Abstract
Biological neural networks translate sensory information into neural code that is held in memory over long timescales. Theories for how this occurs often posit a functional role of neural oscillations. However, recent advances show that neural oscillations are often confounded with non-oscillatory, aperiodic neural activity. Here we analyze a dataset of intracranial human EEG recordings (N = 13; 10 female) to test the hypothesis that aperiodic activity plays a role in visual memory, independent and distinct from oscillations. By leveraging a new approach to time-resolved parameterization of neural spectral activity, we find event-related changes in both oscillations and aperiodic activity during memory encoding. During memory encoding, aperiodic-adjusted alpha oscillatory power significantly decreases while, simultaneously, aperiodic neural activity “flattens out”. These results provide novel evidence for task-related dynamics of both aperiodic and oscillatory activity in human memory, paving the way for future investigations into the unique functional roles of these two neural processes in human cognition.
Significance Statement
Neural oscillations have been extensively implicated in memory encoding. However, recent advances show that oscillations are often confounded with aperiodic activity, motivating further investigation of aperiodic dynamics in memory. Here we analyze a dataset of intracranial human EEG recordings to test the hypothesis that aperiodic activity plays a role in memory, distinct from oscillations. By leveraging a new approach to time-resolved spectral parameterization, we find event-related changes in both oscillations and aperiodic activity. Based on our observations, we posit a speculative role for aperiodic activity in cognition, complementary to that of neural oscillations, in a form of neural communication through aperiodic dynamics.
Introduction
It is unclear how we are able to remember information over moderate timescales up to several minutes. This process requires sensory information to be translated into neural code that is likely moved to the frontal cortex for maintenance, however the nature of this code remains elusive. One widely-studied potential mechanism for this process of neural encoding and maintenance relies on neural oscillations, rhythmic fluctuations in neural activity that have been linked to numerous perceptual and cognitive processes, including memory (Buzsáki and Draguhn, 2004; Hanslmayr and Staudigl, 2014). Traditional approaches relate different oscillation frequency bands to distinct components of memory formation, where low-frequency theta (4–7 Hz), alpha (7–13 Hz), and beta (13–30 Hz) have been said to play functionally distinct roles from high-frequency gamma (>30 Hz; Hanslmayr et al., 2009; Nyhus and Curran, 2010; Roux and Uhlhaas, 2014; Lundqvist et al., 2016; Herweg et al., 2020).
In addition to the well-described functional role of oscillations, a debate has emerged regarding the potential functional role of aperiodic neural activity (He et al., 2010; He, 2014; Donoghue et al., 2020b; Van Bree et al., 2024). Aperiodic activity refers to irregular fluctuation in neural field potentials, and is distinct from oscillations and transients such as evoked potentials. There is strong evidence that traditional analyses conflate oscillations and aperiodic activity (Donoghue et al., 2020b, 2020a; Samaha and Cohen, 2022), which has far-reaching implications given that aperiodic activity has its own distinct dynamics, and has been shown to vary across cortical depth (Halgren, 2021), change during development (Cellier et al., 2021; Schaworonkow and Voytek, 2021; Hill et al., 2022; Shuffrey et al., 2022) and aging (Voytek and Knight, 2015; Tran et al., 2020; Brady and Bardouille, 2022), shift between task states (Gao et al., 2020), and is altered in disease (Smith, 2005; Robertson et al., 2019; Belova et al., 2021; Ostlund et al., 2021). In particular, the power spectrum slope—or the aperiodic exponent—reflects a global aperiodic neuronal process that is modulated during visual processing (Podvalny et al., 2015; Waschke et al., 2021) and working memory (Sheehan et al., 2018; Donoghue et al., 2020b), and is implicated in memory consolidation (Helfrich et al., 2021). The dynamics of this process have been described as a “rotation,” during which broadband power is modulated across all frequencies except a relatively stable rotation point known as the “intersection frequency” (Podvalny et al., 2015).
