deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 4cc7975..35a388e 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
...
Propagation of elastic waves in solids has been described in various fields of physics, including geophysics, soft matter physics or acoustics. 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. Shear waves have drawn a strong interest in medical imaging with the development of shear wave elastography methods \cite{muthupillai1995magnetic}, \cite{sarvazyan1998shear}. The latter technique uses shear waves to measure or map the elastic properties of biological tissues. The measurement of the shear wave speed permits calculation of the tissue shear modulus. Shear wave elastography techniques have been successfully applied to several organs such as the liver \cite{sandrin2003transient}, the breast \cite{berg2012shear}, the arteries \cite{schmitt2010ultrasound} and the prostate \cite{cochlin2002elastography}, to name a few examples. The brain has also been studied, and its elasticity is of strong interest for clinicians \cite{mariappan2010magnetic}, \cite{kruse2008magnetic}. For example, it has been shown that Alzeihmer's disease, hydrocephalus or multiple sclerosis are associated with changes in brain elastic properties \cite{murphy2011decreased}, \cite{taylor2004reassessment}, \cite{wuerfel2010mr}.  Clinical shear wave elastography techniques currently rely on an external vibrator \cite{muthupillai1995magnetic}, \cite{sandrin2003transient} or on a focused acoustic wave \cite{nightingale2002acoustic}, \cite{sarvazyan1998shear} as the shear wave source. However, these techniques are limited in situations where the organ of interest is located behind a strong attenuating medium like the brain behind the skull and surrounded by the cerebrospinal fluid. While external shakers are able to transmit some shear waves, using acoustic, pneumatic, piezoelectric or electromagnetic actuators \cite{kruse2008magnetic}, \cite{20833495}\cite{11548931}, \cite{17067861}, \cite{20833495}, \cite{11548931}, \cite{Braun_2003},  this approach can be uncomfortable for patients. Alternatively, acoustic waves could be transmitted through the skull to induce shear waves inside the brain, but the skull attenuates and deforms the acoustic beam, preventing efficient transmission of energy. Recently, it has also been shown that physiological body motion can be used, via blood pulsation \cite{23008140} or passive elastography \cite{gallot2011passive}, but these techniques still requires further development before clinical application. Recently, it was demonstrated that the combination of an electrical current and a magnetic field could create displacements which propagate as shear waves in biological tissues \cite{basford2005lorentz}, \cite{grasland2014elastoEMarticle}. If the electrical current is induced using a coil, this would allow the technique to remotely induce shear waves. To achieve this objective, we propose to use a transcranial magnetic stimulation (TMS) device \cite{hallett2000transcranial}. This instrument is used to induce an electrical current directly inside the brain by using an external coil. It is currently employed by neurologists to study brain functionality \cite{ilmoniemi1999transcranial} and by psychiatrists to treat depression \cite{sakkas2006repetitive}. TMS is occasionally combined with magnetic resonance imaging (MRI) \cite{devlin2003semantic}, \cite{bohning1997mapping}; however, no study has yet reported the production of shear waves when using TMS and a static magnetic field.