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IntroductionMajor depressive disorder with suicidal ideation (MDD/SI+) is characterized by high prevalence, high recurrence rate, high disability rate and low response rate. There is an urgent need for clarifying the pathogenesis and developing novel treatment methods.MethodsSubjects were recruited for the collection of Magnetic Resonance Imaging data and clinical scales. Individual target-transcranial magnetic stimulation (IT-TMS) using Stanford Neuromodulation Therapy over individualized left dorsolateral prefrontal cortex was performed to treat MDD/SI+ with the ethical approval (KY20212218-C-1). GRETNA software was used to analyze brain network characteristics according to graph theory.ResultsA total of 32 patients (aged 18-55) and 28 healthy controls (aged 20-51) had been recruited. Patients after IT-TMS treatment had significant reduction in suicidal ideation and depressive symptom. The functional network of all three groups conformed to small-world topology. There was a renormalization in topology structure after IT-TMS treatment. Decreased functional connectivity between right insula and left anterior cingulate gyrus correlated with improvement in Beck Scale for Suicide Ideation scores.DiscussionThe current study highlights that MDD/SI+ patients in this cohort showed abnormal brain network connections compared to healthy controls, and that IT-TMS may exert its treatment effects by reducing spontaneous hyper-connectivity in the salience network and insula.

Covering neuroimaging evidence has demonstrated that epileptic symptoms are associated with the disrupted topological architecture of the brain network. Infantile spasms (IS) as an age-specific epileptic encephalopathy also showed abnormal structural or functional connectivity in specific brain regions or specific networks. However, little is known about the topological alterations of whole-brain functional networks in patients with IS. To fill this gap, we used the graph theoretical analysis to investigate the topological properties (whole-brain small-world property and modular interaction) in 17 patients with IS and 34 age- and gender-matched healthy controls. The functional networks in both groups showed efficient small-world architecture over the sparsity range from 0.05 to 0.4. While patients with IS showed abnormal global properties characterized by significantly decreased normalized clustering coefficient, normalized path length, small-worldness, local efficiency, and significantly increased global efficiency, implying a shift toward a randomized network. Modular analysis revealed decreased intramodular connectivity within the default mode network (DMN) and frontoparietal network but increased inter-modular connectivity between the cingulo-opercular network and occipital network. Moreover, the decreased intra-modular connectivity in DMN was significantly negatively correlated with seizure frequency. The inter-modular connectivity between the cinguloopercular and occipital network also showed a significant correlation with epilepsy frequency. Together, the current study revealed the disrupted topological organization of the whole-brain functional network, which greatly advances our understanding of neuronal architecture in IS and may contribute to predict the prognosis of IS as disease biomarkers. [ABSTRACT FROM AUTHOR]

Frontotemporal dementia (FTD) is a spectrum of clinical syndromes that affects personality, behavior, language, and cognition. The current diagnostic criteria recognize three main clinical subtypes: the behavioral variant of FTD (bvFTD), the semantic variant of primary progressive aphasia (svPPA), and the non-fluent/agrammatic variant of PPA (nfvPPA). Patients with FTD display heterogeneous clinical and neuropsychological features that highly overlap with those presented by psychiatric syndromes and other types of dementia. Moreover, up to now there are no reliable disease biomarkers, which makes the diagnosis of FTD particularly challenging. To overcome this issue, different studies have adopted metrics derived from magnetic resonance imaging (MRI) to characterize structural and functional brain abnormalities. Within this field, a growing body of scientific literature has shown that graph theory analysis applied to MRI data displays unique potentialities in unveiling brain network abnormalities of FTD subtypes. Here, we provide a critical overview of studies that adopted graph theory to examine the topological changes of large-scale brain networks in FTD. Moreover, we also discuss the possible role of information arising from brain network organization in the diagnostic algorithm of FTD-spectrum disorders and in investigating the neural correlates of clinical symptoms and cognitive deficits experienced by patients. [ABSTRACT FROM AUTHOR]

Frontotemporal dementia (FTD) is a spectrum of clinical syndromes that affects personality, behavior, language, and cognition. The current diagnostic criteria recognize three main clinical subtypes: the behavioral variant of FTD (bvFTD), the semantic variant of primary progressive aphasia (svPPA), and the non-fluent/agrammatic variant of PPA (nfvPPA). Patients with FTD display heterogeneous clinical and neuropsychological features that highly overlap with those presented by psychiatric syndromes and other types of dementia. Moreover, up to now there are no reliable disease biomarkers, which makes the diagnosis of FTD particularly challenging. To overcome this issue, different studies have adopted metrics derived from magnetic resonance imaging (MRI) to characterize structural and functional brain abnormalities. Within this field, a growing body of scientific literature has shown that graph theory analysis applied to MRI data displays unique potentialities in unveiling brain network abnormalities of FTD subtypes. Here, we provide a critical overview of studies that adopted graph theory to examine the topological changes of large-scale brain networks in FTD. Moreover, we also discuss the possible role of information arising from brain network organization in the diagnostic algorithm of FTD-spectrum disorders and in investigating the neural correlates of clinical symptoms and cognitive deficits experienced by patients.

Background: The efficacy and prognosis of major depressive disorder (MDD) are limited by its heterogeneity. MDD with melancholic features is an important subtype of MDD. The present study aimed to reveal the white matter (WM) network changes in melancholic depression. Materials and Methods: Twenty-three first-onset, untreated melancholic MDD, 59 non-melancholic MDD patients and 63 health controls underwent diffusion tensor imaging (DTI) scans. WM network analysis based on graph theory and support vector machine (SVM) were used for image data analysis. Results: Compared with HC, small-worldness was reduced and abnormal node attributes were in the right orbital inferior frontal gyrus, left orbital superior frontal gyrus, right caudate nucleus, right orbital superior frontal gyrus, right orbital middle frontal gyrus, left rectus gyrus, and left median cingulate and paracingulate gyrus of MDD patients. Compared with non-melancholic MDD, small-worldness was reduced and abnormal node attributes were in right orbital inferior frontal gyrus, left orbital superior frontal gyrus and right caudate nucleus of melancholic MDD. For correlation analysis, the 7th item score of the HRSD-17 (work and interest) was positively associated with increased node betweenness centrality (aBC) values in right orbital inferior frontal gyrus, while negatively associated with the decreased aBC in left orbital superior frontal gyrus. SVM analysis results showed that abnormal aBC in right orbital inferior frontal gyrus and left orbital superior frontal gyrus showed the highest accuracy of 81.0% (69/83), the sensitivity of 66.3%, and specificity of 85.2% for discriminating MDD patients with or without melancholic features. Conclusion: There is a significant difference in WM network changes between MDD patients with and without melancholic features. [ABSTRACT FROM AUTHOR]

