A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The spontaneous emergence of coherence and synchronization across such scales is crucial to neural function, while its anomalies often relate to pathological conditions. Here we provide a numerical study of synchronization dynamics in the human connectome network. Our purpose is to provide a detailed characterization of the recently uncovered broad dynamic regime, interposed between order and disorder, which stems from the hierarchical modular organization of the human connectome. In this regime -similar in essence to a Griffiths phase- synchronization dynamics are trapped within metastable attractors of local coherence. Here we explore the role of noise, as an effective description of external perturbations, and discuss how its presence accounts for the ability of the system to escape intermittently from such attractors and explore complex dynamic repertoires of locally coherent states, in analogy with experimentally recorded patterns of cerebral activity.
The spontaneous emergence of coherent behavior through synchronization plays a key role in neural function, and its anomalies often lie at the basis of pathologies. Here we employ a parsimonious (mesoscopic) approach to study analytically and computationally the synchronization (Kuramoto) dynamics on the actual human-brain connectome network. We elucidate the existence of a so-far-uncovered intermediate phase, placed between the standard synchronous and asynchronous phases, i.e. between order and disorder. This novel phase stems from the hierarchical modular organization of the connectome. Whe…
We have extended the study of the Kuramoto model with additive Gaussian noise running on the KKI-18 large human connectome graph. We determined the dynamical behavior of this model by solving it numerically in an assumed homeostatic state, below the synchronization crossover point we determined previously. The de-synchronization duration distributions exhibit power-law tails, characterized by the exponent in the range $1.1 < τ_t < 2$, overlapping the in vivo human brain activity experiments by Palva et al. We show that these scaling results remain valid, by a transformation of the ultra-slow e…
The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 804092 nodes, in an assumed homeostatic state. Since this graph has a topological dimension $d < 4$, a real synchronization phase transition is not possible in the thermodynamic limit, still we c…
We investigate the synchronization transition of the Shinomoto-Kuramoto model on networks of the fruit-fly and two large human connectomes. This model contains a force term, thus is capable of describing critical behavior in the presence of external excitation. By numerical solution we determine the crackling noise durations with and without thermal noise and show extended non-universal scaling tails characterized by $2< τ_t < 2.8$, in contrast with the Hopf transition of the Kuramoto model, without the force $τ_t=3.1(1)$. Comparing the phase and frequency order parameters we find different tr…
Previous simulation studies on human connectomes suggested, that critical dynamics emerge subcrititcally in the so called Griffiths Phases. %This is the consequence of the strong heterogeneity of the graphs. Now we investigate this on the largest available brain network, the $21.662$ node fruit-fly connectome, using the Kuramoto synchronization model. As this graph is less heterogeneous, lacking modular structure and exhibit high topological dimension, we expect a difference from the previous results. Indeed, the synchronization transition is mean-field like, and the width of the transition re…
In this review, we discuss critical dynamics of simple nonequilibrium models on large connectomes, obtained by diffusion MRI, representing the white matter of the human brain. In the first chapter, we overview graph theoretical and topological analysis of these networks, pointing out that universality allows selecting a representative network, the KKI-18, which has been used for dynamical simulation. The critical and sub-critical behaviour of simple, two- or three-state threshold models is discussed with special emphasis on rare-region effects leading to robust Griffiths Phases (GP). Numerical…
Fluctuation-dissipation of the Kuramoto model on fruit-fly connectomes
Institute of Technical Physics and Materials Science, Center for Energy Research（技术物理与材料科学研究所，能源研究中心）；Center for Brain and Cognition, Theoretical and Computational Group, Universitat Pompeu Fabra / ICREA（脑与认知中心，理论与计算组，庞培法布拉大学/加泰罗尼亚高级研究学院）
Current functional Magnetic Resonance Imaging technology is able to resolve billions of individual functional connections characterizing the human connectome. Classical statistical inferential procedures attempting to make valid inferences across this many measures from a reduced set of observations and from a limited number of subjects can be severely underpowered for any but the largest effect sizes. This manuscript discusses fc-MVPA (functional connectivity Multivariate Pattern Analysis), a novel application of multivariate pattern analysis techniques in the context of brain-wide connectome…
The synchronization of different brain regions is widely observed under both normal and pathological conditions such as epilepsy. However, the relationship between the dynamics of these brain regions, the connectivity between them, and the ability to synchronize remains an open question. We investigated the problem of inter-region synchronization in networks of Wilson-Cowan/Neural field equations with homeostatic plasticity, each of which acts as a model for an isolated brain region. We considered arbitrary connection profiles with only one constraint: the rows of the connection matrices are a…
