From brain topography to brain topology: relevance of graph theory to functional neuroscience

Oxytocin promotes prefrontal population activity via the PVN-PFC pathway to regulate pain

Neurons in the prefrontal cortex (PFC) can provide top-down regulation of sensory-affective experiences such as pain. Bottom-up modulation of sensory coding in the PFC, however, remains poorly understood. Here, we examined how oxytocin (OT) signaling from the hypothalamus regulates nociceptive coding in the PFC. In vivo time-lapse endoscopic calcium imaging in freely behaving rats showed that OT selectively enhanced population activity in the prelimbic PFC in response to nociceptive inputs. This population response resulted from the reduction of evoked GABAergic inhibition and manifested as elevated functional connectivity involving pain-responsive neurons. Direct inputs from OT-releasing neurons in the paraventricular nucleus (PVN) of the hypothalamus are crucial to maintaining this prefrontal nociceptive response. Activation of the prelimbic PFC by OT or direct optogenetic stimulation of oxytocinergic PVN projections reduced acute and chronic pain. These results suggest that oxytocinergic signaling in the PVN-PFC circuit constitutes a key mechanism to regulate cortical sensory processing.

Neuromodulation of brain power topography and network topology by prefrontal transcranial photobiomodulation

Objective.Transcranial photobiomodulation (tPBM) has shown promising benefits, including cognitive improvement, in healthy humans and in patients with Alzheimer's disease. In this study, we aimed to identify key cortical regions that present significant changes caused by tPBM in the electroencephalogram (EEG) oscillation powers and functional connectivity in the healthy human brain.Approach. A 64-channel EEG was recorded from 45 healthy participants during a 13 min period consisting of a 2 min baseline, 8 min tPBM/sham intervention, and 3 min recovery. After pre-processing and normalizing the EEG data at the five EEG rhythms, cluster-based permutation tests were performed for multiple comparisons of spectral power topographies, followed by graph-theory analysis as a topological approach for quantification of brain connectivity metrics at global and nodal/cluster levels.Main results. EEG power enhancement was observed in clusters of channels over the frontoparietal regions in the alpha band and the centroparietal regions in the beta band. The global measures of the network revealed a reduction in synchronization, global efficiency, and small-worldness of beta band connectivity, implying an enhancement of brain network complexity. In addition, in the beta band, nodal graphical analysis demonstrated significant increases in local information integration and centrality over the frontal clusters, accompanied by a decrease in segregation over the bilateral frontal, left parietal, and left occipital regions.Significance.Frontal tPBM increased EEG alpha and beta powers in the frontal-central-parietal regions, enhanced the complexity of the global beta-wave brain network, and augmented local information flow and integration of beta oscillations across prefrontal cortical regions. This study sheds light on the potential link between electrophysiological effects and human cognitive improvement induced by tPBM.

An exploratory study on functional connectivity after mild traumatic brain injury: Preserved global but altered local organization

INTRODUCTION

This study aimed to investigate alterations in whole-brain functional connectivity after a concussion using graph-theory analysis from global and local perspectives and explore the association between changes in the functional network properties and cognitive performance.

METHODS

Individuals with mild traumatic brain injury (mTBI, n = 29) within a month after injury, and age- and sex-matched healthy controls (n = 29) were included. Graph-theory measures on functional connectivity assessed using resting state functional magnetic resonance imaging data were acquired from each participant. These included betweenness centrality, strength, clustering coefficient, local efficiency, and global efficiency. Multi-domain cognitive functions were correlated with the graph-theory measures.

RESULTS

In comparison to the controls, the mTBI group showed preserved network characteristics at a global level. However, in the local network, we observed decreased betweenness centrality, clustering coefficient, and local efficiency in several brain areas, including the fronto-parietal attention network. Network strength at the local level showed mixed-results in different areas. The betweenness centrality of the right parahippocampus showed a significant positive correlation with the cognitive scores of the verbal learning test only in the mTBI group.

CONCLUSION

The intrinsic functional connectivity after mTBI is preserved globally, but is suboptimally organized locally in several areas. This possibly reflects the neurophysiological sequelae of a concussion. The present results may imply that the network property could be used as a potential indicator for clinical outcomes after mTBI.

