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Transient Elasticity Imaging and Time Reversal Habib Ammari

Summary: Transient Elasticity Imaging and Time Reversal
Habib Ammari
Lili Guadarrama Bustos
Hyeonbae Kang§
Hyundae Lee
In this paper we consider a purely quasi-incompressible elasticity model. We rigor-
ously establish asymptotic expansions of near- and far-field measurements of the tran-
sient elastic wave induced by a small elastic anomaly. Our proof uses layer potential
techniques for the modified Stokes system. Based on these formulas, we design asymp-
totic imaging methods leading to a quantitative estimation of elastic and geometrical
parameters of the anomaly.
Mathematics subject classification (MSC2000): 35R30, 74L15, 92C55
Keywords: transient imaging, asymptotic imaging, time-reversal, quasi-incompressible elasticity
1 Introduction
An interesting approach to assessing elasticity is to use the acoustic radiation force of an
ultrasonic focused beam to remotely generate mechanical vibrations in organs [11, 14]. The
acoustic force is due to the momentum transfer from the acoustic wave to the medium. The
radiation force acts as a dipolar source. A spatio-temporal sequence of the propagation
of the induced transient wave can be acquired, leading to a quantitative estimation of the


Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique


Collections: Mathematics