[Mne_analysis] Time-frequency Beamforming - and possible implications for EEG-fMRI

[Dylan Mann-Krzisnik]

        External Email - Use Caution        

Dear MNE experts,

Our group is testing different beamforming approaches to EEG data
simultaneously recorded with fMRI using MNE Python. We'd like to analyze
the time-frequency EEG source-space correlates of BOLD-fMRI, both at rest
and following primary sensory tasks. We are trying to figure out which
beamforming approach would best suite our needs.

There seems to be 3 main candidates of beamformers for our analysis. I'll
lay out what seems to me to be the potential advantages and nuances of
these 3 candidate approaches. Apologies for any conceptual mistakes on my
behalf.

 - LCMV, as suggested for EEG-fMRI in Brookes et al. 2008. The gradient and
ballistocardiogram (BCG) artifacts induced within EEG data by the EPI
sequence can be accounted for by proper design of noise covariance
matrices. Linear time-frequency transforms could be performed in sensor
space and projected into source space before performing additional
non-linear transforms (eg Hilbert > source-space projection > compute
magnitude). Good for blocking out interfering signals.

- DICS, similar to LCMV but in frequency-domain. Moreover, to my knowledge,
DICS differ from LCMV due to their respective linear constraints. DICS à la
Gross et al. 2001 imposes a unit-gain constraint for scanning location *r*,
whereas LCMV further imposes a null-gain constraint onto regions other than
the scanning region (this is my understanding from Sekihara & Nagarajan
2008). Good for reconstructing networks of coherent sources.

- 5D time-frequency beamforming à la Dalal et al. 2008, where weights are
optimized for individual narrowbands in a time-resolved manner. Whereas
DICS use cross-spectra to optimize the fllter weights, this 5D beamforming
use time-domain correlations for optimizing the filters, which are then
later used for frequency-domain analysis. Good for resolving
frequency-specific time-varying source power.

My impression is that the 5D beamforming approach, as implemented by Dalal
and colleagues, could be of interest to us in light of our research
activities. Perhaps this is especially true if we incorporate the EPI
gradient and BCG artifacts into estimation of noise covariance matrices,
similarly to Brookes et al 2008.
The MNE-Python implementation of this method (ie tf_dics) uses DICS for
every time-frequency window rather than SAM, as noted in
https://mne.tools/stable/generated/mne.beamformer.tf_dics.html#r24787c541d0a-1.
This implies that frequency-domain CSD matrices are computed rather than
time-domain covariance matrices for optimizing spatial filters for each
time-frequency window.

In light of all of this, here are a few questions:

- Is it reasonable to incorporate gradient and BCG artifacts within
MNE-Python's tf_dics method?
- If so, does calculating the CSD matrices rather than covariance matrices
for these artifacts make a difference?
- Is the pass-band constraint employed for LCMV desirable for
time-frequency analysis, if the source-space *network coherence* is not of
primary interest?
- Would tf_dics be preferred over time-frequency SAM if source-space
network coherence is of primary interest? Otherwise, would time-frequency
SAM be preferred over tf_dics for resolving time-varying narrowband power?

I have additional thoughts and questions, but the email might start being a
bit heavy. Any clarification, even if partial, is deeply appreciated. I'd
be glad to provide more explanations if this helps clarify any question
I've asked or statement I've mentioned.

Kind regards,

Dylan Mann-Krzisnik - M.Sc. Graduate Researcher
Biosignals and Systems Analysis Lab, McGill University
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