Is the brain macroscopically linear? A system identification of resting state dynamics
University of California, Riverside（加州大学河滨分校）；University of Pennsylvania（宾夕法尼亚大学）；Santa Fe Institute（圣塔菲研究所）
Erfan Nozari, Maxwell A. Bertolero, Jennifer Stiso, Lorenzo Caciagli, Eli J. Cornblath, Xiaosong He, Arun S. Mahadevan, George J. Pappas, Dani Smith Bassett
A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal functioning. An implicit assumption has thus formed that an accurate computational model of whole-brain dynamics must also be highly nonlinear, whereas linear models may provide a first-order approximation. Here, we provide a rigorous and data-driven investigation of this hypothesis at the level of whole-brain blood-oxygen-level-dependent (BOLD) and macroscopic field potential dynamics by leveraging the theory of system identification. Using functional MRI (fMRI) and intracranial EEG (iEEG), we model the resting state activity of 700 subjects in the Human Connectome Project (HCP) and 122 subjects from the Restoring Active Memory (RAM) project using state-of-the-art linear and nonlinear model families. We assess relative model fit using predictive power, computational complexity, and the extent of residual dynamics unexplained by the model. Contrary to our expectations, linear auto-regressive models achieve the best measures across all three metrics, eliminating the trade-off between accuracy and simplicity. To understand and explain this linearity, we highlight four properties of macroscopic neurodynamics which can counteract or mask microscopic nonlinear dynamics: averaging over space, averaging over time, observation noise, and limited data samples. Whereas the latter two are technological limitations and can improve in the future, the former two are inherent to aggregated macroscopic brain activity. Our results, together with the unparalleled interpretability of linear models, can greatly facilitate our understanding of macroscopic neural dynamics and the principled design of model-based interventions for the treatment of neuropsychiatric disorders.
Deep learning and whole-brain networks for biomarker discovery: modeling the dynamics of brain fluctuations in resting-state and cognitive tasks
Electric and Computer Engineering Department, Universidad Nacional del Sur（国家南方大学电子与计算机工程系）；Institute of Computer Science and Engineering, National Scientific and Technological Research Council of Argentina (CONICET)（阿根廷国家科学与技术研究理事会计算机科学与工程研究所）；Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra（庞培法布拉大学脑认知中心、信息与通信技术系计算神经科学组）；Institució Catalana de la Recerca i Estudis Avançats (ICREA)（加泰罗尼亚高级研究与教育研究所）；Department of Information and Communication Technologies, Universitat Pompeu Fabra（庞培法布拉大学信息与通信技术系）；ViRVIG, University of Girona（吉罗纳大学ViRVIG）
The human brain exhibits large-scale spontaneous fluctuations that account for most of its total energy metabolism. Independent of any overt function, this immense ongoing activity likely creates or maintains a potential functional brain reserve to facilitate normal brain function. An important property of spontaneous brain activity is the long-range temporal coherence, which can be characterized by resting state fMRI-based brain entropy mapping (BEN), a relatively new method that has gained increasing research interest. The purpose of this study was to leverage the large resting state fMRI an…
Analysis of brain activity in resting-state is of fundamental importance in identifying functional characteristics of neuronal system. Although resting brain has been extensively investigated for low frequency synchrony between brain regions, namely Functional Connectivity (FC), the other main stream of brain connectivity analysis that seeks causal interactions between brain regions, Effective Connectivity (EC), has been little explored in spontaneous brain oscillations. Inherent complexity of brain activities in resting-state, as is observed in BOLD (Blood Oxygenation-Level Dependant) fluctua…
Stroke-induced disturbances of large-scale cortical networks are known to be associated with the extent of motor deficits. We argue that identifying brain networks representative of motor behavior in the resting brain would provide significant insights for current neurorehabilitation approaches. Particularly, we aim to investigate the global configuration of brain rhythms and their relation to motor skill, instead of learning performance as broadly studied. We empirically approach this problem by conducting a three-dimensional physical space visuomotor learning experiment during electroencepha…
Characterising brain activity at rest is of paramount importance to our understanding both of general principles of brain functioning and of the way brain dynamics is affected in the presence of neurological or psychiatric pathologies. We measured the time-reversal symmetry of spontaneous electroencephalographic brain activity recorded from three groups of patients and their respective control group under two experimental conditions (eyes open and closed). We evaluated differences in time irreversibility in terms of possible underlying physical generating mechanisms. The results showed that re…
University of Rajshahi（拉杰沙希大学）；Hajee Mohammad Danesh Science and Technology University（哈吉·穆罕默德·达内什科技大学）；Deakin University（迪肯大学）；COMSATS University Islamabad（伊斯兰堡COMSATS大学）；Charles Sturt University（查尔斯特大学）
In the last two decades, functional magnetic resonance imaging (fMRI) has emerged as one of the most effective technologies in clinical research of the human brain. fMRI allows researchers to study healthy and pathological brains while they perform various neuropsychological functions. Beyond task-related activations, the human brain has some intrinsic activity at a task-negative (resting) state that surprisingly consumes a lot of energy to support communication among neurons. Recent neuroimaging research has also seen an increase in modeling and analyzing brain activity in terms of a graph or…
University of Cambridge（剑桥大学）；Cambridge University（剑桥大学）
