Why data coherence and quality is critical for understanding interareal cortical networks

Predictability of cortico-cortical connections in the mammalian brain

Despite a five order of magnitude range in size, the brains of mammals share many anatomical and functional characteristics that translate into cortical network commonalities. Here we develop a machine learning framework to quantify the degree of predictability of the weighted interareal cortical matrix. Partial network connectivity data were obtained with retrograde tract-tracing experiments generated with a consistent methodology, supplemented by projection length measurements in a nonhuman primate (macaque) and a rodent (mouse). We show that there is a significant level of predictability embedded in the interareal cortical networks of both species. At the binary level, links are predictable with an area under the ROC curve of at least 0.8 for the macaque. Weighted medium and strong links are predictable with an 85%-90% accuracy (mouse) and 70%-80% (macaque), whereas weak links are not predictable in either species. These observations reinforce earlier observations that the formation and evolution of the cortical network at the mesoscale is, to a large extent, rule based. Using the methodology presented here, we performed imputations on all area pairs, generating samples for the complete interareal network in both species. These are necessary for comparative studies of the connectome with minimal bias, both within and across species.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Mapping Structural Connectivity Using Diffusion MRI: Challenges and Opportunities

Diffusion MRI-based tractography is the most commonly-used technique when inferring the structural brain connectome, i.e., the comprehensive map of the connections in the brain. The utility of graph theory-a powerful mathematical approach for modeling complex network systems-for analyzing tractography-based connectomes brings important opportunities to interrogate connectome data, providing novel insights into the connectivity patterns and topological characteristics of brain structural networks. When applying this framework, however, there are challenges, particularly regarding methodological and biological plausibility. This article describes the challenges surrounding quantitative tractography and potential solutions. In addition, challenges related to the calculation of global network metrics based on graph theory are discussed.Evidence Level: 5Technical Efficacy: Stage 1.

Hierarchical disruption in the cortex of anesthetized monkeys as a new signature of consciousness loss

Anesthesia induces a reconfiguration of the repertoire of functional brain states leading to a high function-structure similarity. However, it is unclear how these functional changes lead to loss of consciousness. Here we suggest that the mechanism of conscious access is related to a general dynamical rearrangement of the intrinsic hierarchical organization of the cortex. To measure cortical hierarchy, we applied the Intrinsic Ignition analysis to resting-state fMRI data acquired in awake and anesthetized macaques. Our results reveal the existence of spatial and temporal hierarchical differences of neural activity within the macaque cortex, with a strong modulation by the depth of anesthesia and the employed anesthetic agent. Higher values of Intrinsic Ignition correspond to rich and flexible brain dynamics whereas lower values correspond to poor and rigid, structurally driven brain dynamics. Moreover, spatial and temporal hierarchical dimensions are disrupted in a different manner, involving different hierarchical brain networks. All together suggest that disruption of brain hierarchy is a new signature of consciousness loss.

Brain connectomes come of age

Databases of consistent, directed- and weighted inter-areal connectivity for mouse, macaque and marmoset monkeys have recently become available and begun to be used to build structural and dynamical models. A structural hierarchy can be defined based by laminar patterns of cortical connections. A large-scale dynamical model of the macaque cortex endowed with a laminar structure accounts for empirically observed frequency-modulated interplay between bottom-up and top-down processes. Signal propagation in the model with spiking neurons displays a threshold of stimulus amplitude for the activity to gain access to the prefrontal cortex, reminiscent of the ignition phenomenon associated with conscious perception. These two examples illustrate how connectomics inform structurally based dynamic models of multi-regional brain systems. Theory raises novel questions for future anatomical and physiological empirical research, in a back-and-forth collaboration between experimentalists and theorists. Directed- and weighted inter-areal cortical connectivity matrices of macaque, marmoset and mouse exhibit similarities as well as marked differences. The new connectomic data provide quantitative information for structural and dynamical modeling of multi-regional cortical circuit providing insight to the global cortical function. Quantification of cortical hierarchy guides investigations of interplay between bottom-up and top-down information processes.