Background: Positron Emission Tomography (PET) with 18F-fluorodeoxyglucose (18F-FDG) reveals metabolic abnormalities in Parkinson's disease (PD) at a systemic level. Previous metabolic connectome studies derived from groups of patients have failed to identify the individual neurophysiological details. We aim to establish an individual metabolic connectome method to characterize the aberrant connectivity patterns and topological alterations of the individual-level brain metabolic connectome and their diagnostic value in PD. Methods: The 18F-FDG PET data of 49 PD patients and 49 healthy controls…
One of the crucial questions in neuroscience is how a rich functional repertoire of brain states relates to its underlying structural organization. How to study the associations between these structural and functional layers is an open problem that involves novel conceptual ways of tackling this question. We here propose an extension of the Connectivity Independent Component Analysis (connICA) framework, to identify joint structural-functional connectivity traits. Here, we extend connICA to integrate structural and functional connectomes by merging them into common hybrid connectivity patterns…
Imaging studies suggest that the functional connectivity patterns of resting state networks (RS-networks) reflect underlying structural connectivity (SC). If the connectome constrains how brain areas are functionally connected, the stimulation of specific brain areas should produce a characteristic wave of activity ultimately resolving into RS-networks. To systematically test this hypothesis, we use a connectome-based network model of the human brain with detailed realistic SC. We systematically activate all possible thalamic and cortical areas with focal stimulation patterns and confirm that …
Visually comparing brain networks, or connectomes, is an essential task in the field of neuroscience. Especially relevant to the field of clinical neuroscience, group studies that examine differences between populations or changes over time within a population enable neuroscientists to reason about effective diagnoses and treatments for a range of neuropsychiatric disorders. In this paper, we specifically explore how visual analytics tools can be used to facilitate various clinical neuroscience tasks, in which observation and analysis of meaningful patterns in the connectome can support patien…
The brain's functional diversity is reflected in the meso-scale architecture of its connectome, i.e. its division into clusters and communities of topologically-related brain regions. The dominant view, and one that is reinforced by current analysis techniques, is that communities are strictly assortative and segregated from one another, purportedly for the purpose of carrying out specialized information processing. Such a view, however, precludes the possibility of non-assortative communities that could engender a richer functional repertoire by allowing for a more complex set of inter-commun…
The relation between large-scale brain structure and function is an outstanding open problem in neuroscience. We approach this problem by studying the dynamical regime under which realistic spatio-temporal patterns of brain activity emerge from the empirically derived network of human brain neuroanatomical connections. The results show that critical dynamics unfolding on the structural connectivity of the human brain allow the recovery of many key experimental findings obtained with functional Magnetic Resonance Imaging (fMRI), such as divergence of the correlation length, anomalous scaling of…
Principles of network topology have been widely studied in the human connectome. Of particular interest is the modularity of the human brain, where the connectome is divided into subnetworks and subsequently changes with development, aging or disease are investigated. We present a weighted network measure, the Network Dependency Index (NDI), to identify an individual region's importance to the global functioning of the network. Importantly, we utilize NDI to differentiate four subnetworks (Tiers) in the human connectome following Gaussian Mixture Model fitting. We analyze the topological aspec…
Neuropsychiatric disorders impact functional connectivity of the brain at the network level. The identification and statistical testing of disorder-related networks remains challenging. We propose novel methods to streamline the detection and testing of the hidden, disorder-related connectivity patterns as network-objects. We define an abnormal connectome subnetwork as a network-object that includes three classes: nodes of brain areas, edges representing brain connectomic features, and an organized graph topology formed by these nodes and edges. Comparing to the conventional statistical method…
We introduce TempoCave, a novel visualization application for analyzing dynamic brain networks, or connectomes. TempoCave provides a range of functionality to explore metrics related to the activity patterns and modular affiliations of different regions in the brain. These patterns are calculated by processing raw data retrieved functional magnetic resonance imaging (fMRI) scans, which creates a network of weighted edges between each brain region, where the weight indicates how likely these regions are to activate synchronously. In particular, we support the analysis needs of clinical psycholo…
