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

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.

Keywords: Bipolar disorder; Computational psychiatry; Generalized Ising model; Major depression; Network neuroscience; Schizophrenia; Transdiagnostic approach.

Figure 1.. Post-processing and Binarization.

All x-axes show time in fMRI volumes, Repetition Time (TR); each TR is 0.735 seconds. A) The preprocessed BOLD signals in amplitude of arbitrary units for a single subject for the 8 bilateral nodes: POS1, p32m aTPOJ3, and PGi in both hemispheres. B) The z-scored nodal time-series has an average centered at zero and is scaled to a standard deviation of one. C) The global signal across all z-scored nodes in the entire brain is shown, followed by D) the z-scores after subtracting this value. Finally, E) the time series are binarized at the threshold of zero, where the y-axis is now node index, rather than amplitude. White cells indicate the “on” nodes at the given time, meaning that the value in D for that node was greater than zero, while black cells indicate “off” nodes.

Figure 2.. MEM Fits.

Bilateral DMN nodes (top row) A: Two histograms, psychiatric disorders group (N=132) in yellow and pooled HC (N=132) in black, are compared and not significantly different by a KS-test (KS=0.152, p=0.087). Fitness (x-axis) is the correlation between predicted P(V_k) according to the model and observed P(V_k) per individual. B) All unique possible states are shown for all subjects according to their probability predicted from the MEM (x-axis) versus their observed probability (y-axis). Black circles represent data from controls, yellow points represent data from the patient group. Left Hemisphere DMN nodes (Middle row) C: Fitness histograms for pooled patient group (yellow) and pooled HC (black) are compared and not significantly different (KS=0.114, p=0.342). D) All unique possible states are shown for all subjects according to their predicted probability (x-axis) versus their observed probability (y-axis). Black circles represent data from controls, yellow points represent data from the patient group. Right Hemisphere DMN nodes (Bottom row) E: Fit histograms for pooled patients (yellow) and pooled HC (black) are compared and not significantly different (KS=0.091, p=0.626). F: All unique possible states are shown for all subjects according to their predicted probability (x-axis) versus their observed probability (y-axis). Black circles represent data from controls, yellow points represent data from the patient group.

Figure 3.. Comparison of MLE- and image-derived MEM coefficients.

Bilateral DMN nodes (top row).A) Two histograms, pooled patients (N=132) in yellow and pooled HC (N=132) in black are compared. Each histogram represents the population-wide distribution of correlations between the second-order J parameter (x-axis) compared to edge weights of the FC (y-axis). B) Scatter plots of all subjects and all parameter values showing a strong relationship between J and FC; black circles are HC; yellow points are patients. C) Histograms for group-wise distributions of correlations between h from the MEM and the image-derived coefficients in equation (3). D) Individual scatter plots for all participants between h (x-axis) and the image-derived coefficients from equation (3) (y-axis). Left Hemisphere DMN nodes (Middle row) E) Group-wise population histograms of J-to-FC similarity. F) All individual-level scatter plot data for corresponding parameters in J (x-axis), and FC (y-axis). G) Histograms for group-wise distributions of correlations between h from the MEM and the image-derived coefficients from equation (3). H) Individual scatter plots for all participants between h (x-axis) and the image-derived coefficients (y-axis). Right Hemisphere DMN nodes (Bottom row) I) Group-wise population histograms of J-to-FC similarity. J) All individual-level scatter plot data for corresponding parameters in J (x-axis), and FC (y-axis). K) Histograms for group-wise distributions of correlations between h from the MEM and the image-derived coefficients from equation (3). H) Individual scatter plots for all participants between h (x-axis) and the image-derived coefficients (y-axis).

Figure 4.. Energy Profiles by Clinical Group.

Bilateral: top row. Left Hemisphere: middle row. Right Hemisphere: bottom row. Statistics reported in plots are KS statistics and associated p-value. A) bilateral: The group-wise average energy profile of depression compared to controls. B) bilateral: bipolar/manic compared to controls. C) bilateral: SZ/SA compared to controls. D) left hemisphere: depression compared to controls. E) left hemisphere: bipolar/manic compared to controls. F) left hemisphere: SZ/SA compared to controls. G) right hemisphere: persons with depression compared to controls. H) right hemisphere: bipolar/manic compared to controls. I) right hemisphere: SZ/SA compared to controls.