Bottom-up vs. top-down connectivity imbalance in individuals with high-autistic traits: An electroencephalographic study

Brain connectivity is often altered in autism spectrum disorder (ASD). However, there is little consensus on the nature of these alterations, with studies pointing to either increased or decreased connectivity strength across the broad autism spectrum. An important confound in the interpretation of these contradictory results is the lack of information about the directionality of the tested connections. Here, we aimed at disambiguating these confounds by measuring differences in directed connectivity using EEG resting-state recordings in individuals with low and high autistic traits. Brain connectivity was estimated using temporal Granger Causality applied to cortical signals reconstructed from EEG. Between-group differences were summarized using centrality indices taken from graph theory (in degree, out degree, authority, and hubness). Results demonstrate that individuals with higher autistic traits exhibited a significant increase in authority and in degree in frontal regions involved in high-level mechanisms (emotional regulation, decision-making, and social cognition), suggesting that anterior areas mostly receive information from more posterior areas. Moreover, the same individuals exhibited a significant increase in the hubness and out degree over occipital regions (especially the left and right pericalcarine regions, where the primary visual cortex is located), suggesting that these areas mostly send information to more anterior regions. Hubness and authority appeared to be more sensitive indices than the in degree and out degree. The observed brain connectivity differences suggest that, in individual with higher autistic traits, bottom-up signaling overcomes top-down channeled flow. This imbalance may contribute to some behavioral alterations observed in ASD.

Graph Theoretical Analysis of Structural Covariance Reveals the Relevance of Visuospatial and Attentional Areas in Essential Tremor Recovery After Stereotactic Radiosurgical Thalamotomy

Essential tremor (ET) is the most common movement disorder. Its pathophysiology is only partially understood. Here, we leveraged graph theoretical analysis on structural covariance patterns quantified from morphometric estimates for cortical thickness, surface area, and mean curvature in patients with ET before and one year after (to account for delayed clinical effect) ventro-intermediate nucleus (Vim) stereotactic radiosurgical thalamotomy. We further contrasted the observed patterns with those from matched healthy controls (HCs). Significant group differences at the level of individual morphometric properties were specific to mean curvature and the post-/pre-thalamotomy contrast, evidencing brain plasticity at the level of the targeted left thalamus, and of low-level visual, high-level visuospatial and attentional areas implicated in the dorsal visual stream. The introduction of cross-correlational analysis across pairs of morphometric properties strengthened the presence of dorsal visual stream readjustments following thalamotomy, as cortical thickness in the right lingual gyrus, bilateral rostral middle frontal gyrus, and left pre-central gyrus was interrelated with mean curvature in the rest of the brain. Overall, our results position mean curvature as the most relevant morphometric feature to understand brain plasticity in drug-resistant ET patients following Vim thalamotomy. They also highlight the importance of examining not only individual features, but also their interactions, to gain insight into the routes of recovery following intervention.

Brain Connectivity and Graph Theory Analysis in Alzheimer’s and Parkinson’s Disease: The Contribution of Electrophysiological Techniques

In recent years, applications of the network science to electrophysiological data have increased as electrophysiological techniques are not only relatively low cost, largely available on the territory and non-invasive, but also potential tools for large population screening. One of the emergent methods for the study of functional connectivity in electrophysiological recordings is graph theory: it allows to describe the brain through a mathematic model, the graph, and provides a simple representation of a complex system. As Alzheimer’s and Parkinson’s disease are associated with synaptic disruptions and changes in the strength of functional connectivity, they can be well described by functional connectivity analysis computed via graph theory. The aim of the present review is to provide an overview of the most recent applications of the graph theory to electrophysiological data in the two by far most frequent neurodegenerative disorders, Alzheimer’s and Parkinson’s diseases.

Disrupted population coding in the prefrontal cortex underlies pain aversion

The prefrontal cortex (PFC) regulates a wide range of sensory experiences. Chronic pain is known to impair normal neural response, leading to enhanced aversion. However, it remains unknown how nociceptive responses in the cortex are processed at the population level and whether such processes are disrupted by chronic pain. Using in vivo endoscopic calcium imaging, we identify increased population activity in response to noxious stimuli and stable patterns of functional connectivity among neurons in the prelimbic (PL) PFC from freely behaving rats. Inflammatory pain disrupts functional connectivity of PFC neurons and reduces the overall nociceptive response. Interestingly, ketamine, a well-known neuromodulator, restores the functional connectivity among PL-PFC neurons in the inflammatory pain model to produce anti-aversive effects. These results suggest a dynamic resource allocation mechanism in the prefrontal representations of pain and indicate that population activity in the PFC critically regulates pain and serves as an important therapeutic target.

