Pol Grasland-Mongrain edited When_a_laser_beam_of__1.tex  over 8 years ago

Commit id: 815c66601139e856b7b72c0135581f97a919886f

deletions | additions      

       

When a laser beam of sufficient energy is incident on a medium, the absorption of the electromagnetic radiation increases the local temperature. This leads to a local dilatation due to thermal expansion, and the resulting displacement can propagate as elastic waves. Elastic waves can be separated in two components in a bulk: compression waves, corresponding to a curl-free propagation; and shear waves, corresponding to a divergence-free propagation \cite{landau1986theory}. This phenomenon has been notably observed in metals. Compression and shear waves induced by laser are even used as a method of inspection to reveal potential cracks in solids.  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, When  a laser beamis 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 sufficient energy is incident on a medium,  the source absorption  of the waves. The optical absorption coefficient electromagnetic radiation leads to an increase  of the tissue depends on local temperature. There is consequently a local dilatation, and  the optical wavelength, so different structures resulting displacement  can be observed by tuning properly the laser wavelength. For example, oxygenated and de-oxygenated haemoglobin propagate as elastic waves. Elastic waves  can be discriminated separated  in this way. The frequency of the elastic waves used two components  inphotoacoustic imaging are typically of  a few megahertz. At this frequency, only bulk: compression waves, corresponding to a curl-free propagation; and shear waves, corresponding to a divergence-free propagation \cite{aki2002quantitative}. This phenomenon has been notably observed in metals. Measuring the  compression and shear  waves can propagate, be used  asshear waves at  a frequency method  of a few megahertz are quickly attenuated, typically over a few microns inspection to reveal potential cracks  in soft tissues. the solid.  In a medical context, induction of compression wave has been studied for the last ten years, with the development of photoacoustic imaging \cite{Xu_2006}. In this technique, a laser beam is absorbed by the tissue, which induces by thermal expansion compression waves, which are themselves 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 \cite{Xu_2006}. At this frequency, only compression waves can propagate over a few centimeters, as shear waves 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 also  induce shear waves. This has Shear waves have drawn  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 \cite{muthupillai1995magnetic}, \cite{10385964}, \cite{sandrin2002shear}. As it names indicates, this  term covers the techniques used to measure or map the elastic properties of biological tissues. tissues using shear wave propagation.  The shear modulus, directly proportional to Young's modulus in soft tissues, varies indeed  of several orders of magnitude in human body. This parameter can be measured by using shear wave. A body and potentially offers an excellent contrast. As a  shear wave propagatesindeed  in an organ at a speed proportional to the square root of the shear modulus,so  measuring the its  speed throughout the organ allows to compute its the  shear modulus \cite{sandrin2002shear}. of the tissue \cite{10385964}.  Shear wave elastography techniques have been successfully applied for the detection of various pathologies  inseveral  organs such as the liver \cite{sandrin2003transient}, the breast \cite{goddi2012breast}, \cite{sinkus2005viscoelastic}, the prostate \cite{cochlin2002elastography}, \cite{souchon2003visualisation} \cite{souchon2003visualisation}, the bladder \cite{25574440}  and the eye cornea \cite{tanter2009high}. \cite{tanter2009high}, \cite{22627517}.  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 tissue-mimicking  phantom made from of  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 laser is absorbed in the medium, and 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)  \end{equation}  where $I_0$ is the incident intensity distribution at the surface and $\gamma$ is the absorption coefficient of the medium. In non-metallic solids, the absorption coefficient $\gamma$ is relatively small, so that the radiation is able to penetrate into the bulk of the material - contrary to metals where the radiation is absorbed within a few nanometres. The absorption of the laser beam by the medium gives then rise to an absorbed optical energy $q$ equal to $\gamma I$.  Assuming that all the optical energy is converted to heat, a local increase of temperature appears. Temperature distribution $T(x,y,z,t)$  can be computed using heat equation \cite{Li_2014}: \begin{equation}  \frac{\partial T}{\partial t} = \frac{k}{\rho C} \nabla ^2 T + \frac{q}{\rho C}  \end{equation}  where$T$ is the temperature distribution,  $c_k$ the thermal wave speed (usually taken as equal to the compression wave speed), $\rho$ the density, $\kappa$ the thermal diffusivity and $C$ the heat capacity. The propagation of the heat is slow compared to the duration of the heating (10 ns) and the thermal expansion duration (), so that the phenomenon can be considered as adiabatic.  %$\kappa$ 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 curl-free  displacement, so no shear wave would occur. However, in our case, the case presented,  the solid is rather semi-infinite. semi-infinite (the laser beam is absorbed on one side of the medium).  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. axis mainly.  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 linked to  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} (\textit{Z}-displacement  or \textit{Y-displacement}). \textit{Y}-displacement).  The laser beam was triggered 10 ms after the beginning of the ultrasound acquisition.