Units after the surface Laplacian transform

[niro...@gmail.com]

Hi,

I have been looking into different implementations of the surface Laplacian (CSD Toolbox, FieldTrip and the code from the book), and there seems to be disagreement about the units of the output.

The CSD Toolbox docs say that if the head radius isn't specified (i.e. the computation is done in the "unit sphere" head) then the units are microvolt/(m^2). The documentation says that the head radius can be provided to change the units of the denominator, but doesn't go into the details.

Page 278 of the book says the "raw" units are microvolt/(mm^2), but looking at the code I didn't see something that would explain that difference, since as far as I can tell both the book's code and the CSD toolbox do the computation in the unit sphere.

FieldTrip's documentation of ft_scalpcurrentdensity() states that if the EEG units are microvolts (the typical unit), and that the electrode position units are mm, then the output would be volt/(m^2), which should be the same as microvolt/(mm^2). FieldTrip's code seems unique in that it first scales to the unit sphere to calculate G and H, then rescales by the head radius it estimated using the electrode positions.

I understand that the units aren't so important, as long as the rest of the analysis involves normalizing, but I wondered which toolbox has the "right" units, and which I should treat as AU. My intuition was that if the head radius isn't incorporated, the denominator should be "head-radius" rather than m, cm or mm. That is because the computation of the surface Laplacian itself depends only on the angles between electrodes, as they are first projected on a unit sphere.

I would greatly appreciate any help in figuring out this puzzle.

Thank you for your time!

[Mike X Cohen]

Hi Nirofir. It's been a long time since I've thought about the units of CSD. It is the case that the code I provide is just an improved version of the Kayser/Tenke implementation (I vectorized computations that they had in for-loops, and eliminated redundant computations), so without spending more time looking into it, my guess is that their reported units are correct and mine was a typo in the book. 

Mike

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[Nir Ofir]

Thanks.

Nir

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