MR methods for studying the modularity and connectivity of the human brain

The brain is organized around two complementary principles: modularity and connectivity. This PhD thesis introduces and evaluates novel methods to study both principles in the human brain in vivo. These methods are based on functional Magnetic Resonance Imaging (MRI), which is sensitive to the activation of brain regions and on diffusion MRI, which is sensitive to the structure of the connections between brain regions. We have first evaluated the usefulness of diffusion MRI in the context of effective connectivity studies. Such studies require an explicit model of how the brain is anatomically connected. We show that tractography based on diffusion MRI provides support for a large number of the connections that were proposed in eight previously published effective connectivity studies and also suggest a number of connections that were not used in these studies. However, the methods used in this study are problematic in regions where multiple pathways are crossing. Moreover they do not quantify the probability of finding a connection between regions. We have therefore developed a probabilistic formulation of Q-Ball Imaging, a diffusion MRI method which can resolve up to three different fibre pathways in each voxel. We have recasted the Q-Ball Imaging method in a Bayesian framework and have developed a Markov Chain Monte Carlo algorithm to sample from the posterior distribution on the fibre directions. This algorithm shows good performance both in simulated data and in real diffusion MRI data. The last two studies in this thesis deal with the modularity of the brain, as defined by patterns of anatomical connectivity and functional connectivity during rest. A large number of studies have shown that the resting brain shows a remarkable degree of organization. More specifically, networks that co-activate during task performance show a high degree of co-activation during rest. The third experimental chapter investigates whether we cannot only define functional networks based on resting-state data, but also functionally-defined regions. This chapter is based on the parcellation of a region on the medial wall of the frontal cortex, the SMA region. This region has been consistently parcellated into two sub-regions in a large number of studies using different modalities. We have developed a clustering method for resting-state fMRI data based on the fuzzy clustering algorithm and the Discrete Wavelet Transform. Using this method, we show that the clustering pattern of the SMA region is highly consistent between diffusion MRI and resting-state fMRI data. The resting-state fMRI signal is dynamic in nature, which potentially leads to inconsistencies in clustering patterns within subjects, which would be highly undesirable. The fourth experimental chapter shows that this is indeed the case and proposes an optimization of the Normalized cuts clustering algorithm that significantly improves the within-subject consistency of clustering patterns. This chapter also introduces a heuristic to determine the appropriate number of clusters for resting-state fMRI data. This heuristic is based on the uniqueness of the functional connectivity pattern of each cluster and stops increasing the number of clusters when the functional connectivity pattern of any two clusters has become statistically identical.