Influence of wiring cost on the large-scale architecture of human cortical connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained (‘random’), connection length preserving (‘spatial’), and connection length optimised (‘reduced’) surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Navigability of temporal networks in hyperbolic space

Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remain largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.Comment: 10 pages, 4 figures. Includes Supplemental Informatio

Small-World Brain Networks Revisited.

It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be widely applied to analysis of neuroimaging and other neuroscience data as part of the rapid growth of the new field of connectomics. Here, we review briefly the foundational concepts of graph theoretical estimation and generation of small-world networks. We take stock of some of the key developments in the field in the past decade and we consider in some detail the implications of recent studies using high-resolution tract-tracing methods to map the anatomical networks of the macaque and the mouse. In doing so, we draw attention to the important methodological distinction between topological analysis of binary or unweighted graphs, which have provided a popular but simple approach to brain network analysis in the past, and the topology of weighted graphs, which retain more biologically relevant information and are more appropriate to the increasingly sophisticated data on brain connectivity emerging from contemporary tract-tracing and other imaging studies. We conclude by highlighting some possible future trends in the further development of weighted small-worldness as part of a deeper and broader understanding of the topology and the functional value of the strong and weak links between areas of mammalian cortex.DSB acknowledges support from the John D. and Catherine T. MacArthur Foundation, the Alfred P. Sloan Foundation, the Army Research Laboratory and the Army Research Office through contract numbers W911NF-10-2-0022 and W911NF-14-1-0679, the National Institute of Health (2-R01-DC-009209-11, 1R01HD086888-01, R01-MH107235, R01-MH107703, and R21-M MH-106799), the Office of Naval Research, and the National Science Foundation (BCS-1441502, CAREER PHY-1554488, and BCS-1631550).This is the final version of the article. It first appeared from Sage at http://dx.doi.org/10.1177/1073858416667720

Topological properties of modular networks, with a focus on networks of functional connections in the human brain

Complex network theory offers useful approaches to analyze the structural and functional properties of real life networks. In this work, we explore some of the mathematical concepts of network theory and study real life systems from a complex network perspective. We pay particular attention to networks of connections within the human brain. We analyze weighted networks calculated from full functional magnetic resonance imaging (fMRI) data acquired during task performance. The first novelty of this study is the fact that we retain all of the connections between all of the voxels in the full brain fMRI data. We then evaluate the extent to which this rich dataset can be described by existing models of scale-free or exponentially truncated scale-free topology, comparing results across a large number of more complex topological models as well. Our results suggest that the novel model presented in this dissertation offers a significantly better fit at the voxel level. Structural characterization of the brain can also give insights into the effects of traumatic injuries. For our second study, we used brain networks to explore the topological consequences of brain damage in computational models. By simulating the effects of several traumatic brain injury (TBI) models we find a variety of disruptions in the modular structure and connectivity of the post-injury networks. In particular, we focused on the effects of focalized injuries, axonal degeneration and diffuse microlesions. Our results suggest that mathematical models can predict, to some extent, the structural and functional effects of TBIs based on the analysis of specific topological measures. Furthermore, these results may be correlated to known cognitive sequelae of TBI. In order to complement the set of topological properties studied, we review the concept of participation of a node in a modular network. The participation coefficient is often used to provide a ranking of the importance of a node; however, we propose a new measure, called the gateway coefficient, to assess the involvement of a node. Our results suggest that the gateway coefficient has a superior ranking power than the participation coefficient since it takes into account a variety of modular properties of the network. These results are illustrated with examples of simulations and real life datasets, such as the air transportation network and the human brain network

Doctor of Philosophy

dissertationThe human brain is the seat of cognition and behavior. Understanding the brain mechanistically is essential for appreciating its linkages with cognitive processes and behavioral outcomes in humans. Mechanisms of brain function categorically represent rich and widely under-investigated biological substrates for neural-driven studies of psychiatry and mental health. Research examining intrinsic connectivity patterns across whole brain systems utilizes functional magnetic resonance imaging (fMRI) to trace spontaneous fluctuations in blood oxygen-level dependent (BOLD) signals. In the first study presented, we reveal patterns of dynamic attractors in resting state functional connectivity data corresponding to well-documented biological networks. We introduce a novel simulation for whole brain dynamics that can be adapted to either group-level analysis or single-subject level models. We describe stability of intrinsic functional architecture in terms of transient and global steady states resembling biological networks. In the second study, we demonstrate plasticity in functional connectivity following a minimum six-week intervention to train cognitive performance in a speed reading task. Long-term modulation of connectivity with language regions indicate functional connectivity as a candidate biomarker for tracking and measuring functional changes in neural systems as outcomes of cognitive training. The third study demonstrates utility of functional biomarkers in predicting individual differences in behavioral and cognitive features. We successfully predict three major domains of personality psychologyintelligence, agreeableness, and conscientiousnessin individual subjects using a large (N=475) open source data sample compiled by the National Institutes of Healths Human Connectome Project

Network Geometry

Networks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others are the geometry of latent spaces underlying many networks and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale invariance, self-similarity and other forms of fundamental symmetries in networks. Network geometry is also of great use in a variety of practical applications, from understanding how the brain works to routing in the Internet. We review the most important theoretical and practical developments dealing with these approaches to network geometry and offer perspectives on future research directions and challenges in this frontier in the study of complexity

Abnormalities in structural covariance of cortical gyrification in schizophrenia

The highly convoluted shape of the adult human brain results from several well-coordinated maturational events that start from embryonic development and extend through the adult life span. Disturbances in these maturational events can result in various neurological and psychiatric disorders, resulting in abnormal patterns of morphological relationship among cortical structures (structural covariance). Structural covariance can be studied using graph theory-based approaches that evaluate topological properties of brain networks. Covariance-based graph metrics allow cross-sectional study of coordinated maturational relationship among brain regions. Disrupted gyrification of focal brain regions is a consistent feature of schizophrenia. However, it is unclear if these localized disturbances result from a failure of coordinated development of brain regions in schizophrenia. We studied the structural covariance of gyrification in a sample of 41 patients with schizophrenia and 40 healthy controls by constructing gyrification-based networks using a 3-dimensional index. We found that several key regions including anterior insula and dorsolateral prefrontal cortex show increased segregation in schizophrenia, alongside reduced segregation in somato-sensory and occipital regions. Patients also showed a lack of prominence of the distributed covariance (hubness) of cingulate cortex. The abnormal segregated folding pattern in the right peri-sylvian regions (insula and fronto-temporal cortex) was associated with greater severity of illness. The study of structural covariance in cortical folding supports the presence of subtle deviation in the coordinated development of cortical convolutions in schizophrenia. The heterogeneity in the severity of schizophrenia could be explained in part by aberrant trajectories of neurodevelopment