High-resolution directed human connectomes and the Consensus Connectome Dynamics

Robust circuitry-based scores of structural importance of human brain areas

We consider the 1015-vertex human consensus connectome computed from the diffusion MRI data of 1064 subjects. We define seven different orders on these 1015 graph vertices, where the orders depend on parameters derived from the brain circuitry, that is, from the properties of the edges (or connections) incident to the vertices ordered. We order the vertices according to their degree, the sum, the maximum, and the average of the fiber counts on the incident edges, and the sum, the maximum and the average length of the fibers in the incident edges. We analyze the similarities of these seven orders by the Spearman correlation coefficient and by their inversion numbers and have found that all of these seven orders have great similarities. In other words, if we interpret the orders as scoring of the importance of the vertices in the consensus connectome, then the scores of the vertices will be similar in all seven orderings. That is, important vertices of the human connectome typically have many neighbors connected with long and thick axonal fibers (where thickness is measured by fiber numbers), and their incident edges have high maximum and average values of length and fiber-number parameters, too. Therefore, these parameters may yield robust ways of deciding which vertices are more important in the anatomy of our brain circuitry than the others.

Analyzing bursting synchronization in structural connectivity matrix of a human brain under external pulsed currents

Cognitive tasks in the human brain are performed by various cortical areas located in the cerebral cortex. The cerebral cortex is separated into different areas in the right and left hemispheres. We consider one human cerebral cortex according to a network composed of coupled subnetworks with small-world properties. We study the burst synchronization and desynchronization in a human neuronal network under external periodic and random pulsed currents. With and without external perturbations, the emergence of bursting synchronization is observed. Synchronization can contribute to the processing of information, however, there are evidences that it can be related to some neurological disorders. Our results show that synchronous behavior can be suppressed by means of external pulsed currents.

Nonlocal models in the analysis of brain neurodegenerative protein dynamics with application to Alzheimer's disease

It is well known that today nearly one in six of the world’s population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the detection, prevention, and treatments of such disorders, some fundamentals of the progression of associated diseases are in urgent need of further clarification. In this paper, we focus on Alzheimer’s disease, where it is believed that the concentration changes in amyloid-beta and tau proteins play a central role in its onset and development. A multiscale model is proposed to analyze the propagation of these concentrations in the brain connectome. In particular, we consider a modified heterodimer model for the protein–protein interactions. Higher toxic concentrations of amyloid-beta and tau proteins destroy the brain cell. We have studied these propagations for the primary and secondary and their mixed tauopathies. We model the damage of a brain cell by the nonlocal contributions of these toxic loads present in the brain cells. With the help of rigorous analysis, we check the stability behaviour of the stationary points corresponding to the homogeneous system. After integrating the brain connectome data into the developed model, we see that the spreading patterns of the toxic concentrations for the whole brain are the same, but their concentrations are different in different regions. Also, the time to propagate the damage in each region of the brain connectome is different.

Coupled Neural–Glial Dynamics and the Role of Astrocytes in Alzheimer’s Disease

Neurodegenerative diseases such as Alzheimer’s (AD) are associated with the propagation and aggregation of toxic proteins. In the case of AD, it was Alzheimer himself who showed the importance of both amyloid beta (Aβ) plaques and tau protein neurofibrillary tangles (NFTs) in what he called the “disease of forgetfulness”. The amyloid beta forms extracellular aggregates and plaques, whereas tau proteins are intracellular proteins that stabilize axons by cross-linking microtubules that can form largely messy tangles. On the other hand, astrocytes and microglial cells constantly clear these plaques and NFTs from the brain. Astrocytes transport nutrients from the blood to neurons. Activated astrocytes produce monocyte chemoattractant protein-1 (MCP-1), which attracts anti-inflammatory macrophages and clears Aβ. At the same time, the microglia cells are poorly phagocytic for Aβ compared to proinflammatory and anti-inflammatory macrophages. In addition to such distinctive neuropathological features of AD as amyloid beta and tau proteins, neuroinflammation has to be brought into the picture as well. Taking advantage of a coupled mathematical modelling framework, we formulate a network model, accounting for the coupling between neurons and astroglia and integrating all three main neuropathological features with the brain connectome data. We provide details on the coupled dynamics involving cytokines, astrocytes, and microglia. Further, we apply the tumour necrosis factor alpha (TNF-α) inhibitor and anti-Aβ drug and analyze their influence on the brain cells, suggesting conditions under which the drug can prevent cell damage. The important role of astrocytes and TNF-α inhibitors in AD pathophysiology is emphasized, along with potentially promising pathways for developing new AD therapies.

