Shear modulus decomposition algorithm in magnetic resonance elastography

Magnetic resonance elastography (MRE) is an imaging modality capable of visualizing the elastic properties of an object using magnetic resonance imaging (MRI) measurements of transverse acoustic strain waves induced in the object by a harmonically oscillating mechanical vibration. Various algorithms have been designed to determine the mechanical properties of the object under the assumptions of linear elasticity, isotropic and local homogeneity. One of the challenging problems in MRE is to reduce the noise effects and to maintain contrast in the reconstructed shear modulus images. In this paper, we propose a new algorithm designed to reduce the degree of noise amplification in the reconstructed shear modulus images without the assumption of local homogeneity. Investigating the relation between the measured displacement data and the stress wave vector, the proposed algorithm uses an iterative reconstruction formula based on a decomposition of the stress wave vector. Numerical simulation experiments and real experiments with agarose gel phantoms and human liver data demonstrate that the proposed algorithm is more robust to noise compared to standard inversion algorithms and stably determines the shear modulus.