Anatomy of nerve fiber bundles at micrometer-resolution in the vervet monkey visual system

Although the primate visual system has been extensively studied, detailed spatial organization of white matter fiber tracts carrying visual information between areas has not been fully established. This is mainly due to the large gap between tracer studies and diffusion-weighted MRI studies, which focus on specific axonal connections and macroscale organization of fiber tracts, respectively. Here we used 3D polarization light imaging (3D-PLI), which enables direct visualization of fiber tracts at micrometer resolution, to identify and visualize fiber tracts of the visual system, such as stratum sagittale, inferior longitudinal fascicle, vertical occipital fascicle, tapetum and dorsal occipital bundle in vervet monkey brains. Moreover, 3D-PLI data provide detailed information on cortical projections of these tracts, distinction between neighboring tracts, and novel short-range pathways. This work provides essential information for interpretation of functional and diffusion-weighted MRI data, as well as revision of wiring diagrams based upon observations in the vervet visual system.

Mapping Connectome in Mammalian Brain: A Novel Approach by Bioengineering Neuro-Glia specific Vectors

The connectome is the comprehensive map of the brain represented by wiring diagram of the full set of neuro-glia and synapses within entire brain of an organism. Some recent scientific efforts have successfully been made to visualize such map at neuro-glial networking level, however, capturing it as one unit of the entire brain have never been elucidated. Moreover, in order to derive structure-function relationship of different brain regions in response to a defined stimulus, there is a need to elucidate the connectome at single neuro-glial ensemble level after brain is challenged with the known memory function. This needs developing molecular approaches to tag neuro-glial activities in response to a conditioned brain function. Such approaches of using specific molecular tags have been tried to visualize independently neuron and glial specific events in response to a memory function, however, they could not tag the connectome together at single neuro-glia ensemble level. Therefore, there is a need to develop new methods for mapping entire connectome up to a single neuro-glial precision and resolution, with a purpose of tagging specific brain region accountable to execute a special memory formation process. The present hypothetical paper aims to propose a novel molecular method to generate the structural connectome at neuro-glial level in mice brain. Herein, we propose to tag the entire connectome at neuro-glia precision by generating a transgenic mice via transposing and recombining engineered novel "Neuro-Glia specific Vectors" (NGVs: specific to excitatory neurons, inhibitory neurons and glial cells) vis a vis "Transcriptional/ Translational Messenger (TMs: specific to metalloproteinases, MMP-9) coupled with different color protein tags, followed by the Clarity. Herein, the NGVs will be translated via Neuro-glia specific promoters, while TMs will be translated via endogenous MMP-9 promoter in all neuro-glial cells. The viability of all constructs will be verified in cortical/ hippocampal culture by inducing them to undergo chemically induced long term potentionation (cLTP) following visualization of different colored pattern. This will be further confirmed by Immunostaning, Western Blot and RT-PCR analysis. Additionally, in this approach, one can decipher the dynamics of molecular and cellular events associated with MMP-9 seretome by monitoring the trafficking of tagged endogenous MMP-9 protein after neuronal stimulation by cLTP in vitro. However, for visualizing complete connectome, the adult transgenic mice will be challenged with fear consolidation (Fear context and contextual cue) tests followed by Clarity coupled Light Sheet Microscopy to analyze neuro-glia ensemble following whole brain imaging.

The Mouse Cortical Connectome, Characterized by an Ultra-Dense Cortical Graph, Maintains Specificity by Distinct Connectivity Profiles

The inter-areal wiring pattern of the mouse cerebral cortex was analyzed in relation to a refined parcellation of cortical areas. Twenty-seven retrograde tracer injections were made in 19 areas of a 47-area parcellation of the mouse neocortex. Flat mounts of the cortex and multiple histological markers enabled detailed counts of labeled neurons in individual areas. The observed log-normal distribution of connection weights to each cortical area spans 5 orders of magnitude and reveals a distinct connectivity profile for each area, analogous to that observed in macaques. The cortical network has a density of 97%, considerably higher than the 66% density reported in macaques. A weighted graph analysis reveals a similar global efficiency but weaker spatial clustering compared with that reported in macaques. The consistency, precision of the connectivity profile, density, and weighted graph analysis of the present data differ significantly from those obtained in earlier studies in the mouse.

