A Novel Hidden Markov Approach to Studying Dynamic Functional Connectivity States in Human Neuroimaging

Abstract

Introduction: Hidden Markov models (HMMs) are a popular choice to extract and examine recurring patterns of activity or functional connectivity in neuroimaging data, both in terms of spatial patterns and their temporal progression. Although many diverse HMMs have been applied to neuroimaging data, most have defined states based on activity levels (intensity-based [IB] states) rather than patterns of functional connectivity between brain areas (connectivity-based states), which is problematic if we want to understand connectivity dynamics: IB states are unlikely to provide comprehensive information about dynamic connectivity patterns. Methods: We addressed this problem by introducing a new HMM that defines states based on full functional connectivity (FFC) profiles among brain regions. We empirically explored the behavior of this new model in comparison to existing approaches based on IB or summed functional connectivity states using the Human Connectome Project unrelated 100 functional magnetic resonance imaging "resting-state" dataset. Results: Our FFC model discovered connectivity states with more distinguishable (i.e., unique and separable from each other) patterns than previous approaches, and recovered simulated connectivity-based states more faithfully than the other models tested. Discussion: Thus, if our goal is to extract and interpret connectivity states in neuroimaging data, our new model outperforms previous methods, which miss crucial information about the evolution of functional connectivity in the brain. Impact statement Hidden Markov models (HMMs) can be used to investigate brain states noninvasively. Previous models "recover" connectivity from intensity-based hidden states, or from connectivity "summed" across nodes. In this study, we introduce a novel connectivity-based HMM and show how it can reveal true connectivity hidden states under minimal assumptions.

Keywords: functional connectivity; hidden Markov model; neuroimaging; resting-state fMRI; state patterns.

FIG. 1.

Verification of HMM connectivity-based states. (A) The artificially induced state sequence depicted which networks exhibited slightly increased within- and/or between-network connectivity. Outputted state sequences from (B) IB HMM, (C) SFC HMM, and (D) FFC HMM when connectivity states were induced. FFC HMM recovers simulated states better than the other two models; see main text for details. FCC, full functional connectivity; HMM, hidden Markov model; IB, intensity based; SFC, summed functional connectivity.

FIG. 2.

Differential functional connectivity states for SFC HMM (top row), FFC HMM (middle row), and IB HMM (bottom row). The summed connectivity vectors (summed across one dimension) are displayed below each state. The summed values for SFC were directly outputted from the model .while those for IB and FFC were calculated as described in Connectivity State Pattern Analysis section.

FIG. 3.

Pairwise comparisons between connectivity states discovered by each HMM show that each model recovered eight unique states. A one-to-one match between two states recovered by two different models would appear as a single orange/yellow square (high Pearson correlation) among seven green/blue squares (low Pearson correlation) in those two states' row or column combination. However, (A) FFC HMM-recovered states showed no unique correspondence based on similarity to those recovered by SFC HMMs by visual inspection, and (D) no stability threshold (see the RAICAR analysis to discover number of hidden states, Preliminary Model Fitting and Analysis and Assessing Model Fits sections and Supplementary Appendices A.3 and C.1) can lead to any semblance of a one-to-one match between FFC HMM-recovered states and those recovered by SFC HMM. Similar results were found for pairwise comparisons between FFC HMM and IB HMM states (B, E) and between SFC HMM and IB HMM states (C, F). RAICAR, Ranking and Averaging Independent Component Analysis by Reproducibility.

FIG. 4.

Viterbi Paths for (A) IB HMMs, (B) SFC HMMs, and (C) FFC HMMs. The Viterbi paths for the SFC and FFC HMMs are much “smoother” (i.e., more spread out in time) than those of IB HMMs. Within the connectivity-based HMMs, FFC HMMs' Viterbi path exhibits fewer and less frequent switches than SFC HMMs, which may have occurred because of the selected number of hidden states or the total number of components fitted. See main text for detailed discussion.