UBC Theses and Dissertations

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UBC Theses and Dissertations

Bi-convex model based reconstruction methods for magnetic resonance elastography Mohammed, Shahed Khan


Magnetic resonance elastography (MRE) is a biomechanical imaging tool that reconstructs the tissue elasticity map by capturing tissue displacement with magnetic resonance imaging (MRI). MRE has the unique advantage of capturing all three directional displacement components with a moveable and deep field of view. In addition, MRE offers the functionality to incorporate other MRI contrast seamlessly to extend MRE for advanced biomechanical models. However, MRE is limited by its long scanning time, low signal-to-noise ratio, and low resolution. This thesis focuses on iterative model-based reconstruction techniques with structured sparsity for faster MRE acquisition and robust elastogram reconstruction. A new optimization technique for elastogram reconstruction is proposed using the bi-convexity of the elastodynamic model and the alternating direction method of multipliers (ADMM). The proposed optimization technique allows easy integration of structured sparsity and is robust to noise and initialization. Four elastography reconstruction methods were implemented in this thesis with different models and regularization prior: (a) scalar 2D shear wave model (2D-ERBA), (b) scalar 3D shear wave model (3D-ERBA), (c) vector 3D elastodynamic wave model (ERSA), and (d) multifrequency vector 3D elastodynamic wave model (MERSA). The former two elastography reconstruction methods used a sparsity prior to the shear modulus, while the latter used sparsity prior on both shear modulus and displacement. These methods were extensively validated for in silico, in vitro, and in vivo datasets and compared with state-of-the-art methods. Experiments showed that MERSA provides higher robustness to noise, higher robustness to wavelength-to-voxel ratio, and higher accuracy for both elasticity and viscosity. A comparison study of diagnostic performance in detecting liver disease of scalar 2D shear wave model, scalar 3D shear wave model, and vector 3D elastodynamic wave model with MERSA implementation concludes the reconstruction part of this thesis. A bi-convex optimization-based displacement regularized compressed sensing (DRCS) method is proposed for fast MRE acquisition. The proposed method uses separate sparsity prior on the magnitude, phase and displacement to recover the MR signal from a highly undersampled k-space. We compare the performance of DRCS with other compressed sensing methods for highly undersampled data from in silico, in vitro and in vivo datasets.

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