BackgroundThe efficacy and prognosis of major depressive disorder (MDD) are limited by its heterogeneity. MDD with melancholic features is an important subtype of MDD. The present study aimed to reveal the white matter (WM) network changes in melancholic depression.Materials and MethodsTwenty-three first-onset, untreated melancholic MDD, 59 non-melancholic MDD patients and 63 health controls underwent diffusion tensor imaging (DTI) scans. WM network analysis based on graph theory and support vector machine (SVM) were used for image data analysis.ResultsCompared with HC, small-worldness was reduced and abnormal node attributes were in the right orbital inferior frontal gyrus, left orbital superior frontal gyrus, right caudate nucleus, right orbital superior frontal gyrus, right orbital middle frontal gyrus, left rectus gyrus, and left median cingulate and paracingulate gyrus of MDD patients. Compared with non-melancholic MDD, small-worldness was reduced and abnormal node attributes were in right orbital inferior frontal gyrus, left orbital superior frontal gyrus and right caudate nucleus of melancholic MDD. For correlation analysis, the 7th item score of the HRSD-17 (work and interest) was positively associated with increased node betweenness centrality (aBC) values in right orbital inferior frontal gyrus, while negatively associated with the decreased aBC in left orbital superior frontal gyrus. SVM analysis results showed that abnormal aBC in right orbital inferior frontal gyrus and left orbital superior frontal gyrus showed the highest accuracy of 81.0% (69/83), the sensitivity of 66.3%, and specificity of 85.2% for discriminating MDD patients with or without melancholic features.ConclusionThere is a significant difference in WM network changes between MDD patients with and without melancholic features.

Node centrality measures are among the most commonly used analytical techniques for networks. They have long helped analysts to identify “important” nodes that hold power in a social context, where damages could have dire consequences for transportation applications, or who should be a focus for prevention in epidemiology. Given the ubiquity of network data, new measures have been proposed, occasionally motivated by emerging applications or by the ability to interpolate existing measures. Before analysts use these measures and interpret results, the fundamental question is: are these measures likely to complete within the time window allotted to the analysis? In this paper, we comprehensively examine how the time necessary to run 18 new measures (introduced from 2005 to 2020) scales as a function of the number of nodes in the network. Our focus is on giving analysts a simple and practical estimate for sparse networks. As the time consumption depends on the properties in the network, we nuance our analysis by considering whether the network is scale-free, small-world, or random. Our results identify that several metrics run in the order of O(nlogn) and could scale to large networks, whereas others can require O(n2) or O(n3) and may become prime targets in future works for approximation algorithms or distributed implementations.

The human brain contains billions of neurons that flexibly interconnect to support local and global computational spans. As neuronal activity propagates through the neural medium, it approaches a critical state hedged between ordered and disordered system regimes. Recent work demonstrates that this criticality coincides with the small-world topology, a network arrangement that accommodates both local (subcritical) and global (supercritical) system properties. On one hand, operating near criticality is thought to offer several neurocomputational advantages, e.g., high-dynamic range, efficient information capacity, and information transfer fidelity. On the other hand, aberrations from the critical state have been linked to diverse pathologies of the brain, such as post-traumatic epileptiform seizures and disorders of consciousness. Modulation of brain activity, through neuromodulation, presents an attractive mode of treatment to alleviate such neurological disorders, but a tractable neural framework is needed to facilitate clinical progress. Using a variation on the generative small-world model of Watts and Strogatz and Kuramoto's model of coupled oscillators, we show that the topological and dynamical properties of the small-world network are divided into two functional domains based on the range of connectivity, and that these domains play distinct roles in shaping the behavior of the critical state. We demonstrate that short-range network connections shape the dynamics of the system, e.g., its volatility and metastability, whereas long-range connections drive the system state, e.g., a seizure. Together, these findings lend support to combinatorial neuromodulation approaches that synergistically normalize the system dynamic while mobilizing the system state.

The human brain contains billions of neurons that flexibly interconnect to support local and global computational spans. As neuronal activity propagates through the neural medium, it approaches a critical state hedged between ordered and disordered system regimes. Recent work demonstrates that this criticality coincides with the small-world topology, a network arrangement that accommodates both local (subcritical) and global (supercritical) system properties. On one hand, operating near criticality is thought to offer several neurocomputational advantages, e.g., high-dynamic range, efficient information capacity, and information transfer fidelity. On the other hand, aberrations from the critical state have been linked to diverse pathologies of the brain, such as post-traumatic epileptiform seizures and disorders of consciousness. Modulation of brain activity, through neuromodulation, presents an attractive mode of treatment to alleviate such neurological disorders, but a tractable neural framework is needed to facilitate clinical progress. Using a variation on the generative small-world model of Watts and Strogatz and Kuramoto's model of coupled oscillators, we show that the topological and dynamical properties of the small-world network are divided into two functional domains based on the range of connectivity, and that these domains play distinct roles in shaping the behavior of the critical state. We demonstrate that short-range network connections shape the dynamics of the system, e.g., its volatility and metastability, whereas long-range connections drive the system state, e.g., a seizure. Together, these findings lend support to combinatorial neuromodulation approaches that synergistically normalize the system dynamic while mobilizing the system state. [ABSTRACT FROM AUTHOR]

Aneurysmal subarachnoid hemorrhage (aSAH) is a common disease causing vascular dementia. Survivors often suffer from cognitive impairment especially working memory deficit. Currently, lack of theoretical support limits the improvement of cognitive intervention or rehabilitation. It is unclear how the large-scale network differs and to what extent is the brain network affected? Our study aims to provide novel information about the topological characteristics of brain organization, especially “small-world” property. A total of 62 aSAH patients are enrolled in this study. They are divided into two groups according to the syndrome of working memory deficit. Their working memory function is evaluated by TMT-B and AVLT (Chinese version). Functional MRI scan is also performed for detecting resting-state cortical plasticity. We utilized ICA to extract functional sub-networks including working memory network from imaging data. And then we establish binarized network and calculate the small-worldness property as well as local and global efficiency of networks. aSAH group with working memory deficit shows no significant difference of clustering coefficient with control group. Our study discovered significant decrease of characteristic path length indicating an increase of overall routing efficiency. We reason that patients with working memory deficit have to recruit more neuronal resources and thus develops higher overall routing efficiency of local network. This study provides novel information about the neural alterations of aSAH patients with working memory deficit. It might contribute to the understanding of neural mechanism and the improvement of current intervention for vascular dementia.

Microvascular complications can accelerate cognitive impairment in patients with type 2 diabetes mellitus (T2DM) and have a high impact on their quality of life; however, the underlying mechanism is still unclear. The complex network in the human brain is the physiological basis for information processing and cognitive expression. Therefore, this study explored the relationship between the functional network topological properties and cognitive function in T2DM patients with and without microvascular complications (T2DM-C and T2DM-NC, respectively). Sixty-seven T2DM patients and 41 healthy controls (HCs) underwent resting-state functional MRI and neuropsychological assessment. Then, graph theoretical network analysis was performed to explore the global and nodal topological alterations in the functional whole brain networks of T2DM patients. Correlation analyses were performed to investigate the relationship between the altered topological parameters and cognitive/clinical variables. The T2DM-C group exhibited significantly higher local efficiency (Eloc), normalized cluster coefficient (γ), and small-world characteristics (σ) than the HCs. Patients with T2DM at different clinical stages (T2DM-C and T2DM-NC) showed varying degrees of abnormalities in node properties. In addition, compared with T2DM-NC patients, T2DM-C patients showed nodal properties disorders in the occipital visual network, cerebellum and middle temporal gyrus. The Eloc metrics were positively correlated with HbA1c level (P = 0.001, r = 0.515) and the NE values in the right paracentral lobule were negatively related with serum creatinine values (P = 0.001, r = −0.517) in T2DM-C patients. This study found that T2DM-C patients displayed more extensive changes at different network topology scales. The visual network and cerebellar may be the central vulnerable regions of T2DM-C patients.

