1
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Zhang J, Posse S, Tatsuoka C. Sliding window functional connectivity inference with nonstationary autocorrelations and cross-correlations. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.06.18.599636. [PMID: 38948863 PMCID: PMC11212997 DOI: 10.1101/2024.06.18.599636] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/02/2024]
Abstract
Functional connectivity (FC) is the degree of synchrony of time series between distinct, spatially separated brain regions. While traditional FC analysis assumes the temporal stationarity throughout a brain scan, there is growing recognition that connectivity can change over time and is not stationary, leading to the concept of dynamic FC (dFC). Resting-state functional magnetic resonance imaging (fMRI) can assess dFC using the sliding window method with the correlation analysis of fMRI signals. Accurate statistical inference of sliding window correlation must consider the autocorrelated nature of the time series. Currently, the dynamic consideration is mainly confined to the point estimation of sliding window correlations. Using in vivo resting-state fMRI data, we first demonstrate the non-stationarity in both the cross-correlation function (XCF) and the autocorrelation function (ACF). Then, we propose the variance estimation of the sliding window correlation considering the nonstationary of XCF and ACF. This approach provides a means to dynamically estimate confidence intervals in assessing dynamic connectivity. Using simulations, we compare the performance of the proposed method with other methods, showing the impact of dynamic ACF and XCF on connectivity inference. Accurate variance estimation can help in addressing the critical issue of false positivity and negativity.
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Affiliation(s)
- Jing Zhang
- Department of Population and Quantitative Health Science, Case Western Reserve University, OH, United States
| | - Stefan Posse
- Department of Neurosurgery, University of New Mexico, NM, United States
| | - Curtis Tatsuoka
- Department of Medicine, Division of Hematology/Oncology, University of Pittsburgh, PA, United States
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2
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Chung MK, Azizi T, Hanson JL, Alexander AL, Pollak SD, Davidson RJ. Altered topological structure of the brain white matter in maltreated children through topological data analysis. Netw Neurosci 2024; 8:355-376. [PMID: 38711544 PMCID: PMC11073548 DOI: 10.1162/netn_a_00355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Accepted: 11/30/2023] [Indexed: 05/08/2024] Open
Abstract
Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in the global topology of the brain white matter structural covariance network among children. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging and diffusion tensor imaging. We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children with a typically developing control group, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly suggest that TDA can be a valuable framework to model altered topological structures of the brain. The MATLAB codes and processed data used in this study can be found at https://github.com/laplcebeltrami/maltreated.
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Affiliation(s)
- Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin–Madison, Madison, WI, USA
| | - Tahmineh Azizi
- Department of Biostatistics and Medical Informatics, University of Wisconsin–Madison, Madison, WI, USA
| | - Jamie L. Hanson
- Department of Psychology, University of Pittsburgh, Pittsburgh, PA, USA
| | - Andrew L. Alexander
- Department of Medical Physics, University of Wisconsin–Madison, Madison, WI, USA
| | - Seth D. Pollak
- Department of Psychology, University of Wisconsin–Madison, Madison, WI, USA
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3
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Simpson SL, Shappell HM, Bahrami M. Statistical Brain Network Analysis. ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION 2023; 11:505-531. [PMID: 39184922 PMCID: PMC11343573 DOI: 10.1146/annurev-statistics-040522-020722] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/27/2024]
Abstract
The recent fusion of network science and neuroscience has catalyzed a paradigm shift in how we study the brain and led to the field of brain network analysis. Brain network analyses hold great potential in helping us understand normal and abnormal brain function by providing profound clinical insight into links between system-level properties and health and behavioral outcomes. Nonetheless, methods for statistically analyzing networks at the group and individual levels have lagged behind. We have attempted to address this need by developing three complementary statistical frameworks-a mixed modeling framework, a distance regression framework, and a hidden semi-Markov modeling framework. These tools serve as synergistic fusions of statistical approaches with network science methods, providing needed analytic foundations for whole-brain network data. Here we delineate these approaches, briefly survey related tools, and discuss potential future avenues of research. We hope this review catalyzes further statistical interest and methodological development in the field.
