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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.

[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!

[Marjanz69]

Hi @MakotoMiyakoshi

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

Refined Hypothesis:
"Different types of network alterations—such as those observed in neurodevelopmental conditions (e.g., ASD, schizophrenia) and neurodegenerative conditions (e.g., Alzheimer’s disease, MS)—will be associated with distinguishable patterns in the 1/f slope across both periodic and aperiodic components of the EEG power spectrum, compared to healthy individuals."

[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?)

[EugenMasherov]

Some problems with loading Aperiodic Summary

[dieloz]

Thanks a lot for your thorough post @antoniosdougalis ! Could you please upload the pdf again? It turns out to be an hyperlink #1
Thanks beforehand

[antoniosdougalis]

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?)

Dear All,

I have been reading with great interest the communications between the parties about 1/f. It is very nice to initiate something like this and I am very happy to participate in such a wide collaboration!

I am interested in E/I balance quantification from electrophysiological data, especially in making inferences from recordings where the direct evaluation of this balance is not possible (e.g. EEG data). I would like to start spinning off the ideas by providing some data.
For your records, I am a cellular and network neurophysiologist that works with human neurosurgical samples. I record whole cell intracellular activity from single neurons (patch-clamp recordings), register synaptic activity (E/I balance) and interrogate network behavior from various areas including cortical areas in human brain slices in vitro via multielectrode recordings.
To simplify the matter and to follow the results of Gao et al., 2017, I have asked the following question. How does 1/f (aperiodic 1/f exponent and linear slope determination) change in a single compartment neuron bombarded by random excitation and varying strength of random inhibition?

For a start, in order to make the models as stripped down as possible, I have used a published substantia Nigra par compacta neuron model that I have constructed in the past (NEURON simulation environment, Ortner et al., 2017 J Neurosci, https://modeldb.science/2017402 ) and added synaptic mechanisms of AMPA and GABA receptors as a two exponential synapse (typical rise tau and decay tau). Synapses are activated by a NEURON NetCon object at random times centered around a mean activation interval (set at 20 ms, i.e. 50 Hz for both types of synapses). Simulations were run for 10 seconds at 50 KHz.

model_parameters =
{‘AMPA_activation_interval’: 20, ‘GABA_activation_interval’: 20, 'rev_syn_AMPA' : 0, 'rev_syn_GABA' : -80, 'tau_rise_AMPA' : 0.3,'tau_decay_AMPA' : 2, 'tau_rise_GABA' : 0.5,'tau_decay_GABA' : 10, 'AMPA_G' : 0.0002, 'GABA_G': VARIABLE }

I have systematically varied the neuron’s inhibitory conductance (in 12 steps) while keeping the AMPAergic drive constant to achieve E/I balances of 1 over [ 0.25, 0.5, 1, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0 ]. I have run 5 replicates of every simulation at each E/I balance for statistical inferences.

I have calculated the extracellular voltage from the somatic voltage trajectory at a distance of 200 micrometers (with extracellular conductivity at typical 0.3 S/m) from the soma using the summation of the transmembrane currents (a manual implementation of the Ness and colleagues method 2022 Exp Med Biol)

i_memb = (i_cap + i_AMPA + i_GABA +
i_NaF * nA_Factor + i_kD * nA_Factor + i_leak * nA_Factor +
i_kA * nA_Factor + i_H * nA_Factor + i_kM * nA_Factor +
i_CaW * nA_Factor + i_NaP * nA_Factor + i_kCa * nA_Factor +
i_capump * nA_Factor)

where nA factor is the conversion factor of the ionic densities to current (nA). Note the neuron operates with ten (10) different conductances including a fast (NaF) and a persistent (NaP) sodium channel, a leak current (leak), combined calcium currents (CaW), a hyperpolarisation activated cation current (H-current), an extruding calcium pump (capump), four potassium currents (a Delayed rectifier type current, an M- type current, a kCa calcium activated potassium current and an A-type current)

Finally, I run two variants of the model, one where the soma has entirely passive properties and one that has all active properties activated (referred herein as active and passive models).

The first two figures attached (the title of figure details the model used, ACTIVE or PASSIVE model). Please note that I tried to keep the figure as short as possible, I could have plotted much more than that (feel free to request the data please!)

The first row shows the Welch PSD of the extracellular voltage (left panel) as well as the PSD of the AMPA (middle panel) and GABA (right panel) current densities (from left to right). The second row (left panel) shows a comparative example of two representative extracellular voltage PSDs (depicting 1:2 and 1:6 E/I balances, chosen to reflect the choices of Gao et al., 2017 Neuroimage). The fitted aperiodic component to the PSD (using the FOOOF library) is depicted in the middle panel and the linear slope determination (fit chosen in range 20 to 70 Hz, it does not change the qualitative results if flexed around> 20 <100 Hz) is shown on the right panel.

Finally, to follow up the results I have also correlated the firing rate with the extracted aperiodic exponent and linear slope on the active model. On the first row, I depict typical action potential firing of the model neuron (intracellular potentials and calculated extracellular potentials 200 micm away from the neuron, left and middle panel respectively) that arise from the stochastic train of AMPA and GABA activations (right panel). On the bottom row, I show an example of overlay of traces of the aforementioned experimental design (left panel) followed by the correlation (Spearman’s correlation rho and probability) of firing rate against aperiodic exponential (middle panel) and linear slope (right panel).

