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Introduction: The Elastography Software Library (ESL) was developed to achieve clinically feasible, super-resolution (SR) Magnetic Resonance Elastography (MRE). ESL was created by accomplishing four objectives: 1. perform a critical analysis of MRE inversion, using discrete-time Fourier transform (DTFT) methods, to enable selection of the wave inversion approach most suitable to high- and SR MRE (Chapter 2) 2. develop a new method for real-time 4D phase unwrapping, to enable large acquisitions to be processed in clinical work ow (Chapter 3) 3. develop a new inversion pipeline that recovers fine features in elastograms (Chapter 4) 4. extend this pipeline with a novel interpolation technique to achieve super-resolution (Chapter 5) The results of these experiments were combined to make the ESL. Over the course of the work, two objectives also resulted in software applications in their own right (PhaseTools for phase unwrapping, and Elastography Software Pipeline (ESP) for fine feature elasticity map recovery). Methods: Critical Analysis: Two-filter cascades were designed to model the signal processing pipelines found in the present MRE literature. These models were subjected to DTFT-based analysis to determine the relative advantage of various mathematical approaches to the MRE inverse problem. Phase Unwrapping: A test data set was developed to measure algorithm performance in 4D on data sets with varying levels of wrap, gradient and noise. The algorithms that performed most accurately and efficiently on test data were then applied to in vivo brain, liver, and muscle data, of both moderate and severe wrap, and inspected for wrap failure. Fine Feature Recovery: A new MRE image processing pipeline was developed that incorporates wavelet-domain denoising, image-driven noise estimation, and feature detection. ESP was first validated using simulated data, including viscoelastic Finite Element Method (FEM) simulations, at multiple noise levels. ESP images were then compared with Multifrequency Dual Elasto-Visco Inversion (MDEV) pipeline images in three ten-subject cohorts of brain, thigh, and liver acquisitions. Finally the proportion of spectral energy at fine frequencies was quantified using the Reduced Energy Ratio (RER) for both ESP and MDEV. Super-Resolution: An extension of the ESP pipeline was developed that incorporated a new image fusion technique to combine non-redundant information. The algorithm was validated on an analytic simulation program developed for the study. An in vivo cross-validation was performed between 1X, 2X and 4X magnification levels measuring both spectral gains and shear modulus values. Results: Critical Analysis: The more complex, heterogeneous FEM models were found to only outperform Algebraic Helmholtz Inversion (AHI) in very low noise, with Gaussian smoothing of σ > 0:8px or Butterworth low-pass cutoffs of < 0:8π negating any advantages from assumption of local heterogeneity. Phase Unwrapping: Three algorithms were determined to perform with sufficient robustness in real-time on 4D data sets with challenging phase wrap. These algorithms were then applied to in vivo brain, skeletal muscle, liver and phantom data and shown to successfully resolve heavy phase wrap within a \real-time" criterion of under 3 minutes. Fine Feature Recovery: For FEM inversions, mean values of background and soft target simulated results remained within 8% of prescribed up to σ = 10% for both jG*j and ϕ, though inspection of the ϕ image showed scatter- and boundary-related artefacts around the soft target. Hard target results showed jG*j means within 7% of prescribed up to σ = 5% but unreliable ϕ means, and inspection showed showed scatter- and boundary-related artefacts. For the in vivo cohorts, ESP results showed mean correlation of R = 0:83 with MDEV and liver stiffness estimates within 7% of Local Frequency Estimation (LFE) results. Finally, ESP showed statistically significant increase in fine feature spectral energy as measured with RER for both jG*j (p < 1X10-9) and ϕ (p < 1X10-3). Super-Resolution: At 4X SR, both brain and liver cohorts showed a highly significant (p ≤ 10-6) increase in both number of recovered frequencies and normalised spectral energy in those recovered frequencies. Both the 2X and 4X SR techniques showed a decrease in stiffness estimate from the original resolution (mean decrease of 11.6% and 14.0%) respectively; however cohort correlations between SR and original values were upwards of R = 0:988. Discussion: Established as a technique highly sensitive to important tissue changes, MR Elastography is now also a finely-featured super resolution technique in two parameters, enabling new clinical and research applications. Future work includes statistical mapping of both localised and diffuse soft tissue changes, rapid computation on heterogeneous processing architectures, and two-parameter super-resolution MRI-based lesion mapping. |