Li et al. reveal that inflammatory pain disrupts the functional connectivity of neurons in the prelimbic prefrontal cortex (PL-PFC) and the overall nociceptive response. Ketamine, meanwhile, restores the functional connectivity of neurons in the PL-PFC in the inflammatory pain state to produce anti-aversive effects.

Cortical autonomic network connectivity predicts symptoms in myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS)

Myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) represents a significant public health challenge given the presence of many unexplained patient symptoms. Research has shown that many features in ME/CFS may result from a dysfunctional autonomic nervous system (ANS). We explored the role of the cortical autonomic network (CAN) involved in higher-order control of ANS functioning in 34 patients with ME/CFS and 34 healthy controls under task-free conditions. All participants underwent resting-state quantitative electroencephalographic (qEEG) scalp recordings during an eyes-closed condition. Source analysis was performed using exact low-resolution electromagnetic tomography (eLORETA), and lagged coherence was used to estimate intrinsic functional connectivity between each node across 7 frequency bands: delta (1-3 Hz), theta (4-7 Hz), alpha-1 (8-10 Hz), alpha-2 (10-12 Hz), beta-1 (13-18 Hz), beta-2 (19-21 Hz), and beta-3 (22-30 Hz). Symptom ratings were measured using the DePaul Symptom Questionnaire and the Short Form (SF-36) health survey. Graph theoretical analysis of weighted, undirected connections revealed significant group differences in baseline CAN organization. Regression results showed that cognitive, affective, and somatomotor symptom cluster ratings were associated with alteration to CAN topology in patients, depending on the frequency band. These findings provide evidence for reduced higher-order homeostatic regulation and adaptability in ME/CFS. If confirmed, these findings address the CAN as a potential therapeutic target for managing patient symptoms.

Altered Functional Topological Organization in Type-2 Diabetes Mellitus With and Without Microvascular Complications

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.

The role of network structure and time delay in a metapopulation Wilson--Cowan model

We study the dynamics of a network Wilson--Cowan model (a system of connected Wilson--Cowan oscillators) for interacting excitatory and inhibitory neuron populations with time delays. Each node in this model corresponds to a population of neurons, including excitatory and inhibitory subpopulations, and hence it can be viewed as a metapopulation model. It is known that information transfer within each cortical area is not instantaneous, and therefore we consider a system of delay differential equations with two different kinds of discrete delays. We account for the time delay in information propagation between individual excitatory and inhibitory subpopulations at each node via intra-node time delays, and we account for time delay in information propagation between neuron populations at different nodes with inter-node time delays. The biologically relevant resting state solutions are oscillatory (stable limit cycles). After determining the influence of the coupling parameters between nodes, the intra-node delays, and the inter-node delays on the dynamics of the two coupled Wilson--Cowan oscillators, we then explore a variety of larger networks of 16 and 100 nodes, in order to determine how the network topology will influence time delayed Wilson--Cowan dynamics. We find that network structure can regularize or deregularize the dynamics, with networks of higher mean degree permitting stable limit cycles and networks with smaller mean degree yielding less regular dynamics (which may range from chaotic solutions, to solutions for which limit cycles collapse into steady states, which are biologically undesirable compared with the preferred stable limit cycles). Furthermore, heterogeneity in the degree distribution of the network (resulting from networks with nodes of varying degree) can result in asynchronous dynamics, even if at each node the local dynamics are that of a limit cycle, in contrast to the synchronization of dynamics between nodes seen when the degree of all nodes is equal. This suggests that homogeneous and well-connected networks permit robust limit cycles under time-delayed Wilson--Cowan dynamics, whereas heterogeneous or poorly connected networks may fail to provide such desirable dynamics, a phenomena akin to structural loss of neuron connections in neurodegenerative diseases.

