Testing covariance models for MEG source reconstruction of hippocampal activity

Beamforming is one of the most commonly used source reconstruction methods for magneto- and electroencephalography (M/EEG). One underlying assumption, however, is that distant sources are uncorrelated and here we tested whether this is an appropriate model for the human hippocampal data. We revised the Empirical Bayesian Beamfomer (EBB) to accommodate specific a-priori correlated source models. We showed in simulation that we could use model evidence (as approximated by Free Energy) to distinguish between different correlated and uncorrelated source scenarios. Using group MEG data in which the participants performed a hippocampal-dependent task, we explored the possibility that the hippocampus or the cortex or both were correlated in their activity across hemispheres. We found that incorporating a correlated hippocampal source model significantly improved model evidence. Our findings help to explain why, up until now, the majority of MEG-reported hippocampal activity (typically making use of beamformers) has been estimated as unilateral.

: Sankey flow diagram depicting the split between MEG studies reporting unilateral and bilateral hippocampal activity and which family of inverse solution was implemented.

2) The effect of not accounting for uncorrelated source variance in prior selection
Within the main manuscript, we summed the variance between uncorrelated and correlated sources when designing our priors for cEBB inversion. Whether this is the most appropriate approach is an open question, but here we characterise what would happen if uncorrelated source variance is not accounted for.
Recall Equation 7 in the main manuscript, where we defined the cEBB source covariance matrix as the sum of the original EBB prior and the variance from a set of correlated sources ′.
For this demonstration we shall define an exclusively correlated EBB (xcEBB) covariance matrix as For simplicity, we compared cEBB and xcEBB on our simulations within Heschl's gyri. Figure S2 shows the changes in model evidence where comparing EBB to either cEBB or xcEBB, we see that the two variations of correlated source inversions agreed with each other when selecting the most plausible model. For single sources and uncorrelated, an uncorrelated model (EBB) won, whereas for correlated sources both the correlated models (cEBB and xcEBB) up until SNR values below -30 dB, where it breaks down and believed the correlated sources are in fact not. We observed that the magnitude of the changes were larger for xcEBB models than cEBB models. Figure S3A shows the spatial distribution of the source variance priors used in the model inversions for the mono simulations. Two points are noteworthy, the variance projected into the contralateral hemisphere of the original source relative to the variance in the ipsilateral hemisphere was higher in the xcEBB model than compared to cEBB, a consequence of the variance from the uncorrelated sources being absent. We also noted that in the ipsilateral hemisphere the variance in xcEBB was projected to be more superficial than for cEBB, which was reflected in the localisation of the power, as shown in Figure S3B.

Figure S3: A comparison of cEBB and xcEBB in a single source simulation in Heschl's gyri. A) Spatial distribution of the priors. The solid black circle represents where the correlated source assumptions tried to project a single source into the other hemisphere. xcEBB did this to a larger extent than cEBB. B) Source reconstructed power of oscillations between 8-22
Hz.

3) The relationships between dipole properties and model evidence
Within the main manuscript we speculated that the difficulty in separating bilateral anterior hippocampal sources is largely attributed to the high correlation of the lead fields between the two areas. Here we probe whether some other properties of the sources may also contribute.

Methods
We repeated the dual uncorrelated source simulations from the main manuscript (SNR fixed to -10 dB), but over 256 randomly sampled homologous source pairs in the cortex and 163 hippocampal homolog pairs. We compared the changes in model evidence between the EBB and cEBB model inversions. We would expect the introduction of a correlated source prior to see a reduction in the model evidence. In particular we focussed on 4 properties of the sources: • The correlation of the lead fields between the source pairs • The 2-norm of the lead fields • The distance between the source pairs • The orientation of the sources relative to the radial direction of a single sphere fitted to the anatomy. Figure S4 shows the scatter plots relations between switching source models and the properties of the bilateral dipole sources, cortical sources in grey and hippocampal sources in dark blue for contrast. We see a clear relationship between the correlations in the sources lead fields and the change in model evidence (Fig. S4A).

Results
Interestingly, we observed that if the two source lead fields were strongly anticorrelated then the correct model EBB (as represented as a reduction in model evidence when switching to cEBB) was selected for these simulations. But if the lead fields were positively correlated, cEBB was regarded as the more plausible solution. We observed that in the hippocampus there was a trend for closer sources to prefer the cEBB model, something that we did not observe in the cortex (Fig 4C). The lead field norms (Fig. 4B) and dipole orientation (Fig. 4D) did not show any obvious preference.