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Hi Michal,
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<div class=""><b class="">Question</b>: </div>
<div class="">What is "the proper" value of the cfg.normalizeparam for ft_prepare_leadfield function (<a href="https://www.fieldtriptoolbox.org/reference/ft_prepare_leadfield/" target="_blank" class="">https://www.fieldtriptoolbox.org/reference/ft_prepare_leadfield/</a>)
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<div class="">OR in other words</div>
<div class="">Should the distribution of the leadfield norms across brain volume be uniform?</div>
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<div>I don’t see why this would need to be the case. It probably depends on the type of analysis you want to perform, and what kind of inverse algorithm you use.</div>
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<div class=""><b class="">Question background:</b></div>
<div class="">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. </div>
<div class="">As <span style="white-space: pre-wrap;" class="">Jörn</span> Horshig pointed (<a href="https://mailman.science.ru.nl/pipermail/fieldtrip/2013-July/006759.html" target="_blank" class="">https://mailman.science.ru.nl/pipermail/fieldtrip/2013-July/006759.html</a>),
there is no correct way of normalizing. </div>
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<div>I agree with Jörn.</div>
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<div class="">I have plotted leadfield norm for different setting:<br class="">
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<div class=""><span id="cid:ii_km0pbzzh0"><normalizeparam_0_0_SVD.png></span><br class="">
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<div class="">Fig.1. cfg.normalizeparam = 0.0 (leadfield norm <b class="">increase</b> radially outwards from the center; 10^{-9} order of magnitude)</div>
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<div class=""><span id="cid:ii_km0pccch1"><normalizeparam_0_5_SVD.png></span><br class="">
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<div class="">Fig.2. cfg.normalizeparam = 0.5 (suggested default value; leadfield norms are more or less <b class="">uniformly distributed</b>)<br class="">
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<div class=""><span id="cid:ii_km0pcpwi2"><normalizeparam_1_0_SVD.png></span></div>
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<div class="">Fig.3. cfg.normalizeparam = 1.0 (the value used in the HCP beamforming; leadfield norm <b class="">decrease</b> radially outwards from the center; 10^{+8} order of magnitude)<br class="">
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<div class=""><b class="">Further details:</b></div>
<div class="">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. </div>
<div class="">As the data come from the Human Connectome Project database, I adapted leadfield computation from their beamforming script (<span style="background-color:transparent" class="">hcp_bfblpenv.m from </span>megconnectome-3.0 pipeline):</div>
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<div class=""><font face="monospace" class="">1. allChansMEG = ft_channelselection({'MEG'}, grad.label);<br class="">
2. cfg = [];<br class="">
3. cfg.grid = grid; % Grid for individual's brain in MEG sensor space<br class="">
4. cfg.vol = vol;<br class="">
5. cfg.grad = grad;<br class="">
6. cfg.reducerank = 2; % (default = 3 for EEG, 2 for MEG)<br class="">
7. cfg.normalize = 'yes' ; % Normalise Leadfield: 'yes' for beamformer<br class="">
8. cfg.normalizeparam = 1; % depth normalization parameter<br class="">
9. cfg.channel = allChansMEG;<br class="">
10. lfg = ft_prepare_leadfield(cfg);<br class="">
11. lfg.label = allChansMEG;<br class="">
12. % optimization of the leadfield orientation (SVD approach) <br class="">
13. ratio = 0.07;<br class="">
14. lambda = ratio * trace(Cy)/size(Cy,1);<br class="">
15. invCy = pinv(Cy + lambda * eye(size(Cy)));<br class="">
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17. for iDip = 1:nDip <br class="">
18. if ~isempty(lfg.leadfield{iDip})<br class="">
19. lf = lfg.leadfield{iDip}(indB,:); <br class="">
20. [u, s, v] = svd(real(pinv(lf' * invCy *lf)));<br class="">
21. eta = u(:,1);<br class="">
22. lf = lf * eta;<br class="">
23. lfgSVD.leadfield{iDip} = lf;<br class="">
24. else<br class="">
25. lfgSVD.leadfield{iDip} = [];<br class="">
26. end<br class="">
27. end<br class="">
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<div class="">Line 8. contains the cfg.normalizeparam setting for which I try to figure out the correct value.</div>
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<div class="">Leadfield norms were computed this way:</div>
<div class=""><font face="monospace" class="">lfgNorm = cellfun(@(x) norm(x, 'fro'), lfgSVD.leadfield);</font></div>
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<div class="">Thank you very much for your hints and suggestions.</div>
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The normalization parameter only affects the ’scale’ of the vector leadfield (as long as you don’t do a per-column normalisation, which does not make sense to begin with in my opinion: since you specified cfg.normalize = ‘yes’ (and not ‘column’, you’re fine),
so the beamformer spatial filter’s shape will not be affected. Thus, the overall spatial filter output will not change in shape (i.e. temporal characteristics), only in amplitude.</div>
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<div>So, in the end it boils down to the question what you want to do with the beamformer output in terms of post-processing, whether or not you need to worry about the normalization parameter to begin with. In an experimental setting we’d always compare across
conditions (or against a baseline), so any location specific (and uninteresting) depth bias (either or not ‘corrected’ by a leadfield normalisation) will drop out of the equation anyhow.</div>
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<div>Best wishes,</div>
<div>Jan-Mathijs</div>
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<div class="">Kind regards,</div>
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<div dir="ltr" class="">Michał Komorowski, MSc
<div class=""><font size="1" class="">Nicolaus Copernicus University in Toruń</font></div>
<div class=""><font size="1" class="">Faculty of Physics, Astronomy and Informatics</font></div>
<div class=""><span style="font-size:x-small" class="">Department of Informatics</span></div>
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