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Gallos IK, Lehmberg D, Dietrich F, Siettos C. Data-driven modelling of brain activity using neural networks, diffusion maps, and the Koopman operator. CHAOS (WOODBURY, N.Y.) 2024; 34:013151. [PMID: 38285718 DOI: 10.1063/5.0157881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Accepted: 12/22/2023] [Indexed: 01/31/2024]
Abstract
We propose a machine-learning approach to construct reduced-order models (ROMs) to predict the long-term out-of-sample dynamics of brain activity (and in general, high-dimensional time series), focusing mainly on task-dependent high-dimensional fMRI time series. Our approach is a three stage one. First, we exploit manifold learning and, in particular, diffusion maps (DMs) to discover a set of variables that parametrize the latent space on which the emergent high-dimensional fMRI time series evolve. Then, we construct ROMs on the embedded manifold via two techniques: Feedforward Neural Networks (FNNs) and the Koopman operator. Finally, for predicting the out-of-sample long-term dynamics of brain activity in the ambient fMRI space, we solve the pre-image problem, i.e., the construction of a map from the low-dimensional manifold to the original high-dimensional (ambient) space by coupling DMs with Geometric Harmonics (GH) when using FNNs and the Koopman modes per se. For our illustrations, we have assessed the performance of the two proposed schemes using two benchmark fMRI time series: (i) a simplistic five-dimensional model of stochastic discrete-time equations used just for a "transparent" illustration of the approach, thus knowing a priori what one expects to get, and (ii) a real fMRI dataset with recordings during a visuomotor task. We show that the proposed Koopman operator approach provides, for any practical purposes, equivalent results to the FNN-GH approach, thus bypassing the need to train a non-linear map and to use GH to extrapolate predictions in the ambient space; one can use instead the low-frequency truncation of the DMs function space of L2-integrable functions to predict the entire list of coordinate functions in the ambient space and to solve the pre-image problem.
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Affiliation(s)
- Ioannis K Gallos
- Institute of Communication and Computer Systems, National Technical University of Athens, Zografos Campus, 15780 Athens, Greece
| | - Daniel Lehmberg
- School of Computation, Information and Technology, Technical University of Munich, Munich 80333, Germany
| | - Felix Dietrich
- School of Computation, Information and Technology, Technical University of Munich, Munich 80333, Germany
| | - Constantinos Siettos
- Dipartimento di Matematica e Applicazioni "Renato Caccioppoli," Universitá degli Studi di Napoli Federico II, Naples 80125, Italy
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2
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Chu C, Zhang Z, Wang J, Wang L, Shen X, Bai L, Li Z, Dong M, Liu C, Yi G, Zhu X. Evolution of brain network dynamics in early Parkinson's disease with mild cognitive impairment. Cogn Neurodyn 2023; 17:681-694. [PMID: 37265660 PMCID: PMC10229513 DOI: 10.1007/s11571-022-09868-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2022] [Revised: 07/13/2022] [Accepted: 07/26/2022] [Indexed: 11/03/2022] Open
Abstract
How mild cognitive impairment (MCI) is instantiated in dynamically interacting and spatially distributed functional brain networks remains an unexplored mystery in early Parkinson's disease (PD). We applied a machine-learning technology based on personalized sliding-window algorithm to track continuously time-varying and overlapping subnetworks under the functional brain networks calculated form resting state electroencephalogram data within a sample of 33 early PD patients (13 early PD patients with MCI and 20 early PD patients without MCI). We decoded a set of subnetworks that captured surprisingly dynamically varying and integrated interactions among certain brain lobes. We observed that the master expressed subnetworks were particularly transient, and flexibly switching between high and low expression during integration into a dynamic brain network. This transience was particularly salient in a subnetwork predominantly linking temporal-parietal-occipital lobes, which decreases in both expression and flexibility in early PD patients with MCI and expresses their degree of cognitive impairment. Moreover, MCI induced a regularly interrupted, slow evolution of subnetworks in functional brain network dynamics in early PD at the individual level, and the dynamic expression characteristics of subnetworks also reflected the degree of cognitive impairment in patients with early PD. Collectively, these results provide novel and deeper insights regarding MCI-induced abnormal dynamical interaction and large-scale changes in functional brain network of early PD.
