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The exploration of brain-heart interactions within various paradigms, including affective computing, human-computer interfaces, and sensorimotor evaluation, stands as a significant milestone in biomarker development and neuroscientific research. A range of techniques, spanning from molecular to behavioral approaches, has been proposed to measure these interactions. Different frameworks use signal processing techniques, from the estimation of brain responses to individual heartbeats to higher-order dynamics linking cardiac inputs to changes in brain organization. This review provides an overview to the most notable signal processing strategies currently used for measuring and modeling brain-heart interactions. It discusses their usability and highlights the main challenges that need to be addressed for future methodological developments. Current methodologies have deepened our understanding of the impact of neural disruptions on brain-heart interactions, solidifying it as a biomarker for evaluation of the physiological state of the nervous system and holding immense potential for disease stratification. The vast outlook of these methods becomes apparent specially in neurological and psychiatric disorders. As we tackle new methodological challenges, gaining a more profound understanding of how these interactions operate, we anticipate further insights into the role of peripheral neurons and the environmental input from the rest of the body in shaping brain functioning., Comment: 16 pages, 5 figures

Graph theoretical methods have proven valuable for investigating alterations in both anatomical and functional brain connectivity networks during Alzheimer's disease (AD). Recent studies suggest that representing brain networks in a suitable geometric space can better capture their connectivity structure. This study introduces a novel approach to characterize brain connectivity changes using low-dimensional, informative representations of networks in a latent geometric space. Specifically, the networks are embedded in the Poincar\'e disk model of hyperbolic geometry. Here, we define a local measure of distortion of the geometric neighborhood of a node following a perturbation. The method is applied to a brain networks dataset of patients with AD and healthy participants, derived from DWI and fMRI scans. We show that, compared with standard graph measures, our method identifies more accurately the brain regions most affected by neurodegeneration. Notably, the abnormality detection in memory-related and frontal areas are robust across multiple brain parcellation scales. Finally, our findings suggest that the geometric perturbation score could serve as a potential biomarker for characterizing disease progression.

Brain-computer interfaces (BCIs) enable users to interact with the external world using brain activity. Despite their potential in neuroscience and industry, BCI performance remains inconsistent in noninvasive applications, often prioritizing algorithms that achieve high classification accuracies while masking the neural mechanisms driving that performance. In this study, we investigated the interpretability of features derived from brain network lateralization, benchmarking against widely used techniques like power spectrum density (PSD), common spatial pattern (CSP), and Riemannian geometry. We focused on the spatial distribution of the functional connectivity within and between hemispheres during motor imagery tasks, introducing network-based metrics such as integration and segregation. Evaluating these metrics across multiple EEG-based BCI datasets, our findings reveal that network lateralization offers neurophysiological plausible insights, characterized by stronger lateralization in sensorimotor and frontal areas contralateral to imagined movements. While these lateralization features did not outperform CSP and Riemannian geometry in terms of classification accuracy, they demonstrated competitive performance against PSD alone and provided biologically relevant interpretation. This study underscores the potential of brain network lateralization as a new feature to be integrated in motor imagery-based BCIs for enhancing the interpretability of noninvasive applications.

This paper proposes a multilayer graph model for the community detection from multiple observations. This is a very frequent situation, when different estimators are applied to infer graph edges from signals at its nodes, or when different signal measurements are carried out. The multilayer network stacks the graph observations at the different layers, and it links replica nodes at adjacent layers. This configuration matches the Cartesian product between the ground truth graph and a path graph, where the number of nodes corresponds to the number of the observations. Stemming on the algebraic structure of the Laplacian of the Cartesian multilayer network, we infer a subset of the eigenvectors of the true graph and perform community detection. Experimental results on synthetic graphs prove the accuracy of the method, which outperforms state-of-the-art approaches in terms of ability of correctly detecting graph communities. Finally, we show the application of our method to discriminate different brain networks derived from real EEG data collected during motor imagery experiments. We conclude that our approach appears promising in identifying graph communities when multiple observations of the graph are available and it results promising for EEG-based motor imagery applications., Comment: This work has been submitted to the IEEE for possible publication

Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and support decision-making. This is typically achieved by rearranging the nodes to minimize the edge crossings responsible of unintelligible and often unaesthetic trends. But when the nodes cannot be moved, as in spatial and physical networks, this procedure is not viable. Here, we overcome this situation by turning the edge crossing problem into a graph filtering optimization. We demonstrate that the presence of longer connections prompt the optimal solution to yield sparser networks, thereby limiting the number of intersections and getting more readable layouts. This theoretical result matches human behavior and provides an ecologically-inspired criterion to visualize and model real-world interconnected systems.

Network controllability is a powerful tool to study causal relationships in complex systems and identify the driver nodes for steering the network dynamics into desired states. However, due to ill-posed conditions, results become unreliable when the number of drivers becomes too small compared to the network size. This is a very common situation, particularly in real-world applications, where the possibility to access multiple nodes at the same time is limited by technological constraints, such as in the human brain. Although targeting smaller network parts might improve accuracy, challenges may remain for extremely unbalanced situations, when for example there is one single driver. To address this problem, we developed a mathematical framework that combines concepts from spectral graph theory and modern network science. Instead of controlling the original network dynamics, we aimed to control its low-dimensional embedding into the topological space derived from the network Laplacian. By performing extensive simulations on synthetic networks, we showed that a relatively low number of projected components is enough to improve the overall control accuracy, notably when dealing with very few drivers. Based on these findings, we introduced alternative low-dimensional controllability metrics and used them to identify the main driver areas of the human connectome obtained from N=6134 healthy individuals in the UK-biobank cohort. Results revealed previously unappreciated influential regions compared to standard approaches, enabled to draw control maps between distinct specialized large-scale brain systems, and yielded an anatomically-based understanding of hemispheric functional lateralization. Taken together, our results offered a theoretically-grounded solution to deal with network controllability in real-life applications and provided insights into the causal interactions of the human brain.

Brain-Computer Interface (BCI) systems allow users to perform actions by translating their brain activity into commands. Such systems usually need a training phase, consisting in training a classification algorithm to discriminate between mental states using specific features from the recorded signals. This phase of feature selection and training is crucial for BCI performance and presents specific constraints to be met in a clinical context, such as post-stroke rehabilitation. In this paper, we present HappyFeat, a software making Motor Imagery (MI) based BCI experiments easier, by gathering all necessary manipulations and analysis in a single convenient GUI and via automation of experiment or analysis parameters. The resulting workflow allows for effortlessly selecting the best features, helping to achieve good BCI performance in time-constrained environments. Alternative features based on Functional Connectivity can be used and compared or combined with Power Spectral Density, allowing a network-oriented approach. We then give details of HappyFeat's main mechanisms, and a review of its performances in typical use cases. We also show that it can be used as an efficient tool for comparing different metrics extracted from the signals, to train the classification algorithm. To this end, we show a comparison between the commonly-used Power Spectral Density and network metrics based on Functional Connectivity. HappyFeat is available as an open-source project which can be freely downloaded on GitHub., Comment: 17 pages, 5 figures, 1 table, "Annex" section

Mental imagery-based brain-computer interfaces (BCIs) allow to interact with the external environment by naturally bypassing the musculoskeletal system. Making BCIs efficient and accurate is paramount to improve the reliability of real-life and clinical applications, from open-loop device control to closed-loop neurorehabilitation. By promoting sense of agency and embodiment, realistic setups including multimodal channels of communication, such as eye-gaze, and robotic prostheses aim to improve BCI performance. However, how the mental imagery command should be integrated in those hybrid systems so as to ensure the best interaction is still poorly understood. To address this question, we performed a hybrid EEG-based BCI experiment involving healthy volunteers enrolled in a reach-and-grasp action operated by a robotic arm. Main results showed that the hand grasping motor imagery timing significantly affects the BCI accuracy as well as the spatiotemporal brain dynamics. Higher control accuracy was obtained when motor imagery is performed just after the robot reaching, as compared to before or during the movement. The proximity with the subsequent robot grasping favored intentional binding, led to stronger motor-related brain activity, and primed the ability of sensorimotor areas to integrate information from regions implicated in higher-order cognitive functions. Taken together, these findings provided fresh evidence about the effects of intentional binding on human behavior and cortical network dynamics that can be exploited to design a new generation of efficient brain-machine interfaces., Comment: 18 pages, 5 figures, 7 supplementary materials

