Electrodiffusion impacts delta range

[MakotoMiyakoshi]

Jorge Riera pointed me to a series of works by Gaute Einevoll, saying that his controversial discovery of 'monopole' turned out years later to be due to electrodiffusion.

Roughly speaking, there are two major contributors to the extracellular space potentials (according to Torbjørn's work; Ness et al., 2022).

1. A drift component (ions migrating in electric fields)
2. A diffusion component (ions diffusing due to concentration gradients)

The former is the main mechanism in convention. For example, in Electric Fields of the Brain (2006) by Nunez and Srinivasan only explains this factor. The second one is present only during a transient phase, during which extracellular space shows non-ohmic behavior.

As you can see in screenshots below, electrodiffusion takes a form of monopole (i.e., all blue in difference) and impacts below delta range.

Solbrå A, Bergersen AW, van den Brink J, Malthe-Sørenssen A, Einevoll GT, Halnes G. 2018. A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons. PLoS Comput Biol. 14:e1006510. DOI: 10.1371/journal.pcbi.1006510, PMID: 30286073, PMCID: PMC6191143

ECS, extracellular space; KNP, Kirchhoff-Nernst-Planck (i.e., a model with electrodiffusion); VC, volume conductor (i.e., without electrodiffusion)

Halnes G, Mäki-Marttunen T, Keller D, Pettersen KH, Andreassen OA, Einevoll GT. 2016. Effect of ionic diffusion on extracellular potentials in neural tissue. PLoS Comput Biol. 12:e1005193. DOI: 10.1371/journal.pcbi.1005193, PMID: 27820827, PMCID: PMC5098741

Selected other papers good for reading

Riera JJ, Ogawa T, Goto T, Sumiyoshi A, Nonaka H, Evans A, Miyakawa H, Kawashima R. 2012. Pitfalls in the dipolar model for the neocortical EEG sources. J Neurophysiol. 108:956-975. DOI: 10.1152/jn.00098.2011, PMID: 22539822

Destexhe A, Bedard C. 2012. Do neurons generate monopolar current sources? Journal of neurophysiology. 108:953-955. DOI: 10.1152/jn.00357.2012

Ness TV, Halnes G, Næss S, Pettersen KH, Einevoll GT. 2022. Computing Extracellular Electric Potentials from Neuronal Simulations. Adv Exp Med Biol. 1359:179-199. DOI: 10.1007/978-3-030-89439-9_8, PMID: 35471540

[EugenMasherov]

The conductivity of scalp tissues includes a capacitive component, which, to a first approximation, is a parallel resistor (intercellular space) and an RC circuit (membranes, like a capacitor, and the intracellular space, like a resistor). However, in the EEG frequency range, the contribution of the capacitive component is small; it is significant at tens and hundreds of kilohertz. Moreover, the capacitive component increases conductivity with increasing frequency. If the frequency dependence of the spectrum were explained by this, there would be a rise with increasing frequency rather than a decrease in the 1/f mode.
I believe that the 1/f mode component is determined by the shape of the elementary signals (EPSPs and IPSPs). If their flow is Poisson (which is, of course, only a first approximation), then the spectrum of the resulting signal will match the spectrum of the elementary signal to within a coefficient.
Taking the EPSP shape as an approximation (A^2/4-(t-A/2)^2)*exp(-t)

and calculating its spectrum, we see a good approximation to the stated dependence.

Taking into account a more precise EPSP shape and the non-Poisson nature of the excitatory impulse flow can give an even better approximation.

[MakotoMiyakoshi]

Hi @EugenMasherov,

I updated this post. Basically, electrodiffusion describes a principle that changes the spike waveform.
Can you read either Solbrå et al. (2018), Halnes et al. (2016), or Ness et al. (2022), and tell me if my explanation above is correct? These papers are math-heavy and I'm too weak to fully digest them.

[EugenMasherov]

The question of the presence of a monopole component in the EEG arose in connection with EEG source localization. The potential of a dipole decreases inversely with the square of the distance, so if we can localize the source in the deep structures of the brain, then its amplitude, assuming a dipole, should be implausibly high. Moreover, the calculation results were verified during neurosurgical operations, and the presence of pathological activity in these areas was confirmed. The potential of a monopole, on the other hand, decreases inversely with distance, and the amplitude of the sources takes on reasonable values. I attempted to outline this approach in a short article published in 2004 as an appendix to L.B. Ivanov's book "Applied Computer Electroencephalography," and then developed it in an article in the journal "Biophysics" in 2019. https://link.springer.com/article/10.1134/S0006350919030138
I hypothesize that the mechanism generating the oscillations is an integral regulator that maintains ion concentration. Moreover, I associate this not only with ultra-slow (below the delta range) oscillations, but also with higher-frequency ones, up to alpha.
In a recently published article
https://www.med-alphabet.com/jour/article/view/4644
(in Russian; the English translation, unfortunately, is poorly edited https://istina.msu.ru/download/805082420/1vMKTe:cFFnZPF0Fi0FicIwr3ApSmioy1QAomA4xzN7f9b78Ik/ ), we attempted to construct a theory of the EEG that incorporates various sources. The low-frequency component is associated with regulatory processes and manifests itself in the form of monopoles, the higher-frequency component is associated with EPSP and IPSP and manifests itself in the form of dipoles, the third component is the action potential, which under normal conditions is not recorded in the EEG, but manifests itself in the ECoG, for example, in the form of bursts of ultra-high-frequency activity before epileptic discharges, and when synchronized, produces peaks and sharp waves, already visible on the scalp EEG.