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Affiliation(s)
- Chunguang Chu
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072 China
| | - Zhen Zhang
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072 China
| | - Jiang Wang
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072 China
| | - Liufang Wang
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072 China
| | - Xiao Shen
- Department of Neurology, Tianjin Neurological Institute, Tianjin Medical University General Hospital, Tianjin, 300052 China
| | - Lipeng Bai
- Department of Neurology, Tianjin Neurological Institute, Tianjin Medical University General Hospital, Tianjin, 300052 China
| | - Zhuo Li
- Department of Neurology, Tianjin Neurological Institute, Tianjin Medical University General Hospital, Tianjin, 300052 China
| | - Mengmeng Dong
- Department of Neurology, Tianjin Neurological Institute, Tianjin Medical University General Hospital, Tianjin, 300052 China
| | - Chen Liu
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072 China
| | - Guosheng Yi
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072 China
| | - Xiaodong Zhu
- Department of Neurology, Tianjin Neurological Institute, Tianjin Medical University General Hospital, Tianjin, 300052 China
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3
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Hybrid machine learning method for a connectivity-based epilepsy diagnosis with resting-state EEG. Med Biol Eng Comput 2022; 60:1675-1689. [DOI: 10.1007/s11517-022-02560-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 03/25/2022] [Indexed: 10/18/2022]
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4
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Decision Tree in Working Memory Task Effectively Characterizes EEG Signals in Healthy Aging Adults. Ing Rech Biomed 2021. [DOI: 10.1016/j.irbm.2021.12.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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5
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Almpanis E, Siettos C. Construction of functional brain connectivity networks from fMRI data with driving and modulatory inputs: an extended conditional Granger causality approach. AIMS Neurosci 2020; 7:66-88. [PMID: 32607412 PMCID: PMC7321769 DOI: 10.3934/neuroscience.2020005] [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: 01/06/2020] [Accepted: 03/25/2020] [Indexed: 11/29/2022] Open
Abstract
We propose a numerical-based approach extending the conditional MVAR Granger causality (MVGC) analysis for the construction of directed connectivity networks in the presence of both exogenous/stimuli and modulatory inputs. The performance of the proposed scheme is validated using both synthetic stochastic data considering also the influence of haemodynamics latencies and a benchmark fMRI dataset related to the role of attention in the perception of visual motion. The particular fMRI dataset has been used in many studies to evaluate alternative model hypotheses using the Dynamic Causal Modelling (DCM) approach. Based on the use of the Bayes factor, we show that the obtained GC connectivity network compares well to a reference model that has been selected through DCM analysis among other candidate models. Thus, our findings suggest that the proposed scheme can be successfully used as a stand-alone or complementary to DCM approach to find directed causal connectivity patterns in task-related fMRI studies.
