[FieldTrip] Leadfield normalization: cfg.normalizeparam value

[Michał Komorowski]

Dear Researchers,

*Question*:
What is "the proper" value of the cfg.normalizeparam for
ft_prepare_leadfield function (
https://www.fieldtriptoolbox.org/reference/ft_prepare_leadfield/) ?
OR in other words
Should the distribution of the leadfield norms across brain volume be
uniform?

*Question background:*
I have noticed that the default value is 0.5, however in the beamforming
routines from the Human Connectome Project the value is set to 1.0.
As Jörn Horshig pointed (
https://mailman.science.ru.nl/pipermail/fieldtrip/2013-July/006759.html),
there is no correct way of normalizing.
I have plotted leadfield norm for different setting:

[image: normalizeparam_0_0_SVD.png]
Fig.1. cfg.normalizeparam = 0.0 (leadfield norm *increase* radially
outwards from the center; 10^{-9} order of magnitude)

[image: normalizeparam_0_5_SVD.png]
Fig.2. cfg.normalizeparam = 0.5 (suggested default value; leadfield norms
are more or less *uniformly distributed*)

[image: normalizeparam_1_0_SVD.png]
Fig.3. cfg.normalizeparam = 1.0 (the value used in the HCP beamforming;
leadfield norm *decrease* radially outwards from the center; 10^{+8} order
of magnitude)


*Further details:*
I am preparing a scalar leadfield (dipole orientations optimized using an
SVD approach) for beamforming of the resting-state MEG data for further
spectral analyses on the reconstructed sources level.
As the data come from the Human Connectome Project  database, I adapted
leadfield computation from their beamforming script (hcp_bfblpenv.m
from megconnectome-3.0
pipeline):

1.    allChansMEG         = ft_channelselection({'MEG'}, grad.label);
2.    cfg = [];
3.    cfg.grid            = grid; % Grid for individual's brain in MEG
sensor space
4.    cfg.vol             = vol;
5.    cfg.grad            = grad;
6.    cfg.reducerank      = 2; % (default = 3 for EEG, 2 for MEG)
7.    cfg.normalize       = 'yes' ; % Normalise Leadfield: 'yes' for
beamformer
8.    cfg.normalizeparam  = 1; % depth normalization parameter
9.    cfg.channel         = allChansMEG;
10.   lfg                 = ft_prepare_leadfield(cfg);
11.   lfg.label           = allChansMEG;
12.   % optimization of the leadfield orientation (SVD approach)
13.   ratio  = 0.07;
14.   lambda = ratio * trace(Cy)/size(Cy,1);
15.   invCy  = pinv(Cy + lambda * eye(size(Cy)));
16.
17.   for iDip = 1:nDip
18.         if ~isempty(lfg.leadfield{iDip})
19.             lf = lfg.leadfield{iDip}(indB,:);
20.             [u, s, v] = svd(real(pinv(lf' * invCy *lf)));
21.             eta = u(:,1);
22.             lf  = lf * eta;
23.             lfgSVD.leadfield{iDip} = lf;
24.         else
25.             lfgSVD.leadfield{iDip} = [];
26.         end
27.   end

Line 8. contains the cfg.normalizeparam setting for which I try to figure
out the correct value.

Leadfield norms were computed this way:
lfgNorm  = cellfun(@(x) norm(x, 'fro'), lfgSVD.leadfield);

Thank you very much for your hints and suggestions.

Kind regards,
Michał Komorowski, MSc
Nicolaus Copernicus University in Toruń
Faculty of Physics, Astronomy and Informatics
Department of Informatics
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