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Theis N, Bahuguna J, Rubin JE, Cape J, Iyengar S, Prasad KM. Diagnostically distinct resting state fMRI energy distributions: A subject-specific maximum entropy modeling study. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.01.23.576937. [PMID: 38328170 PMCID: PMC10849576 DOI: 10.1101/2024.01.23.576937] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/09/2024]
Abstract
Objective Existing neuroimaging studies of psychotic and mood disorders have reported brain activation differences (first-order properties) and altered pairwise correlation-based functional connectivity (second-order properties). However, both approaches have certain limitations that can be overcome by integrating them in a pairwise maximum entropy model (MEM) that better represents a comprehensive picture of fMRI signal patterns and provides a system-wide summary measure called energy. This study examines the applicability of individual-level MEM for psychiatry and identifies image-derived model coefficients related to model parameters. Method MEMs are fit to resting state fMRI data from each individual with schizophrenia/schizoaffective disorder, bipolar disorder, and major depression (n=132) and demographically matched healthy controls (n=132) from the UK Biobank to different subsets of the default mode network (DMN) regions. Results The model satisfactorily explained observed brain energy state occurrence probabilities across all participants, and model parameters were significantly correlated with image-derived coefficients for all groups. Within clinical groups, averaged energy level distributions were higher in schizophrenia/schizoaffective disorder but lower in bipolar disorder compared to controls for both bilateral and unilateral DMN. Major depression energy distributions were higher compared to controls only in the right hemisphere DMN. Conclusions Diagnostically distinct energy states suggest that probability distributions of temporal changes in synchronously active nodes may underlie each diagnostic entity. Subject-specific MEMs allow for factoring in the individual variations compared to traditional group-level inferences, offering an improved measure of biologically meaningful correlates of brain activity that may have potential clinical utility.
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Affiliation(s)
- Nicholas Theis
- Department of Psychiatry, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA
| | - Jyotika Bahuguna
- Department of Neuroscience, Laboratoire de Neurosciences Cognitive et Adaptive, University of Strasbourg, France
| | | | - Joshua Cape
- Department of Statistics, University of Wisconsin-Madison, WI, USA
| | - Satish Iyengar
- Department of Statistics, University of Pittsburgh, PA, USA
| | - Konasale M. Prasad
- Department of Psychiatry, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA
- Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, PA, USA
- Veterans Affairs Pittsburgh Healthcare System, Pittsburgh, PA, USA
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Khanra P, Nakuci J, Muldoon S, Watanabe T, Masuda N. Reliability of energy landscape analysis of resting-state functional MRI data. Eur J Neurosci 2024. [PMID: 38837814 DOI: 10.1111/ejn.16390] [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] [Received: 07/05/2023] [Revised: 04/05/2024] [Accepted: 04/25/2024] [Indexed: 06/07/2024]
Abstract
Energy landscape analysis is a data-driven method to analyse multidimensional time series, including functional magnetic resonance imaging (fMRI) data. It has been shown to be a useful characterization of fMRI data in health and disease. It fits an Ising model to the data and captures the dynamics of the data as movement of a noisy ball constrained on the energy landscape derived from the estimated Ising model. In the present study, we examine test-retest reliability of the energy landscape analysis. To this end, we construct a permutation test that assesses whether or not indices characterizing the energy landscape are more consistent across different sets of scanning sessions from the same participant (i.e. within-participant reliability) than across different sets of sessions from different participants (i.e. between-participant reliability). We show that the energy landscape analysis has significantly higher within-participant than between-participant test-retest reliability with respect to four commonly used indices. We also show that a variational Bayesian method, which enables us to estimate energy landscapes tailored to each participant, displays comparable test-retest reliability to that using the conventional likelihood maximization method. The proposed methodology paves the way to perform individual-level energy landscape analysis for given data sets with a statistically controlled reliability.
