Parameterizing neural power spectra into periodic and aperiodic components

Abstract

Electrophysiological signals exhibit both periodic and aperiodic properties. Periodic oscillations have been linked to numerous physiological, cognitive, behavioral and disease states. Emerging evidence demonstrates that the aperiodic component has putative physiological interpretations and that it dynamically changes with age, task demands and cognitive states. Electrophysiological neural activity is typically analyzed using canonically defined frequency bands, without consideration of the aperiodic (1/f-like) component. We show that standard analytic approaches can conflate periodic parameters (center frequency, power, bandwidth) with aperiodic ones (offset, exponent), compromising physiological interpretations. To overcome these limitations, we introduce an algorithm to parameterize neural power spectra as a combination of an aperiodic component and putative periodic oscillatory peaks. This algorithm requires no a priori specification of frequency bands. We validate this algorithm on simulated data, and demonstrate how it can be used in applications ranging from analyzing age-related changes in working memory to large-scale data exploration and analysis.

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Fig. 1: Overlapping nature of periodic and aperiodic spectral features.
Fig. 2: Algorithm schematic on real data.
Fig. 3: Algorithm performance on simulated data.
Fig. 4: Algorithm performance compared with human raters on real EEG and LFP data.
Fig. 5: Age-related shifts in spectral EEG parameters during resting state.
Fig. 6: Event-related spectral parameterization of working memory in aging.
Fig. 7: Large-scale analysis of MEG resting-state data uncovers cortical spectral features.

Data availability

All empirical behavioral and physiological data reported and analyzed in this manuscript are secondary uses of data that have previously been published and/or were accessed from openly available data repositories. A copy of the simulated data, as well as the code to regenerate it, is available in the GitHub repository (https://github.com/TomDonoghue/SimFOOOF). EEG data were analyzed from a previously described study33. Open-access MEG data were analyzed from the Human Connectome Project63,64, which is described on the project site (https://www.humanconnectome.org/), and are available through the data portal (https://db.humanconnectome.org/). LFP data were analyzed from rhesus monkeys from a previously described study56. Additional LFP data from rats were accessed from the HC-2 dataset54, which is available from the Collaborative Research in Computational Neuroscience (CRCNS) data sharing portal (https://crcns.org/).

Code availability

Custom code used in this manuscript is predominantly using the Python programming language, v.3.7. In addition, some preprocessing of MEG data was done in MATLAB (R2017a), using the Brainstorm package (https://neuroimage.usc.edu/brainstorm/). The algorithm code is openly available and released under the Apache-2.0 open-source software license. The code for the algorithm is available on GitHub (https://github.com/fooof-tools/fooof), and from PyPi (https://pypi.org/project/fooof/), and includes a dedicated documentation site (https://fooof-tools.github.io/). All of the code used for the analyses is openly available, and indexed on Github (https://github.com/fooof-tools/Paper). This includes all of the code used for the simulations (https://github.com/TomDonoghue/SimFOOOF), the EEG analyses (https://github.com/TomDonoghue/EEGFOOOF) and the MEG analyses (https://github.com/TomDonoghue/MEGFOOOF).

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Acknowledgements

We thank S.R. Cole, B. Postle, R. Hammonds, T. Tran, R. van der Meij and numerous other colleagues on GitHub, bioRxiv and Twitter who contributed to usability testing and provided invaluable comments, discussion and code contributions. M.H. is supported by National Science Foundation (NSF) Graduate Research Fellowship grant no. DGE1106400. P.S. is supported by a UC San Diego Frontiers of Innovation Scholars Program fellowship. R.G. is supported by the Natural Sciences and Engineering Research Council of Canada grant no. NSERC PGS-D, the UC San Diego Kavli Innovative Research Grant, the Frontiers for Innovation Scholars Program fellowship and a Katzin Prize. J.D.W. is supported by National Institute of Mental Health (NIMH) grant no. R01-MH121448 and NIMH grant no. R01-MH117763. R.T.K. is supported by a National Institute of Neurological Disorders and Stroke (NINDS) grant no. R37NS21135, NIMH Conte Center grant no. P50MH109429 and U19 Brain Initiative grant no. U19NS107609. A.S. is supported by NIMH grant no. F32MH75317. B.V. is supported by Sloan Research Fellowship grant no. FG-2015-66057, the Whitehall Foundation grant no. 2017-12-73, the National Science Foundation grant no. BCS-1736028 and the National Institute of General Medical Sciences grant no. R01GM134363-01.

