Modular Brain Networks

Spectral synchronicity in brain signals

This paper addresses the problem of identifying brain regions with similar oscillatory patterns detected from electroencephalograms. We introduce the hierarchical spectral merger (HSM) clustering method where the feature of interest is the spectral curve and the similarity metric used is the total variance distance. The HSM method is compared with clustering using features derived from independent-component analysis. Moreover, the HSM method is applied to 2 different electroencephalogram datasets. The first was recorded at resting state where the participant was not engaged in any cognitive task; the second was recorded during a spontaneous epileptic seizure. The results of the analyses using the HSM method demonstrate that clustering could evolve over the duration of the resting state and during epileptic seizure.

Applications of community detection techniques to brain graphs: Algorithmic considerations and implications for neural function

The human brain can be represented as a graph in which neural units such as cells or small volumes of tissue are heterogeneously connected to one another through structural or functional links. Brain graphs are parsimonious representations of neural systems that have begun to offer fundamental insights into healthy human cognition, as well as its alteration in disease. A critical open question in network neuroscience lies in how neural units cluster into densely interconnected groups that can provide the coordinated activity that is characteristic of perception, action, and adaptive behaviors. Tools that have proven particularly useful for addressing this question are community detection approaches, which can identify communities or modules: groups of neural units that are densely interconnected with other units in their own group but sparsely interconnected with units in other groups. In this paper, we describe a common community detection algorithm known as modularity maximization, and we detail its applications to brain graphs constructed from neuroimaging data. We pay particular attention to important algorithmic considerations, especially in recent extensions of these techniques to graphs that evolve in time. After recounting a few fundamental insights that these techniques have provided into brain function, we highlight potential avenues of methodological advancements for future studies seeking to better characterize the patterns of coordinated activity in the brain that accompany human behavior. This tutorial provides a naive reader with an introduction to theoretical considerations pertinent to the generation of brain graphs, an understanding of modularity maximization for community detection, a resource of statistical measures that can be used to characterize community structure, and an appreciation of the usefulness of these approaches in uncovering behaviorally-relevant network dynamics in neuroimaging data.

Fronto-Parietal Subnetworks Flexibility Compensates For Cognitive Decline Due To Mental Fatigue

Fronto-parietal subnetworks were revealed to compensate for cognitive decline due to mental fatigue by community structure analysis. Here, we investigate changes in topology of subnetworks of resting-state fMRI networks due to mental fatigue induced by prolonged performance of a cognitively demanding task, and their associations with cognitive decline. As it is well established that brain networks have modular organization, community structure analyses can provide valuable information about mesoscale network organization and serve as a bridge between standard fMRI approaches and brain connectomics that quantify the topology of whole brain networks. We developed inter- and intramodule network metrics to quantify topological characteristics of subnetworks, based on our hypothesis that mental fatigue would impact on functional relationships of subnetworks. Functional networks were constructed with wavelet correlation and a data-driven thresholding scheme based on orthogonal minimum spanning trees, which allowed detection of communities with weak connections. A change from pre- to posttask runs was found for the intermodule density between the frontal and the temporal subnetworks. Seven inter- or intramodule network metrics, mostly at the frontal or the parietal subnetworks, showed significant predictive power of individual cognitive decline, while the network metrics for the whole network were less effective in the predictions. Our results suggest that the control-type fronto-parietal networks have a flexible topological architecture to compensate for declining cognitive ability due to mental fatigue. This community structure analysis provides valuable insight into connectivity dynamics under different cognitive states including mental fatigue.

Drawing Inspiration from Human Brain Networks: Construction of Interconnected Virtual Networks

Virtualization of wireless sensor networks (WSN) is widely considered as a foundational block of edge/fog computing, which is a key technology that can help realize next-generation Internet of things (IoT) networks. In such scenarios, multiple IoT devices and service modules will be virtually deployed and interconnected over the Internet. Moreover, application services are expected to be more sophisticated and complex, thereby increasing the number of modifications required for the construction of network topologies. Therefore, it is imperative to establish a method for constructing a virtualized WSN (VWSN) topology that achieves low latency on information transmission and high resilience against network failures, while keeping the topological construction cost low. In this study, we draw inspiration from inter-modular connectivity in human brain networks, which achieves high performance when dealing with large-scale networks composed of a large number of modules (i.e., regions) and nodes (i.e., neurons). We propose a method for assigning inter-modular links based on a connectivity model observed in the cerebral cortex of the brain, known as the exponential distance rule (EDR) model. We then choose endpoint nodes of these links by controlling inter-modular assortativity, which characterizes the topological connectivity of brain networks. We test our proposed methods using simulation experiments. The results show that the proposed method based on the EDR model can construct a VWSN topology with an optimal combination of communication efficiency, robustness, and construction cost. Regarding the selection of endpoint nodes for the inter-modular links, the results also show that high assortativity enhances the robustness and communication efficiency because of the existence of inter-modular links of two high-degree nodes.

The Dynamics of Concussion: Mapping Pathophysiology, Persistence, and Recovery With Causal-Loop Diagramming

Despite increasing public awareness and a growing body of literature on the subject of concussion, or mild traumatic brain injury, an urgent need still exists for reliable diagnostic measures, clinical care guidelines, and effective treatments for the condition. Complexity and heterogeneity complicate research efforts and indicate the need for innovative approaches to synthesize current knowledge in order to improve clinical outcomes. Methods from the interdisciplinary field of systems science, including models of complex systems, have been increasingly applied to biomedical applications and show promise for generating insight for traumatic brain injury. The current study uses causal-loop diagramming to visualize relationships between factors influencing the pathophysiology and recovery trajectories of concussive injury, including persistence of symptoms and deficits. The primary output is a series of preliminary systems maps detailing feedback loops, intrinsic dynamics, exogenous drivers, and hubs across several scales, from micro-level cellular processes to social influences. Key system features, such as the role of specific restorative feedback processes and cross-scale connections, are examined and discussed in the context of recovery trajectories. This systems approach integrates research findings across disciplines and allows components to be considered in relation to larger system influences, which enables the identification of research gaps, supports classification efforts, and provides a framework for interdisciplinary collaboration and communication-all strides that would benefit diagnosis, prognosis, and treatment in the clinic.