The stochastic exploration of the configuration space and the exploitation of functional states underlie many biological processes. The evolutionary dynamics stands out as a remarkable example. Here, we introduce a novel formalism that mimics evolution and encodes a general exploration-exploitation dynamics for biological networks. We apply it to the brain wiring problem, focusing on the maturation of that of the nematode C. elegans. We demonstrate that a parsimonious maxent description of the adult brain combined with our framework is able to track down the entire developmental trajectory.

Real-world networks typically exhibit several aspects, or layers, of interactions among their nodes. By permuting the role of the nodes and the layers, we establish a new criterion to construct the dual of a network. This approach allows to examine information from either a node-centric or layer-centric viewpoint. Through rigorous analytical methods and extensive simulations, we demonstrate that nodewise and layerwise connectivity measure different but related aspects of the same system. Leveraging node-layer duality provides complementary insights, enabling a deeper comprehension of diverse networks across social science, technology and biology. Taken together, these findings reveal previously unappreciated features of complex systems and provide a fresh tool for delving into their structure and dynamics.

In many fields of science and technology we are confronted with complex networks. Making sense of these networks often require the ability to visualize and explore their intermingled structure consisting of nodes and links. To facilitate the identification of significant connectivity patterns, many methods have been developed based on the rearrangement of the nodes so as to avoid link criss-cross. However, real networks are often embedded in a geometrical space and the nodes code for an intrinsic physical feature of the system that one might want to preserve. For these spatial networks, it is therefore crucial to find alternative strategies operating on the links and not on the nodes. Here, we introduce Vizaj a javascript web application to visualize spatial networks based on optimized geometrical criteria that reshape the link profiles. While optimized for 3D networks, Vizaj can also be used for 2D networks and offers the possibility to interactively customize the visualization via several controlling parameters, including network filtering and the effect of internode distance on the link trajectories. Vizaj is further equipped with additional options allowing to improve the final aesthetics, such as the color/size of both nodes and links, zooming/rotating/translating, and superimposing external objects. Vizaj is an open-source software which can be freely downloaded and updated via a github repository. Here, we provide a detailed description of its main features and algorithms together with a guide on how to use it. Finally, we validate its potential on several synthetic and real spatial networks from infrastructural to biological systems. We hope that Vizaj will help scientists and practitioners to make sense of complex networks and provide aesthetic while informative visualizations.

The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying network structure is crucial to understand the brain functioning under both healthy and pathological conditions. Yet, analyzing brain networks is challenging, in part because their structure represents only one possible realization of a generative stochastic process which is in general unknown. Having a formal way to cope with such intrinsic variability is therefore central for the characterization of brain network properties. Addressing this issue entails the development of appropriate tools mostly adapted from network science and statistics. Here, we focus on a particular class of maximum entropy models for networks, i.e. exponential random graph models (ERGMs), as a parsimonious approach to identify the local connection mechanisms behind observed global network structure. Efforts are reviewed on the quest for basic organizational properties of human brain networks, as well as on the identification of predictive biomarkers of neurological diseases such as stroke. We conclude with a discussion on how emerging results and tools from statistical graph modeling, associated with forthcoming improvements in experimental data acquisition, could lead to a finer probabilistic description of complex systems in network neuroscience., Comment: 34 pages, 8 figures