Novel Brain Complexity Measures Based on Information Theory

Brain networks are widely used models to understand the topology and organization of the brain. These networks can be represented by a graph, where nodes correspond to brain regions and edges to structural or functional connections. Several measures have been proposed to describe the topological features of these networks, but unfortunately, it is still unclear which measures give the best representation of the brain. In this paper, we propose a new set of measures based on information theory. Our approach interprets the brain network as a stochastic process where impulses are modeled as a random walk on the graph nodes. This new interpretation provides a solid theoretical framework from which several global and local measures are derived. Global measures provide quantitative values for the whole brain network characterization and include entropy, mutual information, and erasure mutual information. The latter is a new measure based on mutual information and erasure entropy. On the other hand, local measures are based on different decompositions of the global measures and provide different properties of the nodes. Local measures include entropic surprise, mutual surprise, mutual predictability, and erasure surprise. The proposed approach is evaluated using synthetic model networks and structural and functional human networks at different scales. Results demonstrate that the global measures can characterize new properties of the topology of a brain network and, in addition, for a given number of nodes, an optimal number of edges is found for small-world networks. Local measures show different properties of the nodes such as the uncertainty associated to the node, or the uniqueness of the path that the node belongs. Finally, the consistency of the results across healthy subjects demonstrates the robustness of the proposed measures.

Multiscale dynamical network mechanisms underlying aging of an online organism from birth to death

We present the continuous-time evolution of an online organism network from birth to death which crosses all organizational and temporal scales, from individual components through to the mesoscopic and entire system scale. These continuous-time data reveal a lifespan driven by punctuated, real-time co-evolution of the structural and functional networks. Aging sees these structural and functional networks gradually diverge in terms of their small-worldness and eventually their connectivity. Dying emerges as an extended process associated with the formation of large but disjoint functional sub-networks together with an increasingly detached core. Our mathematical model quantifies the very different impacts that interventions will have on the overall lifetime, period of initial growth, peak of potency, and duration of old age, depending on when and how they are administered. In addition to their direct relevance to online extremism, our findings may offer insight into aging in other network systems of comparable complexity for which extensive in vivo data is not yet available.

Occipital White Matter Tracts in Human and Macaque

We compare several major white-matter tracts in human and macaque occipital lobe using diffusion magnetic resonance imaging. The comparison suggests similarities but also significant differences in the tracts. There are several apparently homologous tracts in the 2 species, including the vertical occipital fasciculus (VOF), optic radiation, forceps major, and inferior longitudinal fasciculus (ILF). There is one large human tract, the inferior fronto-occipital fasciculus, with no corresponding fasciculus in macaque. We could identify the macaque VOF (mVOF), which has been little studied. Its position is consistent with classical invasive anatomical studies by Wernicke. VOF homology is supported by similarity of the endpoints in V3A and ventral V4 across species. The mVOF fibers intertwine with the dorsal segment of the ILF, but the human VOF appears to be lateral to the ILF. These similarities and differences between the occipital lobe tracts will be useful in establishing which circuitry in the macaque can serve as an accurate model for human visual cortex.

Network Plasticity and Intraoperative Mapping for Personalized Multimodal Management of Diffuse Low-Grade Gliomas

Gliomas are the most frequent primary brain tumors and include a variety of different histological tumor types and malignancy grades. Recent achievements in terms of molecular and imaging fields have created an unprecedented opportunity to perform a comprehensive interdisciplinary assessment of the glioma pathophysiology, with direct implications in terms of the medical and surgical treatment strategies available for patients. The current paradigm shift considers glioma management in a comprehensive perspective that takes into account the intricate connectivity of the cerebral networks. This allowed significant improvement in the outcome of patients with lesions previously considered inoperable. The current review summarizes the current theoretical framework integrating the adult human brain plasticity and functional reorganization within a dynamic individualized treatment strategy for patients affected by diffuse low-grade gliomas. The concept of neuro-oncology as a brain network surgery has major implications in terms of the clinical management and ensuing outcomes, as indexed by the increased survival and quality of life of patients managed using such an approach.

Statistical Analysis of Tract-Tracing Experiments Demonstrates a Dense, Complex Cortical Network in the Mouse

Anatomical tract tracing methods are the gold standard for estimating the weight of axonal connectivity between a pair of pre-defined brain regions. Large studies, comprising hundreds of experiments, have become feasible by automated methods. However, this comes at the cost of positive-mean noise making it difficult to detect weak connections, which are of particular interest as recent high resolution tract-tracing studies of the macaque have identified many more weak connections, adding up to greater connection density of cortical networks, than previously recognized. We propose a statistical framework that estimates connectivity weights and credibility intervals from multiple tract-tracing experiments. We model the observed signal as a log-normal distribution generated by a combination of tracer fluorescence and positive-mean noise, also accounting for injections into multiple regions. Using anterograde viral tract-tracing data provided by the Allen Institute for Brain Sciences, we estimate the connection density of the mouse intra-hemispheric cortical network to be 73% (95% credibility interval (CI): 71%, 75%); higher than previous estimates (40%). Inter-hemispheric density was estimated to be 59% (95% CI: 54%, 62%). The weakest estimable connections (about 6 orders of magnitude weaker than the strongest connections) are likely to represent only one or a few axons. These extremely weak connections are topologically more random and longer distance than the strongest connections, which are topologically more clustered and shorter distance (spatially clustered). Weak links do not substantially contribute to the global topology of a weighted brain graph, but incrementally increased topological integration of a binary graph. The topology of weak anatomical connections in the mouse brain, rigorously estimable down to the biological limit of a single axon between cortical areas in these data, suggests that they might confer functional advantages for integrative information processing and/or they might represent a stochastic factor in the development of the mouse connectome.

