开发可靠方法以区分随时间变化的不同瞬时脑状态，是脑成像研究中神经科学领域的一项关键挑战。拓扑数据分析（Topological Data Analysis，TDA）是一种基于代数拓扑的新型框架，可应对这一挑战。然而，现有TDA在捕捉动态变化脑网络的静态特征总结方面存在一定局限。我们提出一种新型dynamic-TDA框架，在脑网络时间序列上构建持续同调。我们构建了基于Wasserstein距离的推断流程，用于区分不同的网络时间序列。该方法被应用于人脑静息态功能磁共振成像数据。我们证明，所提出的dynamic-TDA方法能够清晰区分男性与女性脑网络的拓扑模式。实现该方法的MATLAB代码可在https://github.com/laplcebeltrami/PH-STAT获取。
英文摘要：
Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology, can handle such a challenge. However, existing TDA has been somewhat limited to capturing the static summary of dynamically changing brain networks. We propose a novel dynamic-TDA framework that builds persistent homology over a time series of brain networks. We construct a Wasserstein distance based inference procedure to discriminate between time series of networks. The method is applied to the resting-state functional magnetic resonance images of human brain. We demonstrate that our proposed dynamic-TDA approach can distinctly discriminate between the topological patterns of male and female brain networks. MATLAB code for implementing this method is available at https://github.com/laplcebeltrami/PH-STAT.
Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This - together with its conceptual simplicity and robustness against measurement noise - makes ordinal time series analysis well suited to improve charac…
The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essent…
Standard neuroimaging techniques provide non-invasive access not only to human brain anatomy but also to its physiology. The activity recorded with these techniques is generally called functional imaging, but what is observed per se is an instance of dynamics, from which functional brain activity should be extracted. Distinguishing between bare dynamics and genuine function is a highly non-trivial task, but a crucially important one when comparing experimental observations and interpreting their significance. Here we illustrate how the ability of neuroimaging to extract genuine functional brai…
This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient topological loss. The use of the proposed loss bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations to assess its effectiveness when discriminating networks with different topology. The method is further demonstrated in a twin brain imaging study where we determine if b…
The velocity of the action potential transduction along myelinated axons in the peripheral nervous system or in the white matter of brain and spinal cord reaches hundreds of meters per second to assure proper functioning of the body, which exceeds the ability of diffusive ion conduction. We propose the new model of the saltatory conduction based on a plasmon-polariton kinetics in myelinated axons, which excludes, however, the white matter form the information storage and its identification in the brain via e-m response. We propose a nonlocal topological approach to information processing in th…
Functional Whole-Brain Models: A New Framework for Unifying Brain Structure and Cognitive Function
Maastricht University（马斯特里赫特大学）；Institute of Biomedical Research August Pi i Sunyer (IDIBAPS)（奥古斯特·皮伊·苏内尔生物医学研究所）；Masaryk University（马萨里克大学）；University of Amsterdam（阿姆斯特丹大学）；The Czech Academy of Sciences（捷克科学院）
In Indian history of arts, Rasas are the aesthetics associated with any auditory, visual, literary or musical piece of art that evokes highly orchestrated emotional states. In this work, we study the functional response of the brain to movie clippings meant to evoke the Rasas through network analysis. We extract functional brain networks using coherence measures on EEG recordings of film clips from popular Indian Bollywood movies representing nine Rasas in the Indian Natyasastra. Structural and functional network measures were computed for these brain networks, averaging over a range of signif…
Rich, spontaneous brain activity has been observed across a range of different temporal and spatial scales. These dynamics are thought to be important t for efficient neural functioning. Experimental evidence suggests that these neural dynamics are maintained across a variety of different cognitive states, in response to alterations of the environment and to changes in brain configuration (e.g., across individuals, development and in many neurological disorders). This suggests that the brain has evolved mechanisms to stabilize dynamics and maintain them across a range of situations. Here, we e…
Estimated connectomes by the means of neuroimaging techniques have enriched our knowledge of the organizational properties of the brain leading to the development of network-based clinical diagnostics. Unfortunately, to date, many of those network-based clinical diagnostics tools, based on the mere description of isolated instances of observed connectomes are noisy estimates of the true connectivity network. Modeling brain connectivity networks is therefore important to better explain the functional organization of the brain and allow inference of specific brain properties. In this report, we …
Higher brain function relies upon the ability to flexibly integrate information across specialized communities of brain regions, however it is unclear how this mechanism manifests over time. In this study, we use time-resolved network analysis of functional magnetic resonance imaging data to demonstrate that the human brain traverses between two functional states that maximize either segregation into tight-knit communities or integration across otherwise disparate neural regions. The integrated state enables faster and more accurate performance on a cognitive task, and is associated with dilat…
Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle topological differences in brain networks. Further, Euclidean distances are sensitive to outliers. A few extreme edge weights may severely affect the distance. Thus it is necessary to use distances and loss functions that recognize topology of data. In this review paper, we survey various topological distance and loss functions from topological data analysis (TDA)…
Already two decades passed since the first applications of graph theory to brain neuroimaging. Since that early description, the characterization of the brain as a very large interacting complex network has evolved in several directions. In this brief review we discuss our contributions to this topic and discuss some perspective for future work.
Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human functional brain networks, the network structure is often inferred from functional magnetic resonance imaging (fMRI) blood oxygen level dependent (BOLD) signal. Since the BOLD signal is a proxy for neuronal activity, it is of interest to learn the latent functional network structure. Additionally, despite a core set of observations about functional networks such…
In this paper we review the preprocessing pipeline through which fMRI data is transformed into a network. We discuss three parameters that mostly affect our understanding of the existence of functional correlations between the brain regions. In the end, we conclude that the existence of functional correlations between pairs of the brain's regions can be modeled with probabilistic edges, not to lose the uncertainty that is inherent in the network generation process.
Characterizing the transcriptome architecture of the human brain is fundamental in gaining an understanding of brain function and disease. A number of recent studies have investigated patterns of brain gene expression obtained from an extensive anatomical coverage across the entire human brain using experimental data generated by the Allen Human Brain Atlas (AHBA) project. In this paper, we propose a new representation of a gene's transcription activity that explicitly captures the pattern of spatial co-expression across different anatomical brain regions. For each gene, we define a Spatial Ex…
Anatomical and functional brain studies have converged to the hypothesis that Autism Spectrum Disorders (ASD) are associated with atypical connectivity. Using a modified resting-state paradigm to drive subjects' attention, we provide evidence of a very marked interaction between ASD brain functional connectivity and cognitive state. We show that functional connectivity changes in opposite ways in ASD and typicals as attention shifts from external world towards one's body generated information. Furthermore, ASD subject alter more markedly than typicals their connectivity across cognitive states…
Emerging evidence shows that cognitive deficits in Alzheimer disease (AD) are associated with disruptions in brain functional connectivity. Thus, the identification of alterations in AD functional networks has become a topic of increasing interest. However, to what extent AD induces disruption of the balance of local and global information processing in the human brain remains elusive. The main objective of this study is to explore the dynamic topological changes of AD networks in terms of brain network segregation and integration. We used electroencephalography (EEG) data recorded from 20 par…
Today the human brain can be modeled as a graph where nodes represent different regions and links stand for statistical interactions between their activities as recorded by different neuroimaging techniques. Empirical studies have lead to the hypothesis that brain functions rely on the coordination of a scattered mosaic of functionally specialized brain regions (modules or sub-networks), forming a web-like structure of coordinated assemblies (a network of networks). The study of brain dynamics would therefore benefit from an inspection of how functional sub-networks interact between them. In t…
ICAR, National Research Council (CNR), Palermo, Italy（国家研究委员会 ICAR 研究所）；Institute of Physics and Astronomy, University of Potsdam, Germany（波茨坦大学物理与天文学研究所）；DSMN, Ca’ Foscari University of Venice, Italy（威尼斯卡福斯卡里大学 DSMN）；VSB Technical University of Ostrava, Czechia（俄斯特拉发 VSB 技术大学）；Potsdam Institute for Climate Impact Research (PIK), Germany（波茨坦气候影响研究所）；Institute of Geosciences, University of Potsdam, Germany（波茨坦大学地球科学研究所）
Functional brain network has been widely studied to understand the relationship between brain organization and behavior. In this paper, we aim to explore the functional connectivity of brain network under a \emph{multi-step} cognitive task involving with consecutive behaviors, and further understand the effect of behaviors on the brain organization. The functional brain networks are constructed base on a high spatial and temporal resolution fMRI dataset and analyzed via complex network based approach. We find that at voxel level the functional brain network shows robust small-worldness and sca…
Functional connectomes capture brain interactions via synchronized fluctuations in the functional magnetic resonance imaging signal. If measured during rest, they map the intrinsic functional architecture of the brain. With task-driven experiments they represent integration mechanisms between specialized brain areas. Analyzing their variability across subjects and conditions can reveal markers of brain pathologies and mechanisms underlying cognition. Methods of estimating functional connectomes from the imaging signal have undergone rapid developments and the literature is full of diverse stra…
The anatomical structure of the brain can be observed via non-invasive techniques such as diffusion imaging. However, these are imperfect because they miss connections that are actually known to exist, especially long range inter-hemispheric ones. In this paper we formulate the inverse problem of inferring the structural connectivity of brain networks from experimentally observed functional connectivity via functional Magnetic Resonance Imaging (fMRI), by formulating it as a convex optimization problem. We show that structural connectivity can be modeled as an optimal sparse representation der…
The estimation of sparse hierarchical components reflecting patterns of the brain's functional connectivity from rsfMRI data can contribute to our understanding of the brain's functional organization, and can lead to biomarkers of diseases. However, inter-scanner variations and other confounding factors pose a challenge to the robust and reproducible estimation of functionally-interpretable brain networks, and especially to reproducible biomarkers. Moreover, the brain is believed to be organized hierarchically, and hence single-scale decompositions miss this hierarchy. The paper aims to use cu…
Understanding the relationship between large-scale structural and functional brain networks remains a crucial issue in modern neuroscience. Recently, there has been growing interest in investigating the role of homeostatic plasticity mechanisms, across different spatiotemporal scales, in regulating network activity and brain functioning against a wide range of environmental conditions and brain states (e.g., during learning, development, ageing, neurological diseases). In the present study, we investigate how the inclusion of homeostatic plasticity in a stochastic whole-brain model, implemente…
