Relation of connectome topology to brain volume across 103 mammalian species.

The brain connectome is an embedded network of anatomically interconnected brain regions, and the study of its topological organization in mammals has become of paramount importance due to its role in scaffolding brain function and behavior. Unlike many other observable networks, brain connections incur material and energetic cost, and their length and density are volumetrically constrained by the skull. Thus, an open question is how differences in brain volume impact connectome topology. We address this issue using the MaMI database, a diverse set of mammalian connectomes reconstructed from 201 animals, covering 103 species and 12 taxonomy orders, whose brain size varies over more than 4 orders of magnitude. Our analyses focus on relationships between volume and modular organization. After having identified modules through a multiresolution approach, we observed how connectivity features relate to the modular structure and how these relations vary across brain volume. We found that as the brain volume increases, modules become more spatially compact and dense, comprising more costly connections. Furthermore, we investigated how spatial embedding shapes network communication, finding that as brain volume increases, nodes' distance progressively impacts communication efficiency. We identified modes of variation in network communication policies, as smaller and bigger brains show higher efficiency in routing- and diffusion-based signaling, respectively. Finally, bridging network modularity and communication, we found that in larger brains, modular structure imposes stronger constraints on network signaling. Altogether, our results show that brain volume is systematically related to mammalian connectome topology and that spatial embedding imposes tighter restrictions on larger brains.

Partial entropy decomposition reveals higher-order information structures in human brain activity.

The standard approach to modeling the human brain as a complex system is with a network, where the basic unit of interaction is a pairwise link between two brain regions. While powerful, this approach is limited by the inability to assess higher-order interactions involving three or more elements directly. In this work, we explore a method for capturing higher-order dependencies in multivariate data: the partial entropy decomposition (PED). Our approach decomposes the joint entropy of the whole system into a set of nonnegative atoms that describe the redundant, unique, and synergistic interactions that compose the system's structure. PED gives insight into the mathematics of functional connectivity and its limitation. When applied to resting-state fMRI data, we find robust evidence of higher-order synergies that are largely invisible to standard functional connectivity analyses. Our approach can also be localized in time, allowing a frame-by-frame analysis of how the distributions of redundancies and synergies change over the course of a recording. We find that different ensembles of regions can transiently change from being redundancy-dominated to synergy-dominated and that the temporal pattern is structured in time. These results provide strong evidence that there exists a large space of unexplored structures in human brain data that have been largely missed by a focus on bivariate network connectivity models. This synergistic structure is dynamic in time and likely will illuminate interesting links between brain and behavior. Beyond brain-specific application, the PED provides a very general approach for understanding higher-order structures in a variety of complex systems.

Multi-modal and multi-subject modular organization of human brain networks.

The human brain is a complex network of anatomically interconnected brain areas. Spontaneous neural activity is constrained by this architecture, giving rise to patterns of statistical dependencies between the activity of remote neural elements. The non-trivial relationship between structural and functional connectivity poses many unsolved challenges about cognition, disease, development, learning and aging. While numerous studies have focused on statistical relationships between edge weights in anatomical and functional networks, less is known about dependencies between their modules and communities. In this work, we investigate and characterize the relationship between anatomical and functional modular organization of the human brain, developing a novel multi-layer framework that expands the classical concept of multi-layer modularity. By simultaneously mapping anatomical and functional networks estimated from different subjects into communities, this approach allows us to carry out a multi-subject and multi-modal analysis of the brain's modular organization. Here, we investigate the relationship between anatomical and functional modules during resting state, finding unique and shared structures. The proposed framework constitutes a methodological advance in the context of multi-layer network analysis and paves the way to further investigate the relationship between structural and functional network organization in clinical cohorts, during cognitively demanding tasks, and in developmental or lifespan studies.

Modularity maximization as a flexible and generic framework for brain network exploratory analysis.

The modular structure of brain networks supports specialized information processing, complex dynamics, and cost-efficient spatial embedding. Inter-individual variation in modular structure has been linked to differences in performance, disease, and development. There exist many data-driven methods for detecting and comparing modular structure, the most popular of which is modularity maximization. Although modularity maximization is a general framework that can be modified and reparamaterized to address domain-specific research questions, its application to neuroscientific datasets has, thus far, been narrow. Here, we highlight several strategies in which the "out-of-the-box" version of modularity maximization can be extended to address questions specific to neuroscience. First, we present approaches for detecting "space-independent" modules and for applying modularity maximization to signed matrices. Next, we show that the modularity maximization frame is well-suited for detecting task- and condition-specific modules. Finally, we highlight the role of multi-layer models in detecting and tracking modules across time, tasks, subjects, and modalities. In summary, modularity maximization is a flexible and general framework that can be adapted to detect modular structure resulting from a wide range of hypotheses. This article highlights multiple frontiers for future research and applications.

The modular organization of brain cortical connectivity across the human lifespan.

The network architecture of the human brain contributes in shaping neural activity, influencing cognitive and behavioral processes. The availability of neuroimaging data across the lifespan allows us to monitor how this architecture reorganizes, influenced by processes like learning, adaptation, maturation, and senescence. Changing patterns in brain connectivity can be analyzed with the tools of network science, which can be used to reveal organizational principles such as modular network topology. The identification of network modules is fundamental, as they parse the brain into coherent sub-systems and allow for both functional integration and segregation among different brain areas. In this work we examined the brain's modular organization by developing an ensemble-based multilayer network approach, allowing us to link changes of structural connectivity patterns to development and aging. We show that modular structure exhibits both linear and nonlinear age-related trends. In the early and late lifespan, communities are more modular, and we track the origins of this high modularity to two different substrates in brain connectivity, linked to the number and the weights of the intra-clusters edges. We also demonstrate that aging leads to a progressive and increasing reconfiguration of modules and a redistribution across hemispheres. Finally, we identify those brain regions that most contribute to network reconfiguration and those that remain more stable across the lifespan.