Given these new findings, even well-established observations regarding the role of oscillations in memory encoding have been called into question, where spectral tilts have been proposed as an alternative—or at least complementary—mechanism to multi-oscillation interpretations (Burke et al., 2015; Herweg et al., 2020; Fig. 1). Here, we leverage recent methodological advances (Donoghue et al., 2020b) that explicitly parameterize both periodic and aperiodic components of the neural power spectrum (Equation 1). We introduce a novel extension of this approach to permit time-resolved, event-related analyses of spectral parameters. We analyzed invasive human electroencephalography (iEEG) data from 13 participants performing a visual memory recall task (Fig. 2). We find that neural power spectra exhibit rapid task-related changes in both oscillatory and aperiodic features, simultaneously. That is, rather than a model where only oscillations change with task (Fig. 1a), or where only aperiodic activity shifts in the presence (Fig. 1b) or absence of oscillations (Fig. 1c), there is clear evidence for a mixed model (Fig. 1d). The change in aperiodic activity manifests as a dynamic, task-related “tilt”, or rotation about an intersection frequency, caused by a decrease in the aperiodic exponent (i.e., a “flattening” of the power spectrum) following stimulus presentation. This phenomenon occurs in conjunction with a decrease in narrowband, aperiodic-adjusted alpha power. These results show that consideration of both periodic and aperiodic spectral features is essential to our understanding of the neural correlates of memory encoding.
Spectral signatures of memory encoding. Simulated power spectra depict hypothesized models of memory encoding. Spectra representing the baseline (gray) and encoding (black) periods are plotted. The alpha (purple) and gamma (green) bands of interest are shaded. The intersection frequency is annotated with a black circle. a, Periodic model: the “spectral fingerprints” model posits that encoding is associated with a reduction in the amplitude of a low-frequency oscillation and an increase in the amplitude of a high-frequency oscillation. b, c, Aperiodic model: the “spectral tilt” model posits that encoding is associated with a flattening of the power spectra (i.e., a decrease in the aperiodic exponent). As depicted in c, this model does not necessitate the presence of peaks in the power spectrum. d, Combined model: here we present a novel third alternative which posits that encoding is associated with both periodic and aperiodic effects. Importantly, each model predicts a decrease in power in the alpha band and an increase in power in the gamma band during encoding.
Dataset details and experimental paradigm. Here we present a reanalysis of a previously reported dataset (Fellner et al., 2019). a, Participants engaged in a subsequent memory paradigm. This task involves an encoding phase and a recognition phase separated by a distractor task. During the encoding phase, participants are sequentially presented with images of unfamiliar faces; during the recognition phase, these same images are presented in a pseudorandom order interleaved with novel items and participants must rate their confidence with respect to whether each image was presented during the encoding phase. This study included two blocks: a face-encoding block and a word-encoding block. b, 13 patients with pharmaco-resistant epilepsy were implanted with intracranial electrodes (695 total electrodes). c, The bipolar referenced virtual electrode locations are plotted for each patient.
Materials and Methods
Experimental design
For this analysis, we reanalyzed data previously collected by Fellner et al. (2019). In the following, we briefly summarize the experimental setup and behavioral paradigm. A more extensive description of the dataset can be found in the original publication (Fellner et al., 2019).
The study protocol was approved by the ethics committee of the Friedrich Alexander University of Erlangen and the National Hospital for Neurology and Neurosurgery. All participants provided written, informed consent.
This dataset includes iEEG recordings from 13 patients (10 female; mean age, 35.54 years; range, 20–60 years) with pharmaco-resistant epilepsy. iEEG was recorded using a combination of surface grid, strip, and depth electrodes, with a total of 695 electrodes across all patients. Data were continuously sampled at 512 Hz (four participants), 1,024 Hz (8 participants), or 4,096 Hz (1 participant). Each recording was referenced to a scalp electrode.
Neural activity was recorded as patients engaged in a subsequent memory paradigm. The task consisted of two blocks: a word- and a face-encoding block. Each block consisted of an encoding, a distractor, and a recognition phase. During the encoding phase, items were sequentially presented for 2 s. After each item, a prompt instructing the participants to rate the pleasantness of the item was presented until the response. During the recognition phase, these items were presented again in a pseudorandom order interleaved with novel items; participants were instructed to rate their confidence with respect to whether they had encountered each item during the encoding phase.