Alterations in white matter network topology contribute to freezing of gait in Parkinson's disease

Freezing of gait (FOG) is a common symptom in advanced Parkinson's disease (PD). Despite current advances, the neural mechanisms underpinning this disturbance remain poorly understood. To this end, we investigated the structural organisation of the white matter connectome in PD freezers and PD non-freezers. We hypothesized that freezers would show an altered network architecture, which could hinder the effective information processing that characterizes the disorder. Twenty-six freezers and twenty-four well-matched non-freezers were included in this study. Using diffusion tensor imaging, we investigated the modularity and integration of the regional connectome by calculating the module degree z score and the participation coefficient, respectively. Compared to non-freezers, freezers demonstrated lower participation coefficients in the right caudate, thalamus, and hippocampus, as well as within superior frontal and parietal cortical regions. Importantly, several of these nodes were found within the brain's 'rich club'. Furthermore, group differences in module degree z scores within cortical frontal and sensory processing areas were found. Together, our results suggest that changes in the structural network topology contribute to the manifestation of FOG in PD, specifically due to a lack of structural integration between key information processing hubs of the brain.

Clustering Coefficients for Correlation Networks

Graph theory is a useful tool for deciphering structural and functional networks of the brain on various spatial and temporal scales. The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighboring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other) measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients (i.e., abundance of triangles around a focal node) are useful in characterizing individual nodes. In contrast, the conventional local clustering coefficients were strongly correlated with and therefore may be confounded by the node's connectivity. The proposed methods are expected to help us to understand clustering and lack thereof in correlational brain networks, such as those derived from functional time series and across-participant correlation in neuroanatomical properties.

Neural Correlates of Unconsciousness in Large-Scale Brain Networks

The biological basis of consciousness is one of the most challenging and fundamental questions in 21st century science. A related pursuit aims to identify the neural correlates and causes of unconsciousness. We review current trends in the investigation of physiological, pharmacological, and pathological states of unconsciousness at the level of large-scale functional brain networks. We focus on the roles of brain connectivity, repertoire, graph-theoretical techniques, and neural dynamics in understanding the functional brain disconnections and reduced complexity that appear to characterize these states. Persistent questions in the field, such as distinguishing true correlates, linking neural scales, and understanding differential recovery patterns, are also addressed.

Classification and characterisation of brain network changes in chronic back pain: A multicenter study

Background. Chronic pain is a common, often disabling condition thought to involve a combination of peripheral and central neurobiological factors. However, the extent and nature of changes in the brain is poorly understood. Methods. We investigated brain network architecture using resting-state fMRI data in chronic back pain patients in the UK and Japan (41 patients, 56 controls), as well as open data from USA. We applied machine learning and deep learning (conditional variational autoencoder architecture) methods to explore classification of patients/controls based on network connectivity. We then studied the network topology of the data, and developed a multislice modularity method to look for consensus evidence of modular reorganisation in chronic back pain. Results. Machine learning and deep learning allowed reliable classification of patients in a third, independent open data set with an accuracy of 63%, with 68% in cross validation of all data. We identified robust evidence of network hub disruption in chronic pain, most consistently with respect to clustering coefficient and betweenness centrality. We found a consensus pattern of modular reorganisation involving extensive, bilateral regions of sensorimotor cortex, and characterised primarily by negative reorganisation - a tendency for sensorimotor cortex nodes to be less inclined to form pairwise modular links with other brain nodes. In contrast, intraparietal sulcus displayed a propensity towards positive modular reorganisation, suggesting that it might have a role in forming modules associated with the chronic pain state. Conclusion. The results provide evidence of consistent and characteristic brain network changes in chronic pain, characterised primarily by extensive reorganisation of the network architecture of the sensorimotor cortex.

Multiresolution Consensus Clustering in Networks

Networks often exhibit structure at disparate scales. We propose a method for identifying community structure at different scales based on multiresolution modularity and consensus clustering. Our contribution consists of two parts. First, we propose a strategy for sampling the entire range of possible resolutions for the multiresolution modularity quality function. Our approach is directly based on the properties of modularity and, in particular, provides a natural way of avoiding the need to increase the resolution parameter by several orders of magnitude to break a few remaining small communities, necessitating the introduction of ad-hoc limits to the resolution range with standard sampling approaches. Second, we propose a hierarchical consensus clustering procedure, based on a modified modularity, that allows one to construct a hierarchical consensus structure given a set of input partitions. While here we are interested in its application to partitions sampled using multiresolution modularity, this consensus clustering procedure can be applied to the output of any clustering algorithm. As such, we see many potential applications of the individual parts of our multiresolution consensus clustering procedure in addition to using the procedure itself to identify hierarchical structure in networks.

The brain as a "hyper-network": the key role of neural networks as main producers of the integrated brain actions especially via the "broadcasted" neuroconnectomics

Investigations of brain complex integrative actions should consider beside neural networks, glial, extracellular molecular, and fluid channels networks. The present paper proposes that all these networks are assembled into the brain hyper-network that has as fundamental components, the tetra-partite synapses, formed by neural, glial, and extracellular molecular networks. Furthermore, peri-synaptic astrocytic processes by modulating the perviousness of extracellular fluid channels control the signals impinging on the tetra-partite synapses. It has also been surmised that global signalling via astrocytes networks and highly pervasive signals, such as electromagnetic fields (EMFs), allow the appropriate integration of the various networks especially at crucial nodes level, the tetra-partite synapses. As a matter of fact, it has been shown that astrocytes can form gap-junction-coupled syncytia allowing intercellular communication characterised by a rapid and possibly long-distance transfer of signals. As far as the EMFs are concerned, the concept of broadcasted neuroconnectomics (BNC) has been introduced to describe highly pervasive signals involved in resetting the information handling of brain networks at various miniaturisation levels. In other words, BNC creates, thanks to the EMFs, generated especially by neurons, different assemblages among the various networks forming the brain hyper-network. Thus, it is surmised that neuronal networks are the "core components" of the brain hyper-network that has as special "nodes" the multi-facet tetra-partite synapses. Furthermore, it is suggested that investigations on the functional plasticity of multi-partite synapses in response to BNC can be the background for a new understanding and perhaps a new modelling of brain morpho-functional organisation and integrative actions.

PAGANI Toolkit: Parallel graph-theoretical analysis package for brain network big data

The recent collection of unprecedented quantities of neuroimaging data with high spatial resolution has led to brain network big data. However, a toolkit for fast and scalable computational solutions is still lacking. Here, we developed the PArallel Graph-theoretical ANalysIs (PAGANI) Toolkit based on a hybrid central processing unit-graphics processing unit (CPU-GPU) framework with a graphical user interface to facilitate the mapping and characterization of high-resolution brain networks. Specifically, the toolkit provides flexible parameters for users to customize computations of graph metrics in brain network analyses. As an empirical example, the PAGANI Toolkit was applied to individual voxel-based brain networks with ∼200,000 nodes that were derived from a resting-state fMRI dataset of 624 healthy young adults from the Human Connectome Project. Using a personal computer, this toolbox completed all computations in ∼27 h for one subject, which is markedly less than the 118 h required with a single-thread implementation. The voxel-based functional brain networks exhibited prominent small-world characteristics and densely connected hubs, which were mainly located in the medial and lateral fronto-parietal cortices. Moreover, the female group had significantly higher modularity and nodal betweenness centrality mainly in the medial/lateral fronto-parietal and occipital cortices than the male group. Significant correlations between the intelligence quotient and nodal metrics were also observed in several frontal regions. Collectively, the PAGANI Toolkit shows high computational performance and good scalability for analyzing connectome big data and provides a friendly interface without the complicated configuration of computing environments, thereby facilitating high-resolution connectomics research in health and disease.