It has become increasingly popular to study the brain as a network due to the realization that functionality cannot be explained exclusively by independent activation of specialized regions. Instead, across a large spectrum of behaviors, function arises due to the dynamic interactions between brain regions. The existing literature on functional brain networks focuses mainly on a battery of network properties characterizing the "resting state" using for example the modularity, clustering, or path length among regions. In contrast, we seek to uncover subgraphs of functional connectivity that pre…
A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. Here, we use nonequilibrium Green's functions to describe the time-dependent functional connectivity of a contin…
Centre for Computational Intelligence, University of Essex（埃塞克斯大学计算智能中心）
The last decades have seen significant advancements in non-invasive neuroimaging technologies that have been increasingly adopted to examine human brain development. However, these improvements have not necessarily been followed by more sophisticated data analysis measures that are able to explain the mechanisms underlying functional brain development. For example, the shift from univariate (single area in the brain) to multivariate (multiple areas in brain) analysis paradigms is of significance as it allows investigations into the interactions between different brain regions. However, despite…
Analysis of data from functional magnetic resonance imaging (fMRI) results in constructing functional brain networks. Principal component analysis (PCA) and independent component analysis (ICA) are widely used to generate functional brain networks. Moreover, dictionary learning and sparse representation provide some latent patterns that rules brain activities and they can be interpreted as brain networks. However, these methods lack modeling dependencies of the discovered networks. In this study an alternative to these conventional methods is presented in which dependencies of the networks are…
The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws. The modular organization, in terms of modular mass, inter-modular, and intra-modular interaction, also obeys fractal nature. The parameters which characterize topological properties of brain networks follow one parameter scaling theory in all levels of network structure which reveals the self-similar rules governing the network structure. The calculated fract…
Brain-like Functional Organization within Large Language Models
School of Automation, Northwestern Polytechnical University（西北工业大学自动化学院）；School of Computing, University of Georgia（佐治亚大学计算学院）；School of Computer and Cyber Sciences, Augusta University（奥古斯塔大学计算机与网络科学学院）
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…
Cognitive neuroscience explores the mechanisms of cognition by studying its structural and functional brain correlates. Here, we report the first systematic review that assesses how information from structural and functional neuroimaging methods can be integrated to investigate the brain substrates of cognition. Web of Science and Scopus databases were searched for studies of healthy young adult populations that collected cognitive data, and structural and functional neuroimaging data. Five percent of screened studies met all inclusion criteria. Next, 54% of included studies related cognitive …
The goal of the present study is to identify autism using machine learning techniques and resting-state brain imaging data, leveraging the temporal variability of the functional connections (FC) as the only information. We estimated and compared the FC variability across brain regions between typical, healthy subjects and autistic population by analyzing brain imaging data from a world-wide multi-site database known as ABIDE (Autism Brain Imaging Data Exchange). Our analysis revealed that patients diagnosed with autism spectrum disorder (ASD) show increased FC variability in several brain regi…
Severe traumatic brain injury can lead to disorders of consciousness (DOC) characterized by deficit in conscious awareness and cognitive impairment including coma, vegetative state, minimally consciousness, and lock-in syndrome. Of crucial importance is to find objective markers that can account for the large-scale disturbances of brain function to help the diagnosis and prognosis of DOC patients and eventually the prediction of the coma outcome. Following recent studies suggesting that the functional organization of brain networks can be altered in comatose patients, this work analyzes brain …
Activity in the human brain moves between diverse functional states to meet the demands of our dynamic environment, but fundamental principles guiding these transitions remain poorly understood. Here, we capitalize on recent advances in network science to analyze patterns of functional interactions between brain regions. We use dynamic network representations to probe the landscape of brain reconfigurations that accompany task performance both within and between four cognitive states: a task-free resting state, an attention-demanding state, and two memory-demanding states. Using the formalism …
Complex functional brain network analyses have exploded over the last eight years, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has facilitated these analyses and enabled examining the brain as an integrated system that produces complex behaviors. While the field of statistics has been integral in advancing activation analyses and some connectivity analyses in functional neuroimaging research, it has yet to play a commensurate role in complex network analyses. Fusing novel statistical methods wi…
Neuroimaging-driven prediction of brain age, defined as the predicted biological age of a subject using only brain imaging data, is an exciting avenue of research. In this work we seek to build models of brain age based on functional connectivity while prioritizing model interpretability and understanding. This way, the models serve to both provide accurate estimates of brain age as well as allow us to investigate changes in functional connectivity which occur during the ageing process. The methods proposed in this work consist of a two-step procedure: first, linear latent variable models, suc…
