Increased network centrality of the anterior insula in early abstinence from alcohol.

Abnormal resting-state functional connectivity, as measured by functional magnetic resonance imaging (MRI), has been reported in alcohol use disorders (AUD), but findings are so far inconsistent. Here, we exploited recent developments in graph-theoretical analyses, enabling improved resolution and fine-grained representation of brain networks, to investigate functional connectivity in 35 recently detoxified alcohol dependent patients versus 34 healthy controls. Specifically, we focused on the modular organization, that is, the presence of tightly connected substructures within a network, and on the identification of brain regions responsible for network integration using an unbiased approach based on a large-scale network composed of more than 600 a priori defined nodes. We found significant reductions in global connectivity and region-specific disruption in the network topology in patients compared with controls. Specifically, the basal brain and the insular-supramarginal cortices, which form tightly coupled modules in healthy subjects, were fragmented in patients. Further, patients showed a strong increase in the centrality of the anterior insula, which exhibited stronger connectivity to distal cortical regions and weaker connectivity to the posterior insula. Anterior insula centrality, a measure of the integrative role of a region, was significantly associated with increased risk of relapse. Exploratory analysis suggests partial recovery of modular structure and insular connectivity in patients after 2 weeks. These findings support the hypothesis that, at least during the early stages of abstinence, the anterior insula may drive exaggerated integration of interoceptive states in AUD patients with possible consequences for decision making and emotional states and that functional connectivity is dynamically changing during treatment.

Scale-resolved analysis of brain functional connectivity networks with spectral entropy.

Functional connectivity is derived from inter-regional correlations in spontaneous fluctuations of brain activity, and can be represented in terms of complete graphs with continuous (real-valued) edges. The structure of functional connectivity networks is strongly affected by signal processing procedures to remove the effects of motion, physiological noise and other sources of experimental error. However, in the absence of an established ground truth, it is difficult to determine the optimal procedure, and no consensus has been reached on the most effective approach to remove nuisance signals without unduly affecting the network intrinsic structural features. Here, we use a novel information-theoretic approach, based on von Neumann entropy, which provides a measure of information encoded in the networks at different scales. We also define a measure of distance between networks, based on information divergence, and optimal null models appropriate for the description of functional connectivity networks, to test for the presence of nontrivial structural patterns that are not the result of simple local constraints. This formalism enables a scale-resolved analysis of the distance between a functional connectivity network and its maximally random counterpart, thus providing a means to assess the effects of noise and image processing on network structure. We apply this novel approach to address a few open questions in the analysis of brain functional connectivity networks. Specifically, we demonstrate a strongly beneficial effect of network sparsification by removal of the weakest links, and the existence of an optimal threshold that maximizes the ability to extract information on large-scale network structures. Additionally, we investigate the effects of different degrees of motion at different scales, and compare the most popular processing pipelines designed to mitigate its deleterious effect on functional connectivity networks. We show that network sparsification, in combination with motion correction algorithms, dramatically improves detection of large scale network structure.

Community detection in weighted brain connectivity networks beyond the resolution limit.

Graph theory provides a powerful framework to investigate brain functional connectivity networks and their modular organization. However, most graph-based methods suffer from a fundamental resolution limit that may have affected previous studies and prevented detection of modules, or "communities", that are smaller than a specific scale. Surprise, a resolution-limit-free function rooted in discrete probability theory, has been recently introduced and applied to brain networks, revealing a wide size-distribution of functional modules (Nicolini and Bifone, 2016), in contrast with many previous reports. However, the use of Surprise is limited to binary networks, while brain networks are intrinsically weighted, reflecting a continuous distribution of connectivity strengths between different brain regions. Here, we propose Asymptotical Surprise, a continuous version of Surprise, for the study of weighted brain connectivity networks, and validate this approach in synthetic networks endowed with a ground-truth modular structure. We compare Asymptotical Surprise with leading community detection methods currently in use and show its superior sensitivity in the detection of small modules even in the presence of noise and intersubject variability such as those observed in fMRI data. We apply our novel approach to functional connectivity networks from resting state fMRI experiments, and demonstrate a heterogeneous modular organization, with a wide distribution of clusters spanning multiple scales. Finally, we discuss the implications of these findings for the identification of connector hubs, the brain regions responsible for the integration of the different network elements, showing that the improved resolution afforded by Asymptotical Surprise leads to a different classification compared to current methods.

Statistical physics of complex information dynamics.

The constituents of a complex system exchange information to function properly. Their signaling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange has been widely modeled by means of distinct spreading processes-such as continuous-time diffusion, random walks, synchronization and consensus-on top of complex networks, a unified and physically grounded framework to study information dynamics and gain insights about the macroscopic effects of microscopic interactions is still eluding us. In this paper, we present this framework in terms of a statistical field theory of information dynamics, unifying a range of dynamical processes governing the evolution of information on top of static or time-varying structures. We show that information operators form a meaningful statistical ensemble and their superposition defines a density matrix that can be used for the analysis of complex dynamics. As a direct application, we show that the von Neumann entropy of the ensemble can be a measure of the functional diversity of complex systems, defined in terms of the functional differentiation of higher-order interactions among their components. Our results suggest that modularity and hierarchy, two key features of empirical complex systems-from the human brain to social and urban networks-play a key role to guarantee functional diversity and, consequently, are favored.

Apomorphine-induced reorganization of striato-frontal connectivity in patients with tremor-dominant Parkinson's disease.