Mild behavioral impairment (MBI), characterized by the late-life onset of sustained and meaningful neuropsychiatric symptoms, is increasingly recognized as a prodromal stage of dementia. However, the underlying neural mechanisms of MBI remain unclear. Here, we examined alterations in the topological organization of the structural covariance networks of patients with MBI (N = 32) compared with normal controls (N = 38). We found that the gray matter structural covariance networks of both the patients with MBI and controls exhibited a small-world topology evidenced by sigma value larger than one. The patients with MBI had significantly decreased clustering coefficients at several network densities and local efficiency at densities ranging from 0.05 to 0.26, indicating decreased local segregation. No significant differences in the characteristic path length, gamma value, sigma value, or global efficiency were detected. Locally, the patients with MBI showed significantly decreased nodal betweenness centrality in the left middle frontal gyrus, right inferior frontal gyrus (opercular part), and left Heschl gyrus and increased betweenness centrality in the left gyrus rectus, right insula, bilateral precuneus, and left thalamus. Moreover, the difference in the bilateral precuneus survived after correcting for multiple comparisons. In addition, a different number and distribution of hubs was identified in patients with MBI, showing more paralimbic hubs than observed in the normal controls. In conclusion, we revealed abnormal topological patterns of the structural covariance networks in patients with MBI and offer new insights into the network dysfunctional mechanisms of MBI.

Aneurysmal subarachnoid hemorrhage (aSAH) is a common disease causing vascular dementia. Survivors often suffer from cognitive impairment especially working memory deficit. Currently, lack of theoretical support limits the improvement of cognitive intervention or rehabilitation. It is unclear how the large-scale network differs and to what extent is the brain network affected? Our study aims to provide novel information about the topological characteristics of brain organization, especially "small-world" property. A total of 62 aSAH patients are enrolled in this study. They are divided into two groups according to the syndrome of working memory deficit. Their working memory function is evaluated by TMT-B and AVLT (Chinese version). Functional MRI scan is also performed for detecting resting-state cortical plasticity. We utilized ICA to extract functional sub-networks including working memory network from imaging data. And then we establish binarized network and calculate the small-worldness property as well as local and global efficiency of networks. aSAH group with working memory deficit shows no significant difference of clustering coefficient with control group. Our study discovered significant decrease of characteristic path length indicating an increase of overall routing efficiency. We reason that patients with working memory deficit have to recruit more neuronal resources and thus develops higher overall routing efficiency of local network. This study provides novel information about the neural alterations of aSAH patients with working memory deficit. It might contribute to the understanding of neural mechanism and the improvement of current intervention for vascular dementia. [ABSTRACT FROM AUTHOR]

Mild behavioral impairment (MBI), characterized by the late-life onset of sustained and meaningful neuropsychiatric symptoms, is increasingly recognized as a prodromal stage of dementia. However, the underlying neural mechanisms of MBI remain unclear. Here, we examined alterations in the topological organization of the structural covariance networks of patients with MBI (N = 32) compared with normal controls (N = 38). We found that the gray matter structural covariance networks of both the patients with MBI and controls exhibited a small-world topology evidenced by sigma value larger than one. The patients with MBI had significantly decreased clustering coefficients at several network densities and local efficiency at densities ranging from 0.05 to 0.26, indicating decreased local segregation. No significant differences in the characteristic path length, gamma value, sigma value, or global efficiency were detected. Locally, the patients with MBI showed significantly decreased nodal betweenness centrality in the left middle frontal gyrus, right inferior frontal gyrus (opercular part), and left Heschl gyrus and increased betweenness centrality in the left gyrus rectus, right insula, bilateral precuneus, and left thalamus. Moreover, the difference in the bilateral precuneus survived after correcting for multiple comparisons. In addition, a different number and distribution of hubs was identified in patients with MBI, showing more paralimbic hubs than observed in the normal controls. In conclusion, we revealed abnormal topological patterns of the structural covariance networks in patients with MBI and offer new insights into the network dysfunctional mechanisms of MBI. [ABSTRACT FROM AUTHOR]

Microvascular complications can accelerate cognitive impairment in patients with type 2 diabetes mellitus (T2DM) and have a high impact on their quality of life; however, the underlying mechanism is still unclear. The complex network in the human brain is the physiological basis for information processing and cognitive expression. Therefore, this study explored the relationship between the functional network topological properties and cognitive function in T2DM patients with and without microvascular complications (T2DM-C and T2DM-NC, respectively). Sixty-seven T2DM patients and 41 healthy controls (HCs) underwent resting-state functional MRI and neuropsychological assessment. Then, graph theoretical network analysis was performed to explore the global and nodal topological alterations in the functional whole brain networks of T2DM patients. Correlation analyses were performed to investigate the relationship between the altered topological parameters and cognitive/clinical variables. The T2DM-C group exhibited significantly higher local efficiency (Eloc), normalized cluster coefficient (γ), and small-world characteristics (σ) than the HCs. Patients with T2DM at different clinical stages (T2DM-C and T2DM-NC) showed varying degrees of abnormalities in node properties. In addition, compared with T2DM-NC patients, T2DM-C patients showed nodal properties disorders in the occipital visual network, cerebellum and middle temporal gyrus. The Eloc metrics were positively correlated with HbA1c level (P = 0.001, r = 0.515) and the NE values in the right paracentral lobule were negatively related with serum creatinine values (P = 0.001, r = −0.517) in T2DM-C patients. This study found that T2DM-C patients displayed more extensive changes at different network topology scales. The visual network and cerebellar may be the central vulnerable regions of T2DM-C patients. [ABSTRACT FROM AUTHOR]

Equilibrium propagation is a learning framework that marks a step forward in the search for a biologically-plausible implementation of deep learning, and could be implemented efficiently in neuromorphic hardware. Previous applications of this framework to layered networks encountered a vanishing gradient problem that has not yet been solved in a simple, biologically-plausible way. In this paper, we demonstrate that the vanishing gradient problem can be mitigated by replacing some of a layered network's connections with random layer-skipping connections in a manner inspired by small-world networks. This approach would be convenient to implement in neuromorphic hardware, and is biologically-plausible.

