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We explore the stability and dynamic properties of a hierarchical, linearized, and analytic spectral graph model for neural oscillations that integrates the structural wiring of the brain. Previously, we have shown that this model can accurately capture the frequency spectra and the spatial patterns of the alpha and beta frequency bands obtained from magnetoencephalography recordings without regionally varying parameters. Here, we show that this macroscopic model based on long-range excitatory connections exhibits dynamic oscillations with a frequency in the alpha band even without any oscillations implemented at the mesoscopic level. We show that depending on the parameters, the model can exhibit combinations of damped oscillations, limit cycles, or unstable oscillations. We determined bounds on model parameters that ensure stability of the oscillations simulated by the model. Finally, we estimated time-varying model parameters to capture the temporal fluctuations in magnetoencephalography activity. We show that a dynamic spectral graph modeling framework with a parsimonious set of biophysically interpretable model parameters can thereby be employed to capture oscillatory fluctuations observed in electrophysiological data in various brain states and diseases.

Human brain connectome studies aim to both explore healthy brains, and extract and analyze relevant features associated with pathologies of interest. Usually this consists of modeling the brain connectome as a graph and using graph metrics as features. A fine brain description requires graph metrics computation at the node level. Given the relatively reduced number of patients in standard cohorts, such data analysis problems fall in the high-dimension, low-sample-size framework. In this context, our goal is to provide a machine learning technique that exhibits flexibility, gives the investigator an understanding of the features and covariates, allows visualization and exploration, and yields insight into the data and the biological phenomena at stake. The retained approach is dimension reduction in a manifold learning methodology; the originality is that the investigator chooses one (or several) reduced variables. The proposed method is illustrated in two studies. The first one addresses comatose patients; the second one compares young and elderly populations. The method sheds light on the differences between brain connectivity graphs using graph metrics and potential clinical interpretations of these differences., Author Summary Human brain connectome studies aim to both explore healthy brains, and extract and analyze relevant features associated with pathologies of interest. Usually this consists of modeling the brain connectome as a graph and using graph metrics as features. A fine brain description requires graph metrics computation at the node level. Given the relatively reduced number of patients in standard cohorts, such data analysis problems fall in the high-dimension, low-sample-size framework. In this context, our goal is to provide a machine learning technique that exhibits flexibility, gives the investigator an understanding of the features and covariates, allows visualization and exploration, and yields insight into the data and the biological phenomena at stake. The retained approach is dimension reduction in a manifold learning methodology; the originality is that the investigator chooses one (or several) reduced variables. The proposed method is illustrated in two studies. The first one addresses comatose patients; the second one compares young and elderly populations. The method sheds light on the differences between brain connectivity graphs using graph metrics and potential clinical interpretations of these differences.

We consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are drawn from a specified model. We achieve this by deriving the joint asymptotic properties of average subgraph counts as the number of observed networks increases but the number of nodes in each network remains finite. In doing so, we do not require that each observed network contains the same number of nodes, or is drawn from the same distribution. Our results yield joint confidence regions for subgraph counts, and therefore methods for testing whether the observations in a network sample are drawn from: a specified distribution, a specified model, or from the same model as another network sample. We present simulation experiments and an illustrative example on a sample of brain networks where we find that highly creative individuals' brains present significantly more short cycles than found in less creative people. for this article are available online.