The dynamics of human cognition: Increasing global integration coupled with decreasing segregation found using iEEG

Cognitive processing requires the ability to flexibly integrate and process information across large brain networks. How do brain networks dynamically reorganize to allow broad communication between many different brain regions in order to integrate information? We record neural activity from 12 epileptic patients using intracranial EEG while performing three cognitive tasks. We assess how the functional connectivity between different brain areas changes to facilitate communication across them. At the topological level, this facilitation is characterized by measures of integration and segregation. Across all patients, we found significant increases in integration and decreases in segregation during cognitive processing, especially in the gamma band (50-90 Hz). We also found higher levels of global synchronization and functional connectivity during task execution, again particularly in the gamma band. More importantly, functional connectivity modulations were not caused by changes in the level of the underlying oscillations. Instead, these modulations were caused by a rearrangement of the mutual synchronization between the different nodes as proposed by the "Communication Through Coherence" Theory.

Efficient communication dynamics on macro-connectome, and the propagation speed

Global communication dynamics in the brain can be captured using fMRI, MEG, or electrocorticography (ECoG), and the global slow dynamics often represent anatomical constraints. Complementary single-/multi-unit recordings have described local fast temporal dynamics. However, global fast temporal dynamics remain incompletely understood with considering of anatomical constraints. Therefore, we compared temporal aspects of cross-area propagations of single-unit recordings and ECoG, and investigated their anatomical bases. First, we demonstrated how both evoked and spontaneous ECoGs can accurately predict latencies of single-unit recordings. Next, we estimated the propagation velocity (1.0–1.5 m/s) from brain-wide data and found that it was fairly stable among different conscious levels. We also found that the shortest paths in anatomical topology strongly predicted the latencies. Finally, we demonstrated that Communicability, a novel graph-theoretic measure, is able to quantify that more than 90% of paths should use shortest paths and the remaining are non-shortest walks. These results revealed that macro-connectome is efficiently wired for detailed communication dynamics in the brain.

Hub connectivity, neuronal diversity, and gene expression in the Caenorhabditis elegans connectome

Studies of nervous system connectivity, in a wide variety of species and at different scales of resolution, have identified several highly conserved motifs of network organization. One such motif is a heterogeneous distribution of connectivity across neural elements, such that some elements act as highly connected and functionally important network hubs. These brain network hubs are also densely interconnected, forming a so-called rich club. Recent work in mouse has identified a distinctive transcriptional signature of neural hubs, characterized by tightly coupled expression of oxidative metabolism genes, with similar genes characterizing macroscale inter-modular hub regions of the human cortex. Here, we sought to determine whether hubs of the neuronal C. elegans connectome also show tightly coupled gene expression. Using open data on the chemical and electrical connectivity of 279 C. elegans neurons, and binary gene expression data for each neuron across 948 genes, we computed a correlated gene expression score for each pair of neurons, providing a measure of their gene expression similarity. We demonstrate that connections between hub neurons are the most similar in their gene expression while connections between nonhubs are the least similar. Genes with the greatest contribution to this effect are involved in glutamatergic and cholinergic signaling, and other communication processes. We further show that coupled expression between hub neurons cannot be explained by their neuronal subtype (i.e., sensory, motor, or interneuron), separation distance, chemically secreted neurotransmitter, birth time, pairwise lineage distance, or their topological module affiliation. Instead, this coupling is intrinsically linked to the identity of most hubs as command interneurons, a specific class of interneurons that regulates locomotion. Our results suggest that neural hubs may possess a distinctive transcriptional signature, preserved across scales and species, that is related to the involvement of hubs in regulating the higher-order behaviors of a given organism.

Cliques and cavities in the human connectome

Encoding brain regions and their connections as a network of nodes and edges captures many of the possible paths along which information can be transmitted as humans process and perform complex behaviors. Because cognitive processes involve large, distributed networks of brain areas, principled examinations of multi-node routes within larger connection patterns can offer fundamental insights into the complexities of brain function. Here, we investigate both densely connected groups of nodes that could perform local computations as well as larger patterns of interactions that would allow for parallel processing. Finding such structures necessitates that we move from considering exclusively pairwise interactions to capturing higher order relations, concepts naturally expressed in the language of algebraic topology. These tools can be used to study mesoscale network structures that arise from the arrangement of densely connected substructures called cliques in otherwise sparsely connected brain networks. We detect cliques (all-to-all connected sets of brain regions) in the average structural connectomes of 8 healthy adults scanned in triplicate and discover the presence of more large cliques than expected in null networks constructed via wiring minimization, providing architecture through which brain network can perform rapid, local processing. We then locate topological cavities of different dimensions, around which information may flow in either diverging or converging patterns. These cavities exist consistently across subjects, differ from those observed in null model networks, and - importantly - link regions of early and late evolutionary origin in long loops, underscoring their unique role in controlling brain function. These results offer a first demonstration that techniques from algebraic topology offer a novel perspective on structural connectomics, highlighting loop-like paths as crucial features in the human brain's structural architecture.

Topographical Information-Based High-Order Functional Connectivity and Its Application in Abnormality Detection for Mild Cognitive Impairment

Temporal synchronization-based functional connectivity (FC) has long been used by the neuroscience community. However, topographical FC information may provide additional information to characterize the advanced relationship between two brain regions. Accordingly, we proposed a novel method, namely high-order functional connectivity (HOFC), to capture this second-level relationship using inter-regional resemblance of the FC topographical profiles. Specifically, HOFC first calculates an FC profile for each brain region, notably between the given brain region and other brain regions. Based on these FC profiles, a second layer of correlations is computed between all pairs of brain regions (i.e., correlation's correlation). On this basis, we generated an HOFC network, where "high-order" network properties were computed. We found that HOFC was discordant with the traditional FC in several links, indicating additional information being revealed by the new metrics. We applied HOFC to identify biomarkers for early detection of Alzheimer's disease by comparing 77 mild cognitive impairment patients with 89 healthy individuals (control group). Sensitivity in detection of group difference was consistently improved by ∼25% using HOFC compared to using FC. An HOFC network analysis also provided complementary information to an FC network analysis. For example, HOFC between olfactory and orbitofrontal cortices was found significantly reduced in patients, besides extensive alterations in HOFC network properties. In conclusion, our results showed promise in using HOFC to comprehensively map the human brain connectome.