INTRODUCTION: Apomorphine is a dopamine agonist used in Parkinson's disease (PD), which matches levodopa in terms of the magnitude of effect on the cardinal motor features, such as tremor and bradykinesia. The beneficial effect of this treatment on PD patients with tremor-dominant has widely been demonstrated, although the underlying neural correlates are unknown. We sought to examine the effects of apomorphine on topological characteristics of resting-state functional connectivity networks in tremor-dominant PD (tdPD) patients. METHODS: Sixteen tdPD patients were examined using a combined electromyography-functional magnetic resonance imaging approach. Patients were scanned twice following either placebo (subcutaneous injection of 1 mL saline solution) or 1 mg of apomorphine injection. Graph analysis methods were employed to investigate the modular organization of functional connectivity networks before and after drug treatment. RESULTS: After injection of apomorphine, evident reduction of tremor symptoms was mirrored by a significant increase in overall connectivity strength and reorganization of the modular structure of the basal ganglia and of the fronto-striatal module. Moreover, we found an increase in the centrality of motor and premotor regions. No differences were found between pre- and post-placebo sessions. CONCLUSION: These results provide new evidence about the effects of apomorphine at a large-scale neural network level showing that drug treatment modifies the brain functional organization of tdPD, increasing the overall resting-state functional connectivity strength, the segregation of striato-frontal regions and the integrative role of motor areas.

Thermodynamics of network model fitting with spectral entropies.

An information-theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does not rely on specific topological features or network descriptors but leverages entropy-based measures of network distance. Entertaining the analogy with thermodynamics, we provide a physical interpretation of model hyperparameters and propose analytical procedures for their estimate. These results enable the practical application of this novel and powerful framework to network model inference. We demonstrate this method in synthetic networks endowed with a modular structure and in real-world brain connectivity networks.

Disrupted modular organization of primary sensory brain areas in schizophrenia.

Abnormal brain resting-state functional connectivity has been consistently observed in patients affected by schizophrenia (SCZ) using functional MRI and other neuroimaging techniques. Graph theoretical methods provide a framework to investigate these defective functional interactions and their effects on the organization of brain connectivity networks. A few studies have shown altered distribution of connectivity within and between functional modules in SCZ patients, an indication of imbalanced functional segregation ad integration. However, no major alterations of modular organization have been reported in patients, and unambiguous identification of the neural substrates affected remains elusive. Recently, it has been demonstrated that current modularity analysis methods suffer from a fundamental and severe resolution limit, as they fail to detect features that are smaller than a scale determined by the size of the entire connectivity network. This resolution limit is likely to have hampered the ability to resolve differences between patients and controls in previous studies. Here, we apply Surprise, a novel resolution limit-free approach, to study the modular organization of resting state functional connectivity networks in a large cohort of SCZ patients and in matched healthy controls. Leveraging these important methodological advances we find new evidence of substantial fragmentation and reorganization involving primary sensory, auditory and visual areas in SCZ patients. Conversely, frontal and prefrontal areas, typically associated with higher cognitive functions, appear to be largely unaffected, with changes selectively involving language and speech processing areas. Our findings support the hypothesis that cognitive dysfunction in SCZ may involve deficits occurring already at early stages of sensory processing.

Graph Analysis and Modularity of Brain Functional Connectivity Networks: Searching for the Optimal Threshold.

Neuroimaging data can be represented as networks of nodes and edges that capture the topological organization of the brain connectivity. Graph theory provides a general and powerful framework to study these networks and their structure at various scales. By way of example, community detection methods have been widely applied to investigate the modular structure of many natural networks, including brain functional connectivity networks. Sparsification procedures are often applied to remove the weakest edges, which are the most affected by experimental noise, and to reduce the density of the graph, thus making it theoretically and computationally more tractable. However, weak links may also contain significant structural information, and procedures to identify the optimal tradeoff are the subject of active research. Here, we explore the use of percolation analysis, a method grounded in statistical physics, to identify the optimal sparsification threshold for community detection in brain connectivity networks. By using synthetic networks endowed with a ground-truth modular structure and realistic topological features typical of human brain functional connectivity networks, we show that percolation analysis can be applied to identify the optimal sparsification threshold that maximizes information on the networks' community structure. We validate this approach using three different community detection methods widely applied to the analysis of brain connectivity networks: Newman's modularity, InfoMap and Asymptotical Surprise. Importantly, we test the effects of noise and data variability, which are critical factors to determine the optimal threshold. This data-driven method should prove particularly useful in the analysis of the community structure of brain networks in populations characterized by different connectivity strengths, such as patients and controls.

Modular structure of brain functional networks: breaking the resolution limit by Surprise.

The modular organization of brain networks has been widely investigated using graph theoretical approaches. Recently, it has been demonstrated that graph partitioning methods based on the maximization of global fitness functions, like Newman's Modularity, suffer from a resolution limit, as they fail to detect modules that are smaller than a scale determined by the size of the entire network. Here we explore the effects of this limitation on the study of brain connectivity networks. We demonstrate that the resolution limit prevents detection of important details of the brain modular structure, thus hampering the ability to appreciate differences between networks and to assess the topological roles of nodes. We show that Surprise, a recently proposed fitness function based on probability theory, does not suffer from these limitations. Surprise maximization in brain co-activation and functional connectivity resting state networks reveals the presence of a rich structure of heterogeneously distributed modules, and differences in networks' partitions that are undetectable by resolution-limited methods. Moreover, Surprise leads to a more accurate identification of the network's connector hubs, the elements that integrate the brain modules into a cohesive structure.