Equilibrium propagation is a learning framework that marks a step forward in the search for a biologically-plausible implementation of deep learning, and could be implemented efficiently in neuromorphic hardware. Previous applications of this framework to layered networks encountered a vanishing gradient problem that has not yet been solved in a simple, biologically-plausible way. In this paper, we demonstrate that the vanishing gradient problem can be mitigated by replacing some of a layered network's connections with random layer-skipping connections in a manner inspired by small-world networks. This approach would be convenient to implement in neuromorphic hardware, and is biologically-plausible. [ABSTRACT FROM AUTHOR]

Modern network science has provided exciting new opportunities for understanding the human brain as a complex network of interacting regions. The improved knowledge of human brain network architecture has made it possible for clinicians to detect the network changes in neurological diseases. Generalized tonic–clonic seizure (GTCS) is a subtype of epilepsy characterized by generalized spike-wave discharge involving the bilateral hemispheres during seizure. Network researches in adults with GTCS exhibited that GTCS can be conceptualized as a network disorder. However, the overall organization of the brain structural covariance network in children with GTCS remains largely unclear. Here, we used a graph theory method to assess the gray matter structural covariance network organization of 14 pediatric patients diagnosed with GTCS and 29 healthy control children. The group differences in regional and global topological properties were investigated. Results revealed significant changes in nodal betweenness locating in brain regions known to be abnormal in GTCS (the right thalamus, bilateral temporal pole, and some regions of default mode network). The network hub analysis results were in accordance with the regional betweenness, which presented a disrupted regional topology of structural covariance network in children with GTCS. To our knowledge, the present study is the first work reporting the changes of structural topological properties in children with GTCS. The findings contribute new insights into the understanding of the neural mechanisms underlying GTCS and highlight critical regions for future neuroimaging research in children with GTCS.

Modern network science has provided exciting new opportunities for understanding the human brain as a complex network of interacting regions. The improved knowledge of human brain network architecture has made it possible for clinicians to detect the network changes in neurological diseases. Generalized tonic–clonic seizure (GTCS) is a subtype of epilepsy characterized by generalized spike-wave discharge involving the bilateral hemispheres during seizure. Network researches in adults with GTCS exhibited that GTCS can be conceptualized as a network disorder. However, the overall organization of the brain structural covariance network in children with GTCS remains largely unclear. Here, we used a graph theory method to assess the gray matter structural covariance network organization of 14 pediatric patients diagnosed with GTCS and 29 healthy control children. The group differences in regional and global topological properties were investigated. Results revealed significant changes in nodal betweenness locating in brain regions known to be abnormal in GTCS (the right thalamus, bilateral temporal pole, and some regions of default mode network). The network hub analysis results were in accordance with the regional betweenness, which presented a disrupted regional topology of structural covariance network in children with GTCS. To our knowledge, the present study is the first work reporting the changes of structural topological properties in children with GTCS. The findings contribute new insights into the understanding of the neural mechanisms underlying GTCS and highlight critical regions for future neuroimaging research in children with GTCS. [ABSTRACT FROM AUTHOR]

Sleep is a complex and dynamic process for maintaining homeostasis, and a lack of sleep can disrupt whole-body functioning. No organ is as vulnerable to the loss of sleep as the brain. Accordingly, we examined a set of task-based functional magnetic resonance imaging (fMRI) data by using graph theory to assess brain topological changes in subjects in a state of chronic sleep restriction, and then identified diurnal variability in the graph-theoretic measures. Task-based fMRI data were collected in a 1.5T MR scanner from the same participants on two days: after a week of fully restorative sleep and after a week with 35% sleep curtailment. Each day included four scanning sessions throughout the day (at approximately 10:00 AM, 2:00 PM, 6:00 PM, and 10:00 PM). A modified spatial cueing task was applied to evaluate sustained attention. After sleep restriction, the characteristic path length significantly increased at all measurement times, and small-worldness significantly decreased. Assortativity, a measure of network fault tolerance, diminished over the course of the day in both conditions. Local graph measures were altered primarily across the limbic system (particularly in the hippocampus, parahippocampal gyrus, and amygdala), default mode network, and visual network.

There is a pressing need to further our understanding of the mechanisms underlying the depression symptoms in patients with post-stroke depression (PSD) in order to inform targeted therapeutic approaches. While previous research has demonstrated a reorganization in the functional brain network of PSD, it remains uncertain whether, or not it also occurs in the structural brain network. We therefore aim to investigate the structural brain network of patients with PSD as compared to post-stroke non-depression (PSND) patients. In addition, our research considers the relationship between network metrics and functional measurements. Thirty-one PSD patients and twenty-three PSND patients were recruited. All patients underwent MRI and functional assessments, including the Barthel index, mini-mental state examination (MMSE), and Hamilton depression rating scale (HAMD). Diffusion tensor imaging was used to construct the structural brain network and to conduct the subsequent graph theoretical analysis. Network measures were computed and compared between PSD and PSND patients. Associations between functional assessments and network measures were studied as well. We successfully detected increased global and local efficiency in patients with PSD. Regions with disrupted local connections were located primarily in the cognitive and limbic systems. More importantly, PSD patients’ global and regional network measures were associated with depression severity, as measured by HAMD. These findings suggest that disrupted global and local network topologies might contribute to PSD patients’ depression symptoms. Therefore, connectome-based network measures could be potential bio-markers for evaluating stroke patients’ depression levels.

BackgroundPrevious diabetes mellitus studies of cognitive impairments in the early stages have focused on changes in brain structure and function, and more recently the focus has shifted to the relationships between encephalic regions and diversification of network topology. However, studies examining network topology in diabetic brain function are still limited.MethodsThe study included 102 subjects; 55 type 2 diabetes mellitus (T2DM) patients plus 47 healthy controls. All subjects were examined by resting-state functional magnetic resonance imaging (rs-fMRI) scan. According to Automated Anatomical Labeling, the brain was divided into 90 anatomical regions, and every region corresponds to a brain network analysis node. The whole brain functional network was constructed by thresholding the correlation matrices of the 90 brain regions, and the topological properties of the network were computed based on graph theory. Then, the topological properties of the network were compared between different groups by using a non-parametric test. Finally, the associations between differences in topological properties and the clinical indicators were analyzed.ResultsThe brain functional networks of both T2DM patients and healthy controls were found to possess small-world characteristics, i.e., normalized clustering coefficient (γ) > 1, and normalized characteristic path length (λ) close to 1. No significant differences were found in the small-world characteristics (σ). Second, the T2DM patient group displayed significant differences in node properties in certain brain regions. Correlative analytic results showed that the node degree of the right inferior temporal gyrus (ITG) and the node efficiencies of the right ITG and superior temporal gyrus of T2DM patients were positively correlated with body mass index.ConclusionThe brain network of T2DM patients has the same small-world characteristics as normal people, but the normalized clustering coefficient is higher and the normalized characteristic path length is lower than that of the normal control group, indicating that the brain function network of the T2DM patients has changed. The changes of node properties were mostly concentrated in frontal lobe, temporal lobe and posterior cingulate gyrus. The abnormal changes in these indices in T2DM patients might be explained as a compensatory behavior to reduce cognitive impairments, which is achieved by mobilizing additional neural resources, such as the excessive activation of the network and the efficient networking of multiple brain regions.