Memory performance was analyzed by Fellner et al. (for additional details see Hanslmayr et al., 2009; Fellner et al., 2013, 2019). Briefly, the authors use a receiver operating characteristic approach to classify trials as “remembered” versus “forgotten.” In this approach, a single-process unequal-variance model is fit to the distribution of behavioral responses (1–6 confidence rating) individually for each patient in order to estimate the criterion (i.e., threshold), above and below which, responses are classified as “remembered” and “forgotten.”
Data preprocessing
Fellner at al. applied the following preprocessing protocol to the iEEG dataset leveraged in this study:
Segmentation: Data were epoched into trials from −1.5 to 2.5 s relative to stimulus onset.
Downsampling: Data were downsampled to 512 Hz to account for the range of sampling rates across participants.
Rereferencing: Bipolar montages were computed by rereferencing each electrode to its neighboring electrode. For grid electrodes, electrodes were rereferenced in both the vertical and horizontal dimension. The electrode locations in this dataset represent the location between the physical electrodes.
Artifact rejection and data exclusion: Electrodes located within or bordering tissue that was identified as the epileptic foci or later resected were excluded from the dataset. Data were manually inspected by a trained neurologist and a second individual to identify epileptogenic activity, and electrodes with epileptogenic activity were excluded from the dataset. Trials that exceeded the mean range, variance, or kurtosis by more than 5 standard deviations were also excluded. Finally, electrodes with <10 trials after artifact rejection were excluded from the dataset.
Code accessibility
The preprocessed dataset was reanalyzed in Python using open-source toolboxes and custom analysis scripts. All the code used for the analyses can be found at https://github.com/voytekresearch/oscillation_vs_exponent. The data from the original publication (Fellner et al., 2019) are available on the Open Science Framework repository (https://osf.io/3csku/).
Data analysis
Spectral analyses were performed using the MNE-Python toolbox v.1.6.1 (Gramfort et al., 2013; Larson et al., 2024). Power spectra were computed for the baseline (−1–0 s) and encoding (0–1 s) periods of each trial. Although stimuli were presented for 2 s, the task design did not include an equivalent baseline period; therefore, one second epochs were used for both trial periods. The multitaper method was applied to balance the bias-variance tradeoff in spectral estimation of short time windows (Babadi and Brown, 2014). The function mne.Epochs.compute_psd was applied, using a frequency bandwidth of 2 Hz. The average power spectral content for each electrode was then computed as the across-trial mean.
We first identified task-modulated electrodes, i.e., electrodes exhibiting significant modulation of alpha and gamma total power during encoding relative to baseline. For all analyses, alpha is defined as 7–13 Hz and gamma is defined as 50–90 Hz. While Fellner et al. analyzed a broader “alpha/beta” range from 8 to 20 Hz, we analyzed a narrower range to isolate a singular process in the alpha band. Total power was computed as the mean power across a given frequency band. For each electrode, significance was determined via permutation testing. A paired permutation test was used to compare the mean difference between time windows (scipy.stats.permutation_test; permutation_type: “samples”; n_resamples: 1000; alternative: “two-sided”). An alpha level of 0.05 was used to determine significance.
Single-electrode power spectra were parameterized using the spectral parameterization method and toolbox developed by Donoghue, Haller, Peterson, et al., v.2.0.0rc0 (Donoghue et al., 2020b). In this approach, the power spectrum is modeled as the combination of an aperiodic component and oscillatory peaks:
For time-resolved analysis, spectrograms were computed for each trial using multitapers. The function mne.time_frequency.tfr_multitaper was applied, using a frequency bandwidth of 4 Hz and a time window length of 500 ms, at 256 linearly spaced frequencies between 0.25 and 256 Hz. A decimation factor of 9 was applied resulting in a sliding window step size of ∼17.6 ms. The across-trial average spectrogram was then computed for each electrode. Next, single-electrode spectrograms were parameterized using the previously described spectral parameterization toolbox and settings. Spectral model fits were computed for each spectrogram time bin, yielding time-resolved estimates of oscillatory power and aperiodic activity.