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Affiliation(s)
- Pitambar Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, USA
| | - Johan Nakuci
- School of Psychology, Georgia Institute of Technology, Atlanta, Georgia, USA
| | - Sarah Muldoon
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, USA
- Institute for Artificial Intelligence and Data Science, State University of New York at Buffalo, Buffalo, New York, USA
| | - Takamitsu Watanabe
- International Research Centre for Neurointelligence, The University of Tokyo, Tokyo, Japan
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, USA
- Institute for Artificial Intelligence and Data Science, State University of New York at Buffalo, Buffalo, New York, USA
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Xing L, Guo Z, Long Z. Energy landscape analysis of brain network dynamics in Alzheimer's disease. Front Aging Neurosci 2024; 16:1375091. [PMID: 38813531 PMCID: PMC11133694 DOI: 10.3389/fnagi.2024.1375091] [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: 01/23/2024] [Accepted: 04/30/2024] [Indexed: 05/31/2024] Open
Abstract
Background Alzheimer's disease (AD) is a common neurodegenerative dementia, characterized by abnormal dynamic functional connectivity (DFC). Traditional DFC analysis, assuming linear brain dynamics, may neglect the complexity of the brain's nonlinear interactions. Energy landscape analysis offers a holistic, nonlinear perspective to investigate brain network attractor dynamics, which was applied to resting-state fMRI data for AD in this study. Methods This study utilized resting-state fMRI data from 60 individuals, comparing 30 Alzheimer's patients with 30 controls, from the Alzheimer's Disease Neuroimaging Initiative. Energy landscape analysis was applied to the data to characterize the aberrant brain network dynamics of AD patients. Results The AD group stayed in the co-activation state for less time than the healthy control (HC) group, and a positive correlation was identified between the transition frequency of the co-activation state and behavior performance. Furthermore, the AD group showed a higher occurrence frequency and transition frequency of the cognitive control state and sensory integration state than the HC group. The transition between the two states was positively correlated with behavior performance. Conclusion The results suggest that the co-activation state could be important to cognitive processing and that the AD group possibly raised cognitive ability by increasing the occurrence and transition between the impaired cognitive control and sensory integration states.
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Affiliation(s)
- Le Xing
- The State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China
| | - Zhitao Guo
- School of Artificial Intelligence, Beijing Normal University, Beijing, China
| | - Zhiying Long
- School of Artificial Intelligence, Beijing Normal University, Beijing, China
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Theis N, Bahuguna J, Rubin JE, Muldoon B, Prasad KM. Energy in functional brain states correlates with cognition in adolescent-onset schizophrenia and healthy persons. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.11.06.565753. [PMID: 37987003 PMCID: PMC10659315 DOI: 10.1101/2023.11.06.565753] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2023]
Abstract
Adolescent-onset schizophrenia (AOS) is a relatively rare and under-studied form of schizophrenia with more severe cognitive impairments and poorer outcome compared to adult-onset schizophrenia. Several neuroimaging studies have reported alterations in regional activations that account for activity in individual regions (first-order model) and functional connectivity that reveals pairwise co-activations (second-order model) in AOS compared to controls. The pairwise maximum entropy model, also called the Ising model, can integrate both first-order and second-order terms to elucidate a comprehensive picture of neural dynamics and captures both individual and pairwise activity measures into a single quantity known as energy, which is inversely related to the probability of state occurrence. We applied the MEM framework to task functional MRI data collected on 23 AOS individuals in comparison with 53 healthy control subjects while performing the Penn Conditional Exclusion Test (PCET), which measures executive function that has been repeatedly shown to be more impaired in AOS compared to adult-onset schizophrenia. Accuracy of PCET performance was significantly reduced among AOS compared to controls as expected. Average cumulative energy achieved for a participant over the course of the fMRI negatively correlated with task performance, and the association was stronger than any first-order associations. The AOS subjects spent more time in higher energy states that represent lower probability of occurrence and were associated with impaired executive function and greater severity of psychopathology suggesting that the neural dynamics may be less efficient compared to controls who spent more time in lower energy states occurring with higher probability and hence are more stable and efficient. The energy landscapes in both conditions featured attractors that corresponded to two distinct subnetworks, namely fronto-temporal and parieto-motor. Attractor basins were larger in the controls than in AOS; moreover, fronto-temporal basin size was significantly correlated with cognitive performance in controls but not among the AOS. The single trial trajectories for the AOS group also showed higher variability in concordance with shallow attractor basins among AOS. These findings suggest that the neural dynamics of AOS features more frequent occurrence of less probable states with shallower attractors, which lack the relation to executive function associated with attractors in control subjects suggesting a diminished capacity of AOS to generate task-effective brain states.
