The development and application of a simulation system for diffusion-weighted MRI Mark Graham A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London. Centre for Medical Image Computing & Department of Computer Science University College London April 22, 2018 2 3 I, Mark Graham, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the work. Abstract Diffusion-weighted MRI (DW-MRI) is a powerful, non-invasive imaging tech- nique that allows us to infer the structure of biological tissue. It is particularly well suited to the brain, and is used by clinicians and researchers studying its structure in health and disease. High quality data is required to accurately characterise tissue structure with DW-MRI. Obtaining such data requires the careful optimisation of the image acquisition and processing pipeline, in order to maximise image quality and minimise artefacts. This thesis extends an existing MRI simulator to create a simulation sys- tem capable of producing realistic DW-MR data, with artefacts, and applies it to improve the acquisition and processing of such data. The simulator is applied in three main ways. Firstly, a novel framework for evaluating post- processing techniques is proposed and applied to assess commonly used strate- gies for the correction of motion, eddy-current and susceptibility artefacts. Secondly, it is used to explore the often overlooked susceptibility-movement interaction. It is demonstrated that this adversely impacts analysis of DW- MRI data, and a simple modification to the acquisition scheme is suggested to mitigate its impact. Finally, the simulation is applied to develop a new tool to perform automatic quality control. Simulated data is used to train a classifier to detect movement artefacts in data, with performance approaching that of a classifier trained on real data whilst requiring much less manually-labelled training data. It is hoped that both the findings in this thesis and the simulation tool itself will benefit the DW-MRI community. To this end, the tool is made freely 6 Abstract available online to aid the development and validation of methods for acquiring and processing DW-MRI data. Acknowledgements I owe thanks to my supervisors, Gary and Ivana. Gary’s time, attention to detail, and high standards greatly improved the quality of my PhD work. Ivana was an invaluable source of knowledge on MR physics and POSSUM, and provided a great amount of advice, academic and otherwise, throughout my time at UCL. I enjoyed a fruitful collaboration with Jesper and MJ from FMRIB, Oxford - thanks for your enthusiasm for the simulator, and the chance to contribute to eddy’s development. MIG provided a great environment for research. I’m glad to have been part of a research group with so many students: thanks for all discussions, cookies and conference fun. I was also fortunate to meet Alex, Eliza, Felix, and Zach: thanks for all the laughter, and ensuring I never took anything too seriously. I am grateful to all my friends and family. Thank you Mum, Dad, and Helen, for all your love, support, and tolerating me never wanting to talk about my thesis! So many friends have made the last four years so fun, but special mention is owed to the residents of the Deptford Commune: Emily, George, Javal, Sinead, and Prev. Lastly, to Lindsay. You’ve provided love, encouragement, and the ideal location for me to start writing this thesis: a hammock in a house in Zanzibar, jealously guarded by a very silly cat. Contents 1 Introduction 17 1.1 Motivation . 17 1.2 Problem statement . 19 1.3 Project aims and scope . 19 1.4 Thesis overview and contributions . 19 2 Background 23 2.1 Magnetic resonance imaging . 23 2.1.1 Protons in a magnetic field . 24 2.1.2 Detection of the magnetization . 25 2.1.3 Spatial encoding . 26 2.1.4 Image formation and contrast . 30 2.2 Diffusion MRI . 34 2.2.1 Diffusion . 35 2.2.2 Measuring diffusion with MRI . 37 2.2.3 Models of diffusion . 40 2.3 Image artefacts . 43 2.4 Simulation systems . 48 2.4.1 MRI . 48 2.4.2 Diffusion MRI . 51 2.4.3 Critical analysis . 53 3 A simulation system for diffusion-weighted MRI 55 10 Contents 3.1 Overview . 55 3.1.1 Research dissemination . 55 3.2 Introduction . 56 3.3 Methods . 57 3.3.1 Framework overview . 