We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the refractory time is on the same order-of-magnitude as the mean link time delays or the heterogeneities of the link time delays, cluster synchronization patterns change, or are suppressed entirely, respectively. We also show that these transitions occur when we only change the properties of a small number of nodes identified by their larger in-degree, hence the …
The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of the human connectome remain incompletely understood. Earlier work in model organisms has suggested that wiring rules based on geometric relationships (distance) can account for many but likely not all topological features. Here we systematically explore a family of generative models of the human connectome that yield synthetic networks designed according to…
Neural systems show a modular and typically also a hierarchical organisation across different levels and across different species. Topology relates to function, but it is also influences dynamics as earlier studies showed its effect on synchrony, oscillation, and activity propagation. Understanding the link between the hierarchical organisation and processing (e.g. does consciousness structurally correlate with the top level of the hierarchy and where is the 'top' in a network?) remains one of the main challenges of the field. In addition, although neuron nodes are often treated as uniform ent…
Large bundles of myelinated axons, called white matter, anatomically connect disparate brain regions together and compose the structural core of the human connectome. We recently proposed a method of measuring the local integrity along the length of each white matter fascicle, termed the local connectome. If communication efficiency is fundamentally constrained by the integrity along the entire length of a white matter bundle, then variability in the functional dynamics of brain networks should be associated with variability in the local connectome. We test this prediction using two statistica…
We exploit flow propagation on the directed neuronal network of the nematode Caenorhabditis elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential cand…
Examining task-free functional connectivity (FC) in the human brain offers insights on how spontaneous integration and segregation of information relate to human cognition, and how this organization may be altered in different conditions, and neurological disorders. This is particularly relevant for patients in disorders of consciousness (DOC) following severe acquired brain damage and coma, one of the most devastating conditions in modern medical care. We present a novel data-driven methodology, connICA, which implements Independent Component Analysis (ICA) for the extraction of robust indepe…
In order to understand the complex cognitive functions of the human brain, it is essential to study the structural connectome, i.e., the wiring of different brain regions to each other through axonal pathways. However, the high degree of plasticity and cross-population variability in human brains makes it difficult to relate structure to function, motivating a search for invariant patterns in the connectivity. At the same time, variability within a population can provide information about generative mechanisms. In this paper we analyze the connection topology and link-weight distribution of hu…
Encoding brain regions and their connections as a network of nodes and edges captures many of the possible paths along which information can be transmitted as humans process and perform complex behaviors. Because cognitive processes involve large and distributed networks of brain areas, examinations of multi-node routes within larger connection patterns can offer fundamental insights into the complexities of brain function. Here, we investigate both densely connected groups of nodes that could perform local computations as well as larger patterns of interactions that would allow for parallel p…
Human brain dynamics can be profitably viewed through the lens of statistical mechanics, where neurophysiological activity evolves around and between local attractors representing preferred mental states. Many physically-inspired models of these dynamics define the state of the brain based on instantaneous measurements of regional activity. Yet, recent work in network neuroscience has provided initial evidence that the brain might also be well-characterized by time-varying states composed of locally coherent activity or functional modules. Here we study this network-based notion of brain state…
The dynamic characteristics of functional network connectivity have been widely acknowledged and studied. Both shared and unique information has been shown to be present in the connectomes. However, very little has been known about whether and how this common pattern can predict the individual variability of the brain, i.e. "brain fingerprinting", which attempts to reliably identify a particular individual from a pool of subjects. In this paper, we propose to enhance the individual uniqueness based on an autoencoder network. More specifically, we rely on the hypothesis that the common neural a…
Evaluating the effects of high-throughput structural neuroimaging predictors on whole-brain functional connectome outcomes via network-based vector-on-matrix regression
Synchronization in neural system plays an important role in many brain functions. Synchronization in the gamma frequency band (30Hz-100Hz) is involved in a variety of cognitive phenomena; abnormalities of the gamma synchronization are found in schizophrenia and autism spectrum disorder. Frequently, the strength of synchronization is not very high and is intermittent even on short time scales (a few cycles of oscillations). That is, the network exhibits intervals of synchronization followed by intervals of desynchronization. Neural circuits dynamics may show different distributions of desynchro…