Amnestic Mild Cognitive Impairment Is Associated With Frequency-Specific Brain Network Alterations in Temporal Poles

There is general agreement that the neuropathological processes leading to Alzheimer’s disease (AD) begin decades before the clinical onset. In order to detect early topological changes, we applied functional connectivity and network analysis to magnetoencephalographic (MEG) data obtained from 16 patients with amnestic Mild Cognitive Impairment (aMCI), a prodromal stage of AD, and 16 matched healthy control (HCs). Significant differences between the two groups were found in the theta band, which is associated with memory processes, in both temporal poles (TPs). In aMCI, the degree and betweenness centrality (BC) were lower in the left superior TP, whereas in the right middle TP the BC was higher. A statistically significant negative linear correlation was found between the BC of the left superior TP and a delayed recall score, a sensitive marker of the “hippocampal memory” deficit in early AD. Our results suggest that the TPs, which are involved early in AD pathology and belong to the memory circuitry, have an altered role in the functional network in aMCI.

Differentiating Alzheimer's Disease from Dementia with Lewy Bodies Using a Deep Learning Technique Based on Structural Brain Connectivity

PURPOSE

Alzheimer's disease (AD) and dementia with Lewy bodies (DLB) are representative disorders of dementia of the elderly and the neuroimaging has contributed to early diagnosis by estimation of alterations of brain volume, blood flow and metabolism. A brain network analysis by MR imaging (MR connectome) is a recently developed technique and can estimate the dysfunction of the brain network in AD and DLB. A graph theory which is a major technique of network analysis is useful for a group study to extract the feature of disorders, but is not necessarily suitable for the disorder differentiation at the individual level. In this investigation, we propose a deep learning technique as an alternative method of the graph analysis for recognition and classification of AD and DLB at the individual subject level.

MATERIALS AND METHODS

Forty-eight brain structural connectivity data of 18 AD, 8 DLB and 22 healthy controls were applied to the machine learning consisting of a six-layer convolution neural network (CNN) model. Estimation of the deep learning model to classify AD, DLB and non-AD/DLB was performed using the 4-fold cross-validation method.

RESULTS

The accuracy, average precision and recall of our CNN model were 0.73, 0.78 and 0.73, and the specificity precision and recall were 0.68 and 0.79 in AD, 0.94 and 0.65 in DLB and 0.73 and 0.75 in non-AD/DLB. The triangular probability map of the MR connectome revealed the probability of AD, DLB and non-AD/DLB in each subject.

CONCLUSION

Our preliminary investigation revealed the adaptation of deep learning to the MR connectome and proposed its utility in the differentiation of dementia disorders at the individual subject level.

Altered topology of the functional speech production network in non-fluent/agrammatic variant of PPA

Non-fluent/agrammatic primary progressive aphasia (nfvPPA) is caused by neurodegeneration within the left fronto-insular speech and language production network (SPN). Graph theory is a branch of mathematics that studies network architecture (topology) by quantifying features based on its elements (nodes and connections). This approach has been recently applied to neuroimaging data to explore the complex architecture of the brain connectome, though few studies have exploited this technique in PPA. Here, we used graph theory on functional MRI resting state data from a group of 20 nfvPPA patients and 20 matched controls to investigate topological changes in response to focal neurodegeneration. We hypothesized that changes in the network architecture would be specific to the affected SPN in nfvPPA, while preserved in the spared default mode network (DMN). Topological configuration was quantified by hub location and global network metrics. Our findings showed a less efficiently wired and less optimally clustered SPN, while no changes were detected in the DMN. The SPN in the nfvPPA group showed a loss of hubs in the left fronto-parietal-temporal area and new critical nodes in the anterior left inferior-frontal and right frontal regions. Behaviorally, speech production score and rule violation errors correlated with the strength of functional connectivity of the left (lost) and right (new) regions respectively. This study shows that focal neurodegeneration within the SPN in nfvPPA is associated with network-specific topological alterations, with the loss and gain of crucial hubs and decreased global efficiency that were better accounted for through functional rather than structural changes. These findings support the hypothesis of selective network vulnerability in nfvPPA and may offer biomarkers for future behavioral intervention.