Understanding how few distributed areas can steer large-scale brain activity is a fundamental question that has practical implications, which range from inducing specific patterns of behavior to counteracting disease. Recent endeavors based on network controllability provided fresh insights into the potential ability of single regions to influence whole brain dynamics through the underlying structural connectome. However, controlling the entire brain activity is often unfeasible and might not always be necessary. The question whether single areas can control specific target subsystems remains crucial, albeit still poorly explored. Furthermore, the structure of the brain network exhibits progressive changes across the lifespan, but little is known about the possible consequences in the controllability properties. To address these questions, we adopted a novel target controllability approach that quantifies the centrality of brain nodes in controlling specific target anatomo-functional systems. We then studied such target control centrality in human connectomes obtained from healthy individuals aged from 5 to 85. Main results showed that the sensorimotor system has a high influencing capacity, but it is difficult for other areas to influence it. Furthermore, we reported that target control centrality varies with age and that temporal-parietal regions, whose cortical thinning is crucial in dementia-related diseases, exhibit lower values in older people. By simulating targeted attacks, such as those 19 occurring in focal stroke, we showed that the ipsilesional hemisphere is the most affected one regardless of the damaged area. Notably, such degradation in target control centrality was more evident in younger people, thus supporting early-vulnerability hypotheses after stroke.

A complete understanding of the brain requires an integrated description of the numerous scales of neural organization. It means studying the interplay of genes, synapses, and even whole brain regions which ultimately leads to different types of behavior, from perception to action, while asleep or awake. Yet, multiscale brain modeling is challenging, in part because of the difficulty to access simultaneously to information from multiple spatiotemporal scales. While some insights have been gained on the role of specific microcircuits (e.g., thalamocortical), a comprehensive characterization of how changes occurring at one scale can have an impact on other ones, remains poorly understood. Recent efforts to address this gap include the development of new analytical tools mostly adapted from network science and dynamical systems theory. These theoretical contributions provide a powerful framework to analyze and model interconnected complex systems exhibiting interactions within and between different scales, or layers. Here, we present recent advances for the characterization of the multiscale brain organization in terms of structure-function, oscillation frequencies and temporal evolution. Efforts are reviewed on the multilayer network properties underlying higher-order organization of neuronal assemblies, as well as on the identification of multimodal network-based biomarkers of brain pathologies, such as Alzheimer's disease. We conclude this Colloquium with a perspective discussion on how recent results from multilayer network theory, involving generative modeling, controllability and machine learning, could be adopted to address new questions in modern neuroscience.

Functional connectivity is a key approach to investigate oscillatory activities of the brain that provides important insights on the underlying dynamic of neuronal interactions and that is mostly applied for brain activity analysis. Building on the advances in information geometry for brain-computer interface, we propose a novel framework that combines functional connectivity estimators and covariance-based pipelines to classify mental states, such as motor imagery. A Riemannian classifier is trained for each estimator and an ensemble classifier combines the decisions in each feature space. A thorough assessment of the functional connectivity estimators is provided and the best performing pipeline, called FUCONE, is evaluated on different conditions and datasets. Using a meta-analysis to aggregate results across datasets, FUCONE performed significantly better than all state-of-the-art methods. The performance gain is mostly imputable to the improved diversity of the feature spaces, increasing the robustness of the ensemble classifier with respect to the inter- and intra-subject variability.

Functional connectivity (FC) can be represented as a network, and is frequently used to better understand the neural underpinnings of complex tasks such as motor imagery (MI) detection in brain-computer interfaces (BCIs). However, errors in the estimation of connectivity can affect the detection performances. In this work, we address the problem of denoising common connectivity estimates to improve the detectability of different connectivity states. Specifically, we propose a denoising algorithm that acts on the network graph Laplacian, which leverages recent graph signal processing results. Further, we derive a novel formulation of the Jensen divergence for the denoised Laplacian under different states. Numerical simulations on synthetic data show that the denoising method improves the Jensen divergence of connectivity patterns corresponding to different task conditions. Furthermore, we apply the Laplacian denoising technique to brain networks estimated from real EEG data recorded during MI-BCI experiments. Using our novel formulation of the J-divergence, we are able to quantify the distance between the FC networks in the motor imagery and resting states, as well as to understand the contribution of each Laplacian variable to the total J-divergence between two states. Experimental results on real MI-BCI EEG data demonstrate that the Laplacian denoising improves the separation of motor imagery and resting mental states, and shortens the time interval required for connectivity estimation. We conclude that the approach shows promise for the robust detection of connectivity states while being appealing for implementation in real-time BCI applications., Comment: This work has been submitted to the IEEE for possible publication