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Affiliation(s)
- Sean L Simpson
- Department of Biostatistics and Data Science, Wake Forest University School of Medicine, Winston-Salem, North Carolina, USA
- Laboratory for Complex Brain Networks, Wake Forest University School of Medicine, Winston-Salem, North Carolina, USA
| | - Heather M Shappell
- Department of Biostatistics and Data Science, Wake Forest University School of Medicine, Winston-Salem, North Carolina, USA
- Laboratory for Complex Brain Networks, Wake Forest University School of Medicine, Winston-Salem, North Carolina, USA
| | - Mohsen Bahrami
- Laboratory for Complex Brain Networks, Wake Forest University School of Medicine, Winston-Salem, North Carolina, USA
- Department of Radiology, Wake Forest University School of Medicine, Winston-Salem, North Carolina, USA
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4
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Chung MK, Azizi T, Hanson JL, Alexander AL, Davidson RJ, Pollak SD. Altered Topological Structure of the Brain White Matter in Maltreated Children through Topological Data Analysis. ARXIV 2023:arXiv:2304.05908v3. [PMID: 37090232 PMCID: PMC10120754] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 04/25/2023]
Abstract
Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in the global topology of the brain white-matter structural covariance network among children. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI). We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children to a typically developing control group, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly suggest that TDA can be a valuable framework to model altered topological structures of the brain. The MATLAB codes and processed data used in this study can be found at https://github.com/laplcebeltrami/maltreated.
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Affiliation(s)
- Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA
| | - Tahmineh Azizi
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA
| | | | | | | | - Seth D. Pollak
- Department of Psychology, University of Wisconsin-Madison, USA
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5
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Liang Y, Long M, Yang P, Wang T, Jiao J, Lei B. Fused Brain Functional Connectivity Network and Edge-attention Graph Convolution Network for Fibromyalgia Syndrome Diagnosis. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2023; 2023:1-5. [PMID: 38083477 DOI: 10.1109/embc40787.2023.10340485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2023]
Abstract
Fibromyalgia syndrome (FMS) is a type of rheumatology that seriously affects the normal life of patients. Due to the complex clinical manifestations of FMS, it is challenging to detect FMS. Therefore, an automatic FMS diagnosis model is urgently needed to assist physicians. Brain functional connectivity networks (BFCNs) constructed by resting-state functional magnetic resonance imaging (rs-fMRI) to describe brain functions have been widely used to identify individuals with relevant diseases from normal control (NC). Therefore, we propose a novel model based on BFCN and graph convolutional network (GCN) for automatic FMS diagnosis. Firstly, a novel fused BFCN method is proposed by fusing Pearson's correlation (PC) and low-rank (LR) BFCN, which retains information and reduces data redundancy to construct BFCN. Then we combine the feature of BFCN with non-image information of subjects to obtain nodes and adjacency matrices, which builds a graph with edge attention. Finally, the graph is sent to the GCN layer for FMS diagnosis. Our model is evaluated on the in-house FMS dataset to achieve 82.48% accuracy. The experimental results show that our method outperforms the state-of-the-art competing methods.
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6
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Wang Y, Guo Y. LOCUS: A REGULARIZED BLIND SOURCE SEPARATION METHOD WITH LOW-RANK STRUCTURE FOR INVESTIGATING BRAIN CONNECTIVITY. Ann Appl Stat 2023; 17:1307-1332. [PMID: 39040949 PMCID: PMC11262594 DOI: 10.1214/22-aoas1670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/24/2024]
Abstract
Network-oriented research has been increasingly popular in many scientific areas. In neuroscience research, imaging-based network connectivity measures have become the key for understanding brain organizations, potentially serving as individual neural fingerprints. There are major challenges in analyzing connectivity matrices, including the high dimensionality of brain networks, unknown latent sources underlying the observed connectivity, and the large number of brain connections leading to spurious findings. In this paper we propose a novel blind source separation method with low-rank structure and uniform sparsity (LOCUS) as a fully data-driven decomposition method for network measures. Compared with the existing method that vectorizes connectivity matrices ignoring brain network topology, LOCUS achieves more efficient and accurate source separation for connectivity matrices using low-rank structure. We propose a novel angle-based uniform sparsity regularization that demonstrates better performance than the existing sparsity controls for low-rank tensor methods. We propose a highly efficient iterative node-rotation algorithm that exploits the block multiconvexity of the objective function to solve the nonconvex optimization problem for learning LOCUS. We illustrate the advantage of LOCUS through extensive simulation studies. Application of LOCUS to Philadelphia Neurodevelopmental Cohort neuroimaging study reveals biologically insightful connectivity traits which are not found using the existing method.
