A state-space model of cross-region dynamic connectivity in MEG/EEG
Cross-region dynamic connectivity, which describes the spatio-temporal dependence of neural activity among multiple brain regions of interest (ROIs), can provide important information for understanding cognition. For estimating such connectivity, magnetoencephalography (MEG) and electroencephalography (EEG) are well-suited tools because of their millisecond temporal resolution. However, localizing source activity in the brain requires solving an under-determined linear problem. In typical two-step approaches, researchers first solve the linear problem with generic priors assuming independence across ROIs, and secondly quantify cross-region connectivity. In this work, we propose a one-step state-space model to improve estimation of dynamic connectivity. The model treats the mean activity in individual ROIs as the state variable and describes non-stationary dynamic dependence across ROIs using time-varying auto-regression. Compared with a two-step method, which first obtains the commonly used minimum-norm estimates of source activity, and then fits the auto-regressive model, our state-space model yielded smaller estimation errors on simulated data where the model assumptions held. When applied on empirical MEG data from one participant in a scene-processing experiment, our state-space model also demonstrated intriguing preliminary results, indicating leading and lagged linear dependence between the early visual cortex and a higher-level scene-sensitive region, which could reflect feedforward and feedback information flow within the visual cortex during scene processing.
The paper elegantly presents an approach to source localization that is applicable to both MEG and EEG data (and other modalities), highly sensitive to temporal variations and allows direct extraction of statistical dependance and time lags, from a set of mutually correlated signals (linearly generated from sources). One of the main attributes advocated in this work is that separation into statistically separable sources need not be done independently of causality, or that of time-lag analysis of sources. Rather, the authors present a single model that decomposes the data into sources and models their time dependence, based on expectation-maximization approach. An application to MEG analysis is presented.  
The Introduction is generally very good (with minor exceptions described below).   Comparison to other models is required. Only one alternative approach is compared to the suggested method and another one-step model (DCM) is not lawfully described.    I suggest the authors discuss other applications beside EEG/MEG as many of the alternative approaches were shown to be useful to many modalities.   Please introduce consistent spacing before citations (in many cases the space doe not exist at all).   Specific comments:  1. 46. Perhaps the authors can also point to the ill-poshness of the problem due to SNR and destructive local activities: even if we had the number of observation roughly equal to the number of sources still unravelling source activity from scalp dynamics would have been a major challenge. Please elaborate if this is not the case.  2. 54. Please expand “based on different assumptions.” or if those assumptions are already mentioned before, say it.  3. 60. Perhaps the authors can add a reference to the claim? 4. 61. Is this claim addressed later? If yes, say so, if not, expand this claim, or give proper reference, or omit this claim altogether.  5. 77. describe the model “in detail”.  6. 69-71. The text seems to undermine Ref 1. Please explain why DCM is irrelevant to the claim. If it’s relevant please expand on this issue.  7. 85. “includes”. 8. 94. In what neighborhood, of the sensor? Not clear: please revise the entire sentence, including the improper use of  “according to the physics” (92), as the discussed notions combine physical (and biophysical) attributes with anatomical ones.  9. 100 “Gaussian distribution”. 10. 108. “The state variable u_t…” In general  I suggest sentences won’t start with symbols.  11. The definition of A_0 should be fixed. It doesn’t make sense to say $l$ and $\forall l$ — Please make it more formal.  12. 122. “Equations…” 13. 123. The way the sentence is written should be “is a 0/1…”. Later the authors can omit “in the lth row and ith column”.  14. 123. The way Q_J is described is not a proper definition (not clear what is the exact value of Q_J for the case corresponding to equation 4). In fact the “only if” could be a wrong assertion, if I understand correctly  what is meant by the authors.   15. I don’t see how the authors “integrated J_t out.” Isn’t it just a substitution?  16. 132-134 is clear but informal. Please improve the text by making the definitions more formal/correct.  17. 134. Do you need the square when designating the Forbenuis norm? Isn’t the norm given by the notation || ||_F ? 18. 142. “and” is repeating twice.  19. 190. Typo: “pericalcarine suci.”  20. 194: Typo: “entries was.” 21. 198-199. It’s not so clear what is meant by “were different.”  22. 200. Do you mean “nanoamper”? 23. 215. “which underlines recognition of what we see” is not entirely clear and also a too bold description. 24. 244-247. The statistical analysis is not presented in a clear manner. It is also not clear how the p-values are derived given that the T^2 observations are statistically dependent. Please make this part clearer and make sure the assumptions of the statistical test are met.  25. 289. The reference to “cognitive processes” as an exceptional case is not clear, whereas the authors suggest a simple dynamical behavior for other neural processes. The DCM model should be extended also here (and earlier in the paper).  26. 290. The reasoning for not comparing against DCM is weak and should be improved (“Part of of the reason…” — the comparison is required). The authors should make efforts to directly compare their results to DCM.     Ref 1. David et al. “Dynamic causal modeling of evoked responses in EEG and MEG”