[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]

Hi Makoto!

Happy New Year!

My arrogance is not so great that I deny the law of conservation of charge. Undoubtedly, the total charge is conserved, but it can be spatially redistributed. For example, the potassium-sodium pump exchanges three sodium ions for two potassium ions, that is, the intracellular charge changes while the extracellular charge changes simultaneously. It seems to me that the operation of the potassium-sodium pump provides one of the possible monopolar sources. Of course, the level of an individual cell is a micro level, but we record the EEG at a macro level. But even in the complete absence of synchronization, the sum of independent sources does not go to zero; it will increase, but in proportion to the square root of the number of sources, and not the number of sources, as with complete synchronization. But it seems to me that synchronization can take place, even if weak, so that fluctuations at the micro level will also manifest themselves at the macro level. One of the possible mechanisms of such synchronization may be the diffusion of ions in the intercellular space.
As for the appearance of fictitious dipoles at the boundary of media with different conductivities, this effect is known and practically used in geophysics, for example, to search for water sources where an equivalent dipole appears. Perhaps this explains the “dipole source” placed by the program in the center of the cerebrospinal fluid bubble filling half the skull in a patient with a congenital absence of the right hemisphere. The conductivity of the cerebrospinal fluid is four or more times higher than that of the gray matter, and this could cause a bias in the estimate of the coordinates of the actual source towards a decrease in resistance. Heterogeneities in the conductivity of an anatomically intact brain can also lead to displacement of the dipoles, albeit to a smaller distance.
Once again, let me thank you for the valuable discussion, useful links, and especially for your critical comments. I realize that the approach I propose may be the product of my misunderstanding of essential patterns and ignorance of important facts, but it still seems to me that there is something sound in it.
Thank you.

Eugen Masherov

> 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
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