[Eeglablist] DIPFIT and residual variance

[Martin Randau]

Dear all

I have a question about the 15% residual variance threshold suggested in the tutorial and used in papers.

It is mentioned in Delorne et al (2012) that the ‘dipolarity’ reflects the quality of decomposition, where dipolarity is defined as "the number of returned components whose scalp maps can be fit to the scalp projection of a single equivalent dipole with less than a specified error threshold (specified as percent residual variance)”.

However, I find the wording in the tutorial and in several papers (Rissling et al (2014), MacLean (2014)) to be confusing, e.g.:

Rissling, 2014:

"For each IC, the 3-Dlocation of the best-fitting equivalent current dipole was estimated using DIPFIT 2.2 (EEGLAB plug-in using Fieldtrip toolbox functions, developed by Robert Oostenveld) using a Montreal Neurological Institute (MNI) template head model. The close resemblance of the projection patterns of many EEG independent component (IC) processes to the projection of a single equivalent current dipole is compatible with an origin in (partially) coherent local field activity across a single cortical area or patch (Delorme et al., 2012). Since the ‘dipolarity’ of the IC scalp maps has been shown to reflect quality of de- composition (Delorme et al., 2012), ICs whose equivalent dipole model when projected to the scalp accounted for less than 85% of the IC scalp map were excluded from further analyses.

MacLean, 2014:

"Once the ICs were calculated, a scalp map for each IC was computed from the inverse of the weight matrix, giving the relative magnitude and polarity of the IC contribution at each electrode. Each scalp map was then compared with the forward solutions for various single equivalent dipoles. The digitized 3-D locations of the electrodes on the scalp were first co-registered with the Montreal Neurological Institute (MNI) average brain. IC sources were then localized with the Dipfit2 algorithm in EEGLAB using a standard boundary element model. Dipfit2 is a BESA derivative in which the location and orientation of an equivalent dipolar source for a given scalp potential distribution is estimated by a gradient descent method. Only ICs with scalp maps having an inverse solution for a single dipole source within Talairach (MRI) space (within the brain) of less than 15% residual variance (RV) were considered to be valid and were included in subsequent analyses. All ICs sourced outside Talairach brain space were rejected as artifactual. These latter included ICs representing ocular and temporo-mandibular joint muscle artifacts whose sources were within the head but not within the brain."

As I understand it, the projected scalp map of a given IC is calculated from the inverse of its weight matrix. Then this scalp map is compared to the scalp map of the DIPFIT-derived best-fitting single equivalent dipole (ECD) of this IC. Commonly, if the RV is greater than 15%, the IC is assumed to be mostly artifactual and is excluded from analysis.

Is this a correct understanding? Or is it not the DIPFIT-derived ECD which is used? Is there a mathematical description for what exactly is going on? :)


Best wishes,
Martin
University of Copenhagen



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