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\section{Material and methods}  In the experimental setup, pictured in Figure \ref{Figure1}-(B), the electrical current was induced by a TMS device using a 2x75 mm diameter butterfly coil (MagPro R100 device with C-B60 Butterfly coil, MagVenture, Farum, Danemark). The coil was placed 1 cm away from the medium, without any contact, and fixed to an independent support. The electrical current in the coil was in "monophasic" mode, i.e., a half cycle of 0.4 ms, as illustrated in Figure \ref{InducedElectricalCurrent}. \ref{InducedElectricalCurrent}-(A).  Alternatively, "biphasic" mode, i.e., a full sinus cycle of 0.4 ms could be used. used, as illustrated in Figure \ref{InducedElectricalCurrent}-(B).  According to the manufacturer's specifications, at 100\% amplitude, current reached a magnitude of 149.10$^6$ A.s$^{-1}$ in the coil, leading to a peak transient magnetic field of 2 T at the surface of the coil and of 0.74 T at 20 mm in depth. The magnetic field was induced by a 5x5x5 cm$^3$ N48 NdFeB magnet (model BY0Y0Y0, K\&J Magnetics, Pipersville, PA, USA). The magnet was placed 1 cm away from the medium, without any contact, and fixed to a second independent support. The magnetic field intensity ranged from 100 to 200 mT at the medium location, as measured by a gaussmeter (Model GM2, AlphaLab, Salt Lake City, UT, USA).   Main tested sample was a 4x8x8 cm$^3$ water-based tissue-mimicking phantom made with 5\% polyvinyl alcohol (PVA), 0.1 \% graphite powder and 5\% salt, giving an electrical conductivity of 5 S.m$^{-1}$. Three freezing/thawing cycles were applied to stiffen the material \cite{fromageau2007estimation}. The graphite powder (\#282863 product, Sigma-Aldrich, Saint-Louis, MO, USA) was made of submillimeter particles, which presented a speckle pattern on ultrasound images. The sample was placed in a rigid plastic box of 2 mm thick layers with an opening on a side to introduce the ultrasound probe. The rigid box simulated a solid interface such as a skull. It was also used to ensure that any observed movement was not due to surrounding displacement of air. Alternatively, we used a similar phantom made of 5\% polyvinyl alcohol (PVA), 0.1 \% graphite powder and 0.9\% salt, giving an electrical conductivity of 1.8 S.m$^{-1}$. A biological tissue sample was also tested. This tissue was an approximately 3x5x5 cm$^3$ chicken breast sample, placed in the plastic box previously described, immersed in saline water (0.9 \% NaCl, giving an electrical conductivity of 1.8 S.m$^{-1}$) NaCl)  at 20$^o$C and degassed during two hours. Each sample was observed with a 5 MHz ultrasonic probe made of 128 elements (ATL L7-4, Philips, Amsterdam, Netherlands) coupled to a Verasonics scanner (Verasonics V-1, Redmond, WA, USA). The probe was in contact with the sample with an ultrasound coupling gel but was fixed on a third independent support. It was used in ultrafast mode \cite{bercoff2004supersonic}, to acquire 1000 frames per second using plane waves and Stolt's fk migration algorithm \cite{garcia2013stolt}. The Z component of the displacement in the sample was observed by performing cross-correlations between radiofrequency images with a speckle-tracking technique \cite{montagnon2012real}. Noise was partly reduced thanks to a low-pass frequency filter. Time $t$ = 0 ms was defined as the electrical burst emission.