Controlling the human connectome with spatially diffuse input signals.

The human brain is never at "rest"; its activity is constantly fluctuating over time, transitioning from one brain state-a whole-brain pattern of activity-to another. Network control theory offers a framework for understanding the effort - energy - associated with these transitions. One branch of control theory that is especially useful in this context is "optimal control", in which input signals are used to selectively drive the brain into a target state. Typically, these inputs are introduced independently to the nodes of the network (each input signal is associated with exactly one node). Though convenient, this input strategy ignores the continuity of cerebral cortex - geometrically, each region is connected to its spatial neighbors, allowing control signals, both exogenous and endogenous, to spread from their foci to nearby regions. Additionally, the spatial specificity of brain stimulation techniques is limited, such that the effects of a perturbation are measurable in tissue surrounding the stimulation site. Here, we adapt the network control model so that input signals have a spatial extent that decays exponentially from the input site. We show that this more realistic strategy takes advantage of spatial dependencies in structural connectivity and activity to reduce the energy (effort) associated with brain state transitions. We further leverage these dependencies to explore near-optimal control strategies such that, on a per-transition basis, the number of input signals required for a given control task is reduced, in some cases by two orders of magnitude. This approximation yields network-wide maps of input site density, which we compare to an existing database of functional, metabolic, genetic, and neurochemical maps, finding a close correspondence. Ultimately, not only do we propose a more efficient framework that is also more adherent to well-established brain organizational principles, but we also posit neurobiologically grounded bases for optimal control.

Connectome topology of mammalian brains and its relationship to taxonomy and phylogeny.

Network models of anatomical connections allow for the extraction of quantitative features describing brain organization, and their comparison across brains from different species. Such comparisons can inform our understanding of between-species differences in brain architecture and can be compared to existing taxonomies and phylogenies. Here we performed a quantitative comparative analysis using the MaMI database (Tel Aviv University), a collection of brain networks reconstructed from ex vivo diffusion MRI spanning 125 species and 12 taxonomic orders or superorders. We used a broad range of metrics to measure between-mammal distances and compare these estimates to the separation of species as derived from taxonomy and phylogeny. We found that within-taxonomy order network distances are significantly closer than between-taxonomy network distances, and this relation holds for several measures of network distance. Furthermore, to estimate the evolutionary divergence between species, we obtained phylogenetic distances across 10,000 plausible phylogenetic trees. The anatomical network distances were rank-correlated with phylogenetic distances 10,000 times, creating a distribution of coefficients that demonstrate significantly positive correlations between network and phylogenetic distances. Collectively, these analyses demonstrate species-level organization across scales and informational sources: we relate brain networks distances, derived from MRI, with evolutionary distances, derived from genotyping data.

A Comprehensive Analysis of Multilayer Community Detection Algorithms for Application to EEG-Based Brain Networks.

Modular organization is an emergent property of brain networks, responsible for shaping communication processes and underpinning brain functioning. Moreover, brain networks are intrinsically multilayer since their attributes can vary across time, subjects, frequency, or other domains. Identifying the modular structure in multilayer brain networks represents a gateway toward a deeper understanding of neural processes underlying cognition. Electroencephalographic (EEG) signals, thanks to their high temporal resolution, can give rise to multilayer networks able to follow the dynamics of brain activity. Despite this potential, the community organization has not yet been thoroughly investigated in brain networks estimated from EEG. Furthermore, at the state of the art, there is still no agreement about which algorithm is the most suitable to detect communities in multilayer brain networks, and a way to test and compare them all under a variety of conditions is lacking. In this work, we perform a comprehensive analysis of three algorithms at the state of the art for multilayer community detection (namely, genLouvain, DynMoga, and FacetNet) as compared with an approach based on the application of a single-layer clustering algorithm to each slice of the multilayer network. We test their ability to identify both steady and dynamic modular structures. We statistically evaluate their performances by means of ad hoc benchmark graphs characterized by properties covering a broad range of conditions in terms of graph density, number of clusters, noise level, and number of layers. The results of this simulation study aim to provide guidelines about the choice of the more appropriate algorithm according to the different properties of the brain network under examination. Finally, as a proof of concept, we show an application of the algorithms to real functional brain networks derived from EEG signals collected at rest with closed and open eyes. The test on real data provided results in agreement with the conclusions of the simulation study and confirmed the feasibility of multilayer analysis of EEG-based brain networks in both steady and dynamic conditions.

Multi-layer analysis of multi-frequency brain networks as a new tool to study EEG topological organization.

Oscillatory activity rising from the interaction among neurons is widely observed in the brain at different scales and is thought to encode distinctive properties of the neural processing. Classical investigations of neuroelectrical activity and connectivity usually focus on specific frequency bands, considered as separate aspects of brain functioning. However, this might not paint the whole picture, preventing to see the brain activity as a whole, as the result of an integrated process. This study aims to provide a new framework for the analysis of the functional interaction between brain regions across frequencies and different subjects. We ground our work on the latest advances in graph theory, exploiting multi-layer community detection. In our multi-layer network model, layers keep track of single frequencies, including all the information in a unique graph. Community detection is then applied by means of a multilayer formulation of modularity. As a proof-of-concept of our approach, we provide here an application to multi-frequency functional brain networks derived from resting state EEG collected in a group of healthy subjects. Our results indicate that α-band selectively characterizes an inter-individual common organization of EEG brain networks during open eyes resting state. Future applications of this new approach may include the extraction of subject-specific features able to capture selected properties of the brain processes, related to physiological or pathological conditions.