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[MakotoMiyakoshi]

Invitation to collaborate on an open paper about EEG’s 1/f

This space continues the EEGLAB mailing-list thread "Invitation to collaborate on an open paper about EEG’s 1/f." We’re moving the discussion here to make collaboration easier — for sharing ideas, asking questions, and posting announcements.

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[AaronGibbings]

Hi Makoto, Thanks so much for suggesting and organizing this project! Looking forward to working with everyone!

[Marjanz69]

Hi all,
“I’ve been thinking about a multi-scale hypothesis for EEG 1/f dynamics, linking dendritic filtering, network E/I balance, and Griffiths-like effects. I’d love to hear your thoughts on whether this could fit within the cable theory subgroup, and whether there are particular analyses you’d suggest to test it.”
@MakotoMiyakoshi

[Marjanz69]

@MakotoMiyakoshi
I’d appreciate hearing your thoughts on this idea whenever convenient.

[Marjanz69]

Introduction and Overall Hypothesis

Here is a proposed multi-scale hypothesis and analysis pipeline for EEG 1/f dynamics. It’s speculative and intended for discussion and collaborative exploration. Based on my reading of relevant papers, my guess is that the origin of 1/f in EEG may start at the neuronal level and seamlessly extend to network scales—this hypothesis requires further empirical testing.

Neuronal and Network Level Mechanisms

At the neuronal level, dendritic filtering based on cable theory (Pettersen et al., 2014) can produce 1/f-like patterns independently, without complex interactions. As neurons aggregate, volume conduction and the collective activity of neurons can amplify this pattern. Transitioning to the network level, this could be stabilized by excitation/inhibition (E/I) balance (Gao et al., 2017), which keeps the network in a controlled critical regime, preventing quiescence or runaway activity. This balance may facilitate Griffiths-like dynamics (Moretti & Muñoz, 2013; Ponce-Alvarez et al., 2018), where hierarchical and modular brain structures create rare regions that sustain stable, long-term activity, resulting in a broader power-frequency spectrum in EEG.

Spectral Components and Mechanisms

Essentially, network dynamics can enhance heterogeneity arising from variations in dendritic filtering across neurons. The neural power spectrum can be parameterized into periodic (e.g., rhythmic oscillations such as alpha, beta, gamma) and aperiodic (e.g., 1/f background slope) components using algorithms like FOOOF (Donoghue et al., 2020). While both components are influenced by overlapping biophysical processes (e.g., cable theory, volume conduction, and network interactions like E/I balance), their primary physiological origins are distinct: the aperiodic 1/f slope primarily arises from large-scale, passive processes such as dendritic filtering, synaptic noise aggregation, and Griffiths-like criticality in hierarchical networks, whereas periodic oscillations originate from active, localized circuit mechanisms (e.g., feedback loops, PING dynamics). These mechanisms differ in their spatial scales, with aperiodic activity occurring globally across the brain as a background substrate, while oscillations are local and cluster-based, often in specific regions like occipital (alpha) or frontal (beta/gamma) areas or within neuronal clusters. This distinction provides a multi-scale framework for understanding 1/f dynamics.

Analytical Pipeline and Methods

For analytical testing of this hypothesis, one could start with standard EEG preprocessing (e.g., filtering ,......), followed by wavelet transforms for time-frequency analysis across frequency bands. Then, apply FOOOF (Donoghue et al., 2020) to separate periodic and aperiodic components.

Network Graphs and Connectivity Analysis

To delve deeper, network graphs can be built on the time-frequency signals from wavelets: for the periodic part (oscillations), define local graphs to compute features like node degree or centrality, highlighting cluster-based dynamics. For the aperiodic part (1/f slope), construct global graphs to extract network-level properties like modularity or small-worldness, emphasizing whole-brain aspects. Effective connectivity methods such as Granger causality or transfer entropy can examine causal influences between neurons or regions.

Graph Neural Networks for Multi-Scale Analysis

After graph construction, Graph Neural Networks (GNN) can be utilized: apply GNN at the node and local level for local features (e.g., cluster oscillations), and at the overall network level for global features (e.g., 1/f slope). This approach can provide comprehensive predictions of multi-scale dynamics and effectively model functional connectivity across time-frequency scales.

[MakotoMiyakoshi]

Hi @Marjanz69,

It is not the case that the source of 1/f-ness are mutually exclusive. We do not need to determine which one is true. Rather, their effects linear sum to produce the final result.

I was told by Jorge to check out electrodiffusion. Apparently, this electrodiffusion was not in my scope due to my ignorance, but it seems a critical concept.

Rather than designing a hypothesis-driven experiment, maybe we should write a simple review paper listing known sources of 1/f-ness in scalp-recorded EEG with minimum explanation. We have been so far talking as if there were only three major factors, but obviously there are more. Just listing a valid factors today, which means for example we correctly reject Gabriel et al. (1996) based on Ness et al. (2022), can be by itself a good work.

Do you want to test a hypothesis with data or simulation, or writing such a summary review satisfying enough? Of course, we can do both, but which one do you want to do primarily?

[Marjanz69]

@MakotoMiyakoshi
I think it maybe best to do both.
A short review will give us a complete overview of all known mechanisms, the gaps in the field, and what has already been tested.
From that broader perspective, we can generate clearer hypotheses and decide which ones are most meaningful to test with data or simulations.

[dieloz]

Hi @MakotoMiyakoshi and @Marjanz69,
Which paper is the Ness et al (2022)? I know Gabriel et al (1996) and the potential issue of frequency dependent tissue impedance it may impact the 1/f. Thanks beforehand!

[MakotoMiyakoshi]

This is the one.

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

[dieloz]

Thank you very much!

[EugenMasherov]

Null hypothesis.
A 1/f dependence arises because the spectrum of a single EPSP or IPSP has this shape (a fairly steep rise upon transmitter arrival and an exponential decay), and therefore the spectrum of the total signal with a Poisson excitatory impulse flow also inherits this shape.
I'd like to rule out such a simple, even primitive, explanation before bringing out the heavy artillery, such as Griffiths phases (if I understand correctly, this comes from solid-state physics, spin glasses, or ferromagnets), or multifractality (the concept of self-similarity is beautiful, but is there really self-similarity here?)

[MakotoMiyakoshi]

@EugenMasherov

"A 1/f dependence arises because the spectrum of a single EPSP or IPSP has this shape" indeed sounds like tautology. But empirically validating this prediction from comp neuroscience to animal and human electrophysiology requires genuine scientific effort. The idea of Gao et al. (2017) is there. In fact, once you know it, then you cannot imagine how we not know it!

I can think of at least 4 source of 1/f-ness.

1. Spatial averaging (higher-frequency spatial network tend to be smaller, hence more prone to cancel out)
2. Cable theory, both subthreshold (conventional) and suprathreshold (relatively new)
3. AMPA/GABA_A receptor responses (Gao et al., 2017)
4. Electrodiffusion (see Electrodiffusion impacts delta range #7)

I hear other people say Griffiths phases and multifractality, but I do not know them (I like you say they are heavy artillery).

As I propose above, one of the papers can focus on just listing the confirmed and potential sources of 1/f with short explanations. That would help ourselves to see the outline of the problem.

[dieloz]

Hi @MakotoMiyakoshi and @EugenMasherov ,
I'm interested about the slope of the PSD as E/I balance after reading this:

Chakravarty, K., Roy, S., Sinha, A., & Kumar, A. (2024). Can we infer excitation-inhibition balance from the spectrum of population activity? biorxiv https://doi.org/10.1101/2024.12.29.630705

I'll try to think of alternatives and complementary measures