Introducing and applying Newtonian blurring: an augmented dataset of 126,000 human connectomes at braingraph.org

Gaussian blurring is a well-established method for image data augmentation: it may generate a large set of images from a small set of pictures for training and testing purposes for Artificial Intelligence (AI) applications. When we apply AI for non-imagelike biological data, hardly any related method exists. Here we introduce the "Newtonian blurring" in human braingraph (or connectome) augmentation: Started from a dataset of 1053 subjects from the public release of the Human Connectome Project, we first repeat a probabilistic weighted braingraph construction algorithm 10 times for describing the connections of distinct cerebral areas, then for every possible set of 7 of these graphs, delete the lower and upper extremes, and average the remaining 7 - 2 = 5 edge-weights for the data of each subject. This way we augment the 1053 graph-set to 120 [Formula: see text] 1053 = 126,360 graphs. In augmentation techniques, it is an important requirement that no artificial additions should be introduced into the dataset. Gaussian blurring and also this Newtonian blurring satisfy this goal. The resulting dataset of 126,360 graphs, each in 5 resolutions (i.e., 631,800 graphs in total), is freely available at the site https://braingraph.org/cms/download-pit-group-connectomes/ . Augmenting with Newtonian blurring may also be applicable in other non-image-related fields, where probabilistic processing and data averaging are implemented.

Identifying super-feminine, super-masculine and sex-defining connections in the human braingraph

For more than a decade now, we can discover and study thousands of cerebral connections with the application of diffusion magnetic resonance imaging (dMRI) techniques and the accompanying algorithmic workflow. While numerous connectomical results were published enlightening the relation between the braingraph and certain biological, medical, and psychological properties, it is still a great challenge to identify a small number of brain connections closely related to those conditions. In the present contribution, by applying the 1200 Subjects Release of the Human Connectome Project (HCP) and Support Vector Machines, we identify just 102 connections out of the total number of 1950 connections in the 83-vertex graphs of 1064 subjects, which-by a simple linear test-precisely, without any error determine the sex of the subject. Next, we re-scaled the weights of the edges-corresponding to the discovered fibers-to be between 0 and 1, and, very surprisingly, we were able to identify two graph edges out of these 102, such that, if their weights are both 1, then the connectome always belongs to a female subject, independently of the other edges. Similarly, we have identified 3 edges from these 102, whose weights, if two of them are 1 and one is 0, imply that the graph belongs to a male subject-again, independently of the other edges. We call the former 2 edges superfeminine and the first two of the 3 edges supermasculine edges of the human connectome. Even more interestingly, the edge, connecting the right Pars Triangularis and the right Superior Parietal areas, is one of the 2 superfeminine edges, and it is also the third edge, accompanying the two supermasculine connections if its weight is 0; therefore, it is also a "switching" edge. Identifying such edge-sets of distinction is the unprecedented result of this work.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11571-021-09687-w.