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Affiliation(s)
- Yikai Wang
- Department of Biostatistics and Bioinformatics, Emory University
| | - Ying Guo
- Department of Biostatistics and Bioinformatics, Emory University
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7
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Weaver C, Xiao L, Lindquist MA. Single-index models with functional connectivity network predictors. Biostatistics 2022; 24:52-67. [PMID: 33948617 PMCID: PMC9748592 DOI: 10.1093/biostatistics/kxab015] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Revised: 03/22/2021] [Accepted: 03/25/2021] [Indexed: 12/16/2022] Open
Abstract
Functional connectivity is defined as the undirected association between two or more functional magnetic resonance imaging (fMRI) time series. Increasingly, subject-level functional connectivity data have been used to predict and classify clinical outcomes and subject attributes. We propose a single-index model wherein response variables and sparse functional connectivity network valued predictors are linked by an unspecified smooth function in order to accommodate potentially nonlinear relationships. We exploit the network structure of functional connectivity by imposing meaningful sparsity constraints, which lead not only to the identification of association of interactions between regions with the response but also the assessment of whether or not the functional connectivity associated with a brain region is related to the response variable. We demonstrate the effectiveness of the proposed model in simulation studies and in an application to a resting-state fMRI data set from the Human Connectome Project to model fluid intelligence and sex and to identify predictive links between brain regions.
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Affiliation(s)
- Caleb Weaver
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27606, USA
| | - Luo Xiao
- Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27606, USA
| | - Martin A Lindquist
- Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, 615 N. Wolfe Street, Baltimore, MD 21205, USA
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8
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Morris EL, Taylor SF, Kang J. On predictability of individual functional connectivity networks from clinical characteristics. Hum Brain Mapp 2022; 43:5250-5265. [PMID: 35811395 PMCID: PMC9812246 DOI: 10.1002/hbm.26000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2021] [Revised: 05/07/2022] [Accepted: 06/06/2022] [Indexed: 01/15/2023] Open
Abstract
In recent years, understanding functional brain connectivity has become increasingly important as a scientific tool with potential clinical implications. Statistical methods, such as graphical models and network analysis, have been adopted to construct functional connectivity networks for single subjects. Here we focus on studying the association between functional connectivity networks and clinical characteristics such as psychiatric symptoms and diagnoses. Utilizing machine learning algorithms, we propose a method to examine predictability of functional connectivity networks from clinical characteristics. Our methods can identify salient clinical characteristics predictive of the whole brain network or specific subnetworks. We illustrate our methods on the analysis of fMRI data in the Philadelphia Neurodevelopmental Cohort study, demonstrating clinically meaningful results.