[MakotoMiyakoshi]

Hi @EugenMasherov,

I zapped your paper translated in English. I did not find it 'poorly edited' maybe you are too modest (and patient, I can tell). I found that many of what you say is what I would say as well but with less clarity and confidence.

I like the elegant introduction celebrating 100 years of human scalp EEG work by Berger, then the subsequently raising question as "The Crisis of the Unitary Concept of Postsynaptic Potentials as the Source of EEG" Yes, after all, that is what interests me: if post-synaptic potential is NOT everything, then what else do we have?

Well, it is actually also related to 1/f-genesis, but I can list these works that predicted and demonstrated contribution of suprathreshold activities in contrast to conventional subthreshold membrane theory (which EFB is based on).

Reimann MW, Anastassiou CA, Perin R, Hill SL, Markram H, Koch C. 2013. A biophysically detailed model of neocortical local field potentials predicts the critical role of active membrane currents. Neuron. 79:375-390. DOI: 10.1016/j.neuron.2013.05.023, PMID: 23889937, PMCID: PMC3732581

Murakami S, Okada Y. 2006. Contributions of principal neocortical neurons to magnetoencephalography and electroencephalography signals. J Physiol. 575: 925-936. DOI: 10.1113/jphysiol.2006.105379, PMID: 16613883, PMCID: PMC1995687

But I'm really not ready to understand the seemingly sinusoidal signals like alpha. 'Thalamocortical dysrhythmia' shifts the alpha peak to the theta peak, as Llinas and colleagues argued, but what does that mean and where is it regulated, and how?

[EugenMasherov]

Thank you for your kind words regarding the article, but I understand that it raises many more questions than answers. My co-authors and I haven't reached a definitive agreement on some of them, and we've set them aside for a time when we can convincingly support our positions or, under pressure from the facts, abandon them.
My personal view regarding sinusoidal signals (which correspond to sharp peaks in the spectrum) is that they are poor for transmitting information, since a wide spectral bandwidth is optimal for transmission; they are poor for synchronizing anything, since synchronization requires a rapidly changing signal; and they are poor for sweeping, since they skip the central field at high speed, slowing down at the periphery. However, they arise naturally as the response function of an integral controller. The object of regulation is the ion concentration.

However, with an intense flow of disturbances, we see a response to these disturbances, and the signal spectrum resembles the spectrum of the disturbances. Only if the flow of input signals is low-intensity and Poissonian do we see the controller's pure response. The cessation of visual impulse flow when the eyes are closed generates an occipital alpha rhythm, which disappears when the eyes are open. The mu rhythm in the motor cortex disappears with hand movement, and I believe the mechanism of alpha coma is the cessation of impulses traveling from the brainstem to the cortex.
However, I find this point of view questionable, although I am trying to find confirmation for it. My co-author on the aforementioned article, Professor Alexandrov, believes that this can explain the delta rhythm, but the occipital alpha rhythm is an interaction between the cortex and the thalamus and nothing more. However, he admits that this could also generate activity in other regions with theta and alpha frequencies, but not the occipital rhythm.

[MakotoMiyakoshi]

@EugenMasherov

since a wide spectral bandwidth is optimal for transmission

Which reminds me of what Claude Shannon said: narrow band can contain less info.

So far, your posts are most academically profound. I enjoy reading them. I have no objection to your information theory-like viewpoint, but that is a story when designing signals under engineering (i.e., artificial) conditions. We do not completely understand principles of information transmission in the brain across spatiotemporal scales. We are not even sure whether our observation is meaningful or not to understand the targeted system.

I feel uneasy yet to discuss network behaviors (i.e., heavy artilleries) because it is an abstract and emerging property. I would rather stick to simpler, lower-level physiological mechanism (i.e., pulses) before jumping to heavy artillery (i.e., oscillations and waves). For me, the problem is that I cannot tell to what extent a discussion of network behavior is an analogy. For example,

Only if the flow of input signals is low-intensity and Poissonian do we see the controller's pure response.

Yes, this is a beautiful summary, and also I can see it is also plausible. But the concept 'controller' bugs me. It is partly because Paul Nunez repeatedly explained, which I did not understand completely, that thalamus is not a pacemaker. If we assume there is thalamo-cortical mutual dependency (a chicken-egg relation), can we consider an existence of a separate controller? Around this line of argument, a mysterious fog suddenly get thickened, and I lose confidence in seeing ahead. Like a process of applying linear approximation to a local region of a non-linear system, we can only assume a linear causality in a spatiotemporally local event of a general neuroscientific phenomenon--hence I understand only pulses.

