Universiteit Antwerpen Faculteit Wetenschappen Departement Fysica Data-driven methods for the analysis of time-resolved mental chronometry fMRI data sets Approaches and techniques based on the Fuzzy Clustering Method and spatial Independent Component Analysis Data-gedreven methodes voor de analyse van tijds-geresolveerde mentale chronometrie fMRI data Aanpak en technieken gebaseerd op de Vage Clustering Methode en spatiale Onafhankelijke Componenten Analyse Proefschrift voorgelegd tot het behalen van de graad van Doctor in de Wetenschappen aan de Universiteit Antwerpen te verdedigen door Alain Smolders Promotor Prof. Dr. Jan Sijbers Copromotors Prof. Dr. Paul Scheunders Prof. Dr. Elia Formisano Antwerpen, 2007 Data-driven methods for the analysis of time-resolved mental chronometry fMRI data sets Approaches and techniques based on the Fuzzy Clustering Method and spatial Independent Component Analysis Alain Smolders PhD Dissertation 2007 University of Antwerp Promotor: Prof. Dr. Jan Sijbers Co-promotors Prof. Dr. Paul Schuenders Prof. Dr. Elia Formisano — To ... — — ... — Acknowledgements Contents Acknowledgements ............................... v Summary ..................................... xi Outline ...................................... xv Terminology ................................... xvii Notations ..................................... xxi Part I Data-driven analysis of BOLD fMRI data sets 1 1. BOLD fMRI measurement of cortical activity .............. 3 1.1 Introduction............................... 3 1.2 Functional imaging techniques . 3 1.2.1 Historical overview . 3 1.2.2 Strength and shortcomings of fMRI . 5 1.3 Functional relationship between BOLD response and underlying neuronal activity . 6 1.3.1 Pooled neuronal activity . 6 1.3.2 Physiological changes during brain activation . 7 1.3.3 Magnetic susceptibility changes accompany metabolic changes 8 1.3.4 BOLD effect . 9 1.4 Characteristics of BOLD signal change . 12 1.4.1 Magnitude of the BOLD signal change . 12 1.4.2 Temporal characteristics of the BOLD response . 12 viii Contents 1.4.3 Nonlinearity in BOLD response . 13 1.5 Brain mapping by BOLD fMRI experiments . 15 1.5.1 Visualising human brain activation . 15 1.5.2 Mapping brain functionality . 16 1.5.3 Block versus event-related paradigms . 17 1.6 Non consistently-task-related BOLD effects . 20 1.6.1 Noise .............................. 21 1.6.1.1 Thermal noise . 21 1.6.1.2 Physiological noise . 24 1.6.2 Neuronal and haemodynamic effects . 26 1.7 Specificity of the BOLD effect . 28 1.7.1 Spatial relationship between BOLD response and neuronal activity ............................. 28 1.7.2 Improving the specificity . 30 1.8 Conclusions............................... 34 Bibliography ................................. 35 2. Data-driven analysis techniques for fMRI data sets ........... 53 2.1 Introduction............................... 53 2.2 Hypothesis versus data-driven approach . 53 2.2.1 Hypothesis-driven approach . 54 2.2.2 Shortcomings of hypothesis-driven approach . 57 2.2.3 Data-driven approach . 59 2.3 Preprocessing the data with Principal Components Analysis . 60 2.3.1 Partitioning variance . 60 2.3.2 Strength and shortcomings of PCA . 61 2.4 Principles and applications of sICA for the analysis of fMRI data sets 62 2.4.1 Searching for statistical independence . 62 2.4.1.1 History of ICA . 62 2.4.1.2 Temporal and spatial ICA . 63 2.4.2 Strength and shortcomings of ICA . 65 2.4.2.1 Comparison to hypothesis-driven techniques . 65 2.4.2.2 Selection of parameters . 65 2.4.2.3 Interpretation of the results . 65 2.4.2.4 Robustness ...................... 67 2.5 Principles and applications of FCM for the analysis of fMRI data sets 67 2.5.1 Searching for similarities . 67 2.5.1.1 C-means ....................... 68 2.5.1.2 Fuzzy C-means . 69 2.5.2 Strength and shortcomings of FCM . 71 2.5.2.1 Comparison to other techniques . 71 2.5.2.2 Parameter selection and methodological approaches 71 2.5.2.3 Interpretation of the results . 74 2.5.2.4 Accuracy, robustness, and convergence speed . 76 2.6 ROCanalysis.............................. 77 Contents ix 2.7 Conclusions............................... 78 Bibliography ................................. 79 Part II FCM and spatial ICA based approaches and techniques for the dissection of the processing stages of a cognitive task 93 3. FCM and sICA based approaches and techniques ............ 95 3.1 Introduction............................... 95 3.2 Spatial and temporal view on fMRI data . 96 3.3 Methodology of sICA-based approaches . 98 3.3.1 Principal Components Analysis . 98 3.3.2 TheICAmodel......................... 99 3.3.2.1 Assumptions for the applicability of ICA to fMRI datasets ....................... 99 3.3.2.2 Conditions for the identifiability of the ICA-model 100 3.3.2.3 Investigating the assumptions . 