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T.D., M.H., A.S., R.T.K. and B.V. initiated and designed the study. M.H. and B.V. conceived of and coded the initial algorithm. T.D. and E.J.P. designed the final algorithm and coding architecture. T.D., M.H., E.J.P., A.S. and B.V. tested and refined the algorithm. T.D. implemented the final version, wrote the tutorials and maintains the GitHub package. T.D., E.J.P., P.V., R.G. and T.N. contributed code and tested the algorithm against real and simulated data. T.D. and P.S. analyzed the EEG and MEG data. B.V. and A.S. analyzed the LFP data. A.H.L. and J.D.W. contributed LFP data and insights into analyzing them. B.V. and A.S. provided overall supervision and guidance throughout the project. All authors contributed to the manuscript.

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Correspondence to Thomas Donoghue or Bradley Voytek.

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Peer review information Nature Neuroscience thanks Peter Lakatos and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 False oscillatory power changes and illusory oscillations.

a, Here we took a real neural PSD (blue) and artificially introduced a change in the aperiodic exponent, similar to what is seen in healthy aging18. This PSD was then inverted back to the time domain (right panels). The exponent change manifests as amplitude differences in the time domain. This affects apparent narrowband power when an a priori filter is applied. This is despite the fact that the true oscillatory power relative to the aperiodic component is unaffected. b, Even when no oscillation is present, such as the case with the white and pink (1/f) noise examples here (blue and green, respectively), narrowband filtering gives rise to illusory oscillations where no periodic feature exists in the actual signal, by definition.

Extended Data Fig. 2 Algorithm performance on simulated data across a broader frequency range.

a-c, Power spectra were simulated across the frequency range (1–100 Hz), with two peaks, one in a low range, and one in a high range (see Methods), across five distinct noise levels (1000 spectra per noise level). a, Example power spectra with simulation parameters as aperiodic [offset, knee, exponent] and periodic [center frequency, power, bandwidth]. b, Absolute error of algorithmically identified peak center frequency, separated for the low (3–35 Hz) and high range (50–90 Hz) peaks. c, Absolute error of algorithmically identified aperiodic parameters, offset, knee, and exponent. All violin plots show full distributions, where small white dots represent median values and small box plots show median, first and third quartiles, and ranges. Note that the error axis is log-scaled in b and c.

Extended Data Fig. 3 Algorithm performance on simulated data that violate model assumptions.

