_applied_  
_sciences_  
_Article_  
**Use of Nanoparticles as Nanoelectrodes in Contact-Less Cell**  
**Membrane Permeability by Time-Varying Magnetic Field: A Computational Study**  
**[PERSON] 1,*,** [PERSON] 1,** [PERSON] 1,** [PERSON] 1,2 [PERSON] 1,2 and [PERSON] 1  
1 Consiglio Nazionale delle Ricerche (CNR), Istituto di Elettronica e di Ingegneria dell'Informazione e delle Telecomunicazioni (IEIT), Piazza L. da Vinci, 32, 20133 Milano, Italy; [EMAIL_ADDRESS] (S.F. ); [EMAIL_ADDRESS] (M.B. ); [PERSON] (S.G.); [PERSON]SS] (M.B. ); [PERSON] (M.F.) 2 Dipartimento di Elettronica, Informazione e Bioingegenria (DEIB), Politecnico di Milano, Piazza L. da Vinci, 32, 20133 Milan, Italy  
* Correspondence: [EMAIL_ADDRESS]  
**Abstract** This paper describes a computational approach for the assessment of electric field enhancement by using highly conductive gold nanoparticles (Au NPs) in time-varying electromagnetic fields cell membrane permeabilization, estimating the influence of the presence of Au NPs on transmembrane potential and on the pore opening dynamics. To account for variability and uncertainty about geometries and relative placement and aggregations of the Au NPs, three different NP configurations were considered: spherical Au NPs equally spaced around the cell; cubic Au NPs, for accounting for the possible edge effect, equally spaced around the cell; and spherical Au NPs grouped in clusters. The results show that the combined use of Au NPs and a time-varying magnetic field can significantly improve the permeabilization of cell membranes. The variability of NPs' geometries and configurations in proximity of the cell membrane showed to have a strong influence on the pore opening mechanism. The study offers a better comprehension of the mechanisms, still not completely understood, underlying cell membrane permeabilization by time-varying magnetic fields. contact-less cell permeabilization; gold nanoparticles; time-varying magnetic fields; computational modeling  
Received: 11 October 2021  
Accepted: 19 November 2021  
in the electrode-electrolyte interfaces [7] or the possible electrical breakdown between the electrodes [8]. An alternative approach to achieving membrane permeabilization is the use of time-varying magnetic fields (Pulsed Electromagnetic Fields (PEMF)) [9; 10; 11; 12; 13; 14]. This is a completely contactless technique, thus avoiding the use of electrodes, with many advantages such as lower costs and less patient discomfort, allowing the use of the techniques in a wide range of treatments. Studies using PEMF in vitro [9; 10; 11; 12; 13] and in vivo [14; 15; 16; 17] have demonstrated that PEMF allows permeabilizing the cell membrane, but the efficiency is much lower than that achieved by the conventional electroporation approach. This is because the amplitude of the electric field induced by PEMF in proximity of the cell membrane is almost two orders of magnitude lower that the one obtained by classical electroporation techniques [18; 19]. A possible strategy to overcome this issue is to exploit the conductive properties of metal nanoparticles--such NPs, acting as nanoelectrodes, would enhance the induced electric field locally, i.e., close to the membrane, thus potentially enabling cell permeabilization. It was recently proved that the addition of highly conductive gold NPs (Au NPs) in conventional electroporation protocol local enhanced the induced electric field, leading to significant cellular permeabilization [18]. Thanks to the local enhancement of the electric field, the presence of Au NPs was found to also ameliorate the complete coverage of the sample in terms of uniformity and intensity of the electric field [20]. Moreover, the presence of Au NPs should cause membrane permeabilization over nanoscale regions without affecting the entire membrane, thus avoiding collateral damage.