102 3.3.2.4 Unmixing the data in an iterative procedure . 102 3.3.2.5 Whitening the data . 103 3.3.2.6 Why Gaussian variables are forbidden . 105 3.3.3 Approaches and algorithms . 106 3.3.3.1 Information maximization . 107 3.3.3.2 Non-Gaussianity maximisation . 112 3.3.3.3 Incorporating spatial information: lagged cross- covariances . 116 3.4 Methodology of FCM-based approaches . 117 3.4.1 Approaches and algorithms . 117 3.4.1.1 Crisp clustering: C-means . 117 3.4.1.2 Fuzzy Clustering: Fuzzy C-means . 118 3.4.2 Incorporating spatial information . 119 3.5 Time-resolved event-related mental chronometry . 120 3.5.1 Single trial events . 120 3.5.2 Mental chronometry . 121 3.5.3 Time-resolvedfMRI . 122 3.6 Visuospatial mental imagery . 123 3.6.1 The visuospatial mental imagery experiment . 123 3.6.2 Cortical regions involved in visuospatial mental imagery . 125 3.7 Conclusions ............................... 126 Bibliography ................................. 128 4. Dissecting cognitive stages: comparison of FCM and sICA ...... 135 4.1 Introduction............................... 136 4.2 Methods................................. 138 4.2.1 Fuzzy clustering . 138 4.2.2 Spatial independent component analysis . 140 x Contents 4.2.3 Functional MRI data . 140 4.2.4 Preprocessing . 141 4.2.5 Fuzzy clustering and spatial ICA: selection of parameters andvisualization ........................ 142 4.2.6 Fuzzy clustering and spatial ICA: selection of clusters / com- ponents and comparison . 143 4.3 ResultsandDiscussion......................... 143 4.3.1 FCM and spatial ICA maps and time-courses . 143 4.3.2 Comparison between methods . 144 4.3.2.1 Within- and between subject consistency . 144 4.3.2.2 Spatial and temporal correspondence between ICA and FCM decompositions . 146 4.4 Conclusions ............................... 148 Bibliography ................................. 149 5. Spatio-temporal fuzzy clustering of fMRI time series .......... 155 5.1 Introduction............................... 156 5.2 Methods and materials . 158 5.2.1 Conventional clustering . 158 5.2.2 Spatio-temporal clustering . 159 5.2.3 Datasets ............................ 160 5.2.4 Setting of parameters common to both FCM methods . 163 5.2.5 Selection and visualisation of clusters . 164 5.2.6 Assessment and comparison of results . 164 5.3 Results and discussion . 165 5.3.1 Simulated data sets . 165 5.3.1.1 Comparison to conventional FCM . 165 5.3.1.2 Difference with spatial smoothing . 168 5.3.2 Realdatasets.......................... 169 5.3.2.1 Comparison to conventional FCM . 169 5.4 Conclusions ............................... 171 Bibliography ................................. 171 6. General conclusions ............................. 177 Nederlandse samenvatting ........................... 181 Summary This dissertation deals with data-driven methods for the analysis of complex Blood Oxygen Level Dependent (BOLD) functional Magnetic Resonance Imaging (fMRI) data sets. It explores and identifies the spatial layout and sequence of brain ac- tivations associated with cognitive tasks. The relationship between the measured haemodynamic effect and the underlying neuronal activity however, is complex and poorly understood. Moreover, the resulting signal change is small and ex- hibits a nonlinear component. Finally, confounding factors and the disturbance of the weak signal by several noise sources hamper the interpretation of the results. These constraints become particularly important when analysing complex, cogni- tive data sets. However, several approaches exist to deal with these constraints, such as a well-considered choice of experimental design, acquisition technique, and analysis method. In this dissertation, the focus lies on the analysis method. Originally, hypothesis-driven analysis techniques were applied. They specify a pri- ori a spatially-invariant model of the haemodynamic response (HR). Its goodness- of-fit is tested at each voxel by statistical methods. However, the assumption of spatial invariance of the HR is suboptimal for the analysis of complex tasks. The latter involve the activation of extended networks of brain regions with widely dif- ferent HRs, exhibiting a substantial degree of trial-by-trial variability. Moreover, hypothesis-driven methods typically ignore interactions between voxels. There- fore, an alternative, data-driven approach was introduced. This shift led to the application of the Fuzzy Clustering Method (FCM) and spatial Independent Com- ponent Analysis (sICA). In both methods the data are decomposed into a set of spatio-temporal modes, without strong a prior assumptions about the temporal profile of the effects of interest. These methods however have a different view on the data. Spatial