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

Area of Science:

• Neuroscience
• Computational Neuroscience
• Biostatistics

Background:

• Resting-state functional magnetic resonance imaging (rsfMRI) reveals complex brain state dynamics.
• Pairwise maximum entropy models (pMEM) are effective for exploring nonlinear brain dynamics but typically require large sample sizes.
• Individual-level analysis of brain dynamics is challenging due to data limitations.

Purpose of the Study:

• To develop and validate an empirical Bayes estimation method (VEM-MEM) for individual pMEM using the variational expectation-maximization algorithm.
• To assess the performance of VEM-MEM in estimating individual brain dynamics with small sample sizes.
• To investigate group differences in nonlinear brain dynamics between children with ADHD and typically developing children.

Main Methods:

• Proposed an empirical Bayes estimation approach, VEM-MEM, for individual pMEM.
• Evaluated VEM-MEM performance through simulations with varying sample and network sizes.
• Applied VEM-MEM to rsfMRI data from children with ADHD and controls, focusing on default mode, executive control, and salient networks.

Main Results:

• VEM-MEM reliably estimates individual pMEM parameters even with small sample sizes by incorporating group information.
• Nonlinear dynamic properties derived from pMEM differ significantly between ADHD and control groups.
• pMEM parameters demonstrated higher sensitivity to group differences and stronger correlations with ADHD behavior scores than traditional functional connectivity.

Conclusions:

• The VEM-MEM method enables reliable estimation of individual pMEM, overcoming sample size limitations.
• This approach effectively characterizes individual brain dynamics by leveraging group-level information.
• VEM-MEM offers a sensitive tool for detecting neuroimaging-based biomarkers for conditions like ADHD.