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Affiliation(s)
- Emily L. Morris
- Department of BiostatisticsUniversity of MichiganAnn ArborMichiganUSA
| | | | - Jian Kang
- Department of BiostatisticsUniversity of MichiganAnn ArborMichiganUSA
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9
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Li Y, Zhang X, Nie J, Zhang G, Fang R, Xu X, Wu Z, Hu D, Wang L, Zhang H, Lin W, Li G. Brain Connectivity Based Graph Convolutional Networks and Its Application to Infant Age Prediction. IEEE TRANSACTIONS ON MEDICAL IMAGING 2022; 41:2764-2776. [PMID: 35500083 PMCID: PMC10041448 DOI: 10.1109/tmi.2022.3171778] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Infancy is a critical period for the human brain development, and brain age is one of the indices for the brain development status associated with neuroimaging data. The difference between the predicted age based on neuroimaging and the chronological age can provide an important early indicator of deviation from the normal developmental trajectory. In this study, we utilize the Graph Convolutional Network (GCN) to predict the infant brain age based on resting-state fMRI data. The brain connectivity obtained from rs-fMRI can be represented as a graph with brain regions as nodes and functional connections as edges. However, since the brain connectivity is a fully connected graph with features on edges, current GCN cannot be directly used for it is a node-based method for sparse graphs. Hence, we propose an edge-based Graph Path Convolution (GPC) method, which aggregates the information from different paths and can be naturally applied on dense graphs. We refer the whole model as Brain Connectivity Graph Convolutional Networks (BC-GCN). Further, two upgraded network structures are proposed by including the residual and attention modules, referred as BC-GCN-Res and BC-GCN-SE to emphasize the information of the original data and enhance influential channels. Moreover, we design a two-stage coarse-to-fine framework, which determines the age group first and then predicts the age using group-specific BC-GCN-SE models. To avoid accumulated errors from the first stage, a cross-group training strategy is adopted for the second stage regression models. We conduct experiments on infant fMRI scans from 6 to 811 days of age. The coarse-to-fine framework shows significant improvements when being applied to several models (reducing error over 10 days). Comparing with state-of-the-art methods, our proposed model BC-GCN-SE with coarse-to-fine framework reduces the mean absolute error of the prediction from >70 days to 49.9 days. The code is now available at https://github.com/SCUT-Xinlab/BC-GCN.
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10
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Shahhosseini Y, Miranda MF. Functional Connectivity Methods and Their Applications in fMRI Data. ENTROPY 2022; 24:e24030390. [PMID: 35327901 PMCID: PMC8946919 DOI: 10.3390/e24030390] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/15/2022] [Revised: 02/23/2022] [Accepted: 03/08/2022] [Indexed: 02/01/2023]
Abstract
The availability of powerful non-invasive neuroimaging techniques has given rise to various studies that aim to map the human brain. These studies focus on not only finding brain activation signatures but also on understanding the overall organization of functional communication in the brain network. Based on the principle that distinct brain regions are functionally connected and continuously share information with each other, various approaches to finding these functional networks have been proposed in the literature. In this paper, we present an overview of the most common methods to estimate and characterize functional connectivity in fMRI data. We illustrate these methodologies with resting-state functional MRI data from the Human Connectome Project, providing details of their implementation and insights on the interpretations of the results. We aim to guide researchers that are new to the field of neuroimaging by providing the necessary tools to estimate and characterize brain circuitry.
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11
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Simpson SL. Mixed Modeling Frameworks for Analyzing Whole-Brain Network Data. Methods Mol Biol 2022; 2393:571-595. [PMID: 34837200 PMCID: PMC9251854 DOI: 10.1007/978-1-0716-1803-5_30] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Brain network analyses have exploded in recent years and hold great potential in helping us understand normal and abnormal brain function. Network science approaches have facilitated these analyses and our understanding of how the brain is structurally and functionally organized. However, the development of statistical methods that allow relating this organization to health outcomes has lagged behind. We have attempted to address this need by developing mixed modeling frameworks that allow relating system-level properties of brain networks to outcomes of interest. These frameworks serve as a synergistic fusion of multivariate statistical approaches with network science, providing a needed analytic (modeling and inferential) foundation for whole-brain network data. In this chapter we delineate these approaches that have been developed for single-task and multitask (longitudinal) brain network data, illustrate their utility with data applications, detail their implementation with a user-friendly Matlab toolbox, and discuss ongoing work to adapt the methods to (within-task) dynamic network analysis.
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Affiliation(s)
- Sean L Simpson
- Department of Biostatistics and Data Science, Wake Forest School of Medicine, Winston-Salem, NC, USA.
