Study On Reconstruction Algorithms And Finite Element Simulation For Harmonic Magnetic Resonance Elastography

Magnetic resonance elastography (MRE) is a newly developed non-invasive imaging technique that can quantitatively measure the biomechanical properties of soft tissues. It can measure the phase displacement due to mechanical wave excitation on the surface of tissue with motion sensitive gradient (MSG) , and then reconstruct the elasticity of tissue by inversing elastic wave equation. Elasticity reconstruction is an important part of MRE. It is very hard to work out all elastic parameters due to the complexity of human body and elastic modulus. Therefore many researchers proposed different assumptions of soft tissue models to simplify reconstruction algorithms.In this thesis , we study the basic principle of MRE, and briefly derive and analyze the biomechanical model of soft tissues,and then discuss some reconstruction algorithms for MRE. We attempt to categorize different reconstruction algorithms according to their mathematical hypotheses. Their advantages and pitfalls will be analyzed carefully. Moreover, the influence of different assumptions on elasticity reconstruction will be investigated by using both simulation and experiment data. In particular, we propose to enhance the reconstruction algorithm of Helmholtz equation direct inversion with Gaussian derivative filtering, and some improvements to the reconstruction algorithm of hybrid one-step inversion. Elastic wave propagation in two and three dimensional models are derived with COMSOL Multiphysics based on the fundamentals of elastic dynamics,the influence of parameters in MRE on elasticity reconstruction will be discussed.