57 3.3.2 Producing DWIs . 58 3.3.3 Incorporating artefacts . 61 3.3.4 Ground truth displacement fields . 62 3.4 Simulator demonstration . 64 3.4.1 Image contrast . 64 3.4.2 Eddy-current artefacts . 65 3.5 Discussion . 65 3.6 Conclusions . 70 4 Application I: assessing motion and eddy-current correction techniques 71 4.1 Overview . 71 4.1.1 Research dissemination . 71 4.2 Introduction . 72 4.3 Experiments and Results . 73 4.3.1 Comparison of correction methods . 73 4.3.2 Evaluation of eddy ..................... 76 4.3.3 Impact of correction on microstructure estimation . 80 4.4 Discussion . 85 4.5 Conclusions . 92 5 Simulating the spin-echo 93 5.1 Overview . 93 5.1.1 Research dissemination . 93 5.2 Introduction . 93 5.3 Methods . 94 Contents 11 5.3.1 Implementation of spin-echo in POSSUM . 94 5.3.2 Incorporation of POSSUM into the DW-MR framework . 97 5.4 Validation . 98 5.5 Discussion . 100 6 Application II: investigating the susceptibility artefact 103 6.1 Overview . 103 6.1.1 Research dissemination . 103 6.2 Introduction . 104 6.3 Methods . 107 6.3.1 Assessment of existing techniques using simulated data . 107 6.3.2 Assessment of existing techniques using real data . 111 6.3.3 Assessment of the susceptibility-movement interaction . 113 6.4 Results . 114 6.4.1 Assessment of techniques with simulated data . 114 6.4.2 Assessment of techniques with real data . 122 6.4.3 Interaction between susceptibility and movement . 122 6.5 Discussion . 125 6.6 Conclusions . 132 7 Application III: a tool for automated quality control 135 7.1 Overview . 135 7.1.1 Research dissemination . 135 7.2 Introduction . 136 7.3 Methods . 138 7.3.1 Data . 138 7.3.2 Classifier . 143 7.4 Results . 145 7.5 Discussion . 147 7.6 Conclusion . 151 12 Contents 8 Conclusions 153 8.1 Summary . 153 8.2 Future directions . 154 8.2.1 Simulator improvements . 154 8.2.2 Simulator object improvements . 155 8.2.3 Further applications . 156 Appendices 158 A Publications 159 Bibliography 161 List of Figures 2.1 Motion of M~ during an 90° pulse in the rotating and lab frames. 27 2.2 The gradient-echo pulse sequence. 29 2.3 Image formation in the case of discrete, finite sampling. 32 2.4 Image contrast as a function of TR and TE............. 35 2.5 Illustration of diffusion in a cylinder. 37 2.6 Variation in contrast with b-value. 38 2.7 Schematic of the Stejskal-Tanner pulse sequence . 40 2.8 A single-shot EPI scheme. 41 3.1 The pipeline for simulating DWIs. 59 3.2 Comparison of real and simulated data. 66 3.3 Comparison of our simulated data to state-of-the-art. 67 3.4 Demonstration of DWIs simulated with EC artefacts. 68 4.1 Mean error in displacement field across the brain. 77 4.2 Spatial errors in displacement field. 78 4.3 Correction errors on real data. 79 4.4 Errors after correction with eddy.................. 81 4.5 Errors after correction with eddy.................. 82 4.6 FA maps for corrected data. 85 4.7 NODDI maps for corrected data. 86 4.8 Parameter maps resulting from fits to real data. 87 4.9 Model residuals after correction. 88 4.10 Mean error field over the brain. 89 14 List of Figures 4.11 Spatial plots of the mean error field. 90 5.1 Flowchart describing the POSSUM simulator. 95 5.2 The new framework for simulating DW-MR data. 98 5.3 Comparison of simulation with theory for a spin-echo experiment. 99 5.4 Comparison between simulated GE-EPI and SE-EPI images. 99 5.5 Simulations both with and without a linear B0 gradient across the FOV. 100 5.6 Comparison between GE-EPI and SE-EPI images with a sus- ceptibility field. 101 6.1 Simulated DWIs. 112 6.2 Displacement field errors. 115 6.3 Errors in image intensity. 118 6.4 Errors in FA metrics. 120 6.5 AP-LR comparison on simulated data. 123 6.6 AP-LR comparison on real data. 124 6.7 Susceptibility-movement interaction. 126 6.8 Errors introduced when failing to account for the susceptibility- movement interaction. 127 6.9 Error distribution. 128 7.1 Example of the intra-volume movement artefact. 139 7.2 Example simulated motion trace. 141 7.3 Real and simulated data with QC labels. 146 7.4 Precision-recall curve for both classifiers. 147 7.5 Sample classifier results for images in the test-set. 148 7.6 Quantitative classifier results on the test set. ..