Diversity of meso-scale architecture in human and non-human connectomes

Brain function is reflected in connectome community structure. The dominant view is that communities are assortative and segregated from one another, supporting specialized information processing. However, this view precludes the possibility of non-assortative communities whose complex inter-community interactions could engender a richer functional repertoire. We use weighted stochastic blockmodels to uncover the meso-scale architecture of Drosophila, mouse, rat, macaque, and human connectomes. We find that most communities are assortative, though others form core-periphery and disassortative structures, which better recapitulate observed patterns of functional connectivity and gene co-expression in human and mouse connectomes compared to standard community detection techniques. We define measures for quantifying the diversity of communities in which brain regions participate, showing that this measure is peaked in control and subcortical systems in humans, and that inter-individual differences are correlated with cognitive performance. Our report paints a more diverse portrait of connectome communities and demonstrates their cognitive relevance.

Spatiotemporal, metabolic, and therapeutic characterization of altered functional connectivity in major depressive disorder

Although imbalanced functional integration has been increasingly reported in major depressive disorder (MDD), there still lacks a general framework to characterize common characteristic and origin shared by the integrative disturbances. Here we examined spatial selectivity, temporal uniqueness, metabolic basis, and therapeutic response of altered functional connectivity (FC) in MDD by analyzing both cross-sectional and longitudinal multimodal functional magnetic resonance imaging data from 35 patients and 34 demographically matched healthy controls. First, based on a voxel-wise, data-driven, graph-based degree centrality approach, the bilateral anterior cingulate gyri, middle frontal gyri and superior frontal gyri, and the right parahippocampal gyrus were robustly identified to show decreased FC in MDD. Further spatiotemporal analyses revealed that these regions exhibited hub-like features and were selectively located in limbic and default mode networks spatially and, relative to other areas in the brain, exhibited unique, frequency-dependent oscillation power (stronger within 0.01-0.027 Hz and weaker within 0.027-0.073 Hz) and less dynamical variability of whole-brain FC profiles temporally. Moreover, a cross-modality fusion analysis showed that all MDD-related FC impairments were associated with reduced cerebral blood flow (CBF); however, there existed multiple regions that showed reduced CBF but had intact FC in the patients, which resulted in a decreased FC-CBF coupling and implied an earlier emergence of reduced CBF than impaired FC in MDD. Finally, the disrupted FC in MDD gradually recovered over the course of drug treatment (2 and 12 weeks). Altogether, these findings could help establish a general framework to provide mechanistic insights into integrative dysfunctions in MDD.

Suprathreshold fiber cluster statistics: Leveraging white matter geometry to enhance tractography statistical analysis

This work presents a suprathreshold fiber cluster (STFC) method that leverages the whole brain fiber geometry to enhance statistical group difference analyses. The proposed method consists of 1) a well-established study-specific data-driven tractography parcellation to obtain white matter tract parcels and 2) a newly proposed nonparametric, permutation-test-based STFC method to identify significant differences between study populations. The basic idea of our method is that a white matter parcel's neighborhood (nearby parcels with similar white matter anatomy) can support the parcel's statistical significance when correcting for multiple comparisons. We propose an adaptive parcel neighborhood strategy to allow suprathreshold fiber cluster formation that is robust to anatomically varying inter-parcel distances. The method is demonstrated by application to a multi-shell diffusion MRI dataset from 59 individuals, including 30 attention deficit hyperactivity disorder patients and 29 healthy controls. Evaluations are conducted using both synthetic and in-vivo data. The results indicate that the STFC method gives greater sensitivity in finding group differences in white matter tract parcels compared to several traditional multiple comparison correction methods.

Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network

We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). However, STDP was not considered in previous works on stochastic burst synchronization (SBS) between noise-induced burstings of sub-threshold neurons. Here, we study the effect of additive STDP on SBS by varying the noise intensity D in the Barabási-Albert scale-free network (SFN). One of our main findings is a Matthew effect in synaptic plasticity which occurs due to a positive feedback process. Good burst synchronization (with higher bursting measure) gets better via long-term potentiation (LTP) of synaptic strengths, while bad burst synchronization (with lower bursting measure) gets worse via long-term depression (LTD). Consequently, a step-like rapid transition to SBS occurs by changing D, in contrast to a relatively smooth transition in the absence of STDP. We also investigate the effects of network architecture on SBS by varying the symmetric attachment degree [Formula: see text] and the asymmetry parameter [Formula: see text] in the SFN, and Matthew effects are also found to occur by varying [Formula: see text] and [Formula: see text]. Furthermore, emergences of LTP and LTD of synaptic strengths are investigated in details via our own microscopic methods based on both the distributions of time delays between the burst onset times of the pre- and the post-synaptic neurons and the pair-correlations between the pre- and the post-synaptic instantaneous individual burst rates (IIBRs). Finally, a multiplicative STDP case (depending on states) with soft bounds is also investigated in comparison with the additive STDP case (independent of states) with hard bounds. Due to the soft bounds, a Matthew effect with some quantitative differences is also found to occur for the case of multiplicative STDP.

Aging and Network Properties: Stability Over Time and Links with Learning during Working Memory Training

Growing evidence suggests that healthy aging affects the configuration of large-scale functional brain networks. This includes reducing network modularity and local efficiency. However, the stability of these effects over time and their potential role in learning remain poorly understood. The goal of the present study was to further clarify previously reported age effects on "resting-state" networks, to test their reliability over time, and to assess their relation to subsequent learning during training. Resting-state fMRI data from 23 young (YA) and 20 older adults (OA) were acquired in 2 sessions 2 weeks apart. Graph-theoretic analyses identified both consistencies in network structure and differences in module composition between YA and OA, suggesting topological changes and less stability of functional network configuration with aging. Brain-wide, OA showed lower modularity and local efficiency compared to YA, consistent with the idea of age-related functional dedifferentiation, and these effects were replicable over time. At the level of individual networks, OA consistently showed greater participation and lower local efficiency and within-network connectivity in the cingulo-opercular network, as well as lower intra-network connectivity in the default-mode network and greater participation of the somato-sensorimotor network, suggesting age-related differential effects at the level of specialized brain modules. Finally, brain-wide network properties showed associations, albeit limited, with learning rates, as assessed with 10 days of computerized working memory training administered after the resting-state sessions, suggesting that baseline network configuration may influence subsequent learning outcomes. Identification of neural mechanisms associated with learning-induced plasticity is important for further clarifying whether and how such changes predict the magnitude and maintenance of training gains, as well as the extent and limits of cognitive transfer in both younger and older adults.

