[Eeglablist] Why most of good 'brain' ICs are 'dipolar' with show 'red'-centerd scalp topos, although 2/3 of the cortex is in sulci?

[Евгений Машеров]

Yes, this problem seems to me important and unresolved. Even for an adult with an intact skull, the conductivity of different areas is very different, and an injury or surgical wound changes the EEG picture very strongly (breach effect). Babies generally have open areas in scull (fontanel). A possible solution would be to measure impedance similar to that used to control the quality of electrode placement, but the measurement would be between all pairs of electrodes, 171 pairs for 10-20, or 210 pairs if ear electrodes are included. The current passes through the electrode-skin contact resistance, then branches into a current flowing through the scalp skin and a current passing through the skull, then through the brain tissue, again through the skull and connecting to the first branch of the current, through the contact resistance of the second electrode with the skin. If we assume that the scalp skin has approximately the same thickness and conductivity, we can calculate the resistance of the skin area between the two electrodes purely geometrically to within an unknown coefficient. Another assumption is that the brain tissue is homogeneous, and the resistance to current flow through the brain for a selected pair of electrodes can also be calculated to within an unknown factor. 

i,j - electode numbers
R(i,j) - measured resistance between ith and jth electrodes
Res(i) - resistance of electrode-skin contact for ith electrode
Rb(i) - resistance of skull bone under ith electrode
Qs - quotients for skin resistance
L(i,j) - geometric parameter for computation of skin resistance between points i and j, rs=Qs*L(i,j)
Qt - quotients for brain tissue resistance
V(i,j) - geometric parameter for computation of brain tissue resistance between points i and j, rt=Qt*V(i,j)


R(i,j)=Res(i)+1/(1/(Qs*L(i,j))+1/(Rb(i)+Qt*V(i,j)+Rb(j))+Res(j)

R(i,j) measured, 
Res(i), Rb(i), Qs, Qt - estimated,
L(i,j), V(i,j) - precomputed (finite elements method or other


That is, we have 171 measurements to estimate 2*19+2=40 parameters (or 210 for 2*21+2=44 parameters), which makes the problem mathematically correct. But how correct are the assumptions regarding the conductivity of skin and brain tissue? Technically, this looks feasible, to some extent similar to an impedance tomograph, but, as far as I know, impedance tomography of the brain has not been brought to practical use.
Some information could also be obtained by comparing the distribution of potential on the scalp caused by a source at a known location with a potential calculated assuming equal conductivity of the skull and meninges. The corneo-retinal potential of the eye can be used as a non-invasive source. Perhaps, by closing the eyes one at a time and asking the subject to look up, down and to the sides, it will be possible to assess the influence of inhomogeneities on the propagation of current. There will likely be simultaneous movements of the other eye, so two dipoles must be taken into account, but if the eye is closed the amplitude will be lower. Of course, the idea is somewhat fantastic, as is the use of the heart's electric field for such sensing, but at least it is completely non-invasive.

Thanks

Eugen Masherov

> Equivalent dipole *depth* is the least well estimated parameter in
> equivalent dipole (or any other source) estimation, and the one that has
> the most effect of source estimation. The reason is that skull conductivity
> is currently only given a template value in EEG inverse software, whereas
> our results suggest it has a range of at least 3:1 across adults - and more
> so in infants, of course. (Tucker's group claimed a possible range of
> 12:1). Brain-to-skull conductivity ratio ranges in our estimation from
> ~20:1 to ~70:1 or more. The effects of this uncertainty, as shown clearly
> in this paper
> <https://urldefense.com/v3/__https://link.springer.com/article/10.1007/s10548-012-0274-6/fulltext.html__;!!Mih3wA!EUn9yGvTSgBO0pIbsPZlgPbP0VXD580VIaATFdFlw8LqObtyVUVFIZ1Tt3y_hzIgfUidyT1YFg1VH75zr671$ >,
> are to alter the implied *depth* of the source (by as much as 2 cm). The
> only noninvasive method for estimating individual skull conductivity
> without using EEG/MEG or a particular stimulation sequence is the SCALE
> algorithm, more recently improved
> <https://sccn.ucsd.edu/~scott/pdf/AkalinAcar_BIBE2020_final.pdf>. We are
> now attempting to make this method freely available through the
> Neuroscience Gateway <https://urldefense.com/v3/__https://www.nsgportal.org__;!!Mih3wA!EUn9yGvTSgBO0pIbsPZlgPbP0VXD580VIaATFdFlw8LqObtyVUVFIZ1Tt3y_hzIgfUidyT1YFg1VH1rzF2S8$ >. Meanwhile, think of the
> zone of uncertainty surrounding an estimated equivalent dipole as shaped
> like a (large) grain of rice (pointed outward.).
> 
> Scott Makeig
>