Sleep is a complex and dynamic process for maintaining homeostasis, and a lack of sleep can disrupt whole-body functioning. No organ is as vulnerable to the loss of sleep as the brain. Accordingly, we examined a set of task-based functional magnetic resonance imaging (fMRI) data by using graph theory to assess brain topological changes in subjects in a state of chronic sleep restriction, and then identified diurnal variability in the graph-theoretic measures. Task-based fMRI data were collected in a 1.5T MR scanner from the same participants on two days: after a week of fully restorative sleep and after a week with 35% sleep curtailment. Each day included four scanning sessions throughout the day (at approximately 10:00 AM, 2:00 PM, 6:00 PM, and 10:00 PM). A modified spatial cueing task was applied to evaluate sustained attention. After sleep restriction, the characteristic path length significantly increased at all measurement times, and small-worldness significantly decreased. Assortativity, a measure of network fault tolerance, diminished over the course of the day in both conditions. Local graph measures were altered primarily across the limbic system (particularly in the hippocampus, parahippocampal gyrus, and amygdala), default mode network, and visual network. [ABSTRACT FROM AUTHOR]

There is a pressing need to further our understanding of the mechanisms underlying the depression symptoms in patients with post-stroke depression (PSD) in order to inform targeted therapeutic approaches. While previous research has demonstrated a reorganization in the functional brain network of PSD, it remains uncertain whether, or not it also occurs in the structural brain network. We therefore aim to investigate the structural brain network of patients with PSD as compared to post-stroke non-depression (PSND) patients. In addition, our research considers the relationship between network metrics and functional measurements. Thirty-one PSD patients and twenty-three PSND patients were recruited. All patients underwent MRI and functional assessments, including the Barthel index, mini-mental state examination (MMSE), and Hamilton depression rating scale (HAMD). Diffusion tensor imaging was used to construct the structural brain network and to conduct the subsequent graph theoretical analysis. Network measures were computed and compared between PSD and PSND patients. Associations between functional assessments and network measures were studied as well. We successfully detected increased global and local efficiency in patients with PSD. Regions with disrupted local connections were located primarily in the cognitive and limbic systems. More importantly, PSD patients' global and regional network measures were associated with depression severity, as measured by HAMD. These findings suggest that disrupted global and local network topologies might contribute to PSD patients' depression symptoms. Therefore, connectome-based network measures could be potential bio-markers for evaluating stroke patients' depression levels. [ABSTRACT FROM AUTHOR]

Background: Analysis of the human connectome using functional magnetic resonance imaging (fMRI) started in the mid-1990s and attracted increasing attention in attempts to discover the neural underpinnings of human cognition and neurological disorders. In general, brain connectivity patterns from fMRI data are classified as statistical dependencies (functional connectivity) or causal interactions (effective connectivity) among various neural units. Computational methods, especially graph theory-based methods, have recently played a significant role in understanding brain connectivity architecture. Objectives: Thanks to the emergence of graph theoretical analysis, the main purpose of the current paper is to systematically review how brain properties can emerge through the interactions of distinct neuronal units in various cognitive and neurological applications using fMRI. Moreover, this article provides an overview of the existing functional and effective connectivity methods used to construct the brain network, along with their advantages and pitfalls. Methods: In this systematic review, the databases Science Direct, Scopus, arXiv, Google Scholar, IEEE Xplore, PsycINFO, PubMed, and SpringerLink are employed for exploring the evolution of computational methods in human brain connectivity from 1990 to the present, focusing on graph theory. The Cochrane Collaboration's tool was used to assess the risk of bias in individual studies. Results: Our results show that graph theory and its implications in cognitive neuroscience have attracted the attention of researchers since 2009 (as the Human Connectome Project launched), because of their prominent capability in characterizing the behavior of complex brain systems. Although graph theoretical approach can be generally applied to either functional or effective connectivity patterns during rest or task performance, to date, most articles have focused on the resting-state functional connectivity. Conclusions: This review provides an insight into how to utilize graph theoretical measures to make neurobiological inferences regarding the mechanisms underlying human cognition and behavior as well as different brain disorders. [ABSTRACT FROM AUTHOR]

Background: Previous diabetes mellitus studies of cognitive impairments in the early stages have focused on changes in brain structure and function, and more recently the focus has shifted to the relationships between encephalic regions and diversification of network topology. However, studies examining network topology in diabetic brain function are still limited. Methods: The study included 102 subjects; 55 type 2 diabetes mellitus (T2DM) patients plus 47 healthy controls. All subjects were examined by resting-state functional magnetic resonance imaging (rs-fMRI) scan. According to Automated Anatomical Labeling, the brain was divided into 90 anatomical regions, and every region corresponds to a brain network analysis node. The whole brain functional network was constructed by thresholding the correlation matrices of the 90 brain regions, and the topological properties of the network were computed based on graph theory. Then, the topological properties of the network were compared between different groups by using a non-parametric test. Finally, the associations between differences in topological properties and the clinical indicators were analyzed. Results: The brain functional networks of both T2DM patients and healthy controls were found to possess small-world characteristics, i.e., normalized clustering coefficient (γ) > 1, and normalized characteristic path length (λ) close to 1. No significant differences were found in the small-world characteristics (σ). Second, the T2DM patient group displayed significant differences in node properties in certain brain regions. Correlative analytic results showed that the node degree of the right inferior temporal gyrus (ITG) and the node efficiencies of the right ITG and superior temporal gyrus of T2DM patients were positively correlated with body mass index. Conclusion: The brain network of T2DM patients has the same small-world characteristics as normal people, but the normalized clustering coefficient is higher and the normalized characteristic path length is lower than that of the normal control group, indicating that the brain function network of the T2DM patients has changed. The changes of node properties were mostly concentrated in frontal lobe, temporal lobe and posterior cingulate gyrus. The abnormal changes in these indices in T2DM patients might be explained as a compensatory behavior to reduce cognitive impairments, which is achieved by mobilizing additional neural resources, such as the excessive activation of the network and the efficient networking of multiple brain regions. [ABSTRACT FROM AUTHOR]

Background: Recent studies have reported altered efficiency in selective brain regions and functional networks in patients with alcohol use disorder (AUD). Inefficient processing can reflect or arise from the disorganization of information being conveyed from place to place. However, it remains unknown whether the efficiency and functional connectivity are altered in large-scale topological organization of patients with AUD.Methods: Resting-state functional magnetic resonance imaging (rsfMRI) data were experimentally collected from 21 right-handed males with AUD and 21 right-handed, age-, gender- and education-matched healthy controls (HCs). Graph theory was used to investigate inter-group differences in the topological parameters (global and nodal) of networks and inter-regional functional connectivity. Correlations between group differences in network properties and clinical variables were also investigated in the AUD group.Results: The brain networks of the AUD group showed decreased global efficiency when compared with the HC group. Besides, increased nodal efficiency was found in the left orbitofrontal cortex (OFC), while reduced nodal efficiency was observed in the right OFC, right fusiform gyrus (FFG), right superior temporal gyrus, right inferior occipital gyrus (IOG), and left insula. Moreover, hypo-connectivity was detected between the right dorsolateral prefrontal cortex (DLPFC) and right superior occipital gyrus (SOG) in the AUD group when compared with the HC group. The nodal efficiency of the left OFC was associated with cognitive performance in the AUD group.Conclusions: AUD patients exhibited alterations in brain network efficiency and functional connectivity, particularly in regions linked to multi-sensory modalities. These disrupted topological properties may help to obtain a more comprehensive understanding of large-scale brain network activity. Furthermore, these data provide a potential neural mechanism of impaired cognition in individuals with AUD.