Mathematical modeling of the relationship between the functional activity and the structural wiring of the brain has largely been undertaken using non-linear and biophysically detailed mathematical models with regionally varying parameters. While this approach provides us a rich repertoire of multistable dynamics that can be displayed by the brain, it is computationally demanding. Moreover, although neuronal dynamics at the microscopic level are nonlinear and chaotic, it is unclear if such detailed nonlinear models are required to capture the emergent meso-(regional population ensemble) and macro-scale (whole brain) behavior, which is largely deterministic and reproducible across individuals. Indeed, recent modeling effort based on spectral graph theory has shown that an analytical model without regionally varying parameters and without multistable dynamics can capture the empirical magnetoencephalography frequency spectra and the spatial patterns of the alpha and beta frequency bands accurately. In this work, we demonstrate an improved hierarchical, linearized, and analytic spectral graph theory-based model that can capture the frequency spectra obtained from magnetoencephalography recordings of resting healthy subjects. We reformulated the spectral graph theory model in line with classical neural mass models, therefore providing more biologically interpretable parameters, especially at the local scale. We demonstrated that this model performs better than the original model when comparing the spectral correlation of modeled frequency spectra and that obtained from the magnetoencephalography recordings. This model also performs equally well in predicting the spatial patterns of the empirical alpha and beta frequency bands.

Flexible behaviors over long timescales are thought to engage recurrent neural networks in deep brain regions, which are experimentally challenging to study. In insects, recurrent circuit dynamics in a brain region called the central complex (CX) enable directed locomotion, sleep, and context- and experience-dependent spatial navigation. We describe the first complete electron microscopy-based connectome of the

The anatomic validity of structural connectomes remains a significant uncertainty in neuroimaging. Edge-centric tractography reconstructs streamlines in bundles between each pair of cortical or subcortical regions. Although edge bundles provides a stronger anatomic embedding than traditional connectomes, calculating them for each region-pair requires exponentially greater computation. We observe that major speedup can be achieved by reducing the number of streamlines used by probabilistic tractography algorithms. To ensure this does not degrade connectome quality, we calculate the identifiability of edge-centric connectomes between test and re-test sessions as a proxy for information content. We find that running PROBTRACKX2 with as few as 1 streamline per voxel per region-pair has no significant impact on identifiability. Variation in identifiability caused by streamline count is overshadowed by variation due to subject demographics. This finding even holds true in an entirely different tractography algorithm using MRTrix. Incidentally, we observe that Jaccard similarity is more effective than Pearson correlation in calculating identifiability for our subject population.

The human brain constitutes one of the most advanced networks produced by nature, consisting of billions of neurons communicating with each other. However, this communication is not in real-time, with different communication or time-delays occurring between neurons in different brain areas. Here, we investigate the impacts of these delays by modeling large interacting neural circuits as neural-field systems which model the bulk activity of populations of neurons. By using a Master Stability Function analysis combined with numerical simulations, we find that delays (1) may actually stabilize brain dynamics by temporarily preventing the onset to oscillatory and pathologically synchronized dynamics and (2) may enhance or diminish synchronization depending on the underlying eigenvalue spectrum of the connectivity matrix. Real eigenvalues with large magnitudes result in increased synchronizability while complex eigenvalues with large magnitudes and positive real parts yield a decrease in synchronizability in the delay vs. instantaneously coupled case. This result applies to networks with fixed, constant delays, and was robust to networks with heterogeneous delays. In the case of real brain networks, where the eigenvalues are predominantly real, owing to the nearly symmetric nature of these weight matrices, biologically plausible, small delays, are likely to increase synchronization, rather than decreasing it.