From Maps to Multi-dimensional Network Mechanisms of Mental Disorders

The development of advanced neuroimaging techniques and their deployment in large cohorts has enabled an assessment of functional and structural brain network architecture at an unprecedented level of detail. Across many temporal and spatial scales, network neuroscience has emerged as a central focus of intellectual efforts, seeking meaningful descriptions of brain networks and explanatory sets of network features that underlie circuit function in health and dysfunction in disease. However, the tools of network science commonly deployed provide insight into brain function at a fundamentally descriptive level, often failing to identify (patho-)physiological mechanisms that link system-level phenomena to the multiple hierarchies of brain function. Here we describe recently developed techniques stemming from advances in complex systems and network science that have the potential to overcome this limitation, thereby contributing mechanistic insights into neuroanatomy, functional dynamics, and pathology. Finally, we build on the Research Domain Criteria framework, highlighting the notion that mental illnesses can be conceptualized as dysfunctions of neural circuitry present across conventional diagnostic boundaries, to sketch how network-based methods can be combined with pharmacological, intermediate phenotype, genetic, and magnetic stimulation studies to probe mechanisms of psychopathology.

New dimensions of connectomics and network plasticity in the central nervous system

Cellular network architecture plays a crucial role as the structural substrate for the brain functions. Therefore, it represents the main rationale for the emerging field of connectomics, defined as the comprehensive study of all aspects of central nervous system connectivity. Accordingly, in the present paper the main emphasis will be on the communication processes in the brain, namely wiring transmission (WT), i.e. the mapping of the communication channels made by cell components such as axons and synapses, and volume transmission (VT), i.e. the chemical signal diffusion along the interstitial brain fluid pathways. Considering both processes can further expand the connectomics concept, since both WT-connectomics and VT-connectomics contribute to the structure of the brain connectome. A consensus exists that such a structure follows a hierarchical or nested architecture, and macro-, meso- and microscales have been defined. In this respect, however, several lines of evidence indicate that a nanoscale (nano-connectomics) should also be considered to capture direct protein-protein allosteric interactions such as those occurring, for example, in receptor-receptor interactions at the plasma membrane level. In addition, emerging evidence points to novel mechanisms likely playing a significant role in the modulation of intercellular connectivity, increasing the plasticity of the system and adding complexity to its structure. In particular, the roamer type of VT (i.e. the intercellular transfer of RNA, proteins and receptors by extracellular vesicles) will be discussed since it allowed us to introduce a new concept of 'transient changes of cell phenotype', that is the transient acquisition of new signal release capabilities and/or new recognition/decoding apparatuses.

Enhanced Network Efficiency of Functional Brain Networks in Primary Insomnia Patients

Accumulating evidence from neuroimaging studies suggests that primary insomnia (PI) affects interregional neural coordination of multiple interacting functional brain networks. However, a complete understanding of the whole-brain network organization from a system-level perspective in PI is still lacking. To this end, we investigated in topological organization changes in brain functional networks in PI. 36 PI patients and 38 age-, sex-, and education-matched healthy controls were recruited. All participants underwent a series of neuropsychological assessments and resting-state functional magnetic resonance imaging scans. Individual whole-brain functional network were constructed and analyzed using graph theory-based network approaches. There were no significant differences with respect to age, sex, or education between groups (P > 0.05). Graph-based analyses revealed that participants with PI had a significantly higher total number of edges (P = 0.022), global efficiency (P = 0.014), and normalized global efficiency (P = 0.002), and a significantly lower normalized local efficiency (P = 0.042) compared with controls. Locally, several prefrontal and parietal regions, the superior temporal gyrus, and the thalamus exhibited higher nodal efficiency in participants with PI (P < 0.05, false discovery rate corrected). In addition, most of these regions showed increased functional connectivity in PI patients (P < 0.05, corrected). Finally, altered network efficiency was correlated with neuropsychological variables of the Epworth Sleepiness Scale and Insomnia Severity Index in patients with PI. PI is associated with abnormal organization of large-scale functional brain networks, which may account for memory and emotional dysfunction in people with PI. These findings provide novel implications for neural substrates associated with PI.

From Default Mode Network to the Basal Configuration: Sex Differences in the Resting-State Brain Connectivity as a Function of Age and Their Clinical Correlates

Connectomics is a framework that models brain structure and function interconnectivity as a network, rather than narrowly focusing on select regions-of-interest. MRI-derived connectomes can be structural, usually based on diffusion-weighted MR imaging, or functional, usually formed by examining fMRI blood-oxygen-level-dependent (BOLD) signal correlations. Recently, we developed a novel method for assessing the hierarchical modularity of functional brain networks-the probability associated community estimation (PACE). PACE uniquely permits a dual formulation, thus yielding equivalent connectome modular structure regardless of whether positive or negative edges are considered. This method was rigorously validated using the 1,000 functional connectomes project data set (F1000, RRID:SCR_005361) (1) and the Human Connectome Project (HCP, RRID:SCR_006942) (2, 3) and we reported novel sex differences in resting-state connectivity not previously reported. (4) This study further examines sex differences in regard to hierarchical modularity as a function of age and clinical correlates, with findings supporting a basal configuration framework as a more nuanced and dynamic way of conceptualizing the resting-state connectome that is modulated by both age and sex. Our results showed that differences in connectivity between men and women in the 22-25 age range were not significantly different. However, these same non-significant differences attained significance in both the 26-30 age group (p = 0.003) and the 31-35 age group (p < 0.001). At the most global level, areas of diverging sex difference include parts of the prefrontal cortex and the temporal lobe, amygdala, hippocampus, inferior parietal lobule, posterior cingulate, and precuneus. Further, we identified statistically different self-reported summary scores of inattention, hyperactivity, and anxiety problems between men and women. These self-reports additionally divergently interact with age and the basal configuration between sexes.

The Emergence of Canalization and Evolvability in an Open-Ended, Interactive Evolutionary System

Many believe that an essential component for the discovery of the tremendous diversity in natural organisms was the evolution of evolvability, whereby evolution speeds up its ability to innovate by generating a more adaptive pool of offspring. One hypothesized mechanism for evolvability is developmental canalization, wherein certain dimensions of variation become more likely to be traversed and others are prevented from being explored (e.g., offspring tend to have similar-size legs, and mutations affect the length of both legs, not each leg individually). While ubiquitous in nature, canalization is rarely reported in computational simulations of evolution, which deprives us of in silico examples of canalization to study and raises the question of which conditions give rise to this form of evolvability. Answering this question would shed light on why such evolvability emerged naturally, and it could accelerate engineering efforts to harness evolution to solve important engineering challenges. In this article, we reveal a unique system in which canalization did emerge in computational evolution. We document that genomes entrench certain dimensions of variation that were frequently explored during their evolutionary history. The genetic representation of these organisms also evolved to be more modular and hierarchical than expected by chance, and we show that these organizational properties correlate with increased fitness. Interestingly, the type of computational evolutionary experiment that produced this evolvability was very different from traditional digital evolution in that there was no objective, suggesting that open-ended, divergent evolutionary processes may be necessary for the evolution of evolvability.

