Imaging of brain electric field networks

Reviewer #1 (Public Review):

The paper proposes a new source reconstruction method for electroencephalography (EEG) data and claims that it can provide far superior spatial resolution than existing approaches and also superior spatial resolution to fMRI. This primarily stems from abandoning the established quasi-static approximation to Maxwell's equations.

The proposed method brings together some very interesting ideas, and the potential impact is high. However, the work does not provide the evaluations expected when validating a new source reconstruction approach. I cannot judge the success or impact of the approach based on the current set of results. This is very important to rectify, especially given that the work is challenging some long-standing and fundamental assumptions made in the field.

I also find that the clarity of the description of the methods, and how they link to what is shown in the main results hard to follow.

I am insufficiently familiar with the intricacies of Maxwell's equations to assess the validity of the assumptions and the equations being used by WETCOW. The work therefore needs assessing by someone more versed in that area. That said, how do we know that the new terms in Maxwell's equations, i.e. the time-dependent terms that are normally missing from established quasi-static-based approaches, are large enough to need to be considered? Where is the evidence for this?

I have not come across EFD, and I am not sure many in the EEG field will have. To require the reader to appreciate the contributions of WETCOW only through the lens of the unfamiliar (and far from trivial) approach of EFD is frustrating. In particular, what impact do the assumptions of WETCOW make compared to the assumptions of EFD on the overall performance of SPECTRE?

The paper needs to provide results showing the improvements obtained when WETCOW or EFD are combined with more established and familiar approaches. For example, EFD can be replaced by a first-order vector autoregressive (VAR) model, i.e. y_t = A y_{t-1} + e_t (where y_t is [num_gridpoints x 1] and A is [num_gridpoints x num_gridpoints] of autoregressive parameters).

The authors' decision not to include any comparisons with established source reconstruction approaches does not make sense to me. They attempt to justify this by saying that the spatial resolution of LORETA would need to be very low compared to the resolution being used in SPECTRE, to avoid compute problems. But how does this stop them from using a spatial resolution typically used by the field that has no compute problems, and comparing with that? This would be very informative. There are also more computationally efficient methods than LORETA that are very popular, such as beamforming or minimum norm.

In short, something like the following methods needs to be compared:

(1) Full SPECTRE (EFD plus WETCOW)
(2) WETCOW + VAR or standard ("simple regression") techniques
(3) Beamformer/min norm plus EFD
(4) Beamformer/min norm plus VAR or standard ("simple regression") techniques

This would also allow for more illuminating and quantitative comparisons of the real data. For example, a metric of similarity between EEG maps and fMRI can be computed to compare the performance of these methods. At the moment, the fMRI-EEG analysis amounts to just showing fairly similar maps.

There are no results provided on simulated data. Simulations are needed to provide quantitative comparisons of the different methods, to show face validity, and to demonstrate unequivocally the new information that SPECTRE can _potentially_ provide on real data compared to established methods. The paper ideally needs at least 3 types of simulations, where one thing is changed at a time, e.g.:

(1) Data simulated using WETCOW plus EFD assumptions
(2) Data simulated using WETCOW plus e.g. VAR assumptions
(3) Data simulated using standard lead fields (based on the quasi-static Maxwell solutions) plus e.g. VAR assumptions

These should be assessed with the multiple methods specified earlier. Crucially the assessment should be quantitative showing the ability to recover the ground truth over multiple realisations of realistic noise. This type of assessment of a new source reconstruction method is the expected standard.

Reviewer #2 (Public Review):

Summary:

The manuscript claims to present a novel method for direct imaging of electric field networks from EEG data with higher spatiotemporal resolution than even fMRI. Validation of the EEG reconstructions with EEG/FMRI, EEG, and iEEG datasets are presented. Subsequently, reconstructions from a large EEG dataset of subjects performing a gambling task are presented.

Strengths:

If true and convincing, the proposed theoretical framework and reconstruction algorithm can revolutionize the use of EEG source reconstructions.

Weaknesses:

There is very little actual information in the paper about either the forward model or the novel method of reconstruction. Only citations to prior work by the authors are cited with absolutely no benchmark comparisons, making the manuscript difficult to read and interpret in isolation from their prior body of work.

Author response:

The authors plan to respond in full in due course.