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 cerebrating 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 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.