Probabilistic thresholding of functional connectomes: Application to schizophrenia

Functional connectomes are commonly analysed as sparse graphs, constructed by thresholding cross-correlations between regional neurophysiological signals. Thresholding generally retains the strongest edges (correlations), either by retaining edges surpassing a given absolute weight, or by constraining the edge density. The latter (more widely used) method risks inclusion of false positive edges at high edge densities and exclusion of true positive edges at low edge densities. Here we apply new wavelet-based methods, which enable construction of probabilistically-thresholded graphs controlled for type I error, to a dataset of resting-state fMRI scans of 56 patients with schizophrenia and 71 healthy controls. By thresholding connectomes to fixed edge-specific P value, we found that functional connectomes of patients with schizophrenia were more dysconnected than those of healthy controls, exhibiting a lower edge density and a higher number of (dis)connected components. Furthermore, many participants' connectomes could not be built up to the fixed edge densities commonly studied in the literature (∼5-30%), while controlling for type I error. Additionally, we showed that the topological randomisation previously reported in the schizophrenia literature is likely attributable to "non-significant" edges added when thresholding connectomes to fixed density based on correlation. Finally, by explicitly comparing connectomes thresholded by increasing P value and decreasing correlation, we showed that probabilistically thresholded connectomes show decreased randomness and increased consistency across participants. Our results have implications for future analysis of functional connectivity using graph theory, especially within datasets exhibiting heterogenous distributions of edge weights (correlations), between groups or across participants.

Improving resolution of dynamic communities in human brain networks through targeted node removal

Current approaches to dynamic community detection in complex networks can fail to identify multi-scale community structure, or to resolve key features of community dynamics. We propose a targeted node removal technique to improve the resolution of community detection. Using synthetic oscillator networks with well-defined “ground truth” communities, we quantify the community detection performance of a common modularity maximization algorithm. We show that the performance of the algorithm on communities of a given size deteriorates when these communities are embedded in multi-scale networks with communities of different sizes, compared to the performance in a single-scale network. We demonstrate that targeted node removal during community detection improves performance on multi-scale networks, particularly when removing the most functionally cohesive nodes. Applying this approach to network neuroscience, we compare dynamic functional brain networks derived from fMRI data taken during both repetitive single-task and varied multi-task experiments. After the removal of regions in visual cortex, the most coherent functional brain area during the tasks, community detection is better able to resolve known functional brain systems into communities. In addition, node removal enables the algorithm to distinguish clear differences in brain network dynamics between these experiments, revealing task-switching behavior that was not identified with the visual regions present in the network. These results indicate that targeted node removal can improve spatial and temporal resolution in community detection, and they demonstrate a promising approach for comparison of network dynamics between neuroscientific data sets with different resolution parameters.

Brain connectivity-informed regularization methods for regression

One of the challenging problems in brain imaging research is a principled incorporation of information from different imaging modalities. Frequently, each modality is analyzed separately using, for instance, dimensionality reduction techniques, which result in a loss of mutual information. We propose a novel regularization-method to estimate the association between the brain structure features and a scalar outcome within the linear regression framework. Our regularization technique provides a principled approach to use external information from the structural brain connectivity and inform the estimation of the regression coefficients. Our proposal extends the classical Tikhonov regularization framework by defining a penalty term based on the structural connectivity-derived Laplacian matrix. Here, we address both theoretical and computational issues. The approach is first illustrated using simulated data and compared with other penalized regression methods. We then apply our regularization method to study the associations between the alcoholism phenotypes and brain cortical thickness using a diffusion imaging derived measure of structural connectivity. Using the proposed methodology in 148 young male subjects with a risk for alcoholism, we found a negative associations between cortical thickness and drinks per drinking day in bilateral caudal anterior cingulate cortex, left lateral OFC and left precentral gyrus.

Intelligence is associated with the modular structure of intrinsic brain networks

General intelligence is a psychological construct that captures in a single metric the overall level of behavioural and cognitive performance in an individual. While previous research has attempted to localise intelligence in circumscribed brain regions, more recent work focuses on functional interactions between regions. However, even though brain networks are characterised by substantial modularity, it is unclear whether and how the brain's modular organisation is associated with general intelligence. Modelling subject-specific brain network graphs from functional MRI resting-state data (N = 309), we found that intelligence was not associated with global modularity features (e.g., number or size of modules) or the whole-brain proportions of different node types (e.g., connector hubs or provincial hubs). In contrast, we observed characteristic associations between intelligence and node-specific measures of within- and between-module connectivity, particularly in frontal and parietal brain regions that have previously been linked to intelligence. We propose that the connectivity profile of these regions may shape intelligence-relevant aspects of information processing. Our data demonstrate that not only region-specific differences in brain structure and function, but also the network-topological embedding of fronto-parietal as well as other cortical and subcortical brain regions is related to individual differences in higher cognitive abilities, i.e., intelligence.

Predicting Long-Term Cognitive Outcome Following Breast Cancer with Pre-Treatment Resting State fMRI and Random Forest Machine Learning

We aimed to determine if resting state functional magnetic resonance imaging (fMRI) acquired at pre-treatment baseline could accurately predict breast cancer-related cognitive impairment at long-term follow-up. We evaluated 31 patients with breast cancer (age 34–65) prior to any treatment, post-chemotherapy and 1 year later. Cognitive testing scores were normalized based on data obtained from 43 healthy female controls and then used to categorize patients as impaired or not based on longitudinal changes. We measured clustering coefficient, a measure of local connectivity, by applying graph theory to baseline resting state fMRI and entered these metrics along with relevant patient-related and medical variables into random forest classification. Incidence of cognitive impairment at 1 year follow-up was 55% and was predicted by classification algorithms with up to 100% accuracy (p < 0.0001). The neuroimaging-based model was significantly more accurate than a model involving patient-related and medical variables (p = 0.005). Hub regions belonging to several distinct functional networks were the most important predictors of cognitive outcome. Characteristics of these hubs indicated potential spread of brain injury from default mode to other networks over time. These findings suggest that resting state fMRI is a promising tool for predicting future cognitive impairment associated with breast cancer. This information could inform treatment decision making by identifying patients at highest risk for long-term cognitive impairment.