Neuroimaging studies in children and adolescents with post-traumatic stress disorder (PTSD) have focused on abnormal structures and the functionality of a few individual brain regions. However, little is known about alterations to the topological organization of whole-brain functional networks in children and adolescents with PTSD. To this end, we investigated the topological properties of brain functional networks derived from resting-state functional magnetic resonance imaging (r-fMRI) in patients suffering from PTSD. The r-fMRI data were obtained from 10 PTSD patients and 16 trauma-exposed non-PTSD subjects. Graph theory analysis was used to investigate the topological properties of the two groups, and group comparisons of topological metrics were performed using nonparametric permutation tests. Both the PTSD and non-PTSD groups showed the functional brain network to have a small-world architecture. However, the PTSD group exhibited alterations in global properties characterized by higher global efficiency, lower clustering coefficient, and characteristic path length, implying a shift toward randomization of the networks. The PTSD group also showed increased nodal centralities, predominately in the left middle frontal gyrus, caudate nucleus, and hippocampus, and decreased nodal centralities in the left anterior cingulate cortex, left paracentral lobule, and bilateral thalami. In addition, the clustering coefficient and nodal betweenness of the left paracentral lobule were found to be negatively and positively correlated with the re-experiencing and hyper-arousal symptoms of PTSD respectively. The findings of disrupted topological properties of functional brain networks may help to better understand the pathophysiological mechanism of PTSD in children and adolescents.

Neuroimaging studies in children and adolescents with post-traumatic stress disorder (PTSD) have focused on abnormal structures and the functionality of a few individual brain regions. However, little is known about alterations to the topological organization of whole-brain functional networks in children and adolescents with PTSD. To this end, we investigated the topological properties of brain functional networks derived from resting-state functional magnetic resonance imaging (r-fMRI) in patients suffering from PTSD. The r-fMRI data were obtained from 10 PTSD patients and 16 trauma-exposed non-PTSD subjects. Graph theory analysis was used to investigate the topological properties of the two groups, and group comparisons of topological metrics were performed using nonparametric permutation tests. Both the PTSD and non-PTSD groups showed the functional brain network to have a small-world architecture. However, the PTSD group exhibited alterations in global properties characterized by higher global efficiency, lower clustering coefficient, and characteristic path length, implying a shift toward randomization of the networks. The PTSD group also showed increased nodal centralities, predominately in the left middle frontal gyrus, caudate nucleus, and hippocampus, and decreased nodal centralities in the left anterior cingulate cortex, left paracentral lobule, and bilateral thalami. In addition, the clustering coefficient and nodal betweenness of the left paracentral lobule were found to be negatively and positively correlated with the re-experiencing and hyper-arousal symptoms of PTSD respectively. The findings of disrupted topological properties of functional brain networks may help to better understand the pathophysiological mechanism of PTSD in children and adolescents. [ABSTRACT FROM AUTHOR]

Executive function (EF) plays vital roles in our everyday adaptation to the ever-changing environment. However, limited existing studies have linked EF to the resting-state brain activity. The functional connectivity in the resting state between the sub-regions of the brain can reveal the intrinsic neural mechanisms involved in cognitive processing of EF without disturbance from external stimuli. The present study investigated the relations between the behavioral executive function (EF) scores and the resting-state functional network topological properties in the Prefrontal Cortex (PFC). We constructed complex brain functional networks in the PFC from 90 healthy young adults using functional near infrared spectroscopy (fNIRS). We calculated the correlations between the typical network topological properties (regional topological properties and global topological properties) and the scores of both the Total EF and components of EF measured by computer-based Cambridge Neuropsychological Test Automated Battery (CANTAB). We found that the Total EF scores were positively correlated with regional properties in the right dorsal superior frontal gyrus (SFG), whereas the opposite pattern was found in the right triangular inferior frontal gyrus (IFG). Different EF components were related to different regional properties in various PFC areas, such as planning in the right middle frontal gyrus (MFG), working memory mainly in the right MFG and triangular IFG, short-term memory in the left dorsal SFG, and task switch in the right MFG. In contrast, there were no significant findings for global topological properties. Our findings suggested that the PFC plays an important role in individuals’ behavioral performance in the executive function tasks. Further, the resting-state functional network can reveal the intrinsic neural mechanisms involved in behavioral EF abilities.

Recent imaging connectomics studies have demonstrated that the spontaneous human brain functional networks derived from resting-state functional MRI (R-fMRI) include many non-trivial topological properties, such as highly efficient small-world architecture and densely connected hub regions. However, very little is known about dynamic functional connectivity (D-FC) patterns of spontaneous human brain networks during rest and about how these spontaneous brain dynamics are constrained by the underlying structural connectivity. Here, we combined sub-second multiband R-fMRI data with graph-theoretical approaches to comprehensively investigate the dynamic characteristics of the topological organization of human whole-brain functional networks, and then employed diffusion imaging data in the same participants to further explore the associated structural substrates. At the connection level, we found that human whole-brain D-FC patterns spontaneously fluctuated over time, while homotopic D-FC exhibited high connectivity strength and low temporal variability. At the network level, dynamic functional networks exhibited time-varying but evident small-world and assortativity architecture, with several regions (e.g., insula, sensorimotor cortex and medial prefrontal cortex) emerging as functionally persistent hubs (i.e., highly connected regions) while possessing large temporal variability in their degree centrality. Finally, the temporal characteristics (i.e., strength and variability) of the connectional and nodal properties of the dynamic brain networks were significantly associated with their structural counterparts. Collectively, we demonstrate the economical, efficient and flexible characteristics of dynamic functional coordination in large-scale human brain networks during rest, and highlight their relationship with underlying structural connectivity, which deepens our understandings of spontaneous brain network dynamics in humans.

Recent studies have suggested that the brain’s structural and functional networks (i.e., connectomics) can be constructed by various imaging technologies (e.g., EEG/MEG; structural, diffusion and functional MRI) and further characterized by graph theory. Given the huge complexity of network construction, analysis and statistics, toolboxes incorporating these functions are largely lacking. Here, we developed the GRaph thEoreTical Network Analysis (GRETNA) toolbox for imaging connectomics. The GRETNA contains several key features as follows: (i) an open-source, Matlab-based, cross-platform (Windows and UNIX OS) package with a graphical user interface; (ii) allowing topological analyses of global and local network properties with parallel computing ability, independent of imaging modality and species; (iii) providing flexible manipulations in several key steps during network construction and analysis, which include network node definition, network connectivity processing, network type selection and choice of thresholding procedure; (iv) allowing statistical comparisons of global, nodal and connectional network metrics and assessments of relationship between these network metrics and clinical or behavioral variables of interest; and (v) including functionality in image preprocessing and network construction based on resting-state functional MRI (R-fMRI) data. After applying the GRETNA to a publicly released R-fMRI dataset of 54 healthy young adults, we demonstrated that human brain functional networks exhibit efficient small-world, assortative, hierarchical and modular organizations and possess highly connected hubs and that these findings are robust against different analytical strategies. With these efforts, we anticipate that GRETNA will accelerate imaging connectomics in an easy, quick and flexible manner. GRETNA is freely available on the NITRC website (http://www.nitrc.org/projects/gretna/).