The neural circuits responsible for animal behavior remain largely unknown. We summarize new methods and present the circuitry of a large fraction of the brain of the fruit fly Drosophila melanogaster. Improved methods include new procedures to prepare, image, align, segment, find synapses in, and proofread such large data sets. We define cell types, refine computational compartments, and provide an exhaustive atlas of cell examples and types, many of them novel. We provide detailed circuits consisting of neurons and their chemical synapses for most of the central brain. We make the data public and simplify access, reducing the effort needed to answer circuit questions, and provide procedures linking the neurons defined by our analysis with genetic reagents. Biologically, we examine distributions of connection strengths, neural motifs on different scales, electrical consequences of compartmentalization, and evidence that maximizing packing density is an important criterion in the evolution of the fly’s brain., eLife digest Animal brains of all sizes, from the smallest to the largest, work in broadly similar ways. Studying the brain of any one animal in depth can thus reveal the general principles behind the workings of all brains. The fruit fly Drosophila is a popular choice for such research. With about 100,000 neurons – compared to some 86 billion in humans – the fly brain is small enough to study at the level of individual cells. But it nevertheless supports a range of complex behaviors, including navigation, courtship and learning. Thanks to decades of research, scientists now have a good understanding of which parts of the fruit fly brain support particular behaviors. But exactly how they do this is often unclear. This is because previous studies showing the connections between cells only covered small areas of the brain. This is like trying to understand a novel when all you can see is a few isolated paragraphs. To solve this problem, Scheffer, Xu, Januszewski, Lu, Takemura, Hayworth, Huang, Shinomiya et al. prepared the first complete map of the entire central region of the fruit fly brain. The central brain consists of approximately 25,000 neurons and around 20 million connections. To prepare the map – or connectome – the brain was cut into very thin 8nm slices and photographed with an electron microscope. A three-dimensional map of the neurons and connections in the brain was then reconstructed from these images using machine learning algorithms. Finally, Scheffer et al. used the new connectome to obtain further insights into the circuits that support specific fruit fly behaviors. The central brain connectome is freely available online for anyone to access. When used in combination with existing methods, the map will make it easier to understand how the fly brain works, and how and why it can fail to work correctly. Many of these findings will likely apply to larger brains, including our own. In the long run, studying the fly connectome may therefore lead to a better understanding of the human brain and its disorders. Performing a similar analysis on the brain of a small mammal, by scaling up the methods here, will be a likely next step along this path.

The relationship between the brain’s structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We examine a hierarchical, linear graph spectral model of brain activity at mesoscopic and macroscopic scales. The model formulation yields an elegant closed-form solution for the structure-function problem, specified by the graph spectrum of the structural connectome’s Laplacian, with simple, universal rules of dynamics specified by a minimal set of global parameters. The resulting parsimonious and analytical solution stands in contrast to complex numerical simulations of high dimensional coupled non-linear neural field models. This spectral graph model accurately predicts spatial and spectral features of neural oscillatory activity across the brain and was successful in simultaneously reproducing empirically observed spatial and spectral patterns of alpha-band (8-12 Hz) and beta-band (15-30Hz) activity estimated from source localized scalp magneto-encephalography (MEG). This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole-brain dynamics.Significance StatementThe relationship between the brain’s structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We examine a hierarchical, linear graph spectral model of brain activity at mesoscopic and macroscopic scales. The model formulation yields an elegant closed-form solution for the structure-function problem, specified by the graph spectrum of the structural connectome’s Laplacian, with simple, universal rules of dynamics specified by a minimal set of global parameters. This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole-brain dynamics.

Connectome-based lesion symptom mapping (CLSM) can be used to relate disruptions of brain network connectivity with clinical measures. We present a novel method that extends current CLSM approaches by introducing a fast reliable and accurate way for computing disconnectomes, i.e. identifying damaged or lesioned connections. We introduce a new algorithm that finds the maximally disconnected subgraph containing regions and region pairs with the greatest shared connectivity loss. After normalizing a stroke patient's segmented MRI lesion into template space, probability weighted structural connectivity matrices are constructed from shortest paths found in white matter voxel graphs of 210 subjects from the Human Connectome Project. Percent connectivity loss matrices are constructed by measuring the proportion of shortest-path probability weighted connections that are lost because of an intersection with the patient's lesion. Maximally disconnected subgraphs of the overall connectivity loss matrix are then derived using a computationally fast greedy algorithm that closely approximates the exact solution. We illustrate the approach in eleven stroke patients with hemiparesis by identifying expected disconnections of the corticospinal tract (CST) with cortical sensorimotor regions. Major disconnections are found in the thalamus, basal ganglia, and inferior parietal cortex. Moreover, the size of the maximally disconnected subgraph quantifies the extent of cortical disconnection and strongly correlates with multiple clinical measures. The methods provide a fast, reliable approach for both visualizing and quantifying the disconnected portion of a patient's structural connectome based on their routine clinical MRI, without reliance on concomitant diffusion weighted imaging. The method can be extended to large databases of stroke patients, multiple sclerosis or other diseases causing focal white matter injuries helping to better characterize clinically relevant white matter lesions and to identify biomarkers for the recovery potential of individual patients., Highlights • Significantly accelerated shortest path tractography approach for constructing connectomes and disconnectomes. • New algorithm extracts the subnetwork containing cortical connections and regions with maximal shared connectivity loss. • The size of the maximally disconnected subnetwork quantifies the extent of disconnection and correlates with stroke measures. • Fast and accurate approach for visualizing and analyzing the disconnected portion of a patient's structural connectome.