Universiti Teknologi Malaysia（马来西亚理工大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
We exploit altered patterns in brain functional connectivity as features for automatic discriminative analysis of neuropsychiatric patients. Deep learning methods have been introduced to functional network classification only very recently for fMRI, and the proposed architectures essentially focused on a single type of connectivity measure. We propose a deep convolutional neural network (CNN) framework for classification of electroencephalogram (EEG)-derived brain connectome in schizophrenia (SZ). To capture complementary aspects of disrupted connectivity in SZ, we explore combination of vario…
The white-matter (micro-)structural architecture of the brain promotes synchrony among neuronal populations, giving rise to richly patterned functional connections. A fundamental problem for systems neuroscience is determining the best way to relate structural and functional networks quantified by diffusion tensor imaging and resting-state functional MRI. As one of the state-of-the-art approaches for network analysis, graph convolutional networks (GCN) have been separately used to analyze functional and structural networks, but have not been applied to explore inter-network relationships. In t…
Institute of Systematic Musicology, University of Hamburg（汉堡大学系统音乐学研究所）；Hamburg University of Applied Sciences（汉堡应用科学大学）
When musicians perform in an ensemble, synchronizing to a mutual pace is the foundation of their musical interaction. Clock generators, e.g., metronomes, or drum machines, might assist such synchronization, but these means, in general, will also distort this natural, self-organized, inter-human synchronization process. In this work, the synchronization of musicians to an external rhythm is modeled using the Impulse Pattern Formulation (IPF), an analytical modeling approach for synergetic systems motivated by research on musical instruments. Nonlinear coupling of system components is described …
We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and the inter-node coupling strengths are derived from Diffusion Tensor Imaging data of the connectome of the human brain. Nodes are coupled using an additive scheme without delays and are driven by background inputs with fixed mean and additive Gaussian noise. Optimal control inputs to nodes are determined by minimizing a cost functional that penalizes the devia…
Università di Siena（锡耶纳大学）；Università Sapienza di Roma（罗马 Sapienza 大学）
Epilepsy is a neurological disorder arising from anomalies of the electrical activity in the brain, affecting about 0.5--0.8\% of the world population. Several studies investigated the relationship between seizures and brainwave synchronization patterns, pursuing the possibility of identifying interictal, preictal, ictal and postictal states. In this work, we introduce a graph-based model of the brain interactions developed to study synchronization patterns in the electroencephalogram (EEG) signals. The aim is to develop a patient-specific approach, also for a real-time use, for the prediction…
Neural synchrony in the brain at rest is usually variable and intermittent, thus intervals of predominantly synchronized activity are interrupted by intervals of desynchronized activity. Prior studies suggested that this temporal structure of the weakly synchronous activity might be functionally significant: many short desynchronizations may be functionally different from few long desynchronizations even if the average synchrony level is the same. In this study, we used computational neuroscience methods to investigate the effects of spike-timing dependent plasticity (STDP) on the temporal pat…
The impact of developmental and aging processes on brain connectivity and the connectome has been widely studied. Network theoretical measures and certain topological principles are computed from the entire brain, however there is a need to separate and understand the underlying subnetworks which contribute towards these observed holistic connectomic alterations. One organizational principle is the rich-club - a core subnetwork of brain regions that are strongly connected, forming a high-cost, high-capacity backbone that is critical for effective communication in the network. Investigations pr…
Signal propagation along the structural connectome of the brain induces changes in the patterns of activity. These activity patterns define global brain states and contain information in accordance with their expected probability of occurrence. The structural connectome, in conjunction with the dynamics, determines the set of possible brain states and constrains the transition between accessible states. Yet, precisely how these structural constraints on state-transitions relate to their information content remains unexplored. To address this gap in knowledge, we defined the information content…
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 concentr…
Networks of fast-spiking interneurons are crucial for the generation of neural oscillations in the brain. Here we study the synchronous behavior of interneuronal networks that are coupled by delayed inhibitory and fast electrical synapses. We find that both coupling modes play a crucial role by the synchronization of the network. In addition, delayed inhibitory synapses affect the emerging oscillatory patterns. By increasing the inhibitory synaptic delay, we observe a transition from regular to mixed oscillatory patterns at a critical value. We also examine how the unreliability of inhibitory …
