A Method of Reducing Model Space for Dynamic Causal Modelling Joseph Whittaker School of Medicine A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Medical and Human Sciences. 2013 Table of Contents List of figures.................................................................................................. 5 Abstract .......................................................................................................... 8 Declaration ..................................................................................................... 9 COPYRIGHT STATEMENT ......................................................................... 10 Acknowledgments ........................................................................................ 11 Abbreviations ............................................................................................... 12 1 Introduction ............................................................................................ 14 1.1 General overview and motivations .................................................. 14 1.2 Structure of the thesis ..................................................................... 15 1.2.1 Background .............................................................................. 16 1.2.2 Main findings ............................................................................ 16 2 Principles of fMRI .................................................................................. 18 2.1 Nuclear Magnetic Resonance ......................................................... 18 2.1.1 Spin angular momentum .......................................................... 18 2.1.2 External magnetic field ............................................................. 19 2.1.3 Excitation and relaxation .......................................................... 22 2.1.4 Echoes ..................................................................................... 25 2.1.5 Forming an image .................................................................... 26 2.1.6 Echo-planar imaging ................................................................ 29 2.1.7 Image contrast.......................................................................... 30 2.2 Functional Magnetic Resonance Imaging ....................................... 31 2.2.1 Neurovascular Coupling ........................................................... 32 2.2.2 Blood-oxygen-level-dependent contrast ................................... 33 3 Brain connectivity .................................................................................. 38 3.1 Functional Specialisation and Integration ....................................... 38 3.2 Structural connectivity ..................................................................... 39 3.3 Functional and effective connectivity .............................................. 40 3.3.1 Seed-Voxel Correlation Maps .................................................. 41 3.3.2 Matrix decomposition based methods ...................................... 42 3.3.3 Psychophysiological interactions .............................................. 43 3.3.4 Structural Equation Modelling .................................................. 44 3.3.5 Multivariate autoregressive modelling ...................................... 45 1 3.3.6 Dynamic Causal Modelling ....................................................... 46 4 Dynamic Causal Modelling .................................................................... 47 4.1 Introduction ..................................................................................... 47 4.2 Neuronal state equations ................................................................ 49 4.2.1 Bilinear model .......................................................................... 49 4.2.2 Non-linear model ...................................................................... 52 4.2.3 Two-state model ....................................................................... 53 4.2.4 Stochastic model ...................................................................... 55 4.3 Haemodynamic model .................................................................... 56 4.4 Parameter estimation ...................................................................... 58 4.5 Model priors .................................................................................... 59 4.6 Inference ......................................................................................... 61 4.6.1 Bayesian Model Selection (BMS) ............................................. 61 4.6.2 Model space ............................................................................. 65 4.6.3 Inference on parameter space ................................................. 68 5 Neuroimaging in Psychiatry ................................................................... 70 5.1 Introduction ..................................................................................... 70 5.1.1 Connectivity .............................................................................. 72 5.2 Depression ...................................................................................... 73 5.2.1 Emotional processing bias ....................................................... 75 5.2.2 Emotional face processing in depression ................................. 77 5.2.3 Effects of antidepressants and fMRI ......................................... 82 5.2.4 Summary .................................................................................. 85 6 Paper 1 .................................................................................................. 87 6.1 Abstract ........................................................................................... 87 6.2 Introduction ..................................................................................... 88 6.3 Methods .......................................................................................... 92 6.3.1 Subjects ................................................................................... 92 6.3.2 N-back task .............................................................................. 93 6.3.3 Implicit emotional face processing task .................................... 94 6.3.4 Image analysis ......................................................................... 95 6.3.5 Dynamic Causal Modelling ....................................................... 95 6.4 Results ............................................................................................ 99 2 6.4.1 fMRI group activations .............................................................. 99 6.4.2 N-back task .............................................................................. 99 6.4.3 Implicit emotional face processing task .................................. 101 6.5 Discussion .................................................................................... 106 6.6 Supplementary material ................................................................ 110 7 Paper 2 ................................................................................................ 111 7.1 Abstract ......................................................................................... 111 7.2 Introduction ................................................................................... 113 7.3 Methods ........................................................................................ 115 7.3.1 Subjects ................................................................................. 115 7.3.2 Task ....................................................................................... 116 7.3.3 Dynamic Causal Modelling ..................................................... 116 7.4 Results .......................................................................................... 120 7.4.1 fMRI group activations ............................................................ 120 7.4.2 BMS results ............................................................................ 120 7.4.3 Free energy correlation results ............................................... 122 7.4.4 BMA results ............................................................................ 125 7.5 Discussion .................................................................................... 128 7.6 Supplementary material ................................................................ 133 8 Paper 3 ................................................................................................ 135 8.1 Abstract ......................................................................................... 135 8.2 Introduction ................................................................................... 137 8.2.1 DCM ....................................................................................... 139 8.3 Methods ........................................................................................ 142 8.3.1 Subjects ................................................................................. 142 8.3.2 Antidepressant treatment ....................................................... 143 8.3.3 Implicit emotional processing faces task ................................ 143 8.3.4 fMRI data acquisition .............................................................. 143 8.3.5 DCM analysis ......................................................................... 144 8.4 Results .........................................................................................