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Affiliation(s)
- Nicholas Theis
- Department of Psychiatry, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA
| | - Jyotika Bahuguna
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA
| | | | - Brendan Muldoon
- Department of Psychiatry, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA
| | - Konasale M. Prasad
- Department of Psychiatry, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA
- Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, PA, USA
- Veterans Affairs Pittsburgh Healthcare System, Pittsburgh, PA, USA
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Fang F, Cammon J, Li R, Zhang Y. Test and re-test reliability of optimal stimulation targets and parameters for personalized neuromodulation. Front Neurosci 2023; 17:1153786. [PMID: 37250412 PMCID: PMC10213310 DOI: 10.3389/fnins.2023.1153786] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 04/25/2023] [Indexed: 05/31/2023] Open
Abstract
Protocols have been proposed to optimize neuromodulation targets and parameters to increase treatment efficacies for different neuropsychiatric diseases. However, no study has investigated the temporal effects of optimal neuromodulation targets and parameters simultaneously via exploring the test-retest reliability of the optimal neuromodulation protocols. In this study, we employed a publicly available structural and resting-state functional magnetic resonance imaging (fMRI) dataset to investigate the temporal effects of the optimal neuromodulation targets and parameters inferred from our customized neuromodulation protocol and examine the test-retest reliability over scanning time. 57 healthy young subjects were included in this study. Each subject underwent a repeated structural and resting state fMRI scan in two visits with an interval of 6 weeks between two scanning visits. Brain controllability analysis was performed to determine the optimal neuromodulation targets and optimal control analysis was further applied to calculate the optimal neuromodulation parameters for specific brain states transition. Intra-class correlation (ICC) measure was utilized to examine the test-retest reliability. Our results demonstrated that the optimal neuromodulation targets and parameters had excellent test-retest reliability (both ICCs > 0.80). The test-retest reliability of model fitting accuracies between the actual final state and the simulated final state also showed a good test-retest reliability (ICC > 0.65). Our results indicated the validity of our customized neuromodulation protocol to reliably identify the optimal neuromodulation targets and parameters between visits, which may be reliably extended to optimize the neuromodulation protocols to efficiently treat different neuropsychiatric disorders.
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Affiliation(s)
- Feng Fang
- Department of Biomedical Engineering, University of Houston, Houston, TX, United States
| | - Jared Cammon
- Department of Biomedical Engineering, University of Houston, Houston, TX, United States
| | - Rihui Li
- Department of Psychiatry and Behavioral Sciences, Center for Interdisciplinary Brain Sciences Research, Stanford University, Stanford, CA, United States
| | - Yingchun Zhang
- Department of Biomedical Engineering, University of Houston, Houston, TX, United States
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Fagerholm ED, Dezhina Z, Moran RJ, Turkheimer FE, Leech R. A primer on entropy in neuroscience. Neurosci Biobehav Rev 2023; 146:105070. [PMID: 36736445 DOI: 10.1016/j.neubiorev.2023.105070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Revised: 01/16/2023] [Accepted: 01/29/2023] [Indexed: 02/04/2023]
Abstract
Entropy is not just a property of a system - it is a property of a system and an observer. Specifically, entropy is a measure of the amount of hidden information in a system that arises due to an observer's limitations. Here we provide an account of entropy from first principles in statistical mechanics with the aid of toy models of neural systems. Specifically, we describe the distinction between micro and macrostates in the context of simplified binary-state neurons and the characteristics of entropy required to capture an associated measure of hidden information. We discuss the origin of the mathematical form of entropy via the indistinguishable re-arrangements of discrete-state neurons and show the way in which the arguments are extended into a phase space description for continuous large-scale neural systems. Finally, we show the ways in which limitations in neuroimaging resolution, as represented by coarse graining operations in phase space, lead to an increase in entropy in time as per the second law of thermodynamics. It is our hope that this primer will support the increasing number of studies that use entropy as a way of characterising neuroimaging timeseries and of making inferences about brain states.
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Affiliation(s)
- Erik D Fagerholm
- Department of Neuroimaging, King's College London, United Kingdom.
| | - Zalina Dezhina
- Department of Neuroimaging, King's College London, United Kingdom
| | - Rosalyn J Moran
- Department of Neuroimaging, King's College London, United Kingdom
| | | | - Robert Leech
- Department of Neuroimaging, King's College London, United Kingdom
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Fan L, Li C, Huang ZG, Zhao J, Wu X, Liu T, Li Y, Wang J. The longitudinal neural dynamics changes of whole brain connectome during natural recovery from poststroke aphasia. NEUROIMAGE: CLINICAL 2022; 36:103190. [PMID: 36174256 PMCID: PMC9668607 DOI: 10.1016/j.nicl.2022.103190] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Revised: 07/24/2022] [Accepted: 09/08/2022] [Indexed: 12/14/2022] Open
Abstract
Poststroke aphasia is one of the most dramatic functional deficits that results from direct damage of focal brain regions and dysfunction of large-scale brain networks. The reconstruction of language function depends on the hierarchical whole-brain dynamic reorganization. However, investigations into the longitudinal neural changes of large-scale brain networks for poststroke aphasia remain scarce. Here we characterize large-scale brain dynamics in left-frontal-stroke aphasia through energy landscape analysis. Using fMRI during an auditory comprehension task, we find that aphasia patients suffer serious whole-brain dynamics perturbation in the acute and subacute stages after stroke, in which the brains were restricted into two major activity patterns. Following spontaneous recovery process, the brain flexibility improved in the chronic stage. Critically, we demonstrated that the abnormal neural dynamics are correlated with the aberrant brain network coordination. Taken together, the energy landscape analysis exhibited that the acute poststroke aphasia has a constrained, low dimensional brain dynamics, which were replaced by less constrained and high dimensional dynamics at chronic aphasia. Our study provides a new perspective to profoundly understand the pathological mechanisms of poststroke aphasia.