Classification of whole-brain functional connectivity MRI data with convolutional neural networks (CNNs) has shown promise, but the complexity of these models impedes understanding of which aspects of brain activity contribute to classification. While visualization techniques have been developed to interpret CNNs, bias inherent in the method of encoding abstract input data, as well as the natural variance of deep learning models, detract from the accuracy of these techniques. We introduce a stochastic encoding method in an ensemble of CNNs to classify functional connectomes by gender. We appli…
The oddball paradigm is widely applied to the investigation of multiple cognitive functions. Prior studies have explored the cortical oscillation and power spectral differing from the resting-state conduction to oddball paradigm, but whether brain networks existing the significant difference is still unclear. Our study addressed how the brain reconfigures its architecture from a resting-state condition (i.e., baseline) to P300 stimulus task in the visual oddball paradigm. In this study, electroencephalogram (EEG) datasets were collected from 24 postgraduate students, who were required to only …
Diverse cognitive processes set different demands on locally segregated and globally integrated brain activity. However, it remains unclear how resting brains configure their functional organization to balance the demands on network segregation and integration to best serve cognition. Here, we use an eigenmode-based approach to identify hierarchical modules in functional brain networks, and quantify the functional balance between network segregation and integration. In a large sample of healthy young adults (n=991), we combine the whole-brain resting state functional magnetic resonance imaging…
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…
Converging research suggests that the resting brain operates at the cusp of dynamic instability signified by scale-free temporal correlations. We asked if the scaling properties of these correlations differ between amplitude and phase fluctuations, which may reflect different aspects of cortical functioning. Using source-reconstructed magneto-encephalographic signals, we found power-law scaling for the collective amplitude and for phase synchronization, both capturing whole-brain activity. The temporal changes of the amplitude comprise slow, persistent memory processes, whereas phase synchroni…
The continuous interaction between brain regions "at rest" defines the so-called resting state networks (RSN) which can be reconstructed from the analysis of functional magnetic resonance imaging (fMRI) data. What dynamical mechanism allows for a flexible large-scale organization of the RSN still remains an important challenge. Here, three key novel properties of the RSN are uncovered. First, the correlation length (i.e., the length at which correlation between two regions vanishes) diverges with the cluster's size considered. Second, this divergence it is observed also for measures of mutual …
In this paper, we present a novel and versatile method to study the dynamics of resting-state fMRI brain connectivity with a high temporal sensitivity. Whereas most existing methods often rely on dividing the time-series into larger segments of data (i.e. so called sliding window techniques), the point-based method (PBM) proposed here provides an estimate of brain connectivity at the level of individual sampled time-points. The achieved increase in temporal sensitivity, together with temporal graph network theory allowed us to study functional integration between, as well as within, resting-st…
The most studies on functional connectivity have been done by analyzing the brain's hemodynamic response to a stimulation. On the other hand, the low-frequency spontaneous fluctuations in the blood oxygen level dependent (BOLD) signals of functional MRI have been observed in the resting state. However, the BOLD signals in resting state are significantly corrupted by huge noises arising from cardiac pulsation, respiration, subject motion, scanner, and so forth. Especially, the noise compounds are stronger in the rat brain than in the human brain. To overcome such an artifact, we assumed that fr…
A variety of resting state neuroimaging data tend to exhibit fractal behavior where its power spectrum follows power-law scaling. Resting state functional connectivity is significantly influenced by fractal behavior which may not directly originate from neuronal population activities of the brain. To describe the fractal behavior, we adopted the fractionally integrated process (FIP) model instead of the fractional Gaussian noise (FGN) since the FIP model covers more general aspects of fractality than the FGN model. We also introduce a novel concept called the nonfractal connectivity which is d…
Scale-free networks (SFN) arise from simple growth processes, which can encourage efficient, centralized and fault tolerant communication (1). Recently its been shown that stable network hub structure is governed by a phase transition at exponents (>2.0) causing a dramatic change in network structure including a loss of global connectivity, an increasing minimum dominating node set, and a shift towards increasing connectivity growth compared to node growth. Is this SFN shift identifiable in atypical brain activity? The Pareto Distribution (P(D)~D^-\b{eta}) on the hub Degree (D) is a signature …
Attention-deficit/hyperactivity disorder (ADHD) is increasingly being diagnosed in both children and adults, but the neural mechanisms that underlie its distinct symptoms and whether children and adults share the same mechanism remain poorly understood. Here, we used a nested-spectral partition (NSP) approach to study the resting-state brain functional networks of ADHD patients (n=97) and healthy controls (HCs, n=97) across the lifespan (7-50 years). Compared to the linear lifespan associations of brain functional segregation and integration with age in HCs, ADHD patients have a quadratic asso…