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Affiliation(s)
- Evangelos Almpanis
- Section of Condensed Matter Physics, National and Kapodistrian University of Athens, Greece.,Institute of Nanoscience and Nanotechnology, NCSR "Demokritos," Athens, Greece
| | - Constantinos Siettos
- Dipartimento di Matematica e Applicazioni "Renato Caccioppoli", Università degli Studi di Napoli Federico II, Italy
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6
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Hejazi M, Motie Nasrabadi A. Prediction of epilepsy seizure from multi-channel electroencephalogram by effective connectivity analysis using Granger causality and directed transfer function methods. Cogn Neurodyn 2019; 13:461-473. [PMID: 31565091 DOI: 10.1007/s11571-019-09534-z] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2018] [Revised: 02/07/2019] [Accepted: 04/25/2019] [Indexed: 01/09/2023] Open
Abstract
Epilepsy is a chronic disorder, which causes strange perceptions, muscle spasms, sometimes seizures, and loss of awareness, associated with abnormal neuronal activity in the brain. The goal of this study is to investigate how effective connectivity (EC) changes effect on unexpected seizures prediction, as this will authorize the patients to play it safe and avoid risk. We approve the hypothesis that EC variables near seizure change significantly so seizure can be predicted in accordance with this variation. We introduce two time-variant coefficients based on standard deviation of EC on Freiburg EEG dataset by using directed transfer function and Granger causality methods and compare index changes over the course of time in five different frequency bands. Comparison of the multivariate and bivariate analysis of factors is implemented in this investigation. The performance based on the suggested methods shows the seizure occurrence period is approximately 50 min that is expected onset stated in, the maximum value of sensitivity approaching ~ 80%, and 0.33 FP/h is the false prediction rate. The findings revealed that greater accuracy and sensitivity are obtained by the designed system in comparison with the results of other works in the same condition. Even though these results still are not sufficient for clinical applications. Based on the conclusions, it can generally be observed that the greater results by DTF method are in the gamma and beta frequency bands.
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Affiliation(s)
- Mona Hejazi
- 1Department of Biomedical Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran
| | - Ali Motie Nasrabadi
- 2Department of Biomedical Engineering, Faculty of Biomedical Engineering, Shahed University, Tehran, Iran
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7
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Li F, Liang Y, Zhang L, Yi C, Liao Y, Jiang Y, Si Y, Zhang Y, Yao D, Yu L, Xu P. Transition of brain networks from an interictal to a preictal state preceding a seizure revealed by scalp EEG network analysis. Cogn Neurodyn 2019; 13:175-181. [PMID: 30956721 DOI: 10.1007/s11571-018-09517-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2018] [Revised: 11/29/2018] [Accepted: 12/19/2018] [Indexed: 11/29/2022] Open
Abstract
Epilepsy is a neurological disorder in the brain that is characterized by unprovoked seizures. Epileptic seizures are attributed to abnormal synchronous neuronal activity in the brain. To detect the seizure as early as possible, the identification of specific electroencephalogram (EEG) dynamics is of great importance in investigating the transition of brain activity as the epileptic seizure approaches. In this study, we investigated the transition of brain activity from interictal to preictal states preceding a seizure by combining EEG network and clustering analyses together in different frequency bands. The findings of this study demonstrated the best clustering performance of k-medoids in the beta band; in addition, compared to the interictal state, the preictal state experienced increased synchronization of EEG network connectivity, characterized by relatively higher network properties. These findings can provide helpful insight into the mechanism of epilepsy, which can also be used in the prediction of epileptic seizures and subsequent intervention.
