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

[Makoto Miyakoshi]

Hi Eugen,

Happy new year!

> I try to take into account that the field of a collection of sources can
be very different from the field of a single source. In a 2019 article, I
try to explain the peak recorded on the scalp by summing up action
potentials, although a single action potential is not detectable at such a
distance.

I want to note that a single 'dipole' source has zero area by definition.
Hence the goodness of dipole approximation depends on the relative spatial
scales you are talking about. The 'transducer array effect' I mentioned
before occurs when this zero-area assumption gets severely violated. In
short, a widely distributed sheet of dipole array can project, via an
almost non-intuitive mechanism, much further than a single dipole. So to
say, the heatmap of the projection profile along with the z-axis (i.e.
normal to the surface of the dipole sheet) shows as if it is 'extended'.
Another related thing that is often forgotten is that a dipole does not
have a parameter to adjust 'projection width' (Maybe this kind of my
wordings are technically wrong but hopefully you see what I mean) along
with the z-axis parallel to the dipole axis. Therefore, in order to
approximate an electric field generated by a sheet of dipoles, a single
dipole needs to go deeper. Again, I have results from numerical simulations
here

https://sccn.ucsd.edu/mediawiki/images/c/cb/SupplementaryFiguresForSimuUDL_BSCR80.pdf
.

This point is often missed when micro- and meso-scopic EEG sources are
compared with its scalp projections. Sorry if I'm repeating myself.

> On the other hand, a dipole can be approximated by a pair of monopoles at
a short distance, and at a recording distance greater than the distance
between the monopole sources, it is almost impossible to distinguish their
field from the dipole field.

When I used Robert Oostenveld's Fieldtrip to simulate dipole projections in
an infinite homogeneous medium, I specified the two monopoles and their
distance. Nothing is wrong there for me.
But when you talk about two independent monopoles interacting together to
form a dipole, they must be a pair of synchronized source and sink! Is that
what you mean? Also, most fundamentally, when you talk about a
meso-/macroscopic monopole, what happens to the law of current
conservation? Or are you talking about monopoles only in microscopic scales
that is so small that a pair of a source and a sink cannot exist together?

In audio engineering, when a distance to a recording position is within a
wavelength of a tone, we say the source of sound is 'acoustically close'.
It relates to the concept of 'near field'. However, because a loudspeaker
covers 4 orders of magnitude in the frequency range, the actual distance of
'acoustically close' changes from 17 m to 1.7 cm for 20Hz and 20kHz
respectively. This is why a bass-reflex port is sometimes located on the
backside of a loudspeaker enclosure; if a resonance frequency is tuned to
100Hz, the wavelength is 3.4 m, for which the distance to the membrane of a
woofer is 'acoustically close'. In the case of an electric dipole, the
definition of 'near field' is the distance that is x3 or x4 of the pole
distance (which is, for the case of a typical pyramidal cell in the
neocortex, 3-4 mm). You have to place your recording electrode outside this
region to make the dipole approximation hold. You probably know this, but
just to make sure.

Figure 2 of the following paper shows a nice comparison across 3 levels of
coarse graining in modeling an extracellular potential field, namely
compartment-based, multi-dipole, and a single dipole. Note that in each
level of coarse graining, pole distances also vary which changes the
effective 'minimum distance' from the pole center for the dipole
approximation to hold.

Næss S, Halnes G, Hagen E, Hagler DJ, Dale AM, Einevoll GT, Ness TV.
(2021). Biophysically detailed forward modeling of the neural origin of EEG
and MEG signals. Neuroimage. Jan 15; 225 117467

> That is, we have an ambiguity in the representation of the field on the
scalp by the system of sources.

If I understand you correctly, I disagree with you. There is no ambiguity
in describing an electric field arising from dynamics of the cortical
sources--or am I too naive?

> Purely mathematically, there are advantages to representing EEG sources
as a system of monopoles. First of all, this is that a monopole is one
parameter, and a dipole with fixed coordinates is three parameters. A
dipole requires 6 parameters: xyz for the position and the moment. In
EEGLAB, they are stored at EEG.dipfit.model(x).posxyz and
EEG.dipfit.model(x).momxyz.

> Then, the decrease in the monopole potential is not so rapid compared to
the dipole, so there is no need to introduce such a strong correction so
that the found sources are not concentrated on the convexital surface. Of
course, mathematical convenience is insignificant compared to physiological
validity, but I still hope, despite solid arguments against, to show the
presence of real, and not just calculated, monopole sources.

But again, can a monopole exist in a meso-/macroscopic spatial scale? Does
it not violate the law of conservation of current? For example, in the case
of Riera et al. (2012) that claimed significant contribution of monopoles,
I am not sure if they carefully handled differences of spatial scales. They
compared LFP and skull EEG using rats whose cortical thickness is 2 mm.
Looks like their electrodes are too close to the sources all the time. How
thick is the rat skull? It is 0.5-1.5 mm. If a pole distance is 1 mm and
measured its activity from the distance of 0.5-1.5 mm, dipole approximation
does not seem to work well.

By the way, most consumer loudspeakers work as monopole sources. There are
dipole speakers, such as Magnepan, Martin Logan, and those designed by
Linkwitz lab. Linkwitz says dipole speakers work better in terms of room
acoustics. After all, field theories matter.

> Regarding the question of dipoles that are placed by the program in the
white matter or in the cerebrospinal fluid inside the ventricles, I see at
least three possible reasons for this. The first is that the accuracy of
calculating dipole coordinates is not absolute; the error can be quite
high, especially if the number of EEG channels is insufficient. At the same
time, increasing the number of channels does not lead to the desired
increase in accuracy due to signal shunting by the scalp and meninges. In
addition, the idea of matter inside the brain as homogeneous and isotropic
is extremely simplified. The resistance of different structures can vary by
an order of magnitude and depend on the direction of current flow. As a
result, the dipole is shown not in the place where it actually is, but
where it is unrealistic to expect it.

All of these factors can be controlled by using a simulation, right? But
even after addressing all of these factors, I could still reproduce the
depth bias. The trick is simple: For the forward model, you use a dipole
sheet with various sizes. For the inverse solution, you use a single dipole
model. The result is, the broader the ground-truth source, the larger the
depth bias.

By the way, this is my favorite study on inaccuracy of the forward model.
In my personal communication with him, he showed me his dissertation that
discussed the effect of the parietal foramen.

Fiederer LDJ, Vorwerk J, Lucka F, Dannhauer M, Yang S, Dümpelmann M,
Schulze-Bonhage A, Aertsen A, Speck O, Wolters CH, Ball T. (2016) The role
of blood vessels in high-resolution volume conductor head modeling of EEG.
Neuroimage. 2016 Mar; 128 193-208

> The second is that inhomogeneities in the conductivity of brain tissue
can form a fictitious dipole.

I have never heard of that. Is that possible? Aren't the layers of Brain,
CSF, Skull, and Skin all passive?

> The third is that the sources may not be dipoles, but since we can only
look for dipoles, then dipoles are found, but they are shifted.

Yes, any far-field measurement will effectively result in a dipole because
(1) monopoles can't exist due to the law of current conservation (2)
higher-order poles decay quickly.

Again I'm not a super specialist on this topic. I'm just repeating what I
read in Nunez and Srinivasan (2006). If you disagree, I'd love to know why.
For example, I want to know why you do not care about the law of
conservation of current? Is there something I'm missing, or are we talking
about things in very different spatial scales: you talk about things in
microscopic scales, while I do in meso/macroscopic scales? I also want to
ask whether near-field and far-field are distinguished in your case.

Makoto