A novel mechanical model for magnetic resonance elastography

In the memory of my professors Dr.C. Beju, Dr. G. Camenschi and Dr. E. Sóos

Abstract

Magnetic resonance elastography is a non-invasive, in vivo imaging technique used to measure the elasticity of soft tissues subject to mechanical stresses. The resulting strains are measured using MR imaging and the elastic modulus is computed from viscoelastic models of tissue mechanics. In this paper we propose a novel model, called the fractional model of continuum mechanics, which is a generalization of the classical continuum mechanics theory in which the classic integer order spatial derivatives are replaced by fractional order spatial derivatives. The fractional model is a non-local, multi-scale model that can be used to solve both direct and inverse problems of importance in practical applications. In particular, our results to the inverse problem of elastography will show that the proposed model is capable to find the correct elastic moduli without having to perform any of the image processing steps required by the use of the classical continuum mechanics theory.