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Affiliation(s)
- Fali Li
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China
| | - Yi Liang
- 2Department of Neurology, Sichuan Academy of Medical Sciences and Sichuan Provincial People's Hospital, Chengdu, China.,3Department of Neurology, Affiliated Hospital of University of Electronic Science and Technology of China, No. 2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu, 611731 Sichuan China
| | - Luyan Zhang
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China
| | - Chanlin Yi
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China
| | - Yuanyuan Liao
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China
| | - Yuanling Jiang
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China
| | - Yajing Si
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China
| | - Yangsong Zhang
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China.,4School of Computer Science and Technology, Southwest University of Science and Technology, Mianyang, China
| | - Dezhong Yao
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China.,5School of Life Science and Technology, Center for Information in Medicine, University of Electronic Science and Technology of China, Chengdu, China
| | - Liang Yu
- 2Department of Neurology, Sichuan Academy of Medical Sciences and Sichuan Provincial People's Hospital, Chengdu, China.,3Department of Neurology, Affiliated Hospital of University of Electronic Science and Technology of China, No. 2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu, 611731 Sichuan China
| | - Peng Xu
- 1The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, China.,5School of Life Science and Technology, Center for Information in Medicine, University of Electronic Science and Technology of China, Chengdu, China
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8
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Wang G, Wang R, Kong W, Zhang J. Simulation of retinal ganglion cell response using fast independent component analysis. Cogn Neurodyn 2018; 12:615-624. [PMID: 30483369 PMCID: PMC6233330 DOI: 10.1007/s11571-018-9490-4] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Revised: 04/23/2018] [Accepted: 06/14/2018] [Indexed: 12/29/2022] Open
Abstract
Advances in neurobiology suggest that neuronal response of the primary visual cortex to natural stimuli may be attributed to sparse approximation of images, encoding stimuli to activate specific neurons although the underlying mechanisms are still unclear. The responses of retinal ganglion cells (RGCs) to natural and random checkerboard stimuli were simulated using fast independent component analysis. The neuronal response to stimuli was measured using kurtosis and Treves-Rolls sparseness, and the kurtosis, lifetime and population sparseness were analyzed. RGCs exhibited significant lifetime sparseness in response to natural stimuli and random checkerboard stimuli. About 65 and 72% of RGCs do not fire all the time in response to natural and random checkerboard stimuli, respectively. Both kurtosis of single neurons and lifetime response of single neurons values were larger in the case of natural than in random checkerboard stimuli. The population of RGCs fire much less in response to random checkerboard stimuli than natural stimuli. However, kurtosis of population sparseness and population response of the entire neurons were larger with natural than random checkerboard stimuli. RGCs fire more sparsely in response to natural stimuli. Individual neurons fire at a low rate, while the occasional "burst" of neuronal population transmits information efficiently.
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Affiliation(s)
- Guanzheng Wang
- Institute for Cognitive Neurodynamics, School of Science, East China University of Science and Technology, Meilong Road 130, Shanghai, 200237 China
| | - Rubin Wang
- College of Computer Science, Hangzhou Dianzi University, Zhejiang, China
- Institute for Cognitive Neurodynamics, School of Science, East China University of Science and Technology, Meilong Road 130, Shanghai, 200237 China
| | - Wanzheng Kong
- College of Computer Science, Hangzhou Dianzi University, Zhejiang, China
- Baiyang Road 1158, Hangzhou, 310018 China
| | - Jianhai Zhang
- College of Computer Science, Hangzhou Dianzi University, Zhejiang, China
- Baiyang Road 1158, Hangzhou, 310018 China
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9
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Teng C, Cheng Y, Wang C, Ren Y, Xu W, Xu J. Aging-related changes of EEG synchronization during a visual working memory task. Cogn Neurodyn 2018; 12:561-568. [PMID: 30483364 DOI: 10.1007/s11571-018-9500-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Revised: 07/12/2018] [Accepted: 08/22/2018] [Indexed: 12/15/2022] Open
Abstract
Differences of EEG synchronization between normal old and young people during a working memory (WM) task were investigated. The synchronization likelihood (SL) is a novel method to assessed synchronization in multivariate time series for non-stationary systems. To evaluate this method to study the mechanisms of WM, we calculated the SL values in brain electrical activity for both resting state and task state. EEG signals were recorded from 14 young adults and 12 old adults during two different states, respectively. SL was used to measure EEG synchronization between 19 electrodes in delta, theta, alpha1, alpha2 and beta frequency bands. Bad task performance and significantly decreased EEG synchronization were found in old group compared to young group in alpha1, alpha2 and beta frequency bands during the WM task. Moreover, significantly decreased EEG synchronization in beta band in the elder was also detected during the resting state. The findings suggested that reduced EEG synchronization may be one of causes for WM capacity decline along with healthy aging.
