A geometric network model of intrinsic grey-matter connectivity of the human brain

Network science provides a general framework for analysing the large-scale brain networks that naturally arise from modern neuroimaging studies, and a key goal in theoretical neuro- science is to understand the extent to which these neural architectures influence the dynamical processes they sustain. To date, brain network modelling has largely been conducted at the macroscale level (i.e. white-matter tracts), despite growing evidence of the role that local grey matter architecture plays in a variety of brain disorders. Here, we present a new model of intrinsic grey matter connectivity of the human connectome. Importantly, the new model incorporates detailed information on cortical geometry to construct ‘shortcuts’ through the thickness of the cortex, thus enabling spatially distant brain regions, as measured along the cortical surface, to communicate. Our study indicates that structures based on human brain surface information differ significantly, both in terms of their topological network characteristics and activity propagation properties, when compared against a variety of alternative geometries and generative algorithms. In particular, this might help explain histological patterns of grey matter connectivity, highlighting that observed connection distances may have arisen to maximise information processing ability, and that such gains are consistent with (and enhanced by) the presence of short-cut connections

Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca

The entropic brain hypothesis holds that the key facts concerning psychedelics are partially explained in terms of increased entropy of the brain's functional connectivity. Ayahuasca is a psychedelic beverage of Amazonian indigenous origin with legal status in Brazil in religious and scientific settings. In this context, we use tools and concepts from the theory of complex networks to analyze resting state fMRI data of the brains of human subjects under two distinct conditions: (i) under ordinary waking state and (ii) in an altered state of consciousness induced by ingestion of Ayahuasca. We report an increase in the Shannon entropy of the degree distribution of the networks subsequent to Ayahuasca ingestion. We also find increased local and decreased global network integration. Our results are broadly consistent with the entropic brain hypothesis. Finally, we discuss our findings in the context of descriptions of "mind-expansion" frequently seen in self-reports of users of psychedelic drugs.Comment: 27 pages, 6 figure

Exponential Random Graph Modeling for Complex Brain Networks

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks

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

Construction of embedded fMRI resting state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling (MDS), Isometric Feature Mapping (ISOMAP) and Diffusion Maps. Furthermore, based on key global graph-theoretical properties of the embedded FCN, we compare their classification potential using machine learning techniques. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the lagged cross-correlation metric. We show that the FCN constructed with Diffusion Maps and the lagged cross-correlation metric outperform the other combinations

Structural Properties of the Caenorhabditis elegans Neuronal Network

Despite recent interest in reconstructing neuronal networks, complete wiring diagrams on the level of individual synapses remain scarce and the insights into function they can provide remain unclear. Even for Caenorhabditis elegans, whose neuronal network is relatively small and stereotypical from animal to animal, published wiring diagrams are neither accurate nor complete and self-consistent. Using materials from White et al. and new electron micrographs we assemble whole, self-consistent gap junction and chemical synapse networks of hermaphrodite C. elegans. We propose a method to visualize the wiring diagram, which reflects network signal flow. We calculate statistical and topological properties of the network, such as degree distributions, synaptic multiplicities, and small-world properties, that help in understanding network signal propagation. We identify neurons that may play central roles in information processing and network motifs that could serve as functional modules of the network. We explore propagation of neuronal activity in response to sensory or artificial stimulation using linear systems theory and find several activity patterns that could serve as substrates of previously described behaviors. Finally, we analyze the interaction between the gap junction and the chemical synapse networks. Since several statistical properties of the C. elegans network, such as multiplicity and motif distributions are similar to those found in mammalian neocortex, they likely point to general principles of neuronal networks. The wiring diagram reported here can help in understanding the mechanistic basis of behavior by generating predictions about future experiments involving genetic perturbations, laser ablations, or monitoring propagation of neuronal activity in response to stimulation

The Influence of Network Topology on Sound Propagation in Granular Materials

Granular materials, whose features range from the particle scale to the force-chain scale to the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with either of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures for their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of meso-scale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by meso-scale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.Comment: 19 pages, 9 figures, and 3 table