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# Pol Grasland-Mongrain$${}^{1}$$, Yuankang Lu$${}^{1,2}$$, Frederic Lesage$${}^{2,3}$$, Stefan Catheline$${}^{4}$$, Guy Cloutier$${}^{1,3,5}$$ (1) Laboratory of Biorheology and Medical Ultrasonics, Montreal Hospital Research Center, Montreal (QC), H1X0A9, Canada (2) Departement of Electrical Engineering, École Polytechnique of Montreal, Montreal (QC), H3C3A7, Canada (3) Institute of Biomedical Engineering, École Polytechnique and University of Montreal, Montreal (QC), H3T1J4, Canada (4) Laboratory of Therapeutic Applications of Ultrasound, Inserm u1032, Inserm, Lyon, F-69003, France (5) Departement of Radiology, Radio-oncology and Nuclear Medicine, University of Montreal, Montreal (QC), H3C3J7, Canada

Abstract

This article describes the generation of elastic shear waves in a soft medium using a laser beam. Our experiments show two different regimes depending on laser energy. Physical modeling of the underlying phenomena reveals a thermoelastic regime caused by a local dilatation resulting from temperature increase, and an ablative regime caused by a partial vaporization of the medium by the laser. Computed theoretical displacements are close to experimental measurements. A numerical study based on the physical modeling gives propagation patterns comparable to those generated experimentally. These results provide a physical basis for the feasibility of a shear wave elastography technique (a technique which measures a soft solid stiffness from shear wave propagation) by using a laser beam.

When a laser beam of sufficient energy is incident on a medium, the absorption of the electromagnetic radiation leads to an increase in the local temperature. Due to thermal effects, displacements occur in the medium, which can then propagate as elastic waves. Elastic waves within a bulk can be separated into two components: compression waves, corresponding to a curl-free propagation, and shear waves, corresponding to a divergence-free propagation (Aki 1980). Measures of the transmission characteristics of compression and shear waves are useful for inspecting solids, such as a metal, to reveal potential cracks or defects (Shan 1993). In biological tissues, induction of compression waves by laser has been studied with the development of photoacoustic imaging (Xu 2006). Elastic waves used in photoacoustic imaging are typically of a few megahertz; at this frequency, shear waves are quickly attenuated in soft tissues, typically over a few microns, and only compression waves can propagate over a few centimeters.

While the induction of surface acoustic waves by laser in soft tissues was recently demonstrated by Li et al. (Li 2012), (Li 2014), a similar phenomenon with shear waves in bulk medium has never been described. This is of great interest for the shear wave elastography technique. As its name indicates, shear wave elastography comprises the techniques used to map the elastic properties of soft media using shear wave propagation (Plewes 1995), (Muthupillai 1995), (Catheline 1999). These techniques typically use low frequency (50-500 Hz) shear waves so that their propagation can be observed over a few centimeters. The shear waves are currently generated using either an external shaker or a focused acoustic wave. However, alternative shear wave generation methods have drawn important attention recently. For example, it has been demonstrated that one can use natural motion of the medium (Hirsch 2012), (Zorgani 2015), the Lorentz force (Basford 2005), (Grasland-Mongrain 2014), (Grasland-Mongrain 2016) or electrolysed-induced bubbles (Montalescot 2016). Compared to these generation sources, a laser presents the advantage of being fully remote, without need of coupling gel; and of being miniaturizable at low cost using an optical fiber.

In our experiment, illustrated in Figure \ref{Figure1}, we used a Q-switch Nd:YAG laser (EverGreen 200, Quantel, Les Ulis, France) to produce a 10-ns pulse of 10 to 200 mJ energy at a central wavelength of 532 nm in a 5-mm diameter circular beam. The laser beam was absorbed in a 4x8x8 cm$${}^{3}$$ black mat phantom composed of water, 5% polyvinyl alcohol, and 1 % black graphite powder. Two freeze/thaw cycles were applied to stiffen the material to a shear modulus of 25$$\pm$$5 kPa (Fromageau 2007). To observe the resulting shear waves, the medium was scanned simultaneously with a 5-MHz ultrasonic probe, consisting of 128 elements, connected to a multi-channeled ultrasound scanner (Verasonics V-1, Redmond, WA, USA), and placed on the other side of the sample. The probe was acquiring 4000 ultrasound images per second during 30 ms. Due to the presence of graphite particles, the medium presented a speckle pattern on the ultrasound image.The computation of displacements along the Z axis (the ultrasound axis) was computed by tracking the speckle spots with the Lucas-Kanade method (Lucas 1981). This method solves basic optical flow equations by least squares criterion in a window of 64*5 pixels centered on each pixel. Displacements over time were then filtered from 200 to 800 Hz using a 5th-order Butterworth filter and averaged over four experiments.

\label{Figure1}Experimental setup. A laser beam is emitted on a soft medium. This generates shear waves following (a) thermoelastic and/or (b) ablative regimes. The medium is observed with an ultrasound probe. A speckle-tracking algorithm calculates displacements from the ultrasound images.