Aperiodic-adjusted power was computed as the average PSD within a given frequency band relative to the aperiodic component of the spectrum. The aperiodic component was computed via spectral parameterization and subtracted from the PSD, resulting in a flattened power spectrum. The mean power within the frequency range of interest was then computed. This procedure isolates narrowband power that exceeds the aperiodic component of the spectrum, effectively separating periodic and aperiodic activity.
The intersection frequency is defined as the frequency at which power remains relatively stable during a spectral tilt/rotation (i.e., a shift in the aperiodic exponent; Podvalny et al., 2015). The intersection frequency was computed by solving for the intersection of the aperiodic power spectra for the baseline and the encoding period. For each electrode, the aperiodic components of the power spectra were computed (Eq. 3) using the previously described spectral parameterization results and the NeuroDSP toolbox 2.2.1 (Cole et al., 2019).
Statistical analyses
For all group-level comparisons, the paired hierarchical bootstrap was used. The hierarchical bootstrap is a nonparametric method to estimate the uncertainty of statistics derived from nested, multilevel, or hierarchical data structures (Saravanan et al., 2019). This method is an extension of the standard bootstrap method that accounts for nonindependence in the dataset by resampling sequentially over all levels of the hierarchical structure. In this case, to account for the statistical dependence of electrodes within the same participant, participants were resampled with replacement and then electrodes resampled within each participant. Furthermore, the paired hierarchical bootstrap accounts for the paired data structure (i.e., measures from the same electrode during the baseline and encoding periods are paired) by keeping paired samples together during the resampling process and then shuffling the condition (baseline v. encoding). The mean difference between surrogate conditions was then used as the test statistic and compared against the null hypothesis of zero. All test statistics were computed using 1,000 iterations. An alpha level of 0.05 was used to determine significance and the Holm–Bonferroni method was used to correct for multiple comparisons (Holm, 1979). To quantify effect size, Cohen's d was computed using the Pingouin toolbox 0.5.4 (Cohen, 2013; Vallat, 2018).
To compare between spectral models with different numbers of parameters, the adjusted R2 measure proposed by Ezekiel was used (Hittner, 2020):
Statistical modeling
Ordinary least-square regression was used to evaluate whether shifts in the aperiodic exponent were related to shifts in alpha and gamma power. For this analysis, we compared models using the aperiodic exponent as the independent variable to predict four different outcome variables: total alpha and gamma power and aperiodic-adjusted alpha and gamma power. Consistent with prior literature, total power was estimated as the mean PSD with the frequency band of interest; consistent with the other analyses in this paper, aperiodic-adjusted power was estimated using spectral parameterization. Bootstrap statistics were then used to evaluate and compare these regression models. For these analyses, a leave-one-out resampling procedure was applied across patients. For each resampled dataset, the regression analysis was repeated and the R2 value computed to build an empirical distribution to compare between total power and aperiodic-adjusted models for a given frequency band.
To examine whether the aperiodic exponent and aperiodic-adjusted alpha/gamma oscillatory power were predictive of memory performance on a trial-by-trial basis, we used logistic regression. For this analysis, single-trial power spectra were parameterized to estimate each spectral feature on every trial. Memory performance was regressed on the change in each spectral feature between baseline and encoding. Spectral measures were z-scored prior to model fitting. A separate model was fit for each task-modulated electrode with all features as predictors. Fivefold cross-validation was employed with a 80−20% train–test split. To account for class imbalances, we used a weighted regression approach, where the weight of each class was inversely proportional to class frequency. For a given electrode, the logistic regression equation can be written as follows:
Results
We reanalyzed a dataset previously collected by Fellner et al. (2019). Neural activity was recorded from 13 patients with pharmaco-resistant epilepsy as they engaged in a subsequent memory paradigm (Fellner et al., 2019; Fig. 2). Briefly, this task involves an encoding phase in which patients view either words or faces sequentially, and a retrieval phase in which patients are presented with these same items in a pseudorandom order, intermixed with novel items. The task requires patients to rate their confidence with respect to whether each item was presented during the encoding phase. A receiver operating characteristic (ROC) approach was used to classify trials as “remembered” versus “forgotten” (see Materials and Methods, Experimental design). This classic memory paradigm is commonly leveraged to investigate the neural correlates of memory encoding and retrieval.
