Separating Neural Oscillations from Aperiodic 1/f Activity: Challenges and Recommendations

Abstract

Electrophysiological power spectra typically consist of two components: An aperiodic part usually following an 1/f power law [Formula: see text] and periodic components appearing as spectral peaks. While the investigation of the periodic parts, commonly referred to as neural oscillations, has received considerable attention, the study of the aperiodic part has only recently gained more interest. The periodic part is usually quantified by center frequencies, powers, and bandwidths, while the aperiodic part is parameterized by the y-intercept and the 1/f exponent [Formula: see text]. For investigation of either part, however, it is essential to separate the two components. In this article, we scrutinize two frequently used methods, FOOOF (Fitting Oscillations & One-Over-F) and IRASA (Irregular Resampling Auto-Spectral Analysis), that are commonly used to separate the periodic from the aperiodic component. We evaluate these methods using diverse spectra obtained with electroencephalography (EEG), magnetoencephalography (MEG), and local field potential (LFP) recordings relating to three independent research datasets. Each method and each dataset poses distinct challenges for the extraction of both spectral parts. The specific spectral features hindering the periodic and aperiodic separation are highlighted by simulations of power spectra emphasizing these features. Through comparison with the simulation parameters defined a priori, the parameterization error of each method is quantified. Based on the real and simulated power spectra, we evaluate the advantages of both methods, discuss common challenges, note which spectral features impede the separation, assess the computational costs, and propose recommendations on how to use them.

Keywords: 1/f exponent; EEG/MEG; FOOOF; IRASA; Neural oscillations; Spectra.

Fig. 1

Algorithms for 1/f estimation. IRASA: a) Simulated time series. b) PSDs of resampled time series on the y-axis and frequencies on the x-axis. In this figure, the time series is upsampled by the resampling factors $h_i$ of the $h_{\text{set}}=\left\{1.3,,,1.6,,,2\right\}$ and downsampled by $1/h_i$. c) The geometric mean of all resampling pairs ($h_i$, $1/h_i$) is calculated. d) The aperiodic component (orange) is the median of the geometric means. A final fit (dashed-blue) estimates the y-intercept and the 1/f exponent $\beta$. FOOOF: e) A PSD is calculated from the time series. f) FOOOF applies an initial linear fit (dashed-blue) to the PSD in log–log space and g) subtracts the obtained linear trend from the spectrum. h) A Gaussian model (dotted-green) is fitted to the largest peak exceeding the thresholds (dashed-grey) and removes it. The relative threshold is recalculated from the peak-removed flattened spectrum (pink). The procedure is repeated until no peak exceeds the relative threshold. d) Subtraction of all Gaussian models from the original PSD yields the aperiodic component, which is then finally re-fit

Fig. 2

The spectral plateau disrupts the 1/f power law. The x-axis and the y-axis indicate frequency and PSD, respectively. a) Simulation of an aperiodic PSD (black) with a plateau starting at $100$ Hz (grey). The spectrum starts to deviate from the ground truth (dashed line) after around $10$ Hz. Applying FOOOF yields smaller 1/f exponent estimates with larger upper fitting range borders. b) A Parkinsonian LFP spectrum from the subthalamic nucleus shows large oscillations that hinder the plateau onset’s precise detection. c) Adding oscillations of various powers and widths on top of different aperiodic ground truths yields the same 1/f estimation of $\beta \approx 0.77$ in FOOOF. The ground truths are $\beta =1$ (blue), $\beta =1.5$ (green), and $\beta =2$ (orange)

Fig. 3

Oscillations must not cross fitting range borders. a) Upper panel: PSD of a simulated spectrum with β = 2 and oscillations at 5 Hz, 15 Hz, and 35 Hz (black). The x-axis and the y-axis indicate frequency and PSD, respectively. Lower panel: The exponent $\beta$ is measured using FOOOF for all 80 frequency ranges from 1–100 Hz to 80–100 Hz (red). The x-axis indicates the lower fitting range border, while the y-axis shows the absolute deviation from the ground truth. b) Various frequency ranges commonly used for E–I estimation are applied to an STN-LFP PSD of a Parkinsonian patient (purple). Since many of the chosen ranges overlap with spectral peaks, the estimated exponents $\beta$ are strongly differing. FOOOF parameters: max_n_peaks = 0 (for 30–45 Hz); max_n_peaks = 1 (for 40–60 Hz); peak_width_limits = (1, 100) (for 1–45 Hz and 1–95 Hz). c) The simulated PSD in the middle panel (green) was tuned to match the empirical PSD in b) (purple). FOOOF estimates a similar aperiodic exponent for the simulated and the real spectrum (β = 0.61). When decreasing the power of the 2 Hz delta oscillation (blue), the estimated aperiodic exponent decreases (β = 0.50) despite a constant exponent for the simulated spectrum. When increasing the power of the delta oscillation (orange), the estimated aperiodic exponent increases (β = 0.72)

