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Advanced Analysis of Diffusion MRI Data Linköping Studies in Science and Technology Dissertation No. 2017 Advanced analysis of diffusion MRI data Xuan Gu Linköping Studies in Science and Technology Dissertaons, No. 2017 Advanced analysis of diffusion MRI data Xuan Gu Linköping University Department of Biomedical Engineering Division of Biomedical Engineering SE-581 83 Linköping, Sweden Linköping 2019 Edition 1:1 © Xuan Gu, 2019 ISBN 978-91-7519-003-7 ISSN 0345-7524 URL http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-161288 Published articles have been reprinted with permission from the respective copyright holder. Typeset using XƎTEX Printed by LiU-Tryck, Linköping 2019 ii POPULÄRVETENSKAPLIG SAMMANFATTNING Diffusions-viktad magnetresonansavbildning (dMRI) är en icke-invasiv metod för att stude- ra hur vattenmolekyler rör sig på grund av diffusion. För att uppnå detta används speciella sekvenser i en magnetkamera, som sätter fart på molekylerna med hjälp av starka magnet- fält. dMRI kan användas som ett verktyg för att studera hjärnkonnektivitet, det vill säga hur olika delar av hjärnan är ihopkopplade via nervfibrer. Denna avhandling presenterar nya metoder för att analysera data från dMRI experiment. En första utmaning är att dMRI data innehåller flera typer av artefakter. Geometriska distortioner skapas via skillnader i hur olika vävnader reagerar på starka magnetfält. Det är även vanligt att försökspersonen rör på huvudet under experimentet. Efter att data har korrigerats för distortioner skattas en diffusions-modell för varje område i hjärnan. Denna modell säger hur stark diffusionen är och om den är starkare i en riktning jämfört med andra riktningar, vilket kan representeras med en tensor. Från tensorn kan man sen räkna ut olika skalära mått, som medeldiffusionen i alla riktningar och hur riktad diffusionen är. Dessa skalära mått kan användas i gruppanalyser med friska kontrollpersoner och personer med en viss sjukdom, för att bättre förstå olika hjärnsjukdomar. Det är även viktigt att veta hur bra en diffusions-modell passar till data, vilket kan kvantifieras som osäkerhet. Denna avhandling presenterar flera sätt att skatta osäkerhet. iii ABSTRACT Diffusion magnetic resonance imaging (diffusion MRI) is a non-invasive imaging modality which can measure diffusion of water molecules, by making the MRI acquisition sensitive to diffusion. Diffusion MRI provides unique possibilities to study structural connectivity of the human brain, e.g. how the white matter connects different parts of the brain. Diffusion MRI enables a range of tools that permit qualitative and quantitative assessments of many neurological disorders, such as stroke and Parkinson. This thesis introduces novel methods for diffusion MRI data analysis. Prior to estimating a diffusion model in each location (voxel) of the brain, the diffusion data needs tobepre- processed to correct for geometric distortions and head motion. A deep learning approach to synthesize diffusion scalar maps from a T1-weighted MR image is proposed, and it is shown that the distortion-free synthesized images can be used for distortion correction. An evaluation, involving both simulated data and real data, of six methods for susceptibility distortion correction is also presented in this thesis. A common problem in diffusion MRI is to estimate the uncertainty of a diffusion model. An empirical evaluation of tractography, a technique that permits reconstruction of white matter pathways in the human brain, is presented in this thesis. The evaluation is based on analyzing 32 diffusion datasets from a single healthy subject, to study how reliable tractography is. In most cases only a single dataset is available for each subject. This thesis presents methods based on frequentistic (bootstrap) as well as Bayesian inference, which can provide uncertainty estimates when only a single dataset is available. These uncertainty measures can then, for example, be used in a group analysis to downweight subjects with a higher uncertainty. iv Acknowledgments Undertaking this PhD has been a truly life-changing experience for me and it would not have been possible to do without the support and guidance that I received from many people. I would like to first say a very big thank you to my supervisor DrAnders Eklund for all the support and encouragement he gave me. Without his guidance and constant feedback this PhD would not have been achievable. My sincere thanks also go to Professor Hans Knutsson who has provided me an opportunity to start the PhD. Many thanks also to Dr Evren Özarslan who has provided insightful discussions and suggestions about the research. My deep appreciation goes out to the present members of the group: Cem Yolcu, David Abramian, Deneb Boito and Magnus Herberthson. I also thank