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With a Focus on Real-Time Fmri and Non-Parametric Statistics Linköping Studies in Science and Technology Dissertation No. 1439 Computational Medical Image Analysis With a Focus on Real-Time fMRI and Non-Parametric Statistics Anders Eklund Department of Biomedical Engineering Linköping University, SE581 85 Linköping, Sweden http://www.imt.liu.se/ Linköping, March 2012 This is not a joke. Linköping Studies in Science and Technology Dissertation No. 1439 Computational Medical Image Analysis c 2012 Anders Eklund Department of Biomedical Engineering Linköping University SE-581 85 Linköping Sweden ISBN 978-91-7519-921-4 ISSN 0345-7524 Printed in Linköping, Sweden, by LiU-Tryck 2012 Abstract Functional magnetic resonance imaging (fMRI) is a prime example of multi disciplinary research. Without the beautiful physics of MRI, there would not be any images to look at in the first place. To obtain images of good quality, it is necessary to fully understand the concepts of the frequency domain. The analysis of fMRI data requires understanding of signal pro cessing, statistics and knowledge about the anatomy and function of the human brain. The resulting brain activity maps are used by physicians, neurologists, psychologists and behaviourists, in order to plan surgery and to increase their understanding of how the brain works. This thesis presents methods for realtime fMRI and non-parametric fMRI analysis. Realtime fMRI places high demands on the signal processing, as all the calculations have to be made in real-time in complex situations. Real-time fMRI can, for example, be used for interactive brain mapping. Another possibility is to change the stimulus that is given to the subject, in realtime, such that the brain and the computer can work together to solve a given task, yielding a brain computer interface (BCI). Non-parametric fMRI analysis, for example, concerns the problem of calculating signifi- cance thresholds and pvalues for test statistics without a parametric null distribution. Two BCIs are presented in this thesis. In the first BCI, the subject was able to balance a virtual inverted pendulum by thinking of activating the left or right hand or resting. In the second BCI, the subject in the MR scanner was able to communicate with a person outside the MR scanner, through a virtual keyboard. A graphics processing unit (GPU) implementation of a random permuta tion test for single subject fMRI analysis is also presented. The random permutation test is used to calculate significance thresholds and pvalues for fMRI analysis by canonical correlation analysis (CCA), and to investigate the correctness of standard parametric approaches. The random permuta tion test was verified by using 10 000 noise datasets and 1484 resting state fMRI datasets. The random permutation test is also used for a non-local CCA approach to fMRI analysis. Populärvetenskaplig sammanfattning Funktionell magnetresonansavbildning (fMRI) är en ickeinvasiv metod för att mäta hjärnaktivitet. Metoden baseras på att blodets magnetiska egen skaper, via syresättningen, förändras när hjärnan är aktiv. fMRI används dels för att öka förståelsen om hjärnan, dels som ett kliniskt verktyg inför borttagning av hjärntumörer. Denna avhandling presenterar metoder för att analysera hjärnaktivitet när försökspersonen ligger i magnetkameran, s.k. realtidsfMRI, till skillnad mot att genomföra analysen efteråt. RealtidsfMRI kan, bland annat, an vändas som ett hjälpmedel för att lära sig att kontrollera sin egen hjär naktivitet, för att till exempel undertrycka smärta. Ett annat framtida användningsområde är att skapa gränssnitt mellan hjärnan och en dator, för att till exempel kunna kontrollera en robotarm med tankekraft. Avhandlingen presenterar även metoder för ickeparametrisk fMRIanalys. Ett problem med vanlig, parametrisk, fMRIanalys är att man måste göra en rad antaganden om sina data. Om dessa antaganden är fel kan man inte lita på resultatet av analysen. Ickeparametrisk fMRIanalys bygger på färre antaganden, men kräver dock att mer beräkningar utförs. För att göra ickeparametrisk fMRIanalys praktiskt möjligt, används beräkn ingskraften hos moderna grafikkort. Acknowledgements Many people have contributed to this thesis, directly or indirectly. First I would like to thank Professor Hans Knutsson for being a never ending source of new ideas and inspiration. Thanks to Dr. Mats Andersson for endless discussions about filter design, snorkeling, photography, motorcy cles, coffee, beer brewing and for conducting my 127 fMRI experiments (yes I’ve counted them). Thanks to Daniel Forsberg for interesting discussions and for proofreading this thesis. Thanks to Joakim Rydell for providing the network interface to the MR scanner and for answering all my questions about MRI and fMRI. This work has been conducted in collaboration with the Center for Medical Image Science and Visualization (CMIV) at Linköping University, Sweden. CMIV