Beyond modularity: Fine-scale mechanisms and rules for brain network reconfiguration

The human brain is in constant flux, as distinct areas engage in transient communication to support basic behaviors as well as complex cognition. The collection of interactions between cortical and subcortical areas forms a functional brain network whose topology evolves with time. Despite the nontrivial dynamics that are germane to this networked system, experimental evidence demonstrates that functional interactions organize into putative brain systems that facilitate different facets of cognitive computation. We hypothesize that such dynamic functional networks are organized around a set of rules that constrain their spatial architecture - which brain regions may functionally interact - and their temporal architecture - how these interactions fluctuate over time. To objectively uncover these organizing principles, we apply an unsupervised machine learning approach called non-negative matrix factorization to time-evolving, resting state functional networks in 20 healthy subjects. This machine learning approach automatically groups temporally co-varying functional interactions into subgraphs that represent putative topological modes of dynamic functional architecture. We find that subgraphs are stratified based on both the underlying modular organization and the topographical distance of their strongest interactions: while many subgraphs are largely contained within modules, others span between modules and are expressed differently over time. The relationship between dynamic subgraphs and modular architecture is further highlighted by the ability of time-varying subgraph expression to explain inter-individual differences in module reorganization. Collectively, these results point to the critical role that subgraphs play in constraining the topography and topology of functional brain networks. More broadly, this machine learning approach opens a new door for understanding the architecture of dynamic functional networks during both task and rest states, and for probing alterations of that architecture in disease.

Organizing principles for the cerebral cortex network of commissural and association connections

Cognition is supported by a network of axonal connections between gray matter regions within and between right and left cerebral cortex. Global organizing principles of this circuitry were examined with network analysis tools applied to monosynaptic association (within one side) and commissural (between sides) connections between all 77 cortical gray matter regions in each hemisphere of the rat brain. The analysis used 32,350 connection reports expertly collated from published pathway tracing experiments, and 5,394 connections of a possible 23,562 were identified, for a connection density of 23%-of which 20% (1,084) were commissural. Network community detection yielded a stable bihemispheric six-module solution, with an identical set in each hemisphere of three modules topographically forming a lateral core and medial shell arrangement of cortical regions. Functional correlations suggest the lateral module deals preferentially with environmental sensory-motor interactions and the ventromedial module deals preferentially with visceral control, affect, and short-term memory, whereas the dorsomedial module resembles the default mode network. Analysis of commissural connections revealed a set of unexpected rules to help generate hypotheses. Most notably, there is an order of magnitude more heterotopic than homotopic projections; all cortical regions send more association than commissural connections, and for each region, the latter are always a subset of the former; the number of association connections from each cortical region strongly correlates with the number of its commissural connections; and the module (dorsomedial) lying closest to the corpus callosum has the most complete set of commissural connections-and apparently the most complex function.

Developmental increases in white matter network controllability support a growing diversity of brain dynamics

As the human brain develops, it increasingly supports coordinated control of neural activity. The mechanism by which white matter evolves to support this coordination is not well understood. Here we use a network representation of diffusion imaging data from 882 youth ages 8-22 to show that white matter connectivity becomes increasingly optimized for a diverse range of predicted dynamics in development. Notably, stable controllers in subcortical areas are negatively related to cognitive performance. Investigating structural mechanisms supporting these changes, we simulate network evolution with a set of growth rules. We find that all brain networks are structured in a manner highly optimized for network control, with distinct control mechanisms predicted in child vs. older youth. We demonstrate that our results cannot be explained by changes in network modularity. This work reveals a possible mechanism of human brain development that preferentially optimizes dynamic network control over static network architecture.

Generative models for network neuroscience: prospects and promise

Network neuroscience is the emerging discipline concerned with investigating the complex patterns of interconnections found in neural systems, and identifying principles with which to understand them. Within this discipline, one particularly powerful approach is network generative modelling, in which wiring rules are algorithmically implemented to produce synthetic network architectures with the same properties as observed in empirical network data. Successful models can highlight the principles by which a network is organized and potentially uncover the mechanisms by which it grows and develops. Here, we review the prospects and promise of generative models for network neuroscience. We begin with a primer on network generative models, with a discussion of compressibility and predictability, and utility in intuiting mechanisms, followed by a short history on their use in network science, broadly. We then discuss generative models in practice and application, paying particular attention to the critical need for cross-validation. Next, we review generative models of biological neural networks, both at the cellular and large-scale level, and across a variety of species including Caenorhabditis elegans, Drosophila, mouse, rat, cat, macaque and human. We offer a careful treatment of a few relevant distinctions, including differences between generative models and null models, sufficiency and redundancy, inferring and claiming mechanism, and functional and structural connectivity. We close with a discussion of future directions, outlining exciting frontiers both in empirical data collection efforts as well as in method and theory development that, together, further the utility of the generative network modelling approach for network neuroscience.

Large-scale DCMs for resting-state fMRI

This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity. This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of Bayesian model reduction to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM—with functional connectivity priors—is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.

Multi-scale brain networks

The network architecture of the human brain has become a feature of increasing interest to the neuroscientific community, largely because of its potential to illuminate human cognition, its variation over development and aging, and its alteration in disease or injury. Traditional tools and approaches to study this architecture have largely focused on single scales-of topology, time, and space. Expanding beyond this narrow view, we focus this review on pertinent questions and novel methodological advances for the multi-scale brain. We separate our exposition into content related to multi-scale topological structure, multi-scale temporal structure, and multi-scale spatial structure. In each case, we recount empirical evidence for such structures, survey network-based methodological approaches to reveal these structures, and outline current frontiers and open questions. Although predominantly peppered with examples from human neuroimaging, we hope that this account will offer an accessible guide to any neuroscientist aiming to measure, characterize, and understand the full richness of the brain's multiscale network structure-irrespective of species, imaging modality, or spatial resolution.

The significance of negative correlations in brain connectivity

Understanding the modularity of functional magnetic resonance imaging (fMRI)-derived brain networks or "connectomes" can inform the study of brain function organization. However, fMRI connectomes additionally involve negative edges, which may not be optimally accounted for by existing approaches to modularity that variably threshold, binarize, or arbitrarily weight these connections. Consequently, many existing Q maximization-based modularity algorithms yield variable modular structures. Here, we present an alternative complementary approach that exploits how frequent the blood-oxygen-level-dependent (BOLD) signal correlation between two nodes is negative. We validated this novel probability-based modularity approach on two independent publicly-available resting-state connectome data sets (the Human Connectome Project [HCP] and the 1,000 functional connectomes) and demonstrated that negative correlations alone are sufficient in understanding resting-state modularity. In fact, this approach (a) permits a dual formulation, leading to equivalent solutions regardless of whether one considers positive or negative edges; (b) is theoretically linked to the Ising model defined on the connectome, thus yielding modularity result that maximizes data likelihood. Additionally, we were able to detect novel and consistent sex differences in modularity in both data sets. As data sets like HCP become widely available for analysis by the neuroscience community at large, alternative and perhaps more advantageous computational tools to understand the neurobiological information of negative edges in fMRI connectomes are increasingly important.