Brain-computer interfaces (BCIs) constitute a promising tool for communication and control. However, mastering non-invasive closed-loop systems remains a learned skill that is difficult to develop for a non-negligible proportion of users. The involved learning process induces neural changes associated with a brain network reorganization that remains poorly understood. To address this inter-subject variability, we adopted a multilayer approach to integrate brain network properties from electroencephalographic (EEG) and magnetoencephalographic (MEG) data resulting from a four-session BCI training program followed by a group of healthy subjects. Our method gives access to the contribution of each layer to multilayer network that tends to be equal with time. We show that regardless the chosen modality, a progressive increase in the integration of somatosensory areas in the alpha band was paralleled by a decrease of the integration of visual processing and working memory areas in the beta band. Notably, only brain network properties in multilayer network correlated with future BCI scores in the alpha2 band: positively in somatosensory and decision-making related areas and negatively in associative areas. Our findings cast new light on neural processes underlying BCI training. Integrating multimodal brain network properties provides new information that correlates with behavioral performance and could be considered as a potential marker of BCI learning., Comment: This is the version of the article before editing, as submitted by an author to the Journal of Neural Engineering. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online athttp://iopscience.iop.org/article/10.1088/1741-2552/abef39

Brain-computer interfaces (BCIs) make possible to interact with the external environment by decoding the mental intention of individuals. BCIs can therefore be used to address basic neuroscience questions but also to unlock a variety of applications from exoskeleton control to neurofeedback (NFB) rehabilitation. In general, BCI usability critically depends on the ability to comprehensively characterize brain functioning and correctly identify the user s mental state. To this end, much of the efforts have focused on improving the classification algorithms taking into account localized brain activities as input features. Despite considerable improvement BCI performance is still unstable and, as a matter of fact, current features represent oversimplified descriptors of brain functioning. In the last decade, growing evidence has shown that the brain works as a networked system composed of multiple specialized and spatially distributed areas that dynamically integrate information. While more complex, looking at how remote brain regions functionally interact represents a grounded alternative to better describe brain functioning. Thanks to recent advances in network science, i.e. a modern field that draws on graph theory, statistical mechanics, data mining and inferential modelling, scientists have now powerful means to characterize complex brain networks derived from neuroimaging data. Notably, summary features can be extracted from these networks to quantitatively measure specific organizational properties across a variety of topological scales. In this topical review, we aim to provide the state-of-the-art supporting the development of a network theoretic approach as a promising tool for understanding BCIs and improve usability.

Identifying the nodes that have the potential to influence the state of a network is a relevant question for many complex systems. In many applications it is often essential to test the ability of an individual node to control a specific target subset of the network. In biological networks, this might provide precious information on how single genes regulate the expression of specific groups of molecules in the cell. Taking into account these constraints, we propose an optimized heuristic based on the Kalman rank condition to quantify the centrality of a node as the number of target nodes it can control. By introducing a hierarchy among the nodes in the target set, and performing a step-wise research, we ensure for sparse and directed networks the identification of a controllable driver-target configuration in a significantly reduced space and time complexity. We show how the method works for simple network configurations, then we use it to characterize the inflammatory pathways in molecular gene networks associated with macrophage dysfunction in patients with multiple sclerosis. Results indicate that the targeted secreted molecules can in general be controlled by a large number of driver nodes (51%) involved in different cell functions, i.e. sensing, signaling and transcription. However, during the inflammatory response only a moderate fraction of all the possible driver-target pairs are significantly coactivated, as measured by gene expression data obtained from human blood samples. Notably, they differ between multiple sclerosis patients and healthy controls, and we find that this is related to the presence of dysregulated genes along the controllable walks. Our method, that we name step-wise target controllability, represents a practical solution to identify controllable driver-target configurations in directed complex networks and test their relevance from a functional perspective.

