Study of brain complexity using information theory tools

The human brain is a complex network that shares and processes information by using the structural paths between areas in order to perform a function. Magnetic resonance imaging techniques allow the in vivo reconstruction of the structural paths by using diffusion MRI and the mapping of the active areas by using functional MRI. The connectome models the brain as a graph where nodes correspond to brain regions and edges to structural or functional connections. In this thesis, we investigate and provide new methods to study the brain complexity and improve the understanding of the brain functioning by using information theory. Firstly, we focus on brain parcellation, which is a key step to perform brain studies since determines the regions to be analyzed. We interpret a brain function as a stochastic process where neural impulses are modeled as a random walk by using the connectivity matrix. Using this interpretation, we first present a new hierarchical clustering method based on the information bottleneck. We describe two versions of the method, the agglomerative approach that merges elements with a minimum loss of mutual information, and the divisive approach that divides the elements with a higher gain of mutual information. The agglomerative version of the method is employed and deeply evaluated to parcellate the brain. We show that the clustered networks preserve the structure and properties of the original network but having higher mutual information. Secondly, we focus on the definition of measures to characterize the complexity of the brain networks. We propose new global and local measures. Global measures provide quantitative values for the whole-brain network and include the entropy, the mutual information, and the erasure mutual information, which is a new measure defined by extending the mutual information. Local measures are based on different decompositions of the global measures and include the entropic surprise, the mutual surprise, the mutual predictability and the erasure surprise. These measures show local properties of the brain regions, such as the uncertainty associated to the node, or the uniqueness of the path that the node belongs to. Finally, the consistency of the results across healthy subjects using functional or structural connectivity data, demonstrates the flexibility and robustness of the proposed methods.