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12
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Xin B, Huang J, Zhang L, Zheng C, Zhou Y, Lu J, Wang X. Dynamic topology analysis for spatial patterns of multifocal lesions on MRI. Med Image Anal 2021; 76:102267. [PMID: 34929461 DOI: 10.1016/j.media.2021.102267] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Revised: 07/26/2021] [Accepted: 10/07/2021] [Indexed: 01/01/2023]
Abstract
Quantitatively analysing the spatial patterns of multifocal lesions on clinical MRI is an important step towards a better understanding of the disease and for precision medicine, which is yet to be properly explored by feature engineering and deep learning methods. Network science addresses this issue by explicitly modeling the inter-lesion topology. However, the construction of the informative graph with optimal edge sparsity and quantification of community graph structures are the current challenges in network science. In this paper, we address these challenges with a novel Dynamic Topology Analysis framework on the basis of persistent homology, aiming to investigate the predictive values of global geometry and local clusters of multifocal lesions. Firstly, Dynamic Hierarchical Network is proposed to construct informative global and community-level topology over multi-scale networks from sparse to dense. Multi-scale global topology is constructed with a nested sequence of Rips complexes, from which a new K-simplex Filtration is designed to generate a higher-level topological abstraction for community identification based on the connectivity of k-simplices in the Rips Complex. Secondly, to quantify multi-scale community structures, we design a new Decomposed Community Persistence algorithm to track the dynamic evolution of communities, and then summarise the evolutionary communities incorporated with a customisable descriptor. The quantified community features are encapsulated with global geometric invariants for topological pattern analysis. The proposed framework was evaluated on both diagnostic differentiation and prognostic prediction for multiple sclerosis that is a typical multifocal disease, and achieved ROC_AUC 0.875 and 0.767, respectively, outperforming seven state-of-the-art persistent homology methods and the reported performance of six feature engineering and deep learning methods.
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Affiliation(s)
- Bowen Xin
- School of Computer Science, The University of Sydney, Sydney, NSW, Australia
| | - Jing Huang
- Department of Radiology, Xuanwu Hospital, Capital Medical University, Beijing, China
| | - Lin Zhang
- School of Computer Science, The University of Sydney, Sydney, NSW, Australia
| | - Chaojie Zheng
- Central Research Institute, United Imaging Healthcare Group Co, Ltd, Shanghai, China
| | - Yun Zhou
- Central Research Institute, United Imaging Healthcare Group Co, Ltd, Shanghai, China
| | - Jie Lu
- Department of Radiology, Xuanwu Hospital, Capital Medical University, Beijing, China.
| | - Xiuying Wang
- School of Computer Science, The University of Sydney, Sydney, NSW, Australia.
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13
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Liang D, Xia S, Zhang X, Zhang W. Analysis of Brain Functional Connectivity Neural Circuits in Children With Autism Based on Persistent Homology. Front Hum Neurosci 2021; 15:745671. [PMID: 34588970 PMCID: PMC8473898 DOI: 10.3389/fnhum.2021.745671] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 08/19/2021] [Indexed: 11/24/2022] Open
Abstract
Autism spectrum disorder (ASD) is a complex neuropsychiatric disorder with a complex and unknown etiology. Statistics demonstrate that the number of people diagnosed with ASD is increasing in countries around the world. Currently, although many neuroimaging studies indicate that ASD is characterized by abnormal functional connectivity (FC) patterns within brain networks rather than local functional or structural abnormalities, the FC characteristics of ASD are still poorly understood. In this study, a Vietoris-Rips (VR) complex filtration model of the brain functional network was established by using resting-state functional magnetic resonance imaging (fMRI) data of children aged 6–13 years old [including 54 ASD patients and 52 typical development (TD) controls] from the Autism Brain Imaging Data Exchange (ABIDE) public database. VR complex filtration barcodes are calculated by using persistent homology to describe the changes in the FC neural circuits of brain networks. The number of FC neural circuits with different length ranges at different threshold values is calculated by using the barcodes, the different brain regions participating in FC neural circuits are discussed, and the connectivity characteristics of brain FC neural circuits in the two groups are compared and analyzed. Our results show that the number of FC neural circuits with lengths of 8–12 is significantly decreased in the ASD group compared with the TD control group at threshold values of 0.7, 0.8 and 0.9, and there is no significant difference in the number of FC neural circuits with lengths of 4–7 and 13–16 and lengths 16. When the thresholds are 0.7, 0.8, and 0.9, the number of FC neural circuits in some brain regions, such as the right orbital part of the superior frontal gyrus, the left supplementary motor area, the left hippocampus, and the right caudate nucleus, involved in the study is significantly decreased in the ASD group compared with the TD control group. The results of this study indicate that there are significant differences in the FC neural circuits of brain networks in the ASD group compared with the TD control group.