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Affiliation(s)
- Liming Fan
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China,National Engineering Research Center of Health Care and Medical Devices. Guangzhou, Guangdong 510500, PR China
| | - Chenxi Li
- Department of the Psychology of Military Medicine, Air Force Medical University, Xi’an, Shaanxi 710032, PR China
| | - Zi-gang Huang
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China,National Engineering Research Center of Health Care and Medical Devices. Guangzhou, Guangdong 510500, PR China
| | - Jie Zhao
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China,National Engineering Research Center of Health Care and Medical Devices. Guangzhou, Guangdong 510500, PR China
| | - Xiaofeng Wu
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China,National Engineering Research Center of Health Care and Medical Devices. Guangzhou, Guangdong 510500, PR China
| | - Tian Liu
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China,National Engineering Research Center of Health Care and Medical Devices. Guangzhou, Guangdong 510500, PR China
| | - Youjun Li
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China,National Engineering Research Center of Health Care and Medical Devices. Guangzhou, Guangdong 510500, PR China,Corresponding authors at: The Key Laboratory of Biomedical Information Engineering of Ministry of Education, and Institute of Biomedical Engineering, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an 710049, PR China.
| | - Jue Wang
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, Institute of Health and Rehabilitation Science, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China,National Engineering Research Center of Health Care and Medical Devices. Guangzhou, Guangdong 510500, PR China,The Key Laboratory of Neuro-informatics & Rehabilitation Engineering of Ministry of Civil Affairs, Xi’an, Shaanxi 710049, PR China,Corresponding authors at: The Key Laboratory of Biomedical Information Engineering of Ministry of Education, and Institute of Biomedical Engineering, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an 710049, PR China.
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Jeong SO, Kang J, Pae C, Eo J, Park SM, Son J, Park HJ. Empirical Bayes estimation of pairwise maximum entropy model for nonlinear brain state dynamics. Neuroimage 2021; 244:118618. [PMID: 34571159 DOI: 10.1016/j.neuroimage.2021.118618] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 09/22/2021] [Accepted: 09/24/2021] [Indexed: 11/16/2022] Open
Abstract
The pairwise maximum entropy model (pMEM) has recently gained widespread attention to exploring the nonlinear characteristics of brain state dynamics observed in resting-state functional magnetic resonance imaging (rsfMRI). Despite its unique advantageous features, the practical application of pMEM for individuals is limited as it requires a much larger sample than conventional rsfMRI scans. Thus, this study proposes an empirical Bayes estimation of individual pMEM using the variational expectation-maximization algorithm (VEM-MEM). The performance of the VEM-MEM is evaluated for several simulation setups with various sample sizes and network sizes. Unlike conventional maximum likelihood estimation procedures, the VEM-MEM can reliably estimate the individual model parameters, even with small samples, by effectively incorporating the group information as the prior. As a test case, the individual rsfMRI of children with attention deficit hyperactivity disorder (ADHD) is analyzed compared to that of typically developed children using the default mode network, executive control network, and salient network, obtained from the Healthy Brain Network database. We found that the nonlinear dynamic properties uniquely established on the pMEM differ for each group. Furthermore, pMEM parameters are more sensitive to group differences and are better associated with the behavior scores of ADHD compared to the Pearson correlation-based functional connectivity. The simulation and experimental results suggest that the proposed method can reliably estimate the individual pMEM and characterize the dynamic properties of individuals by utilizing empirical information of the group brain state dynamics.