a-c, Power spectra were simulated across a broader frequency range (1–100 Hz), with two peaks, one in a low range, and one in a high range (see Methods), across five distinct knees values (1000 spectra per knee value), with a fixed noise level (0.01). Power spectra were parameterized in the ‘fixed’ aperiodic mode (without a knee) to evaluate how sensitive performance is to aperiodic mode. a, Example power spectra with simulation parameters as aperiodic [offset, knee, exponent] and periodic [center frequency, power, bandwidth], showing spectra with knee values of 0 and 150, both fit in the ‘fixed’ aperiodic mode. b, Absolute error of algorithmically identified aperiodic exponent, across spectra with different knee values. Notably, exponent reconstruction is high when spectra with knees are fit without a knee parameter. c, The number of peaks fit by the model, across knee values. Note that all spectra in this group have two peaks, indicating here that the presence of knee’s in ‘fixed’ mode leads to overfitting peaks. d-f, A distinct set of simulations were created in which power spectra were created with asymmetric or skewed peaks (see Methods), across five distinct skew levels (1000 spectra per skew level). d, Example simulated spectra, showing two different skew levels. (e) Absolute error of algorithmically identified peak center frequency, across peak skewness values. f, The number of peaks fit by the model, across peak skewness. Note that all spectra in this set have one peak. g-i, A distinct set of simulations, in which time series were generated with asymmetric oscillations in the time domain, from which power spectra were calculated (see Methods), across five distinct levels of oscillation asymmetry (1000 spectra per asymmetry value). g, Example simulation of an asymmetric oscillation, simulated in the time domain, and the associated power spectrum. Note that the power spectrum displays harmonic peaks. h, Absolute error of algorithmically identified peak center frequency, across oscillation asymmetry values. i, The number of peaks fit by the model, compared across oscillation asymmetry values. Note that these simulations all contained one oscillation in the time domain. All violin plots show full distributions, where small white dots represent median values and small box plots show median, first and third quartiles, and ranges. Note that the error axis is log-scaled in b, e and h.

Extended Data Fig. 4 Oscillation band occurrences and relative powers in the MEG dataset.

a, The proportion of participants for whom an oscillation peak was fit, at each vertex, per band. b, The group level relative power, per band. For each participant, the oscillation power within the band was normalized between 0 and 1, and then averaged across all participants, such that a maximal relative power of 1 would indicate that all participants have the same location of maximal band-specific power. Note that alpha and beta have maximal values approaching 1, reflecting a high level of consistency in location of maximal power, whereas in theta the values are lower, reflecting more variability. The ‘oscillation score’ metric, as presented in Fig. 7, is the result of multiplying the occurrence probability map with the power maps.

Extended Data Fig. 5 Methods comparison of measures of the aperiodic exponent.

a-c, Comparisons of spectral parameterization to a linear fit (in log-log space), as used in BOSC47, on simulated power spectra (1000 per comparison). a, Comparison of a linear fit and spectral parameterization on a low frequency range (2–40 Hz) with one peak. b, Comparison across the same range with multiple (3) peaks. c, Comparison across a broader frequency range (1–150 Hz) with two peaks and an aperiodic knee. In all cases (ac), spectral parameterization outperforms the linear fit. d-f, Comparisons of spectral parameterization to IRASA48. Groups of simulations mirror those used in (ac). Note that for these simulations, the data were simulated as time series (1000 per comparison) (see Methods). IRASA and spectral parameterization are comparable for the one peak cases (d), but spectral parameterization is significantly better in the other cases (e,f). Note that as IRASA has both greater absolute error and a systematic estimation bias (see Supplementary Modeling Note). g-i, Example of IRASA and spectral parameterization applied to real data. (g) The IRASA-decomposed aperiodic component, using default settings, in orange, is compared to the original spectrum, in blue. There are still visible non-aperiodic peaks, meaning IRASA did not fully separate out the periodic and aperiodic components. h, The IRASA-decomposed aperiodic component, with increased resampling. This helps remove the peaks, but also increasingly distorts the aperiodic component, especially at the higher frequencies, due to its multi-fractal properties (the presence of a knee). i, The isolated aperiodic component from spectral parameterization (computed as the peak-removed spectrum), showing parameterization can account for concomitant large peaks and knees, providing a better fit to the data. All violin plots show full distributions, where small white dots represent median values and small box plots show median, first and third quartiles, and ranges. Note that the error axis is log scaled in af. * indicates a significant difference in between the distributions of errors between methods (paired samples t-tests). Discussion of these methods and results are reported in the Supplementary Modeling Note.

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Donoghue, T., Haller, M., Peterson, E.J. et al. Parameterizing neural power spectra into periodic and aperiodic components. Nat Neurosci 23, 1655–1665 (2020). https://doi.org/10.1038/s41593-020-00744-x

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