We consider a network of coupled excitatory and inhibitory theta neurons which is capable of supporting stable spatially-localized "bump" solutions. We randomly add long-range and simultaneously remove short-range connections within the network to form a small-world network and investigate the effects of this rewiring on the existence and stability of the bump solution. We consider two limits in which continuum equations can be derived; bump solutions are fixed points of these equations. We can thus use standard numerical bifurcation analysis to determine the stability of these bumps and to follow them as parameters (such as rewiring probabilities) are varied. We find that under some rewiring schemes bumps are quite robust, whereas in other schemes they can become unstable via Hopf bifurcation or even be destroyed in saddle-node bifurcations. [ABSTRACT FROM AUTHOR]

The authors discuss evidence which shows that behind each stage of Small-World (SW) brain structure lurks fundamental technical, methodological or theoretical stumbling blocks that render the experimental quantification of the SW structure and its interpretation in terms of information processing. They emphasize that a functional brain activity reconstructed with the use of standard system-level brain recording techniques.

Multicellular organisms rely on intercellular communication to regulate important cellular processes critical to life. To further our understanding of those processes there is a need to scrutinize dynamical signaling events and their functions in both cells and organisms. Here, we report a method and provide MATLAB code that analyzes time-lapse microscopy recordings to identify and characterize network structures within large cell populations, such as interconnected neurons. The approach is demonstrated using intracellular calcium (Ca2+) recordings in neural progenitors and cardiac myocytes, but could be applied to a wide variety of biosensors employed in diverse cell types and organisms. In this method, network structures are analyzed by applying cross-correlation signal processing and graph theory to single-cell recordings. The goal of the analysis is to determine if the single cell activity constitutes a network of interconnected cells and to decipher the properties of this network. The method can be applied in many fields of biology in which biosensors are used to monitor signaling events in living cells. Analyzing intercellular communication in cell ensembles can reveal essential network structures that provide important biological insights.

Graph theoretical explorations of functional interactions within the human connectome, are rapidly advancing our understanding of brain architecture. In particular, global and regional topological parameters are increasingly being employed to quantify and characterize inter-individual differences in human brain function. Head motion remains a significant concern in the accurate determination of resting-state fMRI based assessments of the connectome, including those based on graph theoretical analysis (e.g., motion can increase local efficiency, while decreasing global efficiency and small-worldness). This study provides a comprehensive examination of motion correction strategies on the relationship between motion and commonly used topological parameters. At the individual-level, we evaluated different models of head motion regression and scrubbing, as well as the potential benefits of using partial correlation (estimated via graphical lasso) instead of full correlation. At the group-level, we investigated the utility of regression of motion and mean intrinsic functional connectivity before topological parameters calculation and/or after. Consistent with prior findings, none of the explicit motion-correction approaches at individual-level were able to remove motion relationships for topological parameters. Global signal regression (GSR) emerged as an effective means of mitigating relationships between motion and topological parameters; though at the risk of altering the connectivity structure and topological hub distributions when higher densities graphs are employed (e.g., > 6%). Group-level analysis correction for motion was once again found to be a crucial step. Finally, similar to recent work, we found a constellation of findings suggestive of the possibility that some of the motion-relationships detected may reflect neural or trait signatures of motion, rather than simply motion-induced artifact.

Brain network analyses have moved to the forefront of neuroimaging research over the last decade. However, methods for statistically comparing groups of networks have lagged behind. These comparisons have great appeal for researchers interested in gaining further insight into complex brain function and how it changes across different mental states and disease conditions. Current comparison approaches generally either rely on a summary metric or on mass-univariate nodal or edge-based comparisons that ignore the inherent topological properties of the network, yielding little power and failing to make network level comparisons. Gleaning deeper insights into normal and abnormal changes in complex brain function demands methods that take advantage of the wealth of data present in an entire brain network. Here we propose a permutation testing framework that allows comparing groups of networks while incorporating topological features inherent in each individual network. We validate our approach using simulated data with known group differences. We then apply the method to functional brain networks derived from fMRI data.

Schizophrenia is postulated to be the prototypical dysconnection disorder, in which hallucinations are the core symptom. Due to high heterogeneity in methodology across studies and the clinical phenotype, it remains unclear whether the structural brain dysconnection is global or focal and if clinical symptoms result from this dysconnection. In the present work, we attempt to clarify this issue by studying a population considered as a homogeneous genetic sub-type of schizophrenia, namely the 22q11.2 deletion syndrome (22q11.2DS). Cerebral MRIs were acquired for 46 patients and 48 age and gender matched controls (aged 6 to 26, respectively mean age = 15.20 ± 4.53 and 15.28 ± 4.35 years old). Using the Connectome mapper pipeline (connectomics.org) that combines structural and diffusion MRI, we created a whole brain network for each individual. The graph theory was used to quantify the global and local properties in the brain network organization for each participant. A global degree loss of 6% was found in patients’ network along with an increased Characteristic Path Length. After identifying and comparing hubs, a significant loss of degree in patients’ hubs was found in 58% of them. Based on Allen’s brain network model for hallucinations, we explored the association between local efficiency and symptom severity. Negative correlations were found in the Broca’s area (p

Spike-timing dependent plasticity (STDP) is a biologically constrained unsupervised form of learning that potentiates or depresses synaptic connections based on the precise timing of pre-synaptic and post-synaptic firings. The effects of on-going STDP on the topology of evolving model neural networks were assessed in 50 unique simulations which modeled two hours of activity. After a period of stabilization, a number of global and local topological features were monitored periodically to quantify on-going changes in network structure. Global topological features included the total number of remaining synapses, average synaptic strengths, and average number of synapses per neuron (degree). Under a range of different input regimes and initial network configurations, each network maintained a robust and highly stable global structure across time. Local topology was monitored by assessing state changes of all three-neuron subgraphs (triads) present in the networks. Overall counts and the range of triad configurations varied little across the simulations; however, a substantial set of individual triads continued to undergo rapid state changes and revealed a dynamic local topology. In addition, specific small-world properties also fluctuated across time. These findings suggest that on-going STDP provides an efficient means of selecting and maintaining a stable yet flexible network organization.