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Affiliation(s)
- Chaolin Teng
- 1The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Biomedical Engineering, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi Province People's Republic of China
| | - Yao Cheng
- 1The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Biomedical Engineering, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi Province People's Republic of China
| | - Chao Wang
- 1The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Biomedical Engineering, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi Province People's Republic of China
| | - Yijing Ren
- 2Beijing University of Posts and Telecommunications, Beijing, China
| | - Weiyong Xu
- 1The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Biomedical Engineering, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi Province People's Republic of China.,3Department of Psychology, University of Jyväskylä, Jyväskylä, Finland
| | - Jin Xu
- 1The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Biomedical Engineering, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi Province People's Republic of China
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Talebi N, Nasrabadi AM, Mohammad-Rezazadeh I. Estimation of effective connectivity using multi-layer perceptron artificial neural network. Cogn Neurodyn 2017; 12:21-42. [PMID: 29435085 DOI: 10.1007/s11571-017-9453-1] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Revised: 07/30/2017] [Accepted: 09/01/2017] [Indexed: 01/01/2023] Open
Abstract
Studies on interactions between brain regions estimate effective connectivity, (usually) based on the causality inferences made on the basis of temporal precedence. In this study, the causal relationship is modeled by a multi-layer perceptron feed-forward artificial neural network, because of the ANN's ability to generate appropriate input-output mapping and to learn from training examples without the need of detailed knowledge of the underlying system. At any time instant, the past samples of data are placed in the network input, and the subsequent values are predicted at its output. To estimate the strength of interactions, the measure of "Causality coefficient" is defined based on the network structure, the connecting weights and the parameters of hidden layer activation function. Simulation analysis demonstrates that the method, called "CREANN" (Causal Relationship Estimation by Artificial Neural Network), can estimate time-invariant and time-varying effective connectivity in terms of MVAR coefficients. The method shows robustness with respect to noise level of data. Furthermore, the estimations are not significantly influenced by the model order (considered time-lag), and the different initial conditions (initial random weights and parameters of the network). CREANN is also applied to EEG data collected during a memory recognition task. The results implicate that it can show changes in the information flow between brain regions, involving in the episodic memory retrieval process. These convincing results emphasize that CREANN can be used as an appropriate method to estimate the causal relationship among brain signals.
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Affiliation(s)
- Nasibeh Talebi
- 1Department of Biomedical Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
| | - Ali Motie Nasrabadi
- 1Department of Biomedical Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
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Yao Q, Zhu D, Li F, Xiao C, Lin X, Huang Q, Shi J. Altered Functional and Causal Connectivity of Cerebello-Cortical Circuits between Multiple System Atrophy (Parkinsonian Type) and Parkinson's Disease. Front Aging Neurosci 2017; 9:266. [PMID: 28848423 PMCID: PMC5554370 DOI: 10.3389/fnagi.2017.00266] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2017] [Accepted: 07/26/2017] [Indexed: 01/28/2023] Open
Abstract
Lesions of the cerebellum lead to motor and non-motor deficits by influencing cerebral cortex activity via cerebello-cortical circuits. It remains unknown whether the cerebello-cortical “disconnection” underlies motor and non-motor impairments both in the parkinsonian variant of multiple system atrophy (MSA-P) and Parkinson’s disease (PD). In this study, we investigated both the functional and effective connectivity of the cerebello-cortical circuits from resting-state functional magnetic resonance imaging (rs-fMRI) data of three groups (26 MSA-P patients, 31 PD patients, and 30 controls). Correlation analysis was performed between the causal connectivity and clinical scores. PD patients showed a weakened cerebellar dentate nucleus (DN) functional coupling in the posterior cingulate cortex (PCC) and inferior parietal lobe compared with MSA-P or controls. MSA-P patients exhibited significantly enhanced effective connectivity from the DN to PCC compared with PD patients or controls, as well as declined causal connectivity from the left precentral gyrus to right DN compared with the controls, and this value is significantly correlated with the motor symptom scores. Our findings demonstrated a crucial role for the cerebello-cortical networks in both MSA-P and PD patients in addition to striatal-thalamo-cortical (STC) networks and indicated that different patterns of cerebello-cortical loop degeneration are involved in the development of the diseases.
