Empirical Bayes estimation of pairwise maximum entropy model for nonlinear brain state dynamics

Jeong, Seok-Oh; Kang, Jiyoung; Pae, Chongwon; Eo, Jinseok; Park, Sung Min; Son, Junho

doi:10.1016/j.neuroimage.2021.118618

Cited by 7 publications

(16 citation statements)

References 44 publications

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“…The MLE algorithm for inferring Ising model coefficients converged across all node collections considered in every subject, as anticipated (13, 17). The correlation between the predicted and observed P(V k ) distributions at the individual subject level was high ( Figures 2 ) and exceeded the correlation derived directly from FC, suggesting that the Ising model provides a good representation of how often the states of the system arise.…”

Section: Discussionsupporting

confidence: 53%

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Diagnostically distinct resting state fMRI energy distributions: A subject-specific maximum entropy modeling study

Theis,

Bahuguna,

Rubin

et al. 2024

Preprint

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Objective: Existing neuroimaging studies of psychotic and mood disorders have reported regional brain activation differences (first-order properties) and alterations in functional connectivity based on pairwise correlations in activation (second-order properties). This study used a generalized Ising model, also called a pairwise maximum entropy model (MEM), to integrate first- and second-order properties to provide a comprehensive picture of BOLD patterns and a system-wide summary measure called energy. This study examines the usefulness of individual level MEMs, attempts to identify image-derived counterparts of the model, and explores potential applications to psychiatry. Method: MEMs are fit to resting state fMRI data of each individual of a sample of 132 participants consisting of schizophrenia/schizoaffective disorder, bipolar disorder, and major depression, and a demographically matched 132 participants without these diagnoses from the UK Biobank to examine the default mode network (DMN). Results: The model explained observed brain state occurrence probabilities well across all participants, and model parameters were highly correlated to image-derived parameters for all groups. Within clinical groups, schizophrenia/schizoaffective disorder and bipolar disorder patients showed significant differences in averaged energy distribution compared to controls for all sub-systems of the DMN except for depression, where differences in the energy distributions were only detected in the DMN of the regions from the right hemisphere. Conclusions: Subject-specific Ising modeling may offer an improved measure of biological functional correlates relative to traditional approaches. The observation of distinct patterns of energy distribution among the three clinical groups compared to controls suggests relative diagnostic specificity and potential for clinical translation.

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Section: Discussionsupporting

confidence: 53%

“…Fortunately, recent developments have shown it is possible to achieve individual level Ising model fitting (13, 17), which offers great clinical potential for psychiatry. In this study, we focus on the development of image-derived coefficients that can help distinguish apparently divergent pathologies underlying different disorders.…”

Section: Introductionmentioning

confidence: 99%

Diagnostically distinct resting state fMRI energy distributions: A subject-specific maximum entropy modeling study

Theis,

Bahuguna,

Rubin

et al. 2024

Preprint

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“…Previous studies have shown that there are nonlinear dependencies between time series during the resting state. This nonlinear analysis of fMRI signals performs better than linear correlation [19][20][21][22]. Su et al [23] have found that considering nonlinear dependencies between fMRI signals can better discriminate schizophrenic patients from healthy subjects.…”

Section: Introductionmentioning

confidence: 98%

Multivariate Gaussian Copula Mutual Information to Estimate Functional Connectivity with Less Random Architecture

Ashrafi

Soltanian‐Zadeh

2022

Entropy

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Recognition of a brain region’s interaction is an important field in neuroscience. Most studies use the Pearson correlation to find the interaction between the regions. According to the experimental evidence, there is a nonlinear dependence between the activities of different brain regions that is ignored by Pearson correlation as a linear measure. Typically, the average activity of each region is used as input because it is a univariate measure. This dimensional reduction, i.e., averaging, leads to a loss of spatial information across voxels within the region. In this study, we propose using an information-theoretic measure, multivariate mutual information (mvMI), as a nonlinear dependence to find the interaction between regions. This measure, which has been recently proposed, simplifies the mutual information calculation complexity using the Gaussian copula. Using simulated data, we show that the using this measure overcomes the mentioned limitations. Additionally using the real resting-state fMRI data, we compare the level of significance and randomness of graphs constructed using different methods. Our results indicate that the proposed method estimates the functional connectivity more significantly and leads to a smaller number of random connections than the common measure, Pearson correlation. Moreover, we find that the similarity of the estimated functional networks of the individuals is higher when the proposed method is used.

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“…Another resting fMRI study showed different characteristics of the energy landscape in the default mode and frontoparietal networks (Watanabe et al, 2014). Energy and cognitive performance may be related (Jeong et al, 2021), in that energy level may reflect the complexity of the mental work being done or the efficiency of strategies adopted to complete a cognitive task; for example, complex tasks or inefficient strategies may lead to high energy and hence low probability states that would not naturally arise in more typical, less complicated settings. In this work, we provide what is to our knowledge the first study to apply the MEM model to elucidate complex network dynamics in AOS or adult-onset schizophrenia patients using task fMRI data.…”

Section: Introductionmentioning

confidence: 99%

Energy in functional brain states correlates with cognition in adolescent-onset schizophrenia and healthy persons

Theis,

Bahuguna,

Rubin

et al. 2023

Preprint

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Schizophrenia is associated with diverse neuroimage-derived phenotypes such as increased ventricular size, gray matter reduction, reduced white matter anisotropy, and functional differences at rest and while performing a task. Well-established functional MRI analysis methods, including observation of statistically significant differences in first-order regional activation as well as second-order functional connectivity modeling based on correlation of blood oxygenation level dependent (BOLD) signal time-series between pairs of spatially distributed regions, either account for activity in individual regions or pairwise coactivation of regions, respectively. Neither of these methods integrate both first-order and second-order terms to obtain a comprehensive picture of neural dynamics. While it is challenging to incorporate both of these into one framework, the pairwise maximum entropy model (MEM), also called the Ising model, captures both individual and pairwise activity into a single quantity known as energy, which is inversely related to the probability of state occurrence. Here, we apply the MEM framework to task functional MRI data collected on 23 adolescent onset schizophrenia (AOS) since AOS is a more severe form of schizophrenia with more severe cognitive impairments and poorer outcome, in comparison with 53 healthy control subjects while performing the Penn Conditional Exclusion Test (PCET), which measures abstraction and mental flexibility, aspects of executive function that have repeatedly been shown to be impaired in AOS. 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 association. The AOS image-derived phenotype was characterized by spending more time in higher energy brain states that represent lower probability of occurrence and were associated with impaired executive function, suggesting less stable neural dynamics among AOS compared to controls, who spent more time in lower energy states that are more stable. 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, although not among the AOS group. These findings demonstrate that the MEM can integrate and reduce the dimensionality of neuroimaging data, providing information about functional brain states while emphasizing rather than obscuring clinical and cognitive associations, and may shed light on the organizing principles of neural dynamics in patients and controls.

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Empirical Bayes estimation of pairwise maximum entropy model for nonlinear brain state dynamics

Cited by 7 publications

References 44 publications

Diagnostically distinct resting state fMRI energy distributions: A subject-specific maximum entropy modeling study

Diagnostically distinct resting state fMRI energy distributions: A subject-specific maximum entropy modeling study

Multivariate Gaussian Copula Mutual Information to Estimate Functional Connectivity with Less Random Architecture

Energy in functional brain states correlates with cognition in adolescent-onset schizophrenia and healthy persons

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