Multicellular organisms rely on intercellular communication to regulate important cellular processes critical to life. To further our understanding of those processes there is a need to scrutinize dynamical signaling events and their functions in both cells and organisms. Here, we report a method and provide MATLAB code that analyzes time-lapse microscopy recordings to identify and characterize network structures within large cell populations, such as interconnected neurons. The approach is demonstrated using intracellular calcium (Ca2+) recordings in neural progenitors and cardiac myocytes, but could be applied to a wide variety of biosensors employed in diverse cell types and organisms. In this method, network structures are analyzed by applying cross-correlation signal processing and graph theory to single-cell recordings. The goal of the analysis is to determine if the single cell activity constitutes a network of interconnected cells and to decipher the properties of this network. The method can be applied in many fields of biology in which biosensors are used to monitor signaling events in living cells. Analyzing intercellular communication in cell ensembles can reveal essential network structures that provide important biological insights. [ABSTRACT FROM AUTHOR]

We present a biomimetic system that captures essential functional properties of the glomerular layer of the mammalian olfactory bulb, specifically including its capacity to decorrelate similar odor representations without foreknowledge of the statistical distributions of analyte features. Our system is based on a digital neuromorphic chip consisting of 256 leaky-integrate-and-fire neurons, 1024x256 crossbar synapses, and AER communication circuits. The neural circuits configured in the chip reflect established connections among mitral cells, periglomerular cells, external tufted cells and superficial short axon cells within the olfactory bulb, and accept input from convergent sets of sensors configured as olfactory sensory neurons. This configuration generates functional transformations comparable to those observed in the glomerular layer of the mammalian olfactory bulb. Our circuits, consuming only 45 pJ of active power per spike with a power supply voltage of 0.85V, can be used as the first stage of processing in low-power artificial chemical sensing devices inspired by natural olfactory systems.

The human brain has been studied at multiple scales, from neurons, circuits,areas with well defined anatomical and functional boundaries, to large-scalefunctional networks which mediate coherent cognition. In a recent work,we addressed the problem of the hierarchical organization in the brainthrough network analysis. Our analysis identified functional brainmodules of fractal structure that were inter-connected in a small-worldtopology. Here, we provide more details on the use ofnetwork science tools to elaborate on this behavior.We indicate the importance of using percolation theory to highlightthe modular character of the functional brain network.These modules present a fractal, self-similar topology, identified throughfractal network methods.When we lower the threshold of correlations to include weaker ties,the network as a whole assumes a small-world character.These weak ties are organized precisely as predicted by theory maximizing information transfer withminimal wiring costs.

Psychiatric illnesses characterised by disorganized cognition, such as schizophrenia, have been described in terms of fragmentation and hence understood as reduction in functional brain connectivity, particularly in prefrontal and parietal areas. However, as graph-theory shows, relatively small numbers of nonlocal connections are sufficient to ensure global coherence in the modular small world network structure of the brain. We reconsider fragmentation in this perspective. Computational studies have shown that for a given level of connectivity in a model of coupled nonlinear oscillators, modular small-world networks evolve from an initially random organization. Here we demonstrate that with decreasing connectivity, the probability of evolving into a modular small-world network breaks down at a critical point, which scales to the percolation function of random networks with a universal exponent of α=1.17. Thus, according to the model, local modularity systematically breaks down before there is loss of global coherence in network connectivity. We therefore propose that fragmentation may involve, at least in its initial stages, the inability of a dynamically evolving network to sustain a modular small-world structure. The result is in a shift in the balance in schizophrenia from local to global functional connectivity.

Alzheimer’s disease (AD) is the most common form of dementia. As an incurable, progressive and neurodegenerative disease, it causes cognitive and memory deficits. However, the biological mechanisms underlying the disease are not thoroughly understood. In recent years, non-invasive neuroimaging and neurophysiological techniques (e.g., structural MRI, diffusion MRI, functional MRI and EEG/MEG) and graph theory based network analysis have provided a new perspective on structural and functional connectivity patterns of the human brain (i.e., the human connectome) in health and disease. Using these powerful approaches, several recent studies of patients with AD exhibited abnormal topological organization in both global and regional properties of neuronal networks, indicating that AD not only affects specific brain regions, but also alters the structural and functional associations between distinct brain regions. Specifically, disruptive organization in the whole-brain networks in AD is involved in the loss of small-world characters and the re-organization of hub distributions. These aberrant neuronal connectivity patterns were associated with cognitive deficits in patients with AD, even with genetic factors in healthy aging. These studies provide empirical evidence to support the existence of an aberrant connectome of AD. In this review we will summarize recent advances discovered in large-scale brain network studies of AD, mainly focusing on graph theoretical analysis of brain connectivity abnormalities. These studies provide novel insights into the pathophysiological mechanisms of AD and could be helpful in developing imaging biomarkers for disease diagnosis and monitoring.

Tinnitus, the phantom perception of sound, is a prevalent disorder. One in 10 adults has clinically significant subjective tinnitus, and for 1 in 100, tinnitus severely affects their quality of life. Despite the significant unmet clinical need for a safe and effective drug targeting tinnitus relief, there is currently not a single FDA-approved drug on the market. The search for drugs that target tinnitus is hampered by the lack of a deep knowledge of the underlying neural substrates of this pathology. Recent studies are increasingly demonstrating that, as described for other central nervous system disorders, tinnitus is a pathology of brain networks. The application of graph theoretical analysis to brain networks has recently provided new information concerning their topology, their robustness and their vulnerability to attacks. Moreover, the philosophy behind drug design and pharmacotherapy in central nervous system pathologies is changing from that of magic bullets that target individual chemoreceptors or disease-causing genes into that of magic shotguns, promiscuous or dirty drugs that target disease-causing networks, also known as network pharmacology. In the present work we provide some insight into how this knowledge could be applied to tinnitus pathophysiology and pharmacotherapy.

The structure of gene coexpression networks reflects the activation and interaction of multiple cellular systems. Since the pathology of neuropsychiatric disorders is influenced by diverse cellular systems and pathways, we investigated gene coexpression networks in major depression, and searched for putative unifying themes in network connectivity across neuropsychiatric disorders. Specifically, based on the prevalence of the lethality-centrality relationship in disease-related networks, we hypothesized that network changes between control and major depression-related networks would be centered around coexpression hubs, and secondly, that differentially expressed (DE) genes would have a characteristic position and connectivity level in those networks. Mathematically, the first hypothesis tests the relationship of differential coexpression to network connectivity, while the second hybrid expression-and-network hypothesis tests the relationship of differential expression to network connectivity. To answer these questions about the potential interaction of coexpression network structure with differential expression, we utilized all available human post-mortem depression-related datasets appropriate for coexpression analysis, which spanned different microarray platforms, cohorts, and brain regions. Similar studies were also performed in an animal model of depression and in schizophrenia and bipolar disorder microarray datasets. We now provide results which consistently support (1) that genes assemble into small-world and scale-free networks in control subjects, (2) that this efficient network topology is largely resilient to changes in depressed subjects, and (3) that DE genes are positioned on the periphery of coexpression networks. Similar results were observed in a mouse model of depression, and in selected bipolar- and schizophrenia-related networks. Finally, we show that baseline expression variability contributes to the propensity of genes to be network hubs.