deletions | additions       diff --git a/When_a_laser_beam_of__1.tex b/When_a_laser_beam_of__1.tex  index 2ab4dbd..353bcae 100644  --- a/When_a_laser_beam_of__1.tex  +++ b/When_a_laser_beam_of__1.tex 
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In a medical context, induction of compression wave has been studied for the last twenty years, with the development of photoacoustic imaging. In this technique, a laser beam is absorbed by the tissue, which induces local displacements. These displacements can propagate as compression waves which are acquired by acoustic transducers. Time of flight measurements allows then to find the source of the waves. The optical absorption coefficient of the tissue depends on the optical wavelength, so different structures can be observed by tuning properly the laser wavelength. For example, oxygenated and de-oxygenated haemoglobin can be discriminated in this way. The frequency of the elastic waves used in photoacoustic imaging are typically of a few megahertz. At this frequency, only compression waves can propagate, as shear waves at a frequency of a few megahertz are quickly attenuated, typically over a few microns in soft tissues.  We hypothesized in this study that applying a laser beam in a soft tissue can induce shear waves. This has an increasing interest in medical imaging, with the development for the last two decades of shear wave elastography methods \cite{krouskop1987pulsed}, \cite{ophir1991elastography}, \cite{muthupillai1995magnetic}. This term covers the techniques used to measure or map the elastic properties of biological tissues. The shear modulus, directly proportional to Young's modulus in soft tissues, varies of several orders of magnitude in human body. This parameter can be measured by using shear wave. A shear wave propagates indeed in an organ at a speed proportional to the square root of the shear modulus, so measuring the speed throughout the organ allows to compute its shear modulus \cite{sandrin2002shear}. Shear wave elastography techniques have been successfully applied in several organs such as the liver \cite{sandrin2003transient}, the breast \cite{goddi2012breast}, \cite{sinkus2005viscoelastic}, the prostate \cite{cochlin2002elastography}, \cite{souchon2003visualisation} and the eye cornea \cite{tanter2009high}.  In this study, we wanted to show that shear waves can be induced by a laser beam and to characterize the underlying physical phenomenon. Finally, we applied the technique in a biological tissue to evaluate its application in shear wave elastography.  The Z axis is defined here as the laser beam axis, and the ultrasound probe is in the XZ plane, as illustrated by Figure \ref{Figure1}.  In this experiment, we used first a 4x8x8 cm$^3$ water-based phantom made from 5\% polyvinyl alcohol, 0.1 \% 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 beam was emitted by a Nd:YAG laser (EverGreen 200, Quantel, Les Ulis, France), which produced a 200 mJ, 5 mm in diameter Q-switched pulse at a central wavelength of 532 nm during 10 ns. The optical intensity $I(x,y,z,t)$ along position $(x,y,z)$ and time $t$ decays exponentially along medium depth $z$\cite{scruby1990laser}:  \begin{equation}  I=I_0 \exp(- \gamma z) 
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%$\kappa$ is approximately equal to 10${^6}$ m$^2$.s$^{-1}$ for water, the main component of biological tissues; for a 10 ns laser pulse, the thermal diffusion path is then equal to 0.01 to 0.1 $\mu$m. $\gamma^{-1}$ of water is equal to 0.1 m, which is a million times higher; even for melanin and haemoglobin, highly absorbing at 532 nm, $\gamma^{-1}$ is respectively equal to 10 and 100 $\mu$m, far higher than the thermal diffusion path. The thermal conductivity effects are consequently negligible, and increase of temperature lies in laser absorption zone.  The local increase of temperature can lead to two main effects creating elastic waves: (1) Thermoelastic expansion and (2) Ablation of medium. In metals, transition from first to second regime occurs approximately about 10$^7$ W.cm$^{-2}$. This is equal to the energy of the laser we used, so the predominant regime in our experiment cannot be determined yet.  In the thermoelastic expansion, a local dilatation of the medium occurs. In an unbounded solid, this would lead to a rotational-free displacement, so no shear wave would occur. However, in our case, the solid is rather semi-infinite. The local expansion acts as a dipole force parallel to the surface. In the ablative regime, the local increase of temperature is so high that the surface of the medium melts and creates a point-force in the medium. The medium is then displaced locally inside the medium along Z axis. At very high temperatures, even a plasma can occurs. The local force leads to compression and shear waves.  In both cases, the absorption of the laser by the phantom leads to a local displacement which can propagate as elastic wave in the medium. To observe the elastic wave, the medium was scanned with a 5 MHz ultrasonic probe made of 128 elements and a Verasonics scanner (Verasonics V-1, Redmond, WA, USA). The probe was used in ultrafast mode \cite{bercoff2004supersonic}, acquiring 1000 ultrasound frames 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 (\textit{Z-displacement} or \textit{Y-displacement}). The laser beam was triggered 10 ms after the beginning of the ultrasound acquisition.