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Affiliation(s)
- Di Liang
- School of Science, Shandong Jianzhu University, Jinan, China
| | - Shengxiang Xia
- School of Science, Shandong Jianzhu University, Jinan, China
| | - Xianfu Zhang
- School of Control Science and Engineering, Shandong University, Jinan, China
| | - Weiwei Zhang
- School of Science, Shandong Jianzhu University, Jinan, China
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14
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Caputi L, Pidnebesna A, Hlinka J. Promises and pitfalls of topological data analysis for brain connectivity analysis. Neuroimage 2021; 238:118245. [PMID: 34111515 DOI: 10.1016/j.neuroimage.2021.118245] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Revised: 05/30/2021] [Accepted: 06/05/2021] [Indexed: 11/17/2022] Open
Abstract
Developing sensitive and reliable methods to distinguish normal and abnormal brain states is a key neuroscientific challenge. Topological Data Analysis, despite its relative novelty, already generated many promising applications, including in neuroscience. We conjecture its prominent tool of persistent homology may benefit from going beyond analysing structural and functional connectivity to effective connectivity graphs capturing the direct causal interactions or information flows. Therefore, we assess the potential of persistent homology to directed brain network analysis by testing its discriminatory power in two distinctive examples of disease-related brain connectivity alterations: epilepsy and schizophrenia. We estimate connectivity from functional magnetic resonance imaging and electrophysiology data, employ Persistent Homology and quantify its ability to distinguish healthy from diseased brain states by applying a support vector machine to features quantifying persistent homology structure. We show how this novel approach compares to classification using standard undirected approaches and original connectivity matrices. In the schizophrenia classification, topological data analysis generally performs close to random, while classifications from raw connectivity perform substantially better; potentially due to topographical, rather than topological, specificity of the differences. In the easier task of seizure discrimination from scalp electroencephalography data, classification based on persistent homology features generally reached comparable performance to using raw connectivity, albeit with typically smaller accuracies obtained for the directed (effective) connectivity compared to the undirected (functional) connectivity. Specific applications for topological data analysis may open when direct comparison of connectivity matrices is unsuitable - such as for intracranial electrophysiology with individual number and location of measurements. While standard homology performed overall better than directed homology, this could be due to notorious technical problems of accurate effective connectivity estimation.
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Affiliation(s)
- Luigi Caputi
- Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 271/2, Prague 182 07, Czech Republic.
| | - Anna Pidnebesna
- Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 271/2, Prague 182 07, Czech Republic; National Institute of Mental Health, Topolová 748, Klecany 250 67, Czech Republic; Faculty of Electrical Engineering, Czech Technical University, Technická 1902/2, Prague 166 27, Czech Republic.
| | - Jaroslav Hlinka
- Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 271/2, Prague 182 07, Czech Republic; National Institute of Mental Health, Topolová 748, Klecany 250 67, Czech Republic.
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15
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Wang YXR, Li L, Li JJ, Huang H. Network Modeling in Biology: Statistical Methods for Gene and Brain Networks. Stat Sci 2021; 36:89-108. [PMID: 34305304 PMCID: PMC8296984 DOI: 10.1214/20-sts792] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The rise of network data in many different domains has offered researchers new insight into the problem of modeling complex systems and propelled the development of numerous innovative statistical methodologies and computational tools. In this paper, we primarily focus on two types of biological networks, gene networks and brain networks, where statistical network modeling has found both fruitful and challenging applications. Unlike other network examples such as social networks where network edges can be directly observed, both gene and brain networks require careful estimation of edges using covariates as a first step. We provide a discussion on existing statistical and computational methods for edge esitimation and subsequent statistical inference problems in these two types of biological networks.