Spatial Embedding and Wiring Cost Constrain the Functional Layout of the Cortical Network of Rodents and Primates

Mammals show a wide range of brain sizes, reflecting adaptation to diverse habitats. Comparing interareal cortical networks across brains of different sizes and mammalian orders provides robust information on evolutionarily preserved features and species-specific processing modalities. However, these networks are spatially embedded, directed, and weighted, making comparisons challenging. Using tract tracing data from macaque and mouse, we show the existence of a general organizational principle based on an exponential distance rule (EDR) and cortical geometry, enabling network comparisons within the same model framework. These comparisons reveal the existence of network invariants between mouse and macaque, exemplified in graph motif profiles and connection similarity indices, but also significant differences, such as fractionally smaller and much weaker long-distance connections in the macaque than in mouse. The latter lends credence to the prediction that long-distance cortico-cortical connections could be very weak in the much-expanded human cortex, implying an increased susceptibility to disconnection syndromes such as Alzheimer disease and schizophrenia. Finally, our data from tracer experiments involving only gray matter connections in the primary visual areas of both species show that an EDR holds at local scales as well (within 1.5 mm), supporting the hypothesis that it is a universally valid property across all scales and, possibly, across the mammalian class.

Ensemble Tractography

Tractography uses diffusion MRI to estimate the trajectory and cortical projection zones of white matter fascicles in the living human brain. There are many different tractography algorithms and each requires the user to set several parameters, such as curvature threshold. Choosing a single algorithm with specific parameters poses two challenges. First, different algorithms and parameter values produce different results. Second, the optimal choice of algorithm and parameter value may differ between different white matter regions or different fascicles, subjects, and acquisition parameters. We propose using ensemble methods to reduce algorithm and parameter dependencies. To do so we separate the processes of fascicle generation and evaluation. Specifically, we analyze the value of creating optimized connectomes by systematically combining candidate streamlines from an ensemble of algorithms (deterministic and probabilistic) and systematically varying parameters (curvature and stopping criterion). The ensemble approach leads to optimized connectomes that provide better cross-validated prediction error of the diffusion MRI data than optimized connectomes generated using a single-algorithm or parameter set. Furthermore, the ensemble approach produces connectomes that contain both short- and long-range fascicles, whereas single-parameter connectomes are biased towards one or the other. In summary, a systematic ensemble tractography approach can produce connectomes that are superior to standard single parameter estimates both for predicting the diffusion measurements and estimating white matter fascicles.

Diffusion MRI and tractography opened a new avenue for studying white matter fascicles and their tissue properties in the living human brain. There are many different tractography methods, and each requires the user to set several parameters. A limitation of tractography is that the results depend on the selection of algorithms and parameters. Here, we analyze an ensemble method, Ensemble Tractography (ET), that reduces the effect of algorithm and parameter selection. ET creates a large set of candidate streamlines using an ensemble of algorithms and parameter values and then selects the streamlines with strong support from the data using a global fascicle evaluation method. Compared to single parameter connectomes, ET connectomes predict diffusion MRI signals better and cover a wider range of white matter volume. Importantly, ET connectomes include both short- and long-association fascicles, which are not typically found together in single-parameter connectomes.