Control without Controllers: Toward a Distributed Neuroscience of Executive Control

Executive control refers to the regulation of cognition and behavior by mental processes and is a hallmark of higher cognition. Most approaches to understanding its mechanisms begin with the assumption that our brains have anatomically segregated and functionally specialized control modules. The modular approach is intuitive: Control is conceptually distinct from basic mental processing, so an organization that reifies that distinction makes sense. An alternative approach sees executive control as self-organizing principles of a distributed organization. In distributed systems, control and controlled processes are colocalized within large numbers of dispersed computational agents. Control then is often an emergent consequence of simple rules governing the interaction between agents. Because these systems are unfamiliar and unintuitive, here we review several well-understood examples of distributed control systems, group living insects and social animals, and emphasize their parallels with neural systems. We then reexamine the cognitive neuroscience literature on executive control for evidence that its neural control systems may be distributed.

Concussion As a Multi-Scale Complex System: An Interdisciplinary Synthesis of Current Knowledge

Traumatic brain injury (TBI) has been called "the most complicated disease of the most complex organ of the body" and is an increasingly high-profile public health issue. Many patients report long-term impairments following even "mild" injuries, but reliable criteria for diagnosis and prognosis are lacking. Every clinical trial for TBI treatment to date has failed to demonstrate reliable and safe improvement in outcomes, and the existing body of literature is insufficient to support the creation of a new classification system. Concussion, or mild TBI, is a highly heterogeneous phenomenon, and numerous factors interact dynamically to influence an individual's recovery trajectory. Many of the obstacles faced in research and clinical practice related to TBI and concussion, including observed heterogeneity, arguably stem from the complexity of the condition itself. To improve understanding of this complexity, we review the current state of research through the lens provided by the interdisciplinary field of systems science, which has been increasingly applied to biomedical issues. The review was conducted iteratively, through multiple phases of literature review, expert interviews, and systems diagramming and represents the first phase in an effort to develop systems models of concussion. The primary focus of this work was to examine concepts and ways of thinking about concussion that currently impede research design and block advancements in care of TBI. Results are presented in the form of a multi-scale conceptual framework intended to synthesize knowledge across disciplines, improve research design, and provide a broader, multi-scale model for understanding concussion pathophysiology, classification, and treatment.

Role of Graph Architecture in Controlling Dynamical Networks with Applications to Neural Systems

Networked systems display complex patterns of interactions between components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology, supporting a variety of system-wide dynamical behaviors such as synchronization. While descriptions of these behaviors are important, they are only a first step towards understanding and harnessing the relationship between network topology and system behavior. Here, we use linear network control theory to derive accurate closed-form expressions that relate the connectivity of a subset of structural connections (those linking driver nodes to non-driver nodes) to the minimum energy required to control networked systems. To illustrate the utility of the mathematics, we apply this approach to high-resolution connectomes recently reconstructed from Drosophila, mouse, and human brains. We use these principles to suggest an advantage of the human brain in supporting diverse network dynamics with small energetic costs while remaining robust to perturbations, and to perform clinically accessible targeted manipulation of the brain's control performance by removing single edges in the network. Generally, our results ground the expectation of a control system's behavior in its network architecture, and directly inspire new directions in network analysis and design via distributed control.

Multidimensional encoding of brain connectomes

The ability to map brain networks in living individuals is fundamental in efforts to chart the relation between human behavior, health and disease. Advances in network neuroscience may benefit from developing new frameworks for mapping brain connectomes. We present a framework to encode structural brain connectomes and diffusion-weighted magnetic resonance (dMRI) data using multidimensional arrays. The framework integrates the relation between connectome nodes, edges, white matter fascicles and diffusion data. We demonstrate the utility of the framework for in vivo white matter mapping and anatomical computing by evaluating 1,490 connectomes, thirteen tractography methods, and three data sets. The framework dramatically reduces storage requirements for connectome evaluation methods, with up to 40x compression factors. Evaluation of multiple, diverse datasets demonstrates the importance of spatial resolution in dMRI. We measured large increases in connectome resolution as function of data spatial resolution (up to 52%). Moreover, we demonstrate that the framework allows performing anatomical manipulations on white matter tracts for statistical inference and to study the white matter geometrical organization. Finally, we provide open-source software implementing the method and data to reproduce the results.

A Tri-network Model of Human Semantic Processing

Humans process the meaning of the world via both verbal and nonverbal modalities. It has been established that widely distributed cortical regions are involved in semantic processing, yet the global wiring pattern of this brain system has not been considered in the current neurocognitive semantic models. We review evidence from the brain-network perspective, which shows that the semantic system is topologically segregated into three brain modules. Revisiting previous region-based evidence in light of these new network findings, we postulate that these three modules support multimodal experiential representation, language-supported representation, and semantic control. A tri-network neurocognitive model of semantic processing is proposed, which generates new hypotheses regarding the network basis of different types of semantic processes.

Frequency-specific neuromodulation of local and distant connectivity in aging and episodic memory function

A growing literature has focused on the brain's ability to augment processing in local regions by recruiting distant communities of neurons in response to neural decline or insult. In particular, both younger and older adult populations recruit bilateral prefrontal cortex (PFC) as a means of compensating for increasing neural effort to maintain successful cognitive function. However, it remains unclear how local changes in neural activity affect the recruitment of this adaptive mechanism. To address this problem, we combined graph theoretical measures from functional MRI with diffusion weighted imaging and repetitive transcranial magnetic stimulation (rTMS) to resolve a central hypothesis: how do aged brains flexibly adapt to local changes in cortical activity? Specifically, we applied neuromodulation to increase or decrease local activity in a cortical region supporting successful memory encoding (left dorsolateral PFC or DLPFC) using 5 or 1 Hz rTMS, respectively. We then assessed a region's local within-module degree, or the distributed between-module degree (BMD) between distant cortical communities. We predicted that (1) local stimulation-related deficits may be counteracted by boosting BMD between bilateral PFC, and that this effect should be (2) positively correlated with structural connectivity. Both predictions were confirmed; 5 Hz rTMS increased local success-related activity and local increases in PFC connectivity, while 1 Hz rTMS decreases local activity and triggered a more distributed pattern of bilateral PFC connectivity to compensate for this local inhibitory effect. These results provide an integrated, causal explanation for the network interactions associated with successful memory encoding in older adults. Hum Brain Mapp 38:5987-6004, 2017. © 2017 Wiley Periodicals, Inc.