Multidimensional Dynamic Analysis of Human Brain Connectivity

The human brain is one of the most complex system existing in nature. The emergence of cognitive and physiological phenomena is the outcome of a complex series of interactions that occur hierarchically. Hence, explaining cognition is not possible just by taking into account the single parts the brain is composed of, but a comprehensive view of the collective behaviours of its constituents and the interactions with its environment should be considered to study the global system behaviour. A network formulation simplifies the analysis of a complex system by providing mathematical tools able to capture different aspects of its organization in a compact manner. Graph theoretical methods have been extensively applied to many neuroimaging datasets in order to describe the topological properties of both functional and structural brain networks. Although these methods have become a gold standard for analysing the complex behaviour of the human brain, several important issues related to the identification of the networks, their temporal evolution and new complex metrics for their topological description need to be further explored in order to provide a general and comprehensive analysis framework. Indeed, the human brain is a highly flexible dynamic system: executing both complex and simple functions requires the ongoing reconfiguration of the connections among the general- and specific-domain subsystems. In this work, some methodological procedures are proposed to address the outlined issues. Firstly, a new synchronization-based metric is developed to assess the functional connectivity in human brain through functional magnetic resonance imaging (fMRI). In details, the whole brain volume is partitioned into regions of interest (ROIs) and a phase-space framework is used to map pairs of signals of each region of interest, in their reconstructed phase space, i.e. a topological representation of their behaviour under all possible initial conditions. Cross recurrence plots (CRPs) are then employed to reduce the dimensionality of the phase space and compare the trajectories of the interacting systems. The synchronization metric is then extracted from the cross recurrence to assess the coupling behaviour of the time series. The proposed metric is a generalized synchronization measure that takes into account both the amplitude and phase coupling between pairs of fMRI series. It differs from the correlation measures used in the literature, as it seems to be more sensitive to nonlinear coupling phenomena between time series and it is more robust against the physiological noise. Then an extended multidimensional framework is presented to describe completely the functional interactions of couples of signals in the phase space. More specifically, a set of metrics is extracted from the CRP of each couple of signals to form a multilayer connectivity matrix in which each layer is related to a specific complex phenomenon occurring in phase space. Hence, machine-learning algorithms are used to identify markers of the dynamic states in brain activity to characterize pathological conditions in a clinical context. Finally, a new perspective to characterize node centrality in complex networks is discussed and some preliminary results of the application of a new resilience index are shown. This metric quantifies the importance of the node in relation to its survival rate for progressive removal of links in the network and can be useful for identifying the most persistent nodes in a network.