Power-Law Scaling in the Brain Surface Electric Potential
Open accessAbstract
Recent studies have identified broadband phenomena in the electric potentials produced by the brain. We report the finding of power-law scaling in these signals using subdural electrocorticographic recordings from the surface of human cortex. The power spectral density (PSD) of the electric potential has the power-law form P(f ) approximately Af(-chi) from 80 to 500 Hz. This scaling index, chi = 4.0+/-0.1, is conserved across subjects, area in the cortex, and local neural activity levels. The shape of the PSD does not change with increases in local cortical activity, but the amplitude, A, increases. We observe a "knee" in the spectra at f(0) approximately 75 Hz, implying the existence of a characteristic time scale tau = (2pif(0))(-1) approximately 2 - 4ms. Below f(0), we explore two-power-law forms of the PSD, and demonstrate that there are activity-related fluctuations in the amplitude of a power-law process lying beneath the alpha/beta rhythms. Finally, we illustrate through simulation how, small-scale, simplified neuronal models could lead to these power-law observations. This suggests a new paradigm of non-oscillatory "asynchronous," scale-free, changes in cortical potentials, corresponding to changes in mean population-averaged firing rate, to complement the prevalent "synchronous" rhythm-based paradigm.
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The power spectra of neural signals typically follow a power-law form, indicating temporal correlations that persist across multiple timescales.
“The power spectra of neural signals typically follow a power-law form (), indicating temporal correlations that persist across multiple timescales (He et al. 2010; Miller et al. 2009; Linkenkaer-Hansen et al. 2001; Touboul and Destexhe 2010).”
From The myth of the Bayesian brain (2025) · cites this paper as Miller et al. 2009
The Abstract and Results report power-law spectra in human cortical-surface recordings, particularly from 80–500 Hz. The Introduction describes a process with no preferred timescale, but the Discussion links the spectra to possible short characteristic correlation times; it does not establish persistent temporal correlations across multiple timescales or that neural signals generally have this form. Page numbers are unavailable in our copy. (LLM, conf=0.86)
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Mangalam, M. (2025) · European Journal of Applied Physiology · doi:10.1007/s00421-025-05855-6 · Cited by 14 · see citing works
“Scale-free dynamics: The power spectra of neural signals typically follow a power-law form ( 1 ∕ f 𝛽 ), indicating temporal correlations that persist across multiple time-scales (He et al. 2010; Miller et al. 2009; Linkenkaer-Hansen et al. 2001; Touboul and Destexhe 2010).”
- Authors
- Miller, K. J., Sorensen, L. B., Ojemann, J. G., & den Nijs, M.
- Affiliations
- University of Washington (US)
- Corresponding author
- Miller, Kai J.
- Venue
- PLoS Computational Biology
- Publisher
- Public Library of Science (PLoS)
- Published
- 2009-12-18
- Volume
- 5
- Issue
- 12
- Pages
- e1000609
- ISSN
- 1553-734X (ISSN-L)
- 1553-7358
- PMC
- PMC2787015
- OpenAlex
- W2025933288
- Cited by
- 742
- References
- 75
- Citations by year
- 2026: 52 · 2025: 69 · 2024: 71 · 2023: 47 · 2022: 65 · 2021: 51 · 2020: 46 · 2019: 50 · 2018: 42 · 2017: 40 · 2016: 40 · 2015: 39 · 2014: 35 · 2013: 33 · 2012: 22
- FWCI
- 9.84
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS Computational Biology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Figshare (submittedVersion, cc-by)
- Funders
- National Science Foundation (0622252, 0130705)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cognitive Neuroscience › EEG and Brain-Computer Interfaces
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- power-law scaling, power spectral density, subdural electrocorticography, human cortex, characteristic time scales, neuronal firing rate
- MeSH terms
- Action Potentials, Algorithms, Brain Mapping, Cerebral Cortex, Computer Simulation, Electroencephalography, Epilepsy, Humans, Poisson Distribution, Computational Biology
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