deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index d1332d2..6ac3026 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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In this study, we show that shear waves can be induced in soft tissues by a laser beam, with a model of the underlying physical phenomenon. We also 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 laser beam emitted by a Nd:YAG laser (EverGreen 200, Quantel, Les Ulis, France), which produced a Q-switched pulse of energy $E$ = 200 mJ at a central wavelength of 532 nm during 10 ns in a beam of 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 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 was absorbed in the medium with an exponential decay of the optical intensity $I$ along medium depth $r$\cite{scruby1990laser}: $z$\cite{scruby1990laser}:  \begin{equation}  I=I_0 I(z)=I_0  \exp(- \gamma r) z)  \label{eq:opticalIntensity}  \end{equation}  where $I_0=\frac{1}{S}\frac{d E}{dt}$ the incident intensity distribution at the surface (the reflection on the black mat medium being neglected) and $\gamma$ the absorption coefficient of the medium. 
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