[Eeglablist] Source localization and hippocanpus

[Евгений Машеров]

> Hi Yevgeny, Cedric, and Marjan,
> 
> Thank you for your comments!
> 
> I published the L-EEGibility Atlas on Github and Zenodo.
> https://urldefense.com/v3/__https://github.com/MakotoMiyakoshi/L-EEGibility-Atlas/tree/main__;!!Mih3wA!AF89gXQ_Bw1a_fYT3Lwj_tIHdNTuHFcI9VNexSVkbRNU_Eu6Hws2v5AeyUpAd909X_XItKDCYj7xKhNs_QtbXMho29w$
> 
> I also submitted it to the EEGLAB plugin request.
> 
> There was a bug in code, so the initially reported L hippocampal source
> contribution is updated from 1.649 to 2.009 microV.
> 
> For Yevgeny,
> 
> However, the conclusion regarding whether signals from the hippocampus can
> be recorded on the scalp relies on several assumptions, and these can be
> challenged. The first is that the source is necessarily a dipole.
> 
> I do not understand this. An n-pole model is just a model. You choose which
> model to fit, not the brain uses it. Do I miss something?
> 
> The second is that it is a single dipole, not a set of synchronized dipoles
> distributed over a certain area and similarly oriented.
> 
> Typically, a single dipole model may be used because there is no monopole
> (current conservation) and rapid delay of > quadru-poles for scalp EEG
> recording. For intracranial invasive, things are different.
> 
> 1. In addition to the dipole component, a monopole component also
> contributes to the EEG.
> 
> Invasive brain recording may capture near-DC electrodiffusive
> neuron-extracellular-glia (edNEG) current, for example, between dendritic
> and somatic areas (Halnes et al, there are many of them). But this
> edNEG-caused potential field does not propagate. edNEG is a potential
> field, not a current source.
> 
> Likewise, the potential from a system of quadrupoles can propagate over a
> greater distance than from a single dipole.
> 
> I'm curious if this can really happen. It's certainly different from what I
> learned. I think the point is the word 'a system of quadrupoles' What
> system could it be, like an array formed?
> 

Thank you for your reply. I'll try to explain exactly what I meant, but I couldn't formulate it clearly.
The elementary source located in the brain is independent of our conception of it. Our conception determines the simplifications we make to transform the incomprehensible complexity of the real world into a computationally convenient model. In particular, we can represent the complex system of charges or currents of the elementary source by expanding it into an infinite series of spherical Legendre polynomials. We choose which terms of the infinite series we use. The first is the monopole field, spherically symmetric and decreasing inversely with distance. The second is the dipole field, which has a directionality and decreases inversely with the square of the distance. The third is the quadrupole field, which also has a directionality, but not the same as a dipole, and decreases inversely with the cube of the distance. The series can be continued further, complicating the spatial configuration with each term and increasingly accelerating the rate of potential decay with distance. The most common model of the EEG discards all terms except the second, working only with dipoles. This is justified, on the one hand, by the fact that single charges in the electrolyte will be immediately neutralized, and on the other hand, by the fact that the quadrupole potential decays too rapidly with distance to be recorded on the scalp (this was verified when testing an early hypothesis about the genesis of the EEG as a sum of action potentials—the nerve impulse, quadrupole in nature, was not recorded on the scalp). To the first objection, I would say that it is undeniable when applied to static charges, but in dynamics, the possibility of fluctuations arises, so the average is zero. However, since the passage of ions across the membrane is not instantaneous, a non-zero potential can exist at any given moment. To the second objection, I note that a system of quadrupoles will create a field different from a single quadrupole (I attempted to propose such a model in a 2021 article in "Biophysics" to explain the formation of a peak in the spike-wave complex in epilepsy; the synchronization of action potentials, although each of them is quadrupole, creates a more slowly decreasing field, and this, unlike individual action potentials, can be recorded on the scalp, and not only directly from the cortex).

A similar explanation is also possible for the recording of the potential created by a system of dipoles at a distance where the potential of a single dipole is strongly attenuated. For a simple model in which dipoles are uniformly distributed over a circle of radius r and directed perpendicular to the plane of the circle, at a small distance h of the recording point from the center of the circle, dipoles located on the periphery will make a small contribution due to the cosine of the angle between the dipole vector and the direction to the recording point. As a result, the dependence of the potential on distance will be close to 1/h and, as h increases, approach 1/h^2. Therefore, I propose using a more complex model of an elementary source, including, in addition to the second dipole term, the first and third terms of the series expansion.

Tugen Masherov