The structural and functional multilayer modular organization of the human brain

The human brain is an embedded complex system whose functions cannot be reduced to the processes of its fundamental units. Rather, brain functioning emerges as a consequence of complex patterns of interactions involving all its parts at different levels, from neuron cells to larger brain areas. The past years have been characterized by an exponential growth in the field of neuroimaging techniques and the need for robust methods to interpret and manage the increasing complexity of these data nicely met the rise of network science. The intersection of these disciplines led to the modeling of the brain as a network, in which nodes (subcortical, cortical, or scalp regions) interact with each other through a set of edges (structural or functional connections). Thus, the parallel recording of the interactions of many neuronal groups results in datasets forming, under a mathematical/physics point of view, a complex network. Once the brain network has been estimated, its emerging or topological properties can be measured through a rich collection of metrics developed in the field of network science and rooted in the mathematical branch of graph theory. Several measures of the graph theory have been extensively applied to the structural and functional brain networks, but a recent focus has been on identifying their modular structure. Indeed, the brain network’s elements organize themselves in modules that adopt different configurations basing on the type of connectivity, the brain state, and the external environment. In the network science, modules are groups of nodes internally strongly interconnected, but weakly coupled with the other nodes of the network. By supporting balanced mechanisms of integration and segregation within and between different brain areas, modules constitute the building blocks underpinning the brain network’s organization. Many times, modules have been detected in single networks, yet, there is a long way to go in the inference across brain networks. The patterns of human brain connectivity intrinsically evolve across several domains and consequently, brain networks can change their topology and modular structure in time (in ranges spanning from milliseconds to years), across frequencies, tasks, subjects, or across different acquisition modality. The mathematical formalism of multilayer networks addresses this issue. A multilayer network consists of an ensemble of single-layer networks, each one corresponding and encoding a specific attribute of the system (i.e. different time points, frequencies, subjects, tasks, connectivity metrics). While many graph measures have been successfully translated from single- to multi-layer networks, principled frameworks are still needed, that could allow to treat and manipulate dependencies in multilayer networks. In this context takes place this dissertation, which tackles the challenge of uncovering and characterizing modules in multilayer brain networks. It serves a dual purpose. On one side we attempted to broaden our knowledge of the human brain structural and functional organization across different domains, on the other side we enriched the mathematical and statistical methods in the field of multilayer networks. In section I, we report a comparative analysis among different algorithms employed to detect modules in multilayer networks. In fact, despite the presence of some common practice, there is still no agreement about which algorithm is the most reliable, and a way to test and compare them all under a variety of conditions is lacking. We tested their ability to recover both steady and dynamic modules configurations, statistically evaluating their performances by means of ad-hoc implemented benchmark graphs. Results seek to provide guidelines about the choice of the more appropriate algorithm according to the different properties of the brain network under exam. To prove the validity of the results, we applied the algorithms to functional brain networks derived from electroencephalographic (EEG) signals in a controlled condition. Despite modular organization has not been really investigated in EEG based brain networks, we believe they are extremely suited to study the evolution of cognitive processes across time, given their high temporal resolution. In section II we investigated the evolution of the brain structural modular organization across the human lifespan. In doing that, we developed an ensemble-based multilayer network approach, a statistical procedure that allowed us to efficiently link changes of structural connectivity patterns to development and aging. Given the results obtained in section I, where we found the best multilayer community detection algorithm, in section III we extended its formulation to track variations of brain network architecture across two domains simultaneously. In particular, we explored how it changes across subjects and across different types of connectivity (structural and functional).