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

Reliability of energy landscape analysis of resting-state functional MRI data

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.

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

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.

Low-frequency repetitive transcranial magnetic stimulation alters the individual functional dynamical landscape

Repetitive transcranial magnetic stimulation (rTMS) is a noninvasive approach to modulate brain activity and behavior in humans. Still, how individual resting-state brain dynamics after rTMS evolves across different functional configurations is rarely studied. Here, using resting state fMRI data from healthy subjects, we aimed to examine the effects of rTMS to individual large-scale brain dynamics. Using Topological Data Analysis based Mapper approach, we construct the precise dynamic mapping (PDM) for each participant. To reveal the relationship between PDM and canonical functional representation of the resting brain, we annotated the graph using relative activation proportion of a set of large-scale resting-state networks (RSNs) and assigned the single brain volume to corresponding RSN-dominant or a hub state (not any RSN was dominant). Our results show that (i) low-frequency rTMS could induce changed temporal evolution of brain states; (ii) rTMS didn't alter the hub-periphery configurations underlined resting-state brain dynamics; and (iii) the rTMS effects on brain dynamics differ across the left frontal and occipital lobe. In conclusion, low-frequency rTMS significantly alters the individual temporo-spatial dynamics, and our finding further suggested a potential target-dependent alteration of brain dynamics. This work provides a new perspective to comprehend the heterogeneous effect of rTMS.

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

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.