people who were part of the group, including Jens Sjölund, Mats Andersson, Olivier Cros and Snehlata Shakya. I am honored to work with all of you. I also thank the wonderful staff in the Department of Biomedical Engineering for always being so helpful and friendly. I gratefully acknowledge the funding received towards my PhD from the Swedish research council, the ITEA/VINNOVA funded project BENEFIT, and the Seeing Organ Function (SOF) project supported by the Knut and Alice Wallenberg Foundation. I especially thank my parents for their unconditional trust, timely encour- agement, and endless patience. Finally, I would like to thank the unsung hero Harley who works 24/7 in the server room to process my endless analyses. v Contents Abstract iii Acknowledgments v Contents vi List of Figures ix List of Tables xii 1 Introduction 1 1.1 Introduction ............................... 1 1.2 Research questions ........................... 1 1.3 Outline .................................. 2 1.4 Included publications ......................... 2 1.5 Abbreviations .............................. 3 1.6 Reproducibility and ethics ...................... 4 2 Magnetic resonance imaging 5 2.1 History of MRI ............................. 5 2.2 MR physics ............................... 6 2.3 MR signals ............................... 8 2.4 MR spatial encoding .......................... 10 2.5 k-space .................................. 11 3 Diffusion MRI 13 3.1 History of Diffusion MRI ....................... 13 3.2 Diffusion basics ............................. 14 3.3 Diffusion MRI techniques ....................... 15 4 Preprocessing of diffusion MRI data 27 4.1 Introduction ............................... 27 4.2 Susceptibility-induced distortion correction . 28 4.3 Eddy-current-induced distortion correction . 35 vi 4.4 Head motion correction ........................ 36 4.5 Discussion ................................ 37 5 Tractography 39 5.1 Introduction ............................... 39 5.2 Deterministic tractography ...................... 41 5.3 Probabilistic tractography ...................... 43 5.4 Stopping and rejection criteria .................... 48 5.5 Limitations ............................... 51 6 Uncertainty in diffusion models 53 6.1 Introduction ............................... 53 6.2 Bootstrap ................................ 54 6.3 Bayesian methods ........................... 59 6.4 Reducing uncertainty using a spatial model . 63 7 Deep learning in diffusion MRI 67 7.1 Introduction ............................... 67 7.2 Architectures .............................. 68 7.3 Applications ............................... 71 8 Summary of papers 77 8.1 Introduction ............................... 77 8.2 Paper I - Repeated tractography of a single subject: how high is the variance? ............................. 77 8.3 Paper II - Bayesian diffusion tensor estimation with spatial priors 78 8.4 Paper III - Multi-fiber estimation and tractography for diffusion MRI using mixture of non-central Wishart distributions . 78 8.5 Paper IV - Using the wild bootstrap to quantify uncertainty in mean apparent propagator MRI ................... 78 8.6 Paper V - Generating diffusion MRI scalar maps . 79 8.7 Paper VI - Evaluation of six phase encoding based susceptibility distortion correction methods for diffusion MRI . 79 Bibliography 81 Paper I 97 Paper II 123 Paper III 137 Paper IV 145 Paper V 161 vii Paper VI 173 viii List of Figures 2.1 Precession of protons’ magnetic moment (the dotted line) in an external magnetic field B0 (the solid line). ............... 7 2.2 The net magnetization M (in a rotating frame of reference) with a flip angle α in an external magnetic field B0 and a RF pulse magnetic field B1. ............................. 7 ∗ 2.3 T1, T2 and T2 relaxation. ......................... 8 2.4 The free induction decay (FID) signal is oscillating with a constant frequency. Immediately after the pulse, the transverse component of the precessing magnetization will decay and induce an alternat- ing current in the coil. ........................... 9 2.5 Examples of T1- and T2-weighted images from HCP. 10 2.6 An example of an image in k-space and its reconstructed image. 12 3.1 Schematic diagram of the PGSE sequence. Diffusion gradients are applied on both sides of the 180○ pulse. The signal is acquired immediately following the second diffusion gradient. 14 3.2 Examples of diffusion weighted images for different b-values. The images are scaled independently. A higher b-value results in a lower signal to noise ratio. Data is from MGH adult diffusion (Setsompop et al., 2013). ................................. 15 3.3 Diffusion tensor ellipsoids (from left to right): sphere (λ1 = λ2 = λ3), planar (λ1 = λ2 > λ3) and cigar (λ1 > λ2 = λ3). 17 3.4 DTI scalars (from left
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