Fig. 4

FOOOF cannot characterize oscillation peaks that are not clearly distinguishable. a) Left: Time series of an absence seizure measured using EEG. Turquoise: Pre-seizure, red: seizure, yellow: post-seizure activity. Right: Corresponding PSDs and aperiodic FOOOF fits. Note the increase of the 1/f exponent during the seizure. b) Left: Simulated 1/f noise and temporarily (red) added 3 Hz saw-tooth signal. Right: Aperiodic FOOOF fits. Note the increase of the 1/f exponent despite constant ground truth of ${\beta }_{\text{truth}}=1.8$

Fig. 5

IRASA’s evaluated frequency range is larger than the fitting range. a) Upper panel: Same simulation as in Fig. 3a. Lower panel: The lower fitting range border is shown on the x-axis, the absolute deviation from the ground truth on the y-axis. IRASA correctly estimates the 1/f exponent for all used fitting ranges. b) Simulated aperiodic PSD with a ground truth of $\beta =2$. A 1 Hz highpass filter disrupts the 1/f power law. IRASA’s fitting range for the maximum resampling factor $h_{\text{max}}\in \{2,8,15\}$ is indicated as bright-colored lines upon the fitted aperiodic components, with the evaluated frequency ranges after up- and down-sampling indicated in corresponding transparent colors. IRASA’s error of the 1/f estimation increases with larger resampling rates $h_{\text{max}}$ (and lower resampling rates 1/$h_{\text{max}}$, respectively). c) Same as b) with a spectral plateau disrupting the 1/f power law. d) FOOOF 1/f estimate within 1–30 Hz for a spectrum obtained from voxel data after MEG source reconstruction. e) IRASA 1/f estimates for an evaluated frequency range of 1–30 Hz (green) and an evaluated frequency range of 0.3–90 Hz (green-dashed, corresponding to a fitting range of 1–30 Hz at h_max = 3). f) FOOOF (blue) and IRASA (green) estimates of the 1/f exponent for the same fitting range of 1–30 Hz

Fig. 6

Broad peak widths require large resampling factors. a) Upper panel: Similar as in Fig. 5a) but with increasing peak widths from left to right. Note that removal of peaks from the aperiodic component (grey) worsens with broader peak widths. Lower panel: The lower fitting range border is on the x-axis, the absolute deviation from the ground truth on the y-axis. The 1/f exponent estimation error increases with larger peak widths. b) Simulation of a 30 Hz and 300 Hz peak with increasing peak widths from left to right. Larger peak widths require larger resampling factors. Note that not the absolute peak width but rather the logarithmic peak width $\mathrm{\Delta }{f}_{\mathit{log}}$ determines the minimum resampling factors

Fig. 7

IRASA cannot characterize oscillation peaks that are not clearly distinguishable. a) and b) left panel: Same as Fig. 4a) and b) Right panel: Same as Fig. 4 but showing the 1/f fits by IRASA. c) IRASA’s performance on the simulation drops significantly if two strongly overlapping peaks in the alpha (10 Hz) and beta range (25 Hz) are added. Ground truth: ${\beta }_{\text{truth}}=1.8$

Fig. 8

“Easy” and “hard” PSDs. a) Left: Voxel MEG PSD of a Parkinsonian patient on a semilogarithmic scale. Right: Same PSD on a double logarithmic scale. FOOOF, IRASA, and simply connecting the PSD value at 1 Hz to the PSD value at 95 Hz as a straight line (“straight”) yield similar 1/f exponents. We regard such a PSD as “easy” because it avoids all the discussed challenges. b) LFP data of a Parkinsonian patient on a semilogarithmic scale. Right: Same PSD on a double logarithmic scale. FOOOF, IRASA, and “straight” yield different 1/f exponents. We regard such a spectrum as “hard” because it contains many challenges