The following conclusions are made: Increasing the inhibitory drive in either the active or passive model results in a slower aperiodic element (evident by the longer exponential decay fitted on the aperiodic element, bottom row, middle panel), while the linear slope determined becomes steeper (evident by the more negative slope) with increased strength of the inhibitory drive (bottom row, right panel). The firing rate of the neuron strongly and significantly correlated with both aperiodic (negatively) and linear slope (positively) pointing out that the inhibitory conductance sets a tone for neuron output as expected. These results suggest that in a minimalistic single compartment model, inhibitory drive (and by extension E/I balance) is reflected on both the fitted aperiodic exponent and the slope determinants. These results seem to confirm the model of Gao and colleagues where more inhibition results in steeper PSD linear slopes.

I will be happy to hear your thoughts on these! I have in hand a number of morphologically reconstructed models of neurons (with spines) that are morphologically complex and it would be nice to see how these elements may change on more complex environments.

Any ideas on what I am doing or any feedback would be much welcome!

Kindest Regards

Antonios

Dr. Antonios Dougalis,
BSc (Hons) Pharmacy, MRPharmS, Ph.D
Email: antoniosdougalis@gmail.com
Mobile: +358 4131 10657

https://scholar.google.com/citations?user=v_Ys_IYAAAAJ&hl=en&oi=ao
https://orcid.org/0000-0002-2139-1616
https://antoniosdougalis.com/

[antoniosdougalis]

Some problems with loading Aperiodic Summary

Hi, Thank you for pointing it out!. It has now been loaded, apologies for the inconvenience.

Antonios

[antoniosdougalis]

Thanks a lot for your thorough post @antoniosdougalis ! Could you please upload the pdf again? It turns out to be an hyperlink #1 Thanks beforehand

Hi, Thank you for pointing it out!. It has now been loaded, apologies for the inconvenience.

Antonios

[Valewhite86]

Hi everibody! I want to share a thought that can someway contribute to the review proposed by Makoto and concerns the relation between 1/f an ERPs. Indeed, most slow-wave potentials (slow drift, SPN, CNV, SCPs, and even ERP baselines) live down in the very low frequency range (0.1–3 Hz). Because the 1/f aperiodic component gets stronger as frequency goes to zero, it basically dominates that part of the spectrum. So any slow deflection we see at the scalp is probably a mix of:

1. actual physiological slow potentials (DC shifts, sustained synaptic input, glial/vascular stuff)
2. the low-frequency tail of the 1/f background.
   If we don’t account for the 1/f part, we might be misreading slow ERP components. This is the issue raised in tryiing separating oscillatory vs. aperiodic activity. Please let me know if this can contribute to a piece of discussion in case. @MakotoMiyakoshi thanks in advance.

[MakotoMiyakoshi]

Hi @Valewhite86,

I love your handle name. If I follow your rule, I am MakoPalace78.
So, what do you mean by 1/f background? What is the generative mechanism of it?

[Valewhite86]

Hi @MakoPalace78 :)
thanks again for the discussion and the references you are providing in othes replies!
Maybe I wasn’t very clear before, so let me try to restate my point more cleanly.
When I wrote my earlier paper (Sarrias-Arrabal, Bianco & Di Russo, 2023, Cognitive Neurodynamics) I was still coming from a strong ERP tradition. Back then I followed the standard preprocessing pipeline without ever explicitly considering the contribution of the 1/f aperiodic background to the emergence of ERP components across trials. Only later, once I started isolating the frequency contributions to the slow-wave potentials I realized that the very low-frequency tail of the 1/f component can heavily bias or “inflate” the apparent size of slow potentials. . This made me appreciate the importance of explicitly modeling or removing the 1/f part (also for ERP-preprocessig pipeline and not only when working with spectral analysis), otherwise the slowest components of the signal can be exaggerated. Regarding the origin of 1/f: coming from a pharmacological/physiological background, the Gao et al. (2017) model makes a lot of sense to me. Of course, I also agree with you (and others in this thread) that this cannot be the only source. However, you mentioned that you are "investigating physiological mechanism the contributes 1/f-ness other than Gao's AMPA/GABA_A model".. do you already have a paper on this?

[EugenMasherov]

The ability to assess the ratio of excitatory and inhibitory influences using a noninvasive and accessible method like EEG seems incredibly attractive and clinically important. However, first, I would like to understand how the characteristics of EPSPs and IPSPs are reflected in the slope of the frequency dependence of the aperiodic component's power. First, I note that the main difference—the potential sign—has no effect on the spectrum's shape, as the spectrum is the absolute value of the Fourier transform. The signal shape varies, and this may be reflected in the spectrum's shape, but is there truly a common response shape for all excitatory neurotransmitters that differs from that for inhibitory ones?
Borrowing a graph from a well-known textbook and digitizing the curve, we see that they differ in both the position of the extremum (18.8 ms for EPSPs and 30.8 ms for IPSPs) and the decay decrement (0.0444 per millisecond for EPSPs and 0.0304 for IPSPs). However, it is unclear whether these are typical values ​​or the result of a single experiment, and to what extent they are characteristic of other neurotransmitters. The spectrum of the signal generated by a Poisson pulse stream with such a single response can be analytically calculated. This will yield the difference in the dependence indices of the 1/f ^ alpha type. However, the accuracy will depend heavily on the accuracy of the approximation of the shape of the postsynaptic potential.