The extraction of brain functioning features is a crucial step in the definition of brain-computer interfaces (BCIs). In the last decade, functional connectivity (FC) estimators have been increasingly explored based on their ability to capture synchronization between multivariate brain signals. However, the underlying neurophysiological mechanisms and the extent to which they can improve performance in BCI-related tasks, is still poorly understood. To address this gap in knowledge, we considered a group of 20 healthy subjects during an EEG-based hand motor imagery (MI) task. We studied two well-established FC estimators, i.e. spectral- and imaginary-coherence, and investigated how they were modulated by the MI task. We characterized the resulting FC networks by extracting the strength of connectivity of each EEG sensor and compared the discriminant power with respect to standard power spectrum features. At the group level, results showed that while spectral-coherence based network features were increasing the controlateral motor area, those based on imaginary-coherence were decreasing. We demonstrated that this opposite, but complementary, behavior was respectively determined by the increase in amplitude and phase synchronization between the brain signals. At the individual level, we proved that including these network connectivity features in the classification of MI mental states led to an overall improvement in accuracy. Taken together, our results provide fresh insights into the oscillatory mechanisms subserving brain network changes during MI and offer new perspectives to improve BCI performance.

Motor imagery-based brain-computer interfaces (BCIs) use an individuals ability to volitionally modulate localized brain activity as a therapy for motor dysfunction or to probe causal relations between brain activity and behavior. However, many individuals cannot learn to successfully modulate their brain activity, greatly limiting the efficacy of BCI for therapy and for basic scientific inquiry. Previous research suggests that coherent activity across diverse cognitive systems is a hallmark of individuals who can successfully learn to control the BCI. However, little is known about how these distributed networks interact through time to support learning. Here, we address this gap in knowledge by constructing and applying a multimodal network approach to decipher brain-behavior relations in motor imagery-based brain-computer interface learning using MEG. Specifically, we employ a minimally constrained matrix decomposition method (non-negative matrix factorization) to simultaneously identify regularized, covarying subgraphs of functional connectivity, to assess their similarity to task performance, and to detect their time-varying expression. Individuals also displayed marked variation in the spatial properties of subgraphs such as the connectivity between the frontal lobe and the rest of the brain, and in the temporal properties of subgraphs such as the stage of learning at which they reached maximum expression. From these observations, we posit a conceptual model in which certain subgraphs support learning by modulating brain activity in regions important for sustaining attention. To test this model, we use tools that stipulate regional dynamics on a networked system (network control theory), and find that good learners display a single subgraph whose temporal expression tracked performance and whose architecture supports easy modulation of brain regions important for attention.

Plasticity after stroke is a complex phenomenon initiated by the functional reorganization of the brain, especially in the perilesional tissue. At macroscales, the reestablishment of segregation within the affected hemisphere and interhemispheric integration has been extensively documented in the reconfiguration of brain networks. However, the local connection mechanisms generating such global network changes are still largely unknown as well as their potential to better predict the outcome of patients. To address this question, time must be considered as a formal variable of the problem and not just a simple repeated observation. Here, we hypothesize that the temporal formation of basic connection blocks such as intermodule edges and intramodule triangles would be sufficient to determine the large-scale brain reorganization after stroke. To test our hypothesis, we adopted a statistical approach based on temporal exponential random graph models (tERGMs). First, we validated the overall performance on synthetic time-varying networks simulating the reconfiguration process after stroke. Then, using longitudinal functional connectivity measurements of resting-state brain activity, we showed that both the formation of triangles within the affected hemisphere and interhemispheric links are sufficient to reproduce the longitudinal brain network changes from 2 weeks to 1 year after the stroke. Finally, we showed that these temporal connection mechanisms are over-expressed in the subacute phase as compared to healthy controls and predicted the chronic language and visual outcome respectively in patients with subcortical and cortical lesions, whereas static approaches failed to do so. Our results indicate the importance of considering time-varying connection properties when modeling dynamic complex systems and provide fresh insights into the network mechanisms of stroke recovery.