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Affiliation(s)
- Y X Rachel Wang
- School of Mathematics and Statistics, University of Sydney, Australia
| | - Lexin Li
- Department of Biostatistics and Epidemiology, School of Public Health, University of California, Berkeley
| | | | - Haiyan Huang
- Department of Statistics, University of California, Berkeley
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16
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Li J, Bian C, Luo H, Chen D, Cao L, Liang H. Multi-dimensional persistent feature analysis identifies connectivity patterns of resting-state brain networks in Alzheimer's disease. J Neural Eng 2020; 18. [PMID: 33152713 DOI: 10.1088/1741-2552/abc7ef] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 11/05/2020] [Indexed: 01/21/2023]
Abstract
OBJECTIVE The characterization of functional brain network is crucial to understanding the neural mechanisms associated with Alzheimer's disease (AD) and mild cognitive impairment (MCI). Some studies have shown that graph theoretical analysis could reveal changes of the disease-related brain networks by thresholding edge weights. But the choice of threshold depends on ambiguous cognitive conditions, which leads to the lack of interpretability. Recently, persistent homology (PH) was proposed to record the persistence of topological features of networks across every possible thresholds, reporting a higher sensitivity than graph theoretical features in detecting network-level biomarkers of AD. However, most research on PH focused on 0-dimensional features (persistence of connected components) reflecting the intrinsic topology of the brain network, rather than 1-dimensional features (persistence of cycles) with an interesting neurobiological communication pattern. Our aim is to explore the multi-dimensional persistent features of brain networks in the AD and MCI patients, and further to capture valuable brain connectivity patterns. APPROACH We characterized the change rate of the connected component numbers across graph filtration using the functional derivative curves, and examined the persistence landscapes that vectorize the persistence of cycle structures. After that, the multi-dimensional persistent features were validated in disease identification using a K-nearest neighbor algorithm. Furthermore, a connectivity pattern mining framework was designed to capture the disease-specific brain structures. MAIN RESULTS We found that the multi-dimensional persistent features can identify statistical group differences, quantify subject-level distances, and yield disease-specific connectivity patterns. Relatively high classification accuracies were received when compared with graph theoretical features. SIGNIFICANCE This work represents a conceptual bridge linking complex brain network analysis and computational topology. Our results can be beneficial for providing a complementary objective opinion to the clinical diagnosis of neurodegenerative diseases.
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Affiliation(s)
- Jin Li
- Harbin Engineering University, Harbin, Heilongjiang, CHINA
| | - Chenyuan Bian
- Harbin Engineering University, Harbin, Heilongjiang, CHINA
| | - Haoran Luo
- Harbin Engineering University, Harbin, Heilongjiang, CHINA
| | - Dandan Chen
- Harbin Engineering University, Harbin, Heilongjiang, CHINA
| | - Luolong Cao
- Harbin Engineering University, Harbin, Heilongjiang, CHINA
| | - Hong Liang
- Harbin Engineering University, Nantong street 145, Harbin, 150001, CHINA
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Jin W, Zhu H, Shu P, Tong S, Sun J. Extracting Individual Neural Fingerprint Encoded in Functional Connectivity by Silencing Indirect Effects. IEEE Trans Biomed Eng 2020; 67:2253-2265. [DOI: 10.1109/tbme.2019.2958333] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Decoding Task-Specific Cognitive States with Slow, Directed Functional Networks in the Human Brain. eNeuro 2020; 7:ENEURO.0512-19.2019. [PMID: 32265196 PMCID: PMC7358332 DOI: 10.1523/eneuro.0512-19.2019] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2019] [Accepted: 12/12/2019] [Indexed: 12/02/2022] Open
Abstract
Flexible functional interactions among brain regions mediate critical cognitive functions. Such interactions can be measured using functional magnetic resonance imaging (fMRI) data either with instantaneous (zero-lag) or lag-based (time-lagged) functional connectivity. Because the fMRI hemodynamic response is slow, and is sampled at a timescale (seconds) several orders of magnitude slower than the underlying neural dynamics (milliseconds), simulation studies have shown that lag-based fMRI functional connectivity, measured with approaches like Granger–Geweke causality (GC), provides spurious and unreliable estimates of underlying neural interactions. Experimental verification of this claim is challenging because neural ground truth connectivity is often unavailable concurrently with fMRI recordings. Here we demonstrate that, despite these widely held caveats, GC networks estimated from fMRI recordings contain useful information for classifying task-specific cognitive states. We estimated instantaneous and lag-based GC functional connectivity networks using fMRI data from 1000 participants (Human Connectome Project database). A linear classifier, trained on either instantaneous or lag-based GC, reliably discriminated among seven different task and resting brain states, with >80% cross-validation accuracy. With network simulations, we demonstrate that instantaneous and lag-based GC exploited interactions at fast and slow timescales, respectively, to achieve robust classification. With human fMRI data, instantaneous and lag-based GC identified complementary, task–core networks. Finally, variations in GC connectivity explained inter-individual variations in a variety of cognitive scores. Our findings show that instantaneous and lag-based methods reveal complementary aspects of functional connectivity in the brain, and suggest that slow, directed functional interactions, estimated with fMRI, may provide useful markers of behaviorally relevant cognitive states.
