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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's parameter (), (\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 to 9700 N.m$^{-3}$, which leads to respective displacement from 2.9 to 18 $\mu$m. Lorentz force is about one order of magnitude smaller, but stays in the We found in our numerical study a displacement slightly higher than the 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 electrical current amplitude and shape in the coil, as constructor values were used, and about electrical conductivity of the medium, as the electrical conductivity is not entirely determined by the concentration in salt.