The braingraph.org database with more than 1000 robust human connectomes in five resolutions

The human brain is the most complex object of study we encounter today. Mapping the neuronal-level connections between the more than 80 billion neurons in the brain is a hopeless task for science. By the recent advancement of magnetic resonance imaging (MRI), we are able to map the macroscopic connections between about 1000 brain areas. The MRI data acquisition and the subsequent algorithmic workflow contain several complex steps, where errors can occur. In the present contribution we describe and publish 1064 human connectomes, computed from the public release of the Human Connectome Project. Each connectome is available in 5 resolutions, with 83, 129, 234, 463 and 1015 anatomically labeled nodes. For error correction we follow an averaging and extreme value deleting strategy for each edge and for each connectome. The resulting 5320 braingraphs can be downloaded from the https://braingraph.org site. This dataset makes possible the access to this graphs for scientists unfamiliar with neuroimaging- and connectome-related tools: mathematicians, physicists and engineers can use their expertize and ideas in the analysis of the connections of the human brain. Brain scientists and computational neuroscientists also have a robust and large, multi-resolution set for connectomical studies.

The Graph of Our Mind

Graph theory in the last two decades penetrated sociology, molecular biology, genetics, chemistry, computer engineering, and numerous other fields of science. One of the more recent areas of its applications is the study of the connections of the human brain. By the development of diffusion magnetic resonance imaging (diffusion MRI), it is possible today to map the connections between the 1–1.5 cm2 regions of the gray matter of the human brain. These connections can be viewed as a graph. We have computed 1015-vertex graphs with thousands of edges for hundreds of human brains from one of the highest quality data sources: the Human Connectome Project. Here we analyze the male and female braingraphs graph-theoretically and show statistically significant differences in numerous parameters between the sexes: the female braingraphs are better expanders, have more edges, larger bipartition widths, and larger vertex cover than the braingraphs of the male subjects. These parameters are closely related to the quality measures of highly parallel computer interconnection networks: the better expanding property, the large bipartition width, and the large vertex cover characterize high-quality interconnection networks. We apply the data of 426 subjects and demonstrate the statistically significant (corrected) differences in 116 graph parameters between the sexes.

The frequent complete subgraphs in the human connectome

While it is still not possible to describe the neuronal-level connections of the human brain, we can map the human connectome with several hundred vertices, by the application of diffusion-MRI based techniques. In these graphs, the nodes correspond to anatomically identified gray matter areas of the brain, while the edges correspond to the axonal fibers, connecting these areas. In our previous contributions, we have described numerous graph-theoretical phenomena of the human connectomes. Here we map the frequent complete subgraphs of the human brain networks: in these subgraphs, every pair of vertices is connected by an edge. We also examine sex differences in the results. The mapping of the frequent subgraphs gives robust substructures in the graph: if a subgraph is present in the 80% of the graphs, then, most probably, it could not be an artifact of the measurement or the data processing workflow. We list here the frequent complete subgraphs of the human braingraphs of 413 subjects (238 women and 175 men), each with 463 nodes, with a frequency threshold of 80%, and identify 812 complete subgraphs, which are more frequent in male and 224 complete subgraphs, which are more frequent in female connectomes.

Good neighbors, bad neighbors: the frequent network neighborhood mapping of the hippocampus enlightens several structural factors of the human intelligence on a 414-subject cohort

The human connectome has become the very frequent subject of study of brain-scientists, psychologists and imaging experts in the last decade. With diffusion magnetic resonance imaging techniques, united with advanced data processing algorithms, today we are able to compute braingraphs with several hundred, anatomically identified nodes and thousands of edges, corresponding to the anatomical connections of the brain. The analysis of these graphs without refined mathematical tools is hopeless. These tools need to address the high error rate of the MRI processing workflow, and need to find structural causes or at least correlations of psychological properties and cerebral connections. Until now, structural connectomics was only rarely able of identifying such causes or correlations. In the present work we study the frequent neighbor sets of the most deeply investigated brain area, the hippocampus. By applying the Frequent Network Neighborhood mapping method, we identified frequent neighbor-sets of the hippocampus, which may influence numerous psychological parameters, including intelligence-related ones. We have found "Good Neighbor" sets, which correlate with better test results and also "Bad Neighbor" sets, which correlate with worse test results. Our study utilizes the braingraphs, computed from the imaging data of the Human Connectome Project's 414 subjects, each with 463 anatomically identified nodes.