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Ghafouri S, Khasteh SH. A survey on exponential random graph models: an application perspective. PeerJ Comput Sci 2020; 6:e269. [PMID: 33816920 PMCID: PMC7924687 DOI: 10.7717/peerj-cs.269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2019] [Accepted: 03/08/2020] [Indexed: 06/12/2023]
Abstract
The uncertainty underlying real-world phenomena has attracted attention toward statistical analysis approaches. In this regard, many problems can be modeled as networks. Thus, the statistical analysis of networked problems has received special attention from many researchers in recent years. Exponential Random Graph Models, known as ERGMs, are one of the popular statistical methods for analyzing the graphs of networked data. ERGM is a generative statistical network model whose ultimate goal is to present a subset of networks with particular characteristics as a statistical distribution. In the context of ERGMs, these graph's characteristics are called statistics or configurations. Most of the time they are the number of repeated subgraphs across the graphs. Some examples include the number of triangles or the number of cycle of an arbitrary length. Also, any other census of the graph, as with the edge density, can be considered as one of the graph's statistics. In this review paper, after explaining the building blocks and classic methods of ERGMs, we have reviewed their newly presented approaches and research papers. Further, we have conducted a comprehensive study on the applications of ERGMs in many research areas which to the best of our knowledge has not been done before. This review paper can be used as an introduction for scientists from various disciplines whose aim is to use ERGMs in some networked data in their field of expertise.
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Affiliation(s)
- Saeid Ghafouri
- School of computer engineering, K. N. Toosi University of Technology, Tehran, Iran
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Noriega G. Restricted, Repetitive, and Stereotypical Patterns of Behavior in Autism-an fMRI Perspective. IEEE Trans Neural Syst Rehabil Eng 2019; 27:1139-1148. [PMID: 31021772 DOI: 10.1109/tnsre.2019.2912416] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The main objective of this paper is to determine whether resting-state fMRI can identify functional connectivity differences between individuals with autism who experience severe issues with restricted, repetitive, and stereotypical behaviors, those who experience only mild issues, and controls. We use resting-state fMRI data from the ABIDE-I preprocessed repository, with participants grouped according to their ADI-R Restricted, Repetitive, and Stereotyped Patterns of Behavior Subscore. Three processing methods are used for analysis. A time-correlation approach establishes a basic baseline, and we introduce a method based on sliding time windows, with means across time adjusted to consider the fraction of time the correlation measure is above/below average. We complement these with a band-limited coherence approach. For completeness, preprocessing schemes with and without global signal regression are considered. Our results are in line with recent ones which find both over- and under-connectivities in the autistic brain. We find that there are indeed significant differences in connectivity between various regions that differentiate between ASD subjects with severe stereotypical/restrictive behavior issues, those with only mild issues, and controls. Interestingly, for some regions, the "signature" of subjects in the milder of the ASD groups appears to be distinct (i.e., over- or under-connected) relative to both the more severe ASD group and the controls.
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