Complex networks emerge as a natural framework to describe real-life phe- nomena involving a group of entities and their interactions, i.e., a social net- work. Furthermore, other problems involve a collection of networks, such as multi-layer, temporal, or brain networks (connectomes). With the increas- ing availability of graph-shaped data and associated meta-data, i.e., node or edge attributes, machine learning (ML) techniques on networks have risen in popularity. However, there are still several challenging issues to be addressed concerning feature engineering, graph representation, visualization, and general graph mining applications. This thesis contributes to bridging the gap between ML and complex net- works. We investigate dynamics on networks such as discrete and continuous- time random walks, in two directions. First, we develop a multi-scale anomaly detection algorithm on attributed networks. We exploit the link between graph signal processing and the Markov stability framework used in community de- tection, for spotting anomalous nodes in multiple contexts of the network. Second, we introduce a generalization of assortativity on networks operating on scalar and categorical node attributes. These coefficients turn out to be useful descriptors to build network fingerprints, so that we can perform super- vised graph classification, i.e., predicting the toxicity of molecules or classifying Reddit discussion threads. Besides, we develop an unsupervised approach to learn graph embeddings from a collection of networks. By learning a non-linear mapping from input graphs to a lower-dimensional feature space, we obtain useful graphs representa- tions used in graph visualization, clustering, and classification, e.g., predicting people’s gender based on their structural connectome. Finally, we propose a principled approach to identify stable biomarkers for schizophrenia diagnosis in the human connectome. From an ML perspective, the problem is stated as an embedded feature selection scheme for graph classification. By doing so, we identify the affected-core in schizophrenia, highlighting increasing performance when structural and functional neural features are combined. (SC - Sciences) -- UCL, 2019

Brain parcellation divides the brain's spatial domain into small regions, which are represented by nodes within the network analysis framework. While template-based parcellations are widely used, the parcels on the template do not necessarily match individual's functional nodes. A new method is developed to overcome the inconsistent network analysis results by by-passing the difficulties of parcellating the brain into functionally meaningful areas. First, roughly equal-sized parcellations are obtained. Second, these random parcellations are applied to individual subjects multiple times and a pseudo-bootstrap of the network is obtained for statistical inferences. It was found that the variation of mean global network metrics from pseudo-bootstrap sampling is smaller compared with inter-subject variation or within-subject variation between two diffusion MRI scans. Using the mean global network metrics from pseudo-bootstrap sampling, the intra-class correlation is always higher than the average obtained from using a single random parcellation. As one application, the pseudo-bootstrap method was tested on the Human Connectome Project resting state dataset to identify individuals across scan sessions based on the mean functional connectivity – a trivial network property that has little information about the connectivity between nodes. An accuracy rate of ~90% was achieved by simply finding the maximum correlation of mean functional connectivity of pseudo-bootstrap samples between two scan sessions.