Task-related dynamics
The present analyses focus on the encoding phase of the task. Data from an example electrode are shown in Fig. 3a,b. We first epoched the data relative to the stimulus presentation time, isolating the baseline (−1–0 s) and encoding (0–1 s) period of each trial. Raw iEEG time-series for several trials can be seen in Figure 3a, highlighting the shift from slower to faster fluctuations upon stimulus presentation. We then computed the power spectral density (PSD) for each epoch using the multitaper method (Babadi and Brown, 2014). The trial-average PSD for each time period is shown in Figure 3b, showing a simultaneous drop in lower-frequency power and increase in higher frequency power, with relatively stable power ∼30 Hz, hinting at a spectral rotation about an intersection frequency. The broadband rotational effect is most clear for the face-encoding block. Note that traditional, band-limited analyses easily conflate this aperiodic rotation as a coupled, push–pull relationship between a theta/alpha/beta “oscillation” and gamma “oscillation,” even though no oscillations actually need be present to observe this dynamic.
Classification of task-modulated electrodes based on total power modulation. a, Raw iEEG time-series for an example electrode. Five example trials are shown. b, Mean (N = 99 trials) power spectra for the baseline and encoding periods for an example electrode. The across-trial mean is plotted and the standard error is shaded. The alpha (purple) and gamma (green) frequency ranges are shaded. c–f, Results for the word-encoding block. c, Percentage of electrodes exhibiting significant modulation of total alpha power, total gamma power, or both frequency bands simultaneously. d, Average power spectra across all task-modulated electrodes (N = 104) for the baseline and encoding periods. e, Difference in the average power spectra for the baseline and encoding periods (encoding - baseline). The across-electrode mean is plotted and the standard error is shaded. The alpha (purple) and gamma (green) frequency ranges are shaded. f, Spatial location of task-modulated electrodes. Electrodes that are task-modulated in the alpha band only (purple), the gamma band only (green), and both bands simultaneously (black) are shown. g–j, Same as c–f, except for the face-encoding block (N = 97).
Next, we identified task-modulated electrodes, defined as electrodes exhibiting significant modulation of both alpha and gamma total power during encoding. Note that total power here is conflating aperiodic and oscillatory effects and reflects more traditional segregation of the power spectrum into a priori frequency bands rather than adjusting for aperiodic activity. These electrodes were selected for further analysis in order to disentangle oscillatory and aperiodic effects. Here, we computed total power as the average PSD within a given frequency band. For all analyses, alpha is defined as 7–13 Hz and gamma is defined as 50–90 Hz. We then used permutation testing to assess the significance of the observed difference in mean power between the baseline and the encoding period (Materials and Methods, Data analysis). This approach intentionally is agnostic to whether the task-related changes are driven by aperiodic changes, oscillatory changes, or both. For the word-encoding block, of the 695 electrodes analyzed, 248 (35.7%) exhibited significant modulation of alpha power, 238 (34.2%) exhibited significant modulation of the gamma power, and 104 (15.0%) exhibited significant modulation of power in both bands (Fig. 3c). For the face-encoding block, of the 695 electrodes analyzed, 235 (33.8%) exhibited significant modulation of alpha power, 221 (31.8%) exhibited significant modulation of the gamma power, and 97 (14.0%) exhibited significant modulation of power in both bands (Fig. 3g). The average power spectra for task-modulated electrodes are shown in Figure 3d,h; note that while there is a clear alpha peak at baseline, there is no visually apparent gamma peak. Task-modulated electrodes exhibit both narrowband alpha modulation in conjunction with broadband spectral aperiodic changes (“rotations” or “tilts” in the power spectrum; Fig. 3e,i). Task-modulated electrodes were broadly distributed across the cortex (Fig. 3f,j).
