaches a critical value, i.e., \(V_{\text{crit}}=4V_{op}=1032\) mV [24].