Optimal Interplay between Synaptic Strengths and Network Structure Enhances Activity Fluctuations and Information Propagation in Hierarchical Modular Networks

In network models of spiking neurons, the joint impact of network structure and synaptic parameters on activity propagation is still an open problem. Here, we use an information-theoretical approach to investigate activity propagation in spiking networks with a hierarchical modular topology. We observe that optimized pairwise information propagation emerges due to the increase of either (i) the global synaptic strength parameter or (ii) the number of modules in the network, while the network size remains constant. At the population level, information propagation of activity among adjacent modules is enhanced as the number of modules increases until a maximum value is reached and then decreases, showing that there is an optimal interplay between synaptic strength and modularity for population information flow. This is in contrast to information propagation evaluated among pairs of neurons, which attains maximum value at the maximum values of these two parameter ranges. By examining the network behavior under the increase of synaptic strength and the number of modules, we find that these increases are associated with two different effects: (i) the increase of autocorrelations among individual neurons and (ii) the increase of cross-correlations among pairs of neurons. The second effect is associated with better information propagation in the network. Our results suggest roles that link topological features and synaptic strength levels to the transmission of information in cortical networks.

The Frequent Network Neighborhood Mapping of the human hippocampus shows much more frequent neighbor sets in males than in females

In the study of the human connectome, the vertices and the edges of the network of the human brain are analyzed: the vertices of the graphs are the anatomically identified gray matter areas of the subjects; this set is exactly the same for all the subjects. The edges of the graphs correspond to the axonal fibers, connecting these areas. In the biological applications of graph theory, it happens very rarely that scientists examine numerous large graphs on the very same, labeled vertex set. Exactly this is the case in the study of the connectomes. Because of the particularity of these sets of graphs, novel, robust methods need to be developed for their analysis. Here we introduce the new method of the Frequent Network Neighborhood Mapping for the connectome, which serves as a robust identification of the neighborhoods of given vertices of special interest in the graph. We apply the novel method for mapping the neighborhoods of the human hippocampus and discover strong statistical asymmetries between the connectomes of the sexes, computed from the Human Connectome Project. We analyze 413 braingraphs, each with 463 nodes. We show that the hippocampi of men have much more significantly frequent neighbor sets than women; therefore, in a sense, the connections of the hippocampi are more regularly distributed in men and more varied in women. Our results are in contrast to the volumetric studies of the human hippocampus, where it was shown that the relative volume of the hippocampus is the same in men and women.

The frequent subgraphs of the connectome of the human brain

In mapping the human structural connectome, we are in a very fortunate situation: one can compute and compare graphs, describing the cerebral connections between the very same, anatomically identified small regions of the gray matter among hundreds of human subjects. The comparison of these graphs has led to numerous recent results, as the (1) discovery that women's connectomes have deeper and richer connectivity-related graph parameters like those of men, or (2) the description of more and less conservatively connected lobes and cerebral regions, and (3) the discovery of the phenomenon of the consensus connectome dynamics. Today one of the greatest challenges of brain science is the description and modeling of the circuitry of the human brain. For this goal, we need to identify sub-circuits that are present in almost all human subjects and those, which are much less frequent: the former sub-circuits most probably have functions with general importance, the latter sub-circuits are probably related to the individual variability of the brain structure and function. The present contribution describes the frequent connected subgraphs of at most six edges in the human brain. We analyze these frequent graphs and also examine sex differences in these graphs: we demonstrate numerous connected subgraphs that are more frequent in female or male connectomes. While there is no difference in the number of k edge connected subgraphs in males or females for k = 1 , and for k = 2 males have slightly more frequent subgraphs, for k = 6 there is a very strong advantage in the case of female braingraphs. Our data source is the public release of the Human Connectome Project, and we are applying the data of 426 human subjects in this study.