[EugenMasherov]

I have an engineering background rather than a biological one, and this influences my perspective. On the one hand, this is a drawback, but on the other, it allows me to see something new. Of course, one can't expect nature to replicate human technical solutions, but similar problems often lead to similar solutions.
As for the controller, I don't mean its existence as a separate device. It could also be a pattern governing the behavior of an object. Like a pendulum—the force returning it to its vertical position is proportional to the deviation, taken with the opposite sign.
As for the occipital alpha rhythm, I tried to find a compromise between the theory of the thalamic driver and the integral regulator as the source of a sine wave. I imagined something like an old-fashioned bell.
Where the occipital cortex acts like a gong, excited by strikes, creating a sine wave signal that returns to the thalamus, producing an impulse that creates a new sine wave.

[Marjanz69]

Monopole vs. Dipole Representation in EEG: A Structural and Biophysical Question
EEG signals are commonly interpreted as the macroscopic superposition of postsynaptic potentials, while the contributions of action potentials largely cancel out due to their fast temporal dynamics and spatial symmetry. From this perspective, the dominant generators of EEG are dendritic and postsynaptic currents rather than propagating spikes.

This raises a conceptual question regarding source representation at the scalp level. If EEG primarily reflects spatially distributed postsynaptic activity, and if action potential contributions effectively sum to zero, can we still justify modeling the measured signals strictly as equivalent current dipoles? Or, under certain conditions, is it more appropriate to interpret the effective generators at the scalp as monopole-like effective representations arising from dendritic current distributions and electrodiffusive effects?

Related work on electrodiffusion suggests that non-ideal conductive properties of brain tissue can give rise to apparent monopolar components in the effective extracellular potential, without implying true physical monopoles. This leads to a broader question: could the predominance of postsynaptic, dendritic activity—combined with tissue electrodiffusion—provide a mechanistic explanation for observing monopole-like behavior in EEG, rather than purely dipolar source models?

More generally, how should these biophysical considerations influence our interpretation of EEG source models, especially when linking cellular-level mechanisms to macroscopic measurements?

[EugenMasherov]

The EEG generation model, which assumes the presence of elementary sources distributed throughout the brain, seems to me quite realistic and practically useful. However, an elementary source can have a complex charge configuration, and its potential can be expanded in a series of Legendre polynomials. The first term corresponds to a monopole, the second to a dipole, the third to a quadrupole, and so on. Moreover, the potential from higher-order terms decays faster. For a monopole, the magnitude is inversely proportional to the distance, for a dipole, it is inversely proportional to the square of the distance, and for a quadrupole, to the cube. So, at typical EEG distances from the source to the recording electrode, even a quadrupole is usually not visible, much less higher-order terms. Nevertheless, some observations may indicate a contribution from quadrupoles. In particular, some time ago I worked with the BrainLoc source localization program (developed by Yu. M. Koptelov). It utilizes a method for addressing the main difficulty of source localization, which stems from the fact that the number of parameters greatly exceeds the number of available leads. This method differs from the two most common approaches. One popular approach assumes that the position of the dipole source is specified a priori, and only its electrical parameters are estimated. The other approach requires evaluating all possible sources at once, and since the number of estimated parameters exceeds the number of leads by 2-3 orders of magnitude (even with a 10-10 system), it necessitates intensive regularization. In the first approach, we depend on the choice of position; in the second, on the regularization parameters. Attempting to develop a source localization method independent of the arbitrariness of the researcher or software developer, Koptelov calculated the positions of a small number (1-2) of dipoles for all EEG points, but discarded those time points where such a model does not explain the majority of the signal. For the remaining points, it can be assumed that, due to the random nature of the signal, one or two dipoles dominated at these time points so much that the remaining sources can be considered noise. The single-dipole model achieved good accuracy (we work at the Institute of Neurosurgery; the study was conducted for surgical planning, and the results were verified by ECoG during surgery). The dual-dipole model for the 10-20 system was inaccurate, with one exception: a pair of oppositely directed dipoles was recorded for the peaks in the epileptogenic zone.

A possible interpretation is that this is not actually a pair of dipoles, but a quadrupole. The model proposed on this basis requires criticism. The ability to explain from a unified perspective the spikes, spike-wave complexes, and high-frequency activity recorded on the ECoG before a seizure seems very promising, but that's precisely why I'm asking for arguments against it.
https://link.springer.com/article/10.1134/S0006350921040114
I believe that improving the biophysical model of EEG generation has practical significance. This will allow for the development of methods for analyzing the EEG signal that take into account the generation mechanisms and enable the assessment of the underlying biological phenomena. In terms of source localization, a single-pole analog of LORETA will not only invert a matrix three times smaller, but its determinacy will also be higher.