deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 16732f0..e00d679 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
...
In this study, we show that shear waves can be induced in soft tissues by a laser beam. We also propose a model for the underlying physics. We finally applied the technique in a biological tissue to evaluate its potential application in shear wave elastography.  In the first experiment, illustrated by Figure \ref{Figure1}, we used a Q-switch Nd:YAG laser (EverGreen 200, Quantel, Les Ulis, France), which produced a pulse of energy $E$ = 200 mJ at a central wavelength of 532 nm during 10 ns in a 5 mm diameter circular beam of 5 mm diameter (so that section $S$=20 mm$^2$). We defined Z as the laser beam axis, and the laser beam impact on the medium is the origin of coordinates (0,0,0). The laser beam was absorbed in a 4x8x8 cm$^3$ tissue-mimicking black mat  phantom made of water and of 5\% polyvinyl alcohol, 1 \% black graphite powder and 1\% salt. A freezing/thawing cycle was applied to stiffen the material to a value of 15$\pm$5 kPa \cite{17375819}. The laser is absorbed in the medium with an exponential decay of the optical intensity $I(z)=I_0 \exp(- \gamma z)$ along medium depth $z$, where $I_0=\frac{1}{S}\frac{d E}{dt}$ is the incident intensity distribution at the surface (the reflection on the black mat material being neglected) and $\gamma$ the absorption coefficient of the medium. We measured the fraction of light which go through different thicknesses of the medium with a laser beam power measurement device (QE50LP-S-MB-D0 energy detector, Gentec, Québec, QC, Canada): it indicated that $\gamma \approx$ 20 mm$^{-1}$ in our sample, meaning that 63\% of the radiation is absorbed in the first 50 micrometers of the sample. This is quite higher than metals where the radiation is absorbed within a few nanometers. The absorption of the laser beam by the medium gives then rise to an absorbed optical energy $q = \gamma I$. Assuming that all the optical energy is converted to heat, a local increase of temperature appears. Temperature distribution $T$ in absence of convection and of phase transition can be computed using the heat equation:  \begin{equation} 
...