The study of hierarchy in networks of the human brain has been of significant interest among the researchers as numerous studies have pointed out towards a functional hierarchical organization of the human brain. This paper provides a novel method for the extraction of hierarchical connectivity components in the human brain using resting-state fMRI. The method builds upon prior work of Sparse Connectivity Patterns (SCPs) by introducing a hierarchy of sparse overlapping patterns. The components are estimated by deep factorization of correlation matrices generated from fMRI. The goal of the pape…
Thermodynamic criticality describes emergent phenomena in a wide variety of complex systems. In the mammalian brain, the complex dynamics that spontaneously emerge from neuronal interactions have been characterized as neuronal avalanches, a form of critical branching dynamics. Here, we show that neuronal avalanches also reflect that the brain dynamics are organized close to a thermodynamic critical point. We recorded spontaneous cortical activity in monkeys and humans at rest using high-density intracranial microelectrode arrays and magnetoencephalography, respectively. By numerically changing…
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 …
Adaptive behavior, cognition and emotion are the result of a bewildering variety of brain spatiotemporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain's 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must …
Understanding the relationship between the structure and function of the human brain is one of the most important open questions in Neurosciences. In particular, Resting State Networks (RSN) and more specifically the Default Mode Network (DMN) of the brain, which are defined from the analysis of functional data lack a definitive justification consistent with the anatomical structure of the brain. In this work, we show that a possible connection may naturally rest on the idea that information flows in the brain through a neural message-passing dynamics between macroscopic structures, like those…
Symbolic methods of analysis are valuable tools for investigating complex time-dependent signals. In particular, the ordinal method defines sequences of symbols according to the ordering in which values appear in a time series. This method has been shown to yield useful information, even when applied to signals with large noise contamination. Here we use ordinal analysis to investigate the transition between eyes closed (EC) and eyes open (EO) resting states. We analyze two {EEG} datasets (with 71 and 109 healthy subjects) with different recording conditions (sampling rates and the number of e…
We present a computational framework for analysis and visualization of non-linear functional connectivity in the human brain from resting state functional MRI (fMRI) data for purposes of recovering the underlying network community structure and exploring causality between network components. Our proposed methodology of non-linear mutual connectivity analysis (MCA) involves two computational steps. First, the pair-wise cross-prediction performance between resting state fMRI pixel time series within the brain is evaluated. The underlying network structure is subsequently recovered from the affin…
The brain may be thought of as a many-body architecture with a spatio-temporal dynamics described by neuronal structures. The oscillatory nature of brain activity allows these structures (nodes) to be described as a set of coupled oscillators forming a network where the node dynamics, and that of the network topology can be studied. Quantifying its dynamics at various scales is an issue that claims to be explored for several brain activities, e.g., activity at rest. The resting-state associates the underlying brain dynamics of healthy subjects that are not actively compromised with sensory or …
Multi-Scale Graph Theoretical Analysis of Resting-State fMRI for Classification of Alzheimer's Disease, Mild Cognitive Impairment, and Healthy Controls
University of Bojnord（博季努尔德大学）；Munster Technological University（芒斯特理工大学）
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equil…
To explain individual differences in development, behavior, and cognition, most previous studies focused on projecting resting-state functional MRI (fMRI) based functional connectivity (FC) data into a low-dimensional space via linear dimensionality reduction techniques, followed by executing analysis operations. However, linear dimensionality analysis techniques may fail to capture nonlinearity of brain neuroactivity. Moreover, besides resting-state FC, FC based on task fMRI can be expected to provide complementary information. Motivated by these considerations, we nonlinearly fuse resting-st…
Brain activity following stimulus presentation and during resting state are often the result of highly coordinated responses of large numbers of neurons both locally and globally. Coordinated activity of neurons can give rise to oscillations which are captured by electroencephalograms (EEG). In this paper, we examine EEGs as this is the primary data being used by our collaborators who are studying coordination of neuronal response during the execution of tasks such as learning, and memory formation, retention and retrieval. In this paper, we develop the spectral merger clustering (SMC) method …
Experimental fMRI studies have shown that spontaneous brain activity i.e. in the absence of any external input, exhibit complex spatial and temporal patterns of co-activity between segregated brain regions. These so-called large-scale resting-state functional connectivity networks represent dynamically organized neural assemblies interacting with each other in a complex way. It has been suggested that looking at the dynamical properties of complex patterns of brain functional co-activity may reveal neural mechanisms underlying the dynamic changes in functional interactions. Here, we examine ho…
