Dynamic state allocation for MEG source reconstruction

Abstract

Our understanding of the dynamics of neuronal activity in the human brain remains limited, due in part to a lack of adequate methods for reconstructing neuronal activity from noninvasive electrophysiological data. Here, we present a novel adaptive time-varying approach to source reconstruction that can be applied to magnetoencephalography (MEG) and electroencephalography (EEG) data. The method is underpinned by a Hidden Markov Model (HMM), which infers the points in time when particular states re-occur in the sensor space data. HMM inference finds short-lived states on the scale of 100 ms. Intriguingly, this is on the same timescale as EEG microstates. The resulting state time courses can be used to intelligently pool data over these distinct and short-lived periods in time. This is used to compute time-varying data covariance matrices for use in beamforming, resulting in a source reconstruction approach that can tune its spatial filtering properties to those required at different points in time. Proof of principle is demonstrated with simulated data, and we demonstrate improvements when the method is applied to MEG.

Graph theoretical analysis of resting-state MEG data: Identifying interhemispheric connectivity and the default mode

“…Spurious correlation can result from “leakage” of signal from a reference site to nearby locations such that the source signal is sensitive to the same true sources as the reference signal (Hipp et al, 2012). Approaches based on regression in the frequency or time-domain have been proposed as alternative means to correct for signal leakage for seedbased connectivity analyses (Brookes et al, 2012; Hall et al, 2013; Hipp et al, 2012; Woolrich et al, 2013). …”

Non-linear Parameter Estimates from Non-stationary MEG Data

“…We choose the most probable a posteriori state at each time point, u t ∈ ℝ, using Viterbi decoding (Rezek and Roberts, 2005; Woolrich et al, 2013): $u_t={\displaystyle \underset{\forall k\in K}{qopnameargqopnamemax}}\left\{Pfalse({\mathbf{s}}_t=k|\mathbf{Y}false)\right\}.$ The resulting HMM state time courses can then be used to pool the data over distinct and potentially short-live periods on time to compute time-varying data covariance matrices, as follows: ${\mathbf{C}}_{\mathbf{u}false(tfalse)}={\mathbf{C}}_{false(\mathbf{u}false(tfalse)=kfalse)}=\frac{1}{T_{k-1}}{\displaystyle \sum _{j=1}^{T_k}}false({\mathbf{Y}}_k-{\stackrel{-}{\mathbf{Y}}}_{k}false){false({\mathbf{Y}}_k-{\stackrel{-}{\mathbf{Y}}}_{k}false)}^{\top }$ where Y k comprises the time-instants for which the state k is the most probable, T k is the length of Y k , and ${\stackrel{-}{\mathrm{boldY}}}_k\in {ℝ}^{C\times 1}$ is the mean over those time points.…”

“…The data covariance matrices obtained for the HMM states are distinct from one another unlike the short time strategy that shows very similar covariance estimates for all windows. Additionally, to obtain an objective comparison between the covariance matrices, we used the Symmetrised Kullback-Leibler (KL) divergence , which provides a measure of dissimilarities for the different states k, j (Woolrich et al, 2013): $S_{KL}(k,j)=0.5\mathrm{tr}({boldnormal\Sigma }_j^{-1}{boldnormal\Sigma }_k)+0.5\mathrm{tr}({boldnormal\Sigma }_k^{-1}{boldnormal\Sigma }_j)-2C,$ where larger values of S KL ( k, j ) indicate larger differences in the covariance matrices. Figures 5D,E show the symmetric KL computed between all five states and windows, respectively, where it can be seen that there are minimal differences between the covariances estimated with the short time strategy.…”

Quantifying the performance of MEG source reconstruction using resting state data

“…http://dx.doi.org/10.1101/248252 doi: bioRxiv preprint first posted online Jan. 15, 2018; analysis (PCA) to derive 40 components of unit variance and mean (Woolrich et al, 2013 estimates averaged across those four inversions for each subject. As the HMM was performed on 151 individual, rather than group concatenated data, state numbers did not directly correspond across 152 subjects.…”