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Magnetic Resonance Elastography is usually employing continuous shear waves; but induction of a continuous electrical current by the coil could affect MRI measurements, so "repetitive transient" excitations, which would lead to a continuous wave, could be used.  \subsection{Displacement amplitude}  In our numerical study, Lorentz force magnitude reached about 20 N.m$^{-3}$ for a 150 mT permanent magnetic field and a 5 S.m$^{-1}$ medium. Numerous measurements of grey and white matter electrical conductivity have been performed, and results vary from 0.02 to 2 S.m$^{-1}$ \cite{19636081}. Using an average value of 0.5 S.m$^{-1}$, in a 1.5 T MRI system, the Lorentz force would reach a magnitude of about 500 N.m$^{-3}$. We can compare this value with the acoustic radiation force used for shear wave elastography. This force is calculated with the equation $f_{ARF} = 2 \alpha I / c$, where $\alpha$ is the attenuation in the medium, $I$ the ultrasound intensity and $c$ the speed of sound. Using Nightingale et al. parameters \cite{Nightingale_2001} ($\alpha$ = 0.4 Np.cm$^{-1}$, $I$ = 2.4 to 15 W.cm$^{-2}$, $c$ = 1540 m.s$^{-1}$), $f_{ARF}$ ranges from 1500 1200  to 9700 7800  N.m$^{-3}$, which leads led in their experimental study  to respective displacement displacements  from 2.9 to 18 $\mu$m. Lorentz force is about one order of magnitude smaller, but stays in the smaller. Displacement can however still be detected. Moreover, other types of bursts, with longer excitation for example, could lead to higher amplitude displacements.  We found in our numerical study a Note that  displacement slightly higher than the experimental value reached an amplitude of 0.5 $\mu$m  in the phantom. Various factors like viscosity and border effects, which were not included in our model, could explain this difference. Moreover, there are uncertainties chicken sample. Electrical conductivity of muscle,  about electrical current amplitude and shape 0.4 S.m$^{-1}$, decreases notably after animal death, so although placed  in saline water,  the coil, as constructor values were used, and about electrical effective  conductivity of the medium, as the electrical sample is expected to be quite lower than saline  conductivity (1.8 S.m$^{-1}$): this  is not entirely determined by probably  the concentration in salt. explanation of the low amplitude displacement.  Displacement reached an amplitude of 0.5 $\mu$m We found  in our numerical study a displacement slightly higher than  the chicken sample. Electrical conductivity of muscle, experimental value in the phantom. Various factors like viscosity and border effects, which were not included in our model, could explain this difference. Moreover, there are uncertainties  about 0.4 S.m$^{-1}$, decreases notably after animal death, so although placed electrical current amplitude and shape  insaline water,  the effective coil, as constructor values were used, and about electrical  conductivity of the sample is expected to be quite lower than saline medium, as the electrical  conductivity (1.8 S.m$^{-1}$). is not entirely determined by the concentration in salt.  \subsection{Source localization}  In these experiments, the shear wave source was 3 to 4 cm wide. In currently existing TMS coil geometries, it could hardly be lower than 1 cm. While this is higher than acoustic radiation force (1-2 mm), this last technique is hardly applicable in the brain because of the skull. Compared to the current method using external shaker, the shear wave source is far more localized. For whole brain elasticity measurement, source extension should not be a problem; for localized measurement, shear wave source should be placed close to the region of interest, but not inside.