is acknowledged for provision of financial support and access to leading edge research infrastructure. Special thanks to Johan Wiklund for taking care of my computers and helping me with the CMIV homepage. AgoraLink is acknowledged for providing funding for visits to other research groups. Thanks to my colleagues and the personnel at the Department of biomedical engineering for always being kind and helpful. Thanks to Tan Khoa Nguyen and Anders Ynnerman at the Division of visual information technology and applications (VITA), for producing the nice visualization of brain activity which is used in the thesis. I also want to thank my friends and my family, especially my parents Bo and Lilian Eklund, for always being supportive and engaged in my research. Last but not least, thanks to the Swedish foundation for strategic research (SSF), the Swedish research council (VR), NovaMedTech, the research centers MOVIII and CADICS and the Neuroeconomic research group at Linköping university for funding my research. Anders Eklund Linköping, March 2012 Table of Contents 1 Introduction 1 1.1 Introduction . 1 1.2 Outline . 1 1.3 Included publications . 2 1.4 Additional peer reviewed publications . 3 1.5 Abbreviations . 4 2 Magnetic Resonance Imaging 5 2.1 History and basics of MRI . 5 2.2 Spatial encoding . 7 2.3 How to create an image . 8 2.4 Sampling in k-space . 12 2.5 Relaxations . 13 2.6 Sampling patterns . 14 2.7 3D scanning methods . 15 3 Functional Magnetic Resonance Imaging 17 3.1 History of fMRI . 17 3.2 The BOLD signal and the balloon model . 18 3.3 fMRI experiments . 21 3.4 fMRI analysis . 22 3.5 Visualization of brain activity . 22 4 Preprocessing of fMRI Data 23 4.1 Introduction . 23 4.2 Slice timing correction . 23 4.3 Motion correction . 24 4.4 Spatial smoothing . 25 4.5 High-pass filtering, detrending & whitening . 26 4.6 Registration to template brains . 27 5 Phase Based Image Registration 29 5.1 Introduction . 29 5.2 Quadrature filters and local phase . 30 5.3 Optical flow . 33 5.4 Parametric registration . 34 5.5 Nonparametric registration . 35 x Table of Contents 5.6 Extending the local phase idea . 37 6 Parametric fMRI Analysis 41 6.1 Introduction . 41 6.2 The General Linear Model . 41 6.3 Canonical Correlation Analysis . 44 6.4 Testing for activity . 47 6.4.1 Voxel level inference . 48 6.4.2 Cluster level inference . 48 6.4.3 Set level inference . 48 6.5 Multiple testing . 49 7 Non-Parametric fMRI Analysis 51 7.1 Introduction . 51 7.2 Resampling . 52 7.3 Resampling in single subject fMRI . 53 7.4 Multiple testing . 55 7.5 Cluster level inference . 55 7.6 Computational complexity . 57 7.7 Verifying the random permutation test . 58 7.7.1 Simulated data . 58 7.7.2 Real data . 59 7.8 Comparing parametric and nonparametric significance thresholds . 64 7.9 Using the random permutation test for CCA based fMRI analysis . 69 7.10 Multistep permutation tests . 71 8 Non-Local fMRI Analysis 73 8.1 Introduction . 73 8.2 Extending CCA to nonlocal analysis . 73 8.3 Statistical inference and computational complexity . 76 8.4 Simulated data . 78 8.5 Real data . 78 9 Real-time fMRI Analysis 81 9.1 Introduction . 81 9.2 Brain computer interfaces . 82 9.3 Comparing EEG and fMRI . 82 9.4 Combining EEG and fMRI . 83 9.5 Classification of brain activity . 83 9.6 Balancing an inverted pendulum by thinking . 84 9.7 A communication interface . 87 Table of Contents xi 9.8 Visualization of brain activity in realtime . 90 10 Medical Image Processing on the GPU 93 10.1 Introduction . 93 10.2 Parallel calculations . 93 10.3 Memory types . 94 10.4 The CUDA programming language . 97 10.5 Image registration on the GPU . 98 10.6 Image denoising on the GPU . 99 10.7 fMRI analysis on the GPU . 100 11 Summary of Papers 101 11.1 Introduction . 101 11.2 Paper I - Using RealTime fMRI to Control a Dynamical System by Brain Activity Classification . 101 11.3 Paper II - A Brain Computer Interface for Communication Using Real-Time fMRI . 102 11.4 Paper III - Using the Local Phase of the Magnitude of the Local Structure Tensor for Image Regis tration . 102 11.5 Paper V - True 4D Image Denoising on the GPU . 102 11.6 Paper IV - fMRI Analysis on the GPU - Possibilities and Challenges . 103 11.7 Paper VI - Fast Random Permutation Tests Enable Objec tive Evaluation of Methods for Single Subject fMRI Analysis . 103 11.8 Paper VII - Does Parametric fMRI Analysis with SPM Yield Valid Results? - An Empirical Study of 1484 Rest Datasets . 103 11.9 Paper VIII - A Functional Connectivity Inspired Approach to NonLocal fMRI Analysis . 104 12 Discussion 105 1 Introduction "Yes. Terribly wrong. Your brain is not on file." The Doctor (Emergency Medical Hologram) 1.1 Introduction The area of functional magnetic resonance imaging (fMRI) started in the 1990’s and is still developing fast. fMRI has, so far, been a tremendous tool for understanding of the brain, but a lot of problems remain to be solved.
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