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Affiliation(s)
- Seok-Oh Jeong
- Department of Statistics, Hankuk University of Foreign Studies, Yong-In, Republic of Korea
| | - Jiyoung Kang
- Center for Systems and Translational Brain Science, Institute of Human Complexity and Systems Science, Yonsei University, Seoul, Republic of Korea; Department of Nuclear Medicine, Department of Psychiatry, Yonsei University College of Medicine, Seoul, Republic of Korea
| | - Chongwon Pae
- Center for Systems and Translational Brain Science, Institute of Human Complexity and Systems Science, Yonsei University, Seoul, Republic of Korea; Department of Nuclear Medicine, Department of Psychiatry, Yonsei University College of Medicine, Seoul, Republic of Korea
| | - Jinseok Eo
- Center for Systems and Translational Brain Science, Institute of Human Complexity and Systems Science, Yonsei University, Seoul, Republic of Korea; Department of Nuclear Medicine, Department of Psychiatry, Yonsei University College of Medicine, Seoul, Republic of Korea; Graduate School of Medical Science, Yonsei University College of Medicine, Brain Korea 21 Project, Seoul, Republic of Korea
| | - Sung Min Park
- Center for Systems and Translational Brain Science, Institute of Human Complexity and Systems Science, Yonsei University, Seoul, Republic of Korea
| | - Junho Son
- Center for Systems and Translational Brain Science, Institute of Human Complexity and Systems Science, Yonsei University, Seoul, Republic of Korea; Department of Nuclear Medicine, Department of Psychiatry, Yonsei University College of Medicine, Seoul, Republic of Korea; Graduate School of Medical Science, Yonsei University College of Medicine, Brain Korea 21 Project, Seoul, Republic of Korea
| | - Hae-Jeong Park
- Center for Systems and Translational Brain Science, Institute of Human Complexity and Systems Science, Yonsei University, Seoul, Republic of Korea; Department of Nuclear Medicine, Department of Psychiatry, Yonsei University College of Medicine, Seoul, Republic of Korea; Graduate School of Medical Science, Yonsei University College of Medicine, Brain Korea 21 Project, Seoul, Republic of Korea; Department of Cognitive Science, Yonsei University, Seoul, Republic of Korea.
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Kang J, Jeong S, Pae C, Park H. Bayesian estimation of maximum entropy model for individualized energy landscape analysis of brain state dynamics. Hum Brain Mapp 2021; 42:3411-3428. [PMID: 33934421 PMCID: PMC8249903 DOI: 10.1002/hbm.25442] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 03/25/2021] [Accepted: 03/29/2021] [Indexed: 11/24/2022] Open
Abstract
The pairwise maximum entropy model (MEM) for resting state functional MRI (rsfMRI) has been used to generate energy landscape of brain states and to explore nonlinear brain state dynamics. Researches using MEM, however, has mostly been restricted to fixed‐effect group‐level analyses, using concatenated time series across individuals, due to the need for large samples in the parameter estimation of MEM. To mitigate the small sample problem in analyzing energy landscapes for individuals, we propose a Bayesian estimation of individual MEM using variational Bayes approximation (BMEM). We evaluated the performances of BMEM with respect to sample sizes and prior information using simulation. BMEM showed advantages over conventional maximum likelihood estimation in reliably estimating model parameters for individuals with small sample data, particularly utilizing the empirical priors derived from group data. We then analyzed individual rsfMRI of the Human Connectome Project to show the usefulness of MEM in differentiating individuals and in exploring neural correlates for human behavior. MEM and its energy landscape properties showed high subject specificity comparable to that of functional connectivity. Canonical correlation analysis identified canonical variables for MEM highly associated with cognitive scores. Inter‐individual variations of cognitive scores were also reflected in energy landscape properties such as energies, occupation times, and basin sizes at local minima. We conclude that BMEM provides an efficient method to characterize dynamic properties of individuals using energy landscape analysis of individual brain states.
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Affiliation(s)
- Jiyoung Kang
- Center for Systems and Translational Brain ScienceInstitute of Human Complexity and Systems Science, Yonsei UniversitySeoulSouth Korea
- Department of Nuclear Medicine, PsychiatryYonsei University College of MedicineSeoulSouth Korea
| | - Seok‐Oh Jeong
- Department of StatisticsHankuk University of Foreign StudiesYong‐In, SeoulSouth Korea
| | - Chongwon Pae
- Center for Systems and Translational Brain ScienceInstitute of Human Complexity and Systems Science, Yonsei UniversitySeoulSouth Korea
- Department of Nuclear Medicine, PsychiatryYonsei University College of MedicineSeoulSouth Korea
| | - Hae‐Jeong Park
- Center for Systems and Translational Brain ScienceInstitute of Human Complexity and Systems Science, Yonsei UniversitySeoulSouth Korea
- Department of Nuclear Medicine, PsychiatryYonsei University College of MedicineSeoulSouth Korea
- Graduate School of Medical Science, Brain Korea 21 ProjectYonsei University College of MedicineSeoulSouth Korea
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