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Affiliation(s)
- Qun Yao
- Department of Neurology, Affiliated Brain Hospital of Nanjing Medical UniversityNanjing, China
| | - Donglin Zhu
- Department of Neurology, Affiliated Brain Hospital of Nanjing Medical UniversityNanjing, China
| | - Feng Li
- Department of Neurology, Affiliated Brain Hospital of Nanjing Medical UniversityNanjing, China
| | - Chaoyong Xiao
- Department of Radiology, Affiliated Brain Hospital of Nanjing Medical UniversityNanjing, China
| | - Xingjian Lin
- Department of Neurology, Affiliated Brain Hospital of Nanjing Medical UniversityNanjing, China
| | - Qingling Huang
- Department of Radiology, Affiliated Brain Hospital of Nanjing Medical UniversityNanjing, China
| | - Jingping Shi
- Department of Neurology, Affiliated Brain Hospital of Nanjing Medical UniversityNanjing, China
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12
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Sohrabpour A, Ye S, Worrell GA, Zhang W, He B. Noninvasive Electromagnetic Source Imaging and Granger Causality Analysis: An Electrophysiological Connectome (eConnectome) Approach. IEEE Trans Biomed Eng 2016; 63:2474-2487. [PMID: 27740473 PMCID: PMC5152676 DOI: 10.1109/tbme.2016.2616474] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
OBJECTIVE Combined source-imaging techniques and directional connectivity analysis can provide useful information about the underlying brain networks in a noninvasive fashion. Source-imaging techniques have been used successfully to either determine the source of activity or to extract source time-courses for Granger causality analysis, previously. In this work, we utilize source-imaging algorithms to both find the network nodes [regions of interest (ROI)] and then extract the activation time series for further Granger causality analysis. The aim of this work is to find network nodes objectively from noninvasive electromagnetic signals, extract activation time-courses, and apply Granger analysis on the extracted series to study brain networks under realistic conditions. METHODS Source-imaging methods are used to identify network nodes and extract time-courses and then Granger causality analysis is applied to delineate the directional functional connectivity of underlying brain networks. Computer simulations studies where the underlying network (nodes and connectivity pattern) is known were performed; additionally, this approach has been evaluated in partial epilepsy patients to study epilepsy networks from interictal and ictal signals recorded by EEG and/or Magnetoencephalography (MEG). RESULTS Localization errors of network nodes are less than 5 mm and normalized connectivity errors of ∼20% in estimating underlying brain networks in simulation studies. Additionally, two focal epilepsy patients were studied and the identified nodes driving the epileptic network were concordant with clinical findings from intracranial recordings or surgical resection. CONCLUSION Our study indicates that combined source-imaging algorithms with Granger causality analysis can identify underlying networks precisely (both in terms of network nodes location and internodal connectivity). SIGNIFICANCE The combined source imaging and Granger analysis technique is an effective tool for studying normal or pathological brain conditions.
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Affiliation(s)
- Abbas Sohrabpour
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455 USA
| | - Shuai Ye
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455 USA
| | | | - Wenbo Zhang
- Minnesota Epilepsy Group, United Hospital, MN 55102 USA and also with the Department of Neurology, University of Minnesota, Minneapolis, 55455 USA
| | - Bin He
- Department of Biomedical Engineering, and the Institute for Engineering in Medicine, University of Minnesota, Minneapolis, MN 55455 USA
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13
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Siettos C, Starke J. Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2016; 8:438-58. [PMID: 27340949 DOI: 10.1002/wsbm.1348] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2016] [Revised: 05/01/2016] [Accepted: 05/14/2016] [Indexed: 11/09/2022]
Abstract
The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website.
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Affiliation(s)
- Constantinos Siettos
- School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Athens, Greece
| | - Jens Starke
- School of Mathematical Sciences, Queen Mary University of London, London, UK
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