Embedding of Functional Human Brain Networks on a Sphere

Human brain activity is often measured using the blood-oxygen-level dependent (BOLD) signals obtained through functional magnetic resonance imaging (fMRI). The strength of connectivity between brain regions is then measured and represented as Pearson correlation matrices. As the number of brain regions increases, the dimension of matrix increases. It becomes extremely cumbersome to even visualize and quantify such weighted complete networks. To remedy the problem, we propose to embedded brain networks onto a hypersphere, which is a Riemannian manifold with constant positive curvature

Heritability of "small-world" networks in the brain: A graph theoretical analysis of resting-state EEG functional connectivity.

Recent studies have shown that resting-state functional networks as studied with fMRI, EEG, and MEG may be so-called small-world networks. We investigated to what extent the characteristic features of small-world networks are genetically determined. To represent functional connectivity between brain areas, we measured resting EEG in 574 twins and their siblings and calculated the synchronization likelihood between each pair of electrodes. We applied a threshold to obtain a binary graph from which we calculated the clustering coefficient C (describing local interconnectedness) and average path length L (describing global interconnectedness) for each individual. Modeling of MZ and DZ twin and sibling resemblance indicated that across various frequency bands 46-89% of the individual differences in C and 37-62% of the individual differences in L are heritable. It is asserted that C, L, and a small-world organization are viable markers of genetic differences in brain organization. © 2007 Wiley-Liss, Inc

Investigating Brain Functional Networks in a Riemannian Framework

The brain is a complex system of several interconnected components which can be categorized at different Spatio-temporal levels, evaluate the physical connections and the corresponding functionalities. To study brain connectivity at the macroscale, Magnetic Resonance Imaging (MRI) technique in all the different modalities has been exemplified to be an important tool. In particular, functional MRI (fMRI) enables to record the brain activity either at rest or in different conditions of cognitive task and assist in mapping the functional connectivity of the brain. The information of brain functional connectivity extracted from fMRI images can be defined using a graph representation, i.e. a mathematical object consisting of nodes, the brain regions, and edges, the link between regions. With this representation, novel insights have emerged about understanding brain connectivity and providing evidence that the brain networks are not randomly linked. Indeed, the brain network represents a small-world structure, with several different properties of segregation and integration that are accountable for specific functions and mental conditions. Moreover, network analysis enables to recognize and analyze patterns of brain functional connectivity characterizing a group of subjects. In recent decades, many developments have been made to understand the functioning of the human brain and many issues, related to the biological and the methodological perspective, are still need to be addressed. For example, sub-modular brain organization is still under debate, since it is necessary to understand how the brain is functionally organized. At the same time a comprehensive organization of functional connectivity is mostly unknown and also the dynamical reorganization of functional connectivity is appearing as a new frontier for analyzing brain dynamics. Moreover, the recognition of functional connectivity patterns in patients affected by mental disorders is still a challenging task, making plausible the development of new tools to solve them. Indeed, in this dissertation, we proposed novel methodological approaches to answer some of these biological and neuroscientific questions. We have investigated methods for analyzing and detecting heritability in twin's task-induced functional connectivity profiles. in this approach we are proposing a geodesic metric-based method for the estimation of similarity between functional connectivity, taking into account the manifold related properties of symmetric and positive definite matrices. Moreover, we also proposed a computational framework for classification and discrimination of brain connectivity graphs between healthy and pathological subjects affected by mental disorder, using geodesic metric-based clustering of brain graphs on manifold space. Within the same framework, we also propose an approach based on the dictionary learning method to encode the high dimensional connectivity data into a vectorial representation which is useful for classification and determining regions of brain graphs responsible for this segregation. We also propose an effective way to analyze the dynamical functional connectivity, building a similarity representation of fMRI dynamic functional connectivity states, exploiting modular properties of graph laplacians, geodesic clustering, and manifold learning

Genetic influences on cost-efficient organization of human cortical functional networks

The human cerebral cortex is a complex network of functionally specialized regions interconnected by axonal fibers, but the organizational principles underlying cortical connectivity remain unknown. Here, we report evidence that one such principle for functional cortical networks involves finding a balance between maximizing communication efficiency and minimizing connection cost, referred to as optimization of network cost-efficiency. We measured spontaneous fluctuations of the blood oxygenation level-dependent signal using functional magnetic resonance imaging in healthy monozygotic (16 pairs) and dizygotic (13 pairs) twins and characterized cost-efficient properties of brain network functional connectivity between 1041 distinct cortical regions. At the global network level, 60% of the interindividual variance in cost-efficiency of cortical functional networks was attributable to additive genetic effects. Regionally, significant genetic effects were observed throughout the cortex in a largely bilateral pattern, including bilateral posterior cingulate and medial prefrontal cortices, dorsolateral prefrontal and superior parietal cortices, and lateral temporal and inferomedial occipital regions. Genetic effects were stronger for cost-efficiency than for other metrics considered, and were more clearly significant in functional networks operating in the 0.09–0.18 Hz frequency interval than at higher or lower frequencies. These findings are consistent with the hypothesis that brain networks evolved to satisfy competitive selection criteria of maximizing efficiency and minimizing cost, and that optimization of network cost-efficiency represents an important principle for the brain's functional organization