Altered degree centrality in childhood absence epilepsy: A resting-state fMRI study

Modern network studies have suggested that the pathology of many neurological diseases is in fact not equally distributed over the brain but preferentially affects the hub regions. This study aims to investigate how hub regions were affected in Children with Childhood absence epilepsy (CAE) using resting-state fMRI (rs-fMRI). As one important measures obtained from rs-fMRI, degree centrality (DC) calculates the number of direct connections between a given node and the rest of the brain within the entire connectivity matrix of the brain. In this study, twenty-five CAE children and 25 healthy controls were recruited to investigate the DC changes in CAE patients. Compared with healthy controls, children with CAE showed significantly decreased DC in default mode network (DMN, medial prefrontal cortex, posterior cingulate cortex, precuneus and middle temporal cortex) and increased DC in thalamus. Importantly, significant negative correlation between the epilepsy duration and DC was found in precuneus. Our results suggested selective and specific disruption of hub nodes, especially thalamus and the highly connected brain regions within DMN, might underlie the pathophysiological mechanism of CAE.

Cognitive eloquence in neurosurgery: Insight from graph theoretical analysis of complex brain networks

The structure and function of the brain can be described by complex network models, and the topological properties of these models can be quantified by graph theoretical analysis. This has given insight into brain regions, known as hubs, which are critical for integrative functioning and information transfer, both fundamental aspects of cognition. In this manuscript a hypothesis is put forward for the concept of cognitive eloquence in neurosurgery; that is regions (cortical, subcortical and white matter) of the brain which may not necessarily have readily identifiable neurological function, but if injured may result in disproportionate cognitive morbidity. To this end, the effects of neurosurgical resection on cognition is reviewed and an overview of the role of complex network analysis in the understanding of brain structure and function is provided. The literature describing network, behavioral, and cognitive effects resulting from lesions to, and disconnections of, centralized hub regions will be emphasized as evidence for the espousal of the concept of cognitive eloquence.

White matter structural network abnormalities underlie executive dysfunction in amyotrophic lateral sclerosis

Research in amyotrophic lateral sclerosis (ALS) suggests that executive dysfunction, a prevalent cognitive feature of the disease, is associated with abnormal structural connectivity and white matter integrity. In this exploratory study, we investigated the white matter constructs of executive dysfunction, and attempted to detect structural abnormalities specific to cognitively impaired ALS patients. Eighteen ALS patients and 22 age and education matched healthy controls underwent magnetic resonance imaging on a 4.7 Tesla scanner and completed neuropsychometric testing. ALS patients were categorized into ALS cognitively impaired (ALSci, n = 9) and ALS cognitively competent (ALScc, n = 5) groups. Tract-based spatial statistics and connectomics were used to compare white matter integrity and structural connectivity of ALSci and ALScc patients. Executive function performance was correlated with white matter FA and network metrics within the ALS group. Executive function performance in the ALS group correlated with global and local network properties, as well as FA, in regions throughout the brain, with a high predilection for the frontal lobe. ALSci patients displayed altered local connectivity and structural integrity in these same frontal regions that correlated with executive dysfunction. Our results suggest that executive dysfunction in ALS is related to frontal network disconnectivity, which potentially mediates domain-specific, or generalized cognitive impairment, depending on the degree of global network disruption. Furthermore, reported co-localization of decreased network connectivity and diminished white matter integrity suggests white matter pathology underlies this topological disruption. We conclude that executive dysfunction in ALSci is associated with frontal and global network disconnectivity, underlined by diminished white matter integrity. Hum Brain Mapp 38:1249-1268, 2017. © 2016 Wiley Periodicals, Inc.

Network Connectivity of the Right STS in Three Social Perception Localizers

The posterior STS (pSTS) is an important brain region for perceptual analysis of social cognitive cues. This study seeks to characterize the pattern of network connectivity emerging from the pSTS in three core social perception localizers: biological motion perception, gaze recognition, and the interpretation of moving geometric shapes as animate. We identified brain regions associated with all three of these localizers and computed the functional connectivity pattern between them and the pSTS using a partial correlations metric that characterizes network connectivity. We find a core pattern of cortical connectivity that supports the hypothesis that the pSTS serves as a hub of the social brain network. The right pSTS was the most highly connected of the brain regions measured, with many long-range connections to pFC. Unlike other highly connected regions, connectivity to the pSTS was distinctly lateralized. We conclude that the functional importance of right pSTS is revealed when considering its role in the large-scale network of brain regions involved in various aspects of social cognition.

