Three must-read papers for understanding EEG 1/f-ness

[MakotoMiyakoshi]

This is just my opinion. Comments are welcome!

For the E/I balance interpretation,

Gao R, Peterson EJ, Voytek B. 2017. Inferring synaptic excitation/inhibition balance from field potentials. Neuroimage. 2017 Sep; 158 70-78. DOI: 10.1016/j.neuroimage.2017.06.078, PMID: 28676297

Donoghue T, Haller M, Peterson EJ, Varma P, Sebastian P, Gao R, Noto T, Lara AH, Wallis JD, Knight RT, Shestyuk A, Voytek B. 2020. Parameterizing neural power spectra into periodic and aperiodic components. Nat Neurosci. 2020 Dec; 23(12) 1655-1665
DOI: 10.1038/s41593-020-00744-x, PMID: 33230329, PMCID: PMC8106550

For the cable theory, I would list Electric Fields of the Brain (2006) by Nunez and Srinivasan, but it is a 600-page book with full of mathematical descriptions. If someone know a good paper, please comment. Marjan mentioned this paper in his post to the original mailing list, which I have never read yet.

Pettersen KH, Lindén H, Tetzlaff T, Einevoll GT. 2014. Power laws from linear neuronal cable theory: power spectral densities of the soma potential, soma membrane current and single-neuron contribution to the EEG. PLoS Comput Biol. 2014 Nov 13; 10(11) e1003928
DOI: 10.1371/journal.pcbi.1003928, PMID: 25393030, PMCID: PMC4230751

[EugenMasherov]

There's a point in Donoghue's article that confused me. He considers a 1/f ^chi dependence. But he gives the parameters of the aperiodic component (fig.2) as exponent = 1.12 a.u. Hz^(−1). That is, it's an exponential dependence, not a power law. For a power law, the exponent would be dimensionless. So is it an exponential dependence or a hyperbola?

[dieloz]

Hi @EugenMasherov,
I'm not a math person but simulating the Lorentzian (Donoghue) and the power one, one gets the same result if the knee of the power spectrum is set to zero. Could it be just that the label you refer is wrong?

b = 0;    % broadband offset
chi = 1.12; % aperiodic exponent (what the paper reports)
k = 0;     % no knee  -> pure power law
F = logspace(-1, 2, 400);   % 0.1 to 100 Hz

% Pure power law (reference)  P(f) = A * f^(-chi)
A = 10^b;
P_powerlaw = A .* F.^(-chi);

% Lorentzian model (Donoghue)
L = b - log10(k + F.^chi);
P = 10.^L; % Donoghue with k = 0


figure;
subplot(1,2,1)
loglog(F, P_powerlaw, 'k--', 'LineWidth', 2); hold on
loglog(F, P, 'r-', 'LineWidth', 1.5);
hold off
grid on
legend('Power law 1/f^{\chi}', ['Donoghue, k = ' num2str(k)], 'Location', 'southwest')

k=2;
L = b - log10(k + F.^chi);
P = 10.^L;

subplot(1,2,2)
loglog(F, P_powerlaw, 'k--', 'LineWidth', 2); hold on
loglog(F, P, 'b-', 'LineWidth', 1.5);
legend('Power law 1/f^{\chi}', ['Donoghue, k = ' num2str(k)], 'Location', 'southwest')

[EugenMasherov]

The only thing that confuses me is the indication of the dimensions. The exponent in a power law is dimensionless. And the dimension of 1/Hz corresponds to the exponential dependence exp (-k * f )

[dieloz]

Ok I see. Can't help with that but may be it's just an inintentional labeling mistake.

[dieloz]

Thanks to the fruitfull conversations among all threads, I found this paper that strongly overlap with some of our interests:

Gerster, M., Waterstraat, G., Litvak, V. et al. Separating Neural Oscillations from Aperiodic 1/f Activity: Challenges and Recommendations. Neuroinform 20, 991–1012 (2022). https://doi.org/10.1007/s12021-022-09581-8 (python code)

I'm only halfway through reading it, but it's very clear that both IRASA and FOOOF will fail when modeling Power Spectral Density (PSD) with overlapping and broad peaks or a high-frequency spectral plateau (see Figs 2 and 3). It will be very interesting to learn from this to see if we can come up with reasonable solutions.

[MakotoMiyakoshi]

Hi @dieloz,

Yes, I remember I've read a response by Brad's group--unless I am thinking of something different. At least I know that in the case of FOOOF, users need to determine key geometric parameters for generalized Gaussian to subtract. So users are to be blamed for any bad results :-)

[mgy42]

Thank you for highlighting these resources, Makoto!

Not to toot our own horn, but I wanted to flag this paper too: Gyurkovics et al., 2021, NeuroImage - https://www.sciencedirect.com/science/article/pii/S1053811921004699 - just because this is the paper that catalysed this whole discussion. This is more relevant to discussion about whether we conceptualise the generative mechanisms of the (scalp-level) oscillations and 1/f as independent or strongly dependent. We argue they are largely independent (and this has methodological consequences), and strangely, more and more papers seem to find empirical results in line with this notion of additivity - e.g., https://www.jneurosci.org/content/43/37/6447.abstract , https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3002964 , or https://www.biorxiv.org/content/10.1101/2025.09.24.678322v1.abstract.

[MakotoMiyakoshi]

Hi @mgy42,

I agree with you. Demonstrating independence of 'oscillations' from '1/f' is a solid advancement in understanding the mechanism.

[EugenMasherov]

Regarding the 1/f slope estimate.
I have some doubts about both IRASA and FOOOF. FOOOF uses a lot of tuning parameters and postulates a peak shape (Gaussian). How much does the answer depend on prior choices? As far as I understand, the fundamental assumption underlying IRASA is self-similarity. But self-similarity is precisely what we want to prove. Isn't there a circulus vitiosus here?
Methods that use as few a priori assumptions as possible seem more credible to me. For example, as Gao suggested, using robust regression.
Another possible approach is autoregression. A 2n-order model describes n peaks corresponding to n pairs of complex roots of an auxiliary algebraic equation. Their arguments (phases) determine the peak frequency, and their magnitudes (amplitudes) determine the damping decrement. But if we take the order of the model 2n +1, then another real root appears, corresponding to an aperiodic oscillation.