deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 5de5d89..da2f5cd 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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Similarly to the thermoelastic regime, this leads to a displacement $u_z$:  \begin{equation}  u_z = \frac{\zeta}{\rho (\lambda + 2 \mu)}\frac{I^2}{(L+C(T_V-T_0))^2}\approx \frac{\zeta}{\rho \lambda}\frac{E^2/S^2 \tau^2}{(L+C(T_V-T_0))^2}  \label{eq:deplAbla}  \end{equation}  As in a biological soft tissues, $\mu \ll \lambda$, the displacement $u_z$ can be approximated as $\frac{\zeta}{\rho \lambda}\frac{E^2/S^2 \tau^2}{(L+C(T_V-T_0))^2}$.  Estimating $\zeta$ equal to 50 $\mu$m (average depth of absorption), $\lambda$ = 2 GPa (first Lamé's coefficient of water), $L$ = 2.2 MJ.kg$^{-1}$ (vaporization latent heat of water), $C$ = 4180 J.kg$^{-1}$.K$^{-1}$ (water heat capacity), $T_V-T_0$ = 373-293 = 80 K (water vaporization temperature minus laboratory temperature), $\rho$ = 1000 kg.m$^{-3}$ (water density), $E$ = 200 mJ, $S$ = 20 mm$^2$ and $\tau$ = 10 ns, we obtain a displacement $u_z$ approximately equal to 3.9 $\mu$m. This value is eight times higher than the one obtained with thermoelastic expansion. In both cases, absorption of the laser by the phantom leads to a local displacement which can propagate as elastic waves in the medium. To observe the shear waves, the medium was scanned with a 5 MHz ultrasonic probe made of 128 elements connected to a Verasonics scanner (Verasonics V-1, Redmond, WA, USA). The probe was used in ultrafast mode \cite{bercoff2004supersonic}, acquiring 1500 ultrasound images per second. Due to the presence of graphite particles, the medium presented a speckle pattern on the ultrasound image. Tracking the speckle spots with an optical flow technique (Lucas-Kanade method) allowed to compute one component of the displacement in the medium (Z-displacement or Y-displacement, depending on the position of the probe on the medium). The laser beam was triggered 10 ms after the first ultrasound acquisition, $t$ = 0 ms being defined as the laser emission.   
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