Recent studies have proposed that one can summarize brain activity into dynamics among a relatively small number of hidden states and that such an approach is a promising tool for revealing brain function. Hidden Markov models (HMMs) are a prevalent approach to inferring such neural dynamics among discrete brain states. However, the impact of assuming Markovian structure in neural time series data has not been sufficiently examined. Here, to address this situation and examine the performance of the HMM, we compare the model with the Gaussian mixture model (GMM), which is with no temporal regul…
Functional brain networks exhibit dynamics on the sub-second temporal scale and are often assumed to embody the physiological substrate of cognitive processes. Here we analyse the temporal and spatial dynamics of these states, as measured by EEG, with a hidden Markov model and compare this approach to classical EEG microstate analysis. We find dominating state lifetimes of 100--150\,ms for both approaches. The state topographies show obvious similarities. However, they also feature distinct spatial and especially temporal properties. These differences may carry physiological meaningful informa…
Functional magnetic resonance imaging (fMRI) techniques have contributed significantly to our understanding of brain function. Current methods are based on the analysis of \emph{gradual and continuous} changes in the brain blood oxygenated level dependent (BOLD) signal. Departing from that approach, recent work has shown that equivalent results can be obtained by inspecting only the relatively large amplitude BOLD signal peaks, suggesting that relevant information can be condensed in \emph{discrete} events. This idea is further explored here to demonstrate how brain dynamics at resting state c…
A great improvement to the insight on brain function that we can get from fMRI data can come from effective connectivity analysis, in which the flow of information between even remote brain regions is inferred by the parameters of a predictive dynamical model. As opposed to biologically inspired models, some techniques as Granger causality (GC) are purely data-driven and rely on statistical prediction and temporal precedence. While powerful and widely applicable, this approach could suffer from two main limitations when applied to BOLD fMRI data: confounding effect of hemodynamic response func…
Deep Learning Inductive Biases for fMRI Time Series Classification during Resting-state and Movie-watching
School of Electrical and Computer Engineering, University of Tehran（埃特瓦尔大学电气与计算机工程学院）；School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所（IPM）认知科学学院）
We conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer's disease and mild cognitive impairment. We develop an analysis of longitudinal resting-state functional magnetic resonance imaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects with a total of 319 rs-fMRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRI scans to estimate effective brain connectivity within the DMN and related…
Brain regions are often topographically connected: nearby locations within one brain area connect with nearby locations in another area. Mapping these connection topographies, or 'connectopies' in short, is crucial for understanding how information is processed in the brain. Here, we propose principled, fully data-driven methods for mapping connectopies using functional magnetic resonance imaging (fMRI) data acquired at rest by combining spectral embedding of voxel-wise connectivity 'fingerprints' with a novel approach to spatial statistical inference. We applied the approach in human primary …
Recently we developed a novel method for assessing the hierarchical modularity of functional brain networks - the probability associated community estimation(PACE). The PACE algorithm is unique in that it permits a dual formulation, thus yielding equivalent connectome modular structure regardless of whether considering positive or negative edges. This method was rigorously validated using F1000 and HCP data. We detected novel sex differences in resting-state connectivity that were not previously reported. This current study more thoroughly examined sex differences as a function of age and thei…
Accurate early diagnosis and monitoring of neurodegenerative conditions is essential for effective disease management and delivery of medication and treatment. This research develops automatic methods for detecting brain imaging preclinical biomarkers for Parkinson's disease (PD) by considering the novel application of evolutionary algorithms. A fundamental novel element of this work is the use of evolutionary algorithms to both map and predict the functional connectivity in patients using resting state functional MRI data taken from the PPMI to identify PD progression biomarkers. Specifically…
What makes a network complex, in addition to its size, is the interconnected interactions between elements, disruption of which inevitably results in dysfunction. Likewise, the brain networks' complexity arises from interactions beyond pair connections, as it is simplistic to assume that in complex networks state of a link is independently determined only according to its two constituting nodes. This is particularly of note in genetically complex brain impairments, such as the autism spectrum disorder (ASD), which has a surprising heterogeneity in manifestations with no clear-cut neuropatholog…
A brain microstate is characterized by a unique, fixed spatial distribution of electrically active neurons with time varying amplitude. It is hypothesized that a microstate implements a functional/physiological state of the brain during which specific neural computations are performed. Based on this hypothesis, brain electrical activity is modeled as a time sequence of non-overlapping microstates with variable, finite durations (Lehmann and Skrandies 1980, 1984; Lehmann et al 1987). In this study, EEG recordings from 109 participants during eyes closed resting condition are modeled with four m…
