Anderson localization of shear waves observed by magnetic resonance imaging

¹ Department of Radiology, Charité University Medicine - Charitéplatz 1, 10117 Berlin, Germany, EU
² Institute of Medical Informatics, Charité University Medicine - Hindenburgdamm 30, 12203 Berlin, Germany, EU

^a sebastian.papazoglou@charite.de

Received: 26 March 2010
Accepted: 2 July 2010

Abstract

In this letter we present for the first time an experimental investigation of shear wave localization using motion-sensitive magnetic resonance imaging (MRI). Shear wave localization was studied in gel phantoms containing arrays of randomly positioned parallel glass rods. The phantoms were exposed to continuous harmonic vibrations in a frequency range from 25 to 175 Hz, yielding wavelengths on the order of the elastic mean free path, i.e. the Ioffe-Regel criterion of Anderson localization was satisfied. The experimental setup was further chosen such that purely shear horizontal waves were induced to avoid effects due to mode conversion and pressure waves. Analysis of the distribution of shear wave intensity in experiments and simulations revealed a significant deviation from Rayleigh statistics indicating that shear wave energy is localized. This observation is further supported by experiments on weakly scattering samples exhibiting Rayleigh statistics and an analysis of the multifractality of wave functions. Our results suggest that motion-sensitive MRI is a promising tool for studying Anderson localization of time-harmonic shear waves, which are increasingly used in dynamic elastography.