2012 Proceedings - International Tissue Elasticity Conference

085 SUB–WAVELENGTH RESOLUTION IN SHEAR WAVE IMAGING: THE TIME REVERSAL
APPROACH.
Stefan Catheline 1 , Rémi Souchon 1 , Jean–Yves Chapelon 1 .
1 INSERM U1032, University of Lyon, Lyon, France.
Background: When a wave field is measured within the propagative medium, for instance in seismology,
magnetic resonance elastography (MRE) or ultrasound (US) based elastography, it is known that, the
resolution is ultimately limited by the measuring point density and not the wavelength [1]. Indeed, in
contrast with far field conventional imaging systems, in situ measurement enables the retrieval of the
near field details needed for super resolution. From a time reversal interpretation point of view, because
of diffraction, even if the source is point–like, the wave refocuses on a spot size that cannot be smaller
than half a wavelength except in the presence of an acoustic sink. The acoustic sink plays the inverse
role of a source: it absorbs the energy of an incoming wave. Thus surpassing the diffraction limit for
imaging implies that the acoustic sink can be recreated.
Aims: Here we report numerical and experimental results obtained with a passive acoustic sink where a
focal spot size only depends on the spatial sampling of the field.
Methods: The experiment is as follows: in the first step, a diffuse wave field is created inside the sample
by random finger impacts given from the surface for 10 seconds. The 2D displacement field is then
measured inside the soft solid using speckle tracking algorithms developed in elastography. It involves a
64 channel array working at 5MHz with a repetition frequency of 2000Hz. In the second step, the
displacement at one point chosen as a virtual source is correlated to the other points of the image in
order to compute a time reversal field in the computer. In the third and last step, the decomposition of
the time reversal field into the causal and anticausal Green’s function is computed from a spatial Fourier
transform. Thus, these functions imply the existence of a source and a sink respectively that both
overcome the diffraction limit.
Results: The refocusing spots issued from the Green' s function retrieval are compared to time reversal,
Figure 1. The effect of the windowing inherent to the imaging technique of elastography on the Fourier
transform will be discussed. Although no new information is brought by this approach, it is shown that
imaging with an evanescent wave is possible and that it conserves the symmetry properties of the source.
Conclusions: So the conclusion is that, in the absence of noise in the data, the tomography resolution of
the in situ imaging technique depends only on the spatial sampling of the field inside the medium of
propagation; in MRE it depends on the MR image, in US elastography on the sonogram and in seismology
on the distance between geophones and not on the shear and Rayleigh wavelength, respectively.
Figure 1: Focus spots along x and z directions are obtained from time reversal. They are compared to the anticausal
Green's function (TR+passive sink). The size of the focus spot depends only on the spatial sampling of the
field.
Reference:
[1] Tanter et al.: Médecine Nucléaire, 31 , pp. 132–141, 2007.
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