2.7. State spatial maps

Following Baker et al. (2014), anatomical regions exhibiting state-specific activity (i.e., changes in oscillatory amplitudes during an HMM state, relative to what is happening on average over time) were mapped by computing partial correlations within the general linear modeling (GLM) framework. Several types of maps were derived. First, to determine which of the 38 a priori ROIs show activity changes during each network state, partial correlations were computed using the time-courses of the HMM states and the time-courses of the wide-band oscillatory amplitudes in each ROI. While the HMM was inferred on ROI time-courses in order to reduce the dimensionality of the data to a computationally manageable amount, this did somewhat limit the potential spatial resolution. Therefore, to map state-specific activity within the ROIs with higher resolution, we also calculated the partial correlations of the HMM state time-courses using the wide-band amplitude envelope at each brain voxel. An additional map was created based on correlations of each HMM state time-course with the wide-band amplitude envelope at each brain voxel that were computed selectively within time-intervals of the high occurrence rate of the state (presented in the Appendix D, Fig. D.3). Finally, to map frequency-specific activity during HMM states, the partial correlations of the HMM state time-courses were computed with the narrow-band amplitude envelope at each voxel separately for the theta, alpha, and beta frequency bands.

A similar approach was employed to map the regions where the time-courses of the ultra-slow electrophysiological potentials correlate with the occurrence rates of the fast HMM states. The long timescale time-course of the occurrence rate fluctuations for each HMM state was quantified as changes in the proportion of time spent in the state within 5-sec-long sliding windows (half a cycle length in 0.1 Hz oscillation). Partial correlations were computed between these state-rate time-courses and the lowpass filtered (<0.1 Hz) electrophysiological signal fluctuations at each voxel (the analysis of the long timescale structure of the HMM states is presented in the Appendix D).

In all GLM analyses conducted to compute the cortical maps, we employed a design matrix (T × K), where K is the number of states and each of the K columns is a state time-course with T time-points (Brookes et al., 2004; Friston et al., 1996). For each participant, at each ROI/voxel, a multiple linear regression was performed with the time-course of the electrophysiological activity as the dependent variable. Prior to fitting the GLM, both the design matrix and the ROI/voxel data were normalized to have zero mean and unit variance. Estimates of the partial correlation coefficients between each state and the ROI/voxel data yielded a set of K spatial maps. These maps were averaged across participants and visualized on the cerebral cortex. In the ultra-slow analysis, averaging across participants was based on the absolute values of the coefficients to account for the ± π phase ambiguity of MEG-based estimates of the cortical activity, which are influenced by the arbitrary default orientation of elementary current dipole sources constrained to the local cortical anatomy (Baillet et al., 2001).