A Large-Scale Circuit Mechanism for Hierarchical Dynamical Processing in the Primate Cortex

We developed a large-scale dynamical model of the macaque neocortex, which is based on recently acquired directed- and weighted-connectivity data from tract-tracing experiments, and which incorporates heterogeneity across areas. A hierarchy of timescales naturally emerges from this system: sensory areas show brief, transient responses to input (appropriate for sensory processing), whereas association areas integrate inputs over time and exhibit persistent activity (suitable for decision-making and working memory). The model displays multiple temporal hierarchies, as evidenced by contrasting responses to visual versus somatosensory stimulation. Moreover, slower prefrontal and temporal areas have a disproportionate impact on global brain dynamics. These findings establish a circuit mechanism for "temporal receptive windows" that are progressively enlarged along the cortical hierarchy, suggest an extension of time integration in decision making from local to large circuits, and should prompt a re-evaluation of the analysis of functional connectivity (measured by fMRI or electroencephalography/magnetoencephalography) by taking into account inter-areal heterogeneity.

Wiring cost and topological participation of the mouse brain connectome

Brain connectomes are topologically complex systems, anatomically embedded in 3D space. Anatomical conservation of "wiring cost" explains many but not all aspects of these networks. Here, we examined the relationship between topology and wiring cost in the mouse connectome by using data from 461 systematically acquired anterograde-tracer injections into the right cortical and subcortical regions of the mouse brain. We estimated brain-wide weights, distances, and wiring costs of axonal projections and performed a multiscale topological and spatial analysis of the resulting weighted and directed mouse brain connectome. Our analysis showed that the mouse connectome has small-world properties, a hierarchical modular structure, and greater-than-minimal wiring costs. High-participation hubs of this connectome mediated communication between functionally specialized and anatomically localized modules, had especially high wiring costs, and closely corresponded to regions of the default mode network. Analyses of independently acquired histological and gene-expression data showed that nodal participation colocalized with low neuronal density and high expression of genes enriched for cognition, learning and memory, and behavior. The mouse connectome contains high-participation hubs, which are not explained by wiring-cost minimization but instead reflect competitive selection pressures for integrated network topology as a basis for higher cognitive and behavioral functions.

Graph analysis of the anatomical network organization of the hippocampal formation and parahippocampal region in the rat

Graph theory was used to analyze the anatomical network of the rat hippocampal formation and the parahippocampal region (van Strien et al., Nat Rev Neurosci 10(4):272-282, 2009). For this analysis, the full network was decomposed along the three anatomical axes, resulting in three networks that describe the connectivity within the rostrocaudal, dorsoventral and laminar dimensions. The rostrocaudal network had a connection density of 12% and a path length of 2.4. The dorsoventral network had a high cluster coefficient (0.53), a relatively high path length (1.62) and a rich club was identified. The modularity analysis revealed three modules in the dorsoventral network. The laminar network contained most information. The laminar dimension revealed a network with high clustering coefficient (0.47), a relatively high path length (2.11) and four significantly increased characteristic network building blocks (structural motifs). Thirteen rich club nodes were identified, almost all of them situated in the parahippocampal region. Six connector hubs were detected and all of them were located in the entorhinal cortex. Three large modules were revealed, indicating a close relationship between the perirhinal and postrhinal cortex as well as between the lateral and medial entorhinal cortex. These results confirmed the central position of the entorhinal cortex in the (para)hippocampal network and this possibly explains why pathology in this region has such profound impact on cognitive function, as seen in several brain diseases. The results also have implications for the idea of strict separation of the "spatial" and the "non-spatial" information stream into the hippocampus. This two-stream memory model suggests that the information influx from, respectively, the postrhinal-medial entorhinal cortex and the perirhinal-lateral entorhinal cortex is separate, but the current analysis shows that this apparent separation is not determined by anatomical constraints.

Spatial embedding of structural similarity in the cerebral cortex

Recent anatomical tracing studies have yielded substantial amounts of data on the areal connectivity underlying distributed processing in cortex, yet the fundamental principles that govern the large-scale organization of cortex remain unknown. Here we show that functional similarity between areas as defined by the pattern of shared inputs or outputs is a key to understanding the areal network of cortex. In particular, we report a systematic relation in the monkey, human, and mouse cortex between the occurrence of connections from one area to another and their similarity distance. This characteristic relation is rooted in the wiring distance dependence of connections in the brain. We introduce a weighted, spatially embedded random network model that robustly gives rise to this structure, as well as many other spatial and topological properties observed in cortex. These include features that were not accounted for in any previous model, such as the wide range of interareal connection weights. Connections in the model emerge from an underlying distribution of spatially embedded axons, thereby integrating the two scales of cortical connectivity--individual axons and interareal pathways--into a common geometric framework. These results provide insights into the origin of large-scale connectivity in cortex and have important implications for theories of cortical organization.