To facilitate the comparison of white matter morphologic connectivity across target populations, it is invaluable to map the data to a standardized neuroanatomical space. Here, we evaluated direct streamline normalization (DSN), where the warping was applied directly to the streamlines, with two publically available approaches that spatially normalize the diffusion data and then reconstruct the streamlines. Prior work has shown that streamlines generated after normalization from reoriented diffusion data do not reliably match the streamlines generated in native space. To test the impact of these different normalization methods on quantitative tractography measures, we compared the reproducibility of the resulting normalized connectivity matrices and network metrics with those originally obtained in native space. The two methods that reconstruct streamlines after normalization led to significant differences in network metrics with large to huge standardized effect sizes, reflecting a dramatic alteration of the same subject’s native connectivity. In contrast, after normalizing with DSN we found no significant difference in network metrics compared with native space with only very small-to-small standardized effect sizes. DSN readily outperformed the other methods at preserving native space connectivity and introduced novel opportunities to define connectome networks without relying on gray matter parcellations., Author Summary Direct streamline normalization (DSN) directly warps the streamlines into any template space by using the transformations output from Advanced Normalization Tools (ANTs). DSN overcomes the limitations of diffusion weighted images (DWI) spatial normalization. It allows DWIs to be acquired with any desired sampling scheme. Fiber orientation distributions (FODs) or orientation distribution functions (ODFs) can also be reconstructed using any desired method and streamlines generated using any algorithm. Most importantly, it avoids the problem of generating tracts from FODs or ODFs that have become distorted because of spatial normalization. Our results show that DSN has minimal influence on tractography measures such as tract count and structure and does not significantly alter structural networks with only very small to small effect sizes. We have developed a framework in Python that works with most diffusion software platforms. It is available at http://github.com/clintg6/DSN.

This paper presents a novel method for the reconstruction of a neural network connectivity using calcium fluorescence data. We introduce a fast unsupervised method to integrate different networks that reconstructs structural connectivity from neuron activity. Our method improves the state-of-the-art reconstruction method General Transfer Entropy (GTE). We are able to better eliminate indirect links, improving therefore the quality of the network via a normalization and ensemble process of GTE and three new informative features. The approach is based on a simple combination of networks, which is remarkably fast. The performance of our approach is benchmarked on simulated time series provided at the connectomics challenge and also submitted at the public competition

See Lytton (doi:10.1093/awx018) for a scientific commentary on this article. Patients with drug-resistant epilepsy show different seizure propagation patterns and postsurgical outcomes. Proix et al. merge structural information from brain imaging with mathematical modelling to generate personalized brain network models. Validation of the models against presurgical stereotactic EEGs and clinical data shows that they can account for the variability observed., See Lytton (doi:10.1093/awx018) for a scientific commentary on this article. Neural network oscillations are a fundamental mechanism for cognition, perception and consciousness. Consequently, perturbations of network activity play an important role in the pathophysiology of brain disorders. When structural information from non-invasive brain imaging is merged with mathematical modelling, then generative brain network models constitute personalized in silico platforms for the exploration of causal mechanisms of brain function and clinical hypothesis testing. We here demonstrate with the example of drug-resistant epilepsy that patient-specific virtual brain models derived from diffusion magnetic resonance imaging have sufficient predictive power to improve diagnosis and surgery outcome. In partial epilepsy, seizures originate in a local network, the so-called epileptogenic zone, before recruiting other close or distant brain regions. We create personalized large-scale brain networks for 15 patients and simulate the individual seizure propagation patterns. Model validation is performed against the presurgical stereotactic electroencephalography data and the standard-of-care clinical evaluation. We demonstrate that the individual brain models account for the patient seizure propagation patterns, explain the variability in postsurgical success, but do not reliably augment with the use of patient-specific connectivity. Our results show that connectome-based brain network models have the capacity to explain changes in the organization of brain activity as observed in some brain disorders, thus opening up avenues towards discovery of novel clinical interventions.

Over the last two decades, a large variety of type I error rates and control procedures have been proposed in the field of multiple hypotheses testing. This paper proposes a framework that includes many existing proposals by investigating procedures in which the orderedp-values are compared to an arbitrary positive and non-decreasing threshold sequence. For this case, we derive the error rate being controlled under different assumptions on thep-values. Our focus will be on step-up procedures. The new formulation gives insight into the relations between existing error rates and opens new perspectives for the whole field of multiple testing.