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Pol Grasland-Mongrain edited Body_Lorentz_force_m.tex
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\label{Figure3}Body Lorentz force $\mathbf{f}$ was computed from the combination of $\mathbf{j}$ and $\mathbf{B}$. Then, displacement $\mathbf{u}(\mathbf{r},t)$ was determined analytically along space and time by solving Equation \ref{Equation3} with the Green operator \cite{aki1980quantitative}. It used a medium density $\rho$ of 1000 kg.m$^{-3}$, a bulk modulus $K$ of 2.3 GPa and a shear modulus $\mu$ of 16 kPa, corresponding to a shear wave speed of 4 m.s$^{-1}$.
\section{Results}
Z component maps of the displacements over time are illustrated in Figure
\ref{Figure4}, \ref{Figure7}, respectively 1, 2, 4, 8 and 12 ms after current emission, as given by the simulation (A), experiment in the PVA phantom (B) and experiment in the chicken breast sample (C). Initial displacements were close to the Lorentz force excitation location, on the opposite side of the ultrasound probe. They reached an amplitude of 5 $\mu$m in the phantom and 0.5 $\mu$m in the chicken sample. They propagated as shear waves, whose speed was 4.0 m.s$^{-1}$ for the simulation, 4.0$\pm$1.0 m.s$^{-1}$ for the PVA phantom and 6.5$\pm$1.5 m.s$^{-1}$ for the chicken breast along Z axis.