Evolutionary appearance of von Economo's neurons in the mammalian cerebral cortex

von Economo’s neurons (VENs) are large, spindle-shaped projection neurons in layer V of the frontoinsular (FI) cortex, and the anterior cingulate cortex. During human ontogenesis, the VENs can first be differentiated at late stages of gestation, and increase in number during the first eight postnatal months. VENs have been identified in humans, chimpanzee, bonobos, gorillas, orangutan and, more recently, in the macaque. Their distribution in great apes seems to correlate with human-like social cognitive abilities and self-awareness. VENs are also found in whales, in a number of different cetaceans, and in the elephant. This phylogenetic distribution may suggest a correlation among the VENs, brain size and the “social brain.” VENs may be involved in the pathogenesis of specific neurological and psychiatric diseases, such as autism, callosal agenesis and schizophrenia. VENs are selectively affected in a behavioral variant of frontotemporal dementia in which empathy, social awareness and self-control are seriously compromised, thus associating VENs with the social brain. However, the presence of VENs has also been related to special functions such as mirror self-recognition. Areas containing VENs have been related to motor awareness or sense-of-knowing, discrimination between self and other, and between self and the external environment. Along this line, VENs have been related to the “global Workspace” architecture: in accordance the VENs have been correlated to emotional and interoceptive signals by providing fast connections (large axons = fast communication) between salience-related insular and cingulate and other widely separated brain areas. Nevertheless, the lack of a characterization of their physiology and anatomical connectivity allowed only to infer their functional role based on their location and on the functional magnetic resonance imaging data. The recent finding of VENs in the anterior insula of the macaque opens the way to new insights and experimental investigations.

Functional connectomics from resting-state fMRI

Spontaneous fluctuations in activity in different parts of the brain can be used to study functional brain networks. We review the use of resting-state functional MRI (rfMRI) for the purpose of mapping the macroscopic functional connectome. After describing MRI acquisition and image-processing methods commonly used to generate data in a form amenable to connectomics network analysis, we discuss different approaches for estimating network structure from that data. Finally, we describe new possibilities resulting from the high-quality rfMRI data being generated by the Human Connectome Project and highlight some upcoming challenges in functional connectomics.

Cortical high-density counterstream architectures

Small-world networks provide an appealing description of cortical architecture owing to their capacity for integration and segregation combined with an economy of connectivity. Previous reports of low-density interareal graphs and apparent small-world properties are challenged by data that reveal high-density cortical graphs in which economy of connections is achieved by weight heterogeneity and distance-weight correlations. These properties define a model that predicts many binary and weighted features of the cortical network including a core-periphery, a typical feature of self-organizing information processing systems. Feedback and feedforward pathways between areas exhibit a dual counterstream organization, and their integration into local circuits constrains cortical computation. Here, we propose a bow-tie representation of interareal architecture derived from the hierarchical laminar weights of pathways between the high-efficiency dense core and periphery.

A predictive network model of cerebral cortical connectivity based on a distance rule

Recent advances in neuroscience have engendered interest in large-scale brain networks. Using a consistent database of cortico-cortical connectivity, generated from hemisphere-wide, retrograde tracing experiments in the macaque, we analyzed interareal weights and distances to reveal an important organizational principle of brain connectivity. Using appropriate graph theoretical measures, we show that although very dense (66%), the interareal network has strong structural specificity. Connection weights exhibit a heavy-tailed lognormal distribution spanning five orders of magnitude and conform to a distance rule reflecting exponential decay with interareal separation. A single-parameter random graph model based on this rule predicts numerous features of the cortical network: (1) the existence of a network core and the distribution of cliques, (2) global and local binary properties, (3) global and local weight-based communication efficiencies modeled as network conductance, and (4) overall wire-length minimization. These findings underscore the importance of distance and weight-based heterogeneity in cortical architecture and processing.

Human connectomics - what will the future demand?

Significant resources are now being devoted to large-scale international studies attempting to map the connectome — the brain's wiring diagram. This review will focus on the use of human neuroimaging approaches to map the connectome at a macroscopic level. This emerging field of human connectomics brings both opportunities and challenges. Opportunities arise from the ability to apply a powerful toolkit of mathematical and computational approaches to interrogate these rich datasets, many of which are being freely shared with the scientific community. Challenges arise in methodology, interpretability and biological or clinical validity. This review discusses these challenges and opportunities and highlights potential future directions.

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Human connectomics bring both opportunities and challenges.

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Biological interpretation remains challenging.

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More work needed to demonstrate clinical utility