Methods and utility of EEG-fMRI in epilepsy

Brain activity data in general and more specifically in epilepsy can be represented as a matrix that includes measures of electrophysiology, anatomy and behaviour. Each of these sub-matrices has a complex interaction depending upon the brain state i.e., rest, cognition, seizures and interictal periods. This interaction presents significant challenges for interpretation but also potential for developing further insights into individual event types. Successful treatments in epilepsy hinge on unravelling these complexities, and also on the sensitivity and specificity of methods that characterize the nature and localization of underlying physiological and pathological networks. Limitations of pharmacological and surgical treatments call for refinement and elaboration of methods to improve our capability to localise the generators of seizure activity and our understanding of the neurobiology of epilepsy. Simultaneous electroencephalography and functional magnetic resonance imaging (EEG-fMRI), by potentially circumventing some of the limitations of EEG in terms of sensitivity, can allow the mapping of haemodynamic networks over the entire brain related to specific spontaneous and triggered epileptic events in humans, and thereby provide new localising information. In this work we review the published literature, and discuss the methods and utility of EEG-fMRI in localising the generators of epileptic activity. We draw on our experience and that of other groups, to summarise the spectrum of information provided by an increasing number of EEG-fMRI case-series, case studies and group studies in patients with epilepsy, for its potential role to elucidate epileptic generators and networks. We conclude that EEG-fMRI provides a multidimensional view that contributes valuable clinical information to localize the epileptic focus with potential important implications for the surgical treatment of some patients with drug-resistant epilepsy, and insights into the resting state and cognitive network dynamics.

Pathway and network approaches for identification of cancer signature markers from omics data

The advancement of high throughput omic technologies during the past few years has made it possible to perform many complex assays in a much shorter time than the traditional approaches. The rapid accumulation and wide availability of omic data generated by these technologies offer great opportunities to unravel disease mechanisms, but also presents significant challenges to extract knowledge from such massive data and to evaluate the findings. To address these challenges, a number of pathway and network based approaches have been introduced. This review article evaluates these methods and discusses their application in cancer biomarker discovery using hepatocellular carcinoma (HCC) as an example.

The contribution of TMS-EEG coregistration in the exploration of the human cortical connectome

Recent developments in neuroscience have emphasised the importance of integrated distributed networks of brain areas for successful cognitive functioning. Our current understanding is that the brain has a modular organisation in which segregated networks supporting specialised processing are linked through a few long-range connections, ensuring processing integration. Although such architecture is structurally stable, it appears to be flexible in its functioning, enabling long-range connections to regulate the information flow and facilitate communication among the relevant modules, depending on the contingent cognitive demands. Here we show how insights brought by the coregistration of transcranial magnetic stimulation and electroencephalography (TMS-EEG) integrate and support recent models of functional brain architecture. Moreover, we will highlight the types of data that can be obtained through TMS-EEG, such as the timing of signal propagation, the excitatory/inhibitory nature of connections and causality. Last, we will discuss recent emerging applications of TMS-EEG in the study of brain disorders.

Modern network science of neurological disorders

Modern network science has revealed fundamental aspects of normal brain-network organization, such as small-world and scale-free patterns, hierarchical modularity, hubs and rich clubs. The next challenge is to use this knowledge to gain a better understanding of brain disease. Recent developments in the application of network science to conditions such as Alzheimer's disease, multiple sclerosis, traumatic brain injury and epilepsy have challenged the classical concept of neurological disorders being either 'local' or 'global', and have pointed to the overload and failure of hubs as a possible final common pathway in neurological disorders.

Fast computation of voxel-level brain connectivity maps from resting-state functional MRI using l₁-norm as approximation of Pearson's temporal correlation: proof-of-concept and example vector hardware implementation

An outstanding issue in graph-based analysis of resting-state functional MRI is choice of network nodes. Individual consideration of entire brain voxels may represent a less biased approach than parcellating the cortex according to pre-determined atlases, but entails establishing connectedness for 1(9)-1(11) links, with often prohibitive computational cost. Using a representative Human Connectome Project dataset, we show that, following appropriate time-series normalization, it may be possible to accelerate connectivity determination replacing Pearson correlation with l1-norm. Even though the adjacency matrices derived from correlation coefficients and l1-norms are not identical, their similarity is high. Further, we describe and provide in full an example vector hardware implementation of l1-norm on an array of 4096 zero instruction-set processors. Calculation times <1000 s are attainable, removing the major deterrent to voxel-based resting-sate network mapping and revealing fine-grained node degree heterogeneity. L1-norm should be given consideration as a substitute for correlation in very high-density resting-state functional connectivity analyses.