Using the identified electrodes that showed task modulation in both frequency bands (N = 104 for word encoding; N = 97 for face encoding), we set out to compare the dynamics of conventionally used total power, aperiodic-adjusted power, and aperiodic exponent measures between baseline and encoding period. We focused on these task-modulated electrodes, as here a clear dissociation between these measures for both frequency bands is possible, enabling us to examine codependencies across frequencies. We applied spectral parameterization to quantify these features of the PSD (Donoghue et al., 2020b). Spectral parameterization directly addresses previous challenges of estimating spectral slope separate from oscillations by incorporating spectral peaks and nonlinearities into the model (see Materials and Methods, Data analysis). Specifically, narrowband peaks in the power spectrum (i.e., putative oscillations) are modeled as Gaussian functions (Equation 2) and removed prior to aperiodic fitting. The aperiodic component is then modeled as a Lorentzian function characterized by a broadband offset, spectral knee, and aperiodic exponent (Eq. 3). The aperiodic exponent describes the power spectrum slope and is the focus of the present analysis.
We performed a group-level contrast of the spectral parameters between the baseline and encoding period using a paired hierarchical bootstrap to determine whether observed differences in total alpha and gamma power, aperiodic-adjusted power, and the aperiodic exponent were statistically significant. The Holm–Bonferroni method was used to correct for multiple comparisons (reported as padj) and Cohen’s d used to measure effect size. Here, aperiodic-adjusted power refers to the mean power within a given frequency range exceeding the aperiodic component of the power spectrum (Materials and Methods, Data analysis). For the word-encoding block, we show that both total alpha power (padj = 0.021, d = 0.144) and aperiodic-adjusted alpha power (padj = 0.016, d = 0.255) significantly decrease during encoding; while for the face-encoding block, we show that total alpha power (padj = 0.024, d = 0.173) but not aperiodic-adjusted alpha power (padj = 0.12, d = 0.207) significantly decreases during encoding (Fig. 4a,b). Furthermore, we show that total gamma power (word: padj = 0.021, d = −0.090; face: padj = 0.021, d = −0.141) but not aperiodic-adjusted gamma power (word: padj = 0.292, d = −0.286; face: padj = 0.292, d = −0.131) significantly increases during encoding (Fig. 4c,d). Finally, we show that the aperiodic exponent decreases during the encoding of items that were later successfully retrieved, resulting in a flatter power spectra, for both the word-encoding (padj = 0.010, d = 0.359) and face-encoding blocks (padj = 0.010, d = 0.440; Fig. 4e). These results suggest that, at the group level, modulation of spectral power during word encoding is largely driven by aperiodic effects.
The aperiodic exponent and alpha power are modulated in a task-relevant manner. Spectral parameters are contrasted between the baseline and encoding periods, separately for the word-encoding (brown; N = 104) and face-encoding (blue; N = 97) blocks. a, Total alpha power. b, Aperiodic-adjusted alpha power. c, Total gamma power. d, Aperiodic-adjusted gamma power. e, Aperiodic exponent. Single-electrode parameters were estimated from trial-averaged power spectra. See Extended Data Figure 4-1 for details on aperiodic model selection. Histograms depict the within-electrode difference between the baseline and encoding period; the vertical red line represents the across-electrode mean difference. p values are included for the contrast between baseline and encoding, using the paired hierarchical bootstrap with participant as the upper level. f, Pie chart depicting the percentage of electrodes exhibiting significant modulation of the aperiodic exponent during encoding.
Figure 4-1
Aperiodic model selection. Comparison of “knee” and “fixed” spectral parameterization models. a, Adjusted R2 values for single-electrode spectral fits for each model; the adjusted R2 was used to account for the fact that these models have a different number of parameters (see Materials and Methods, Statistical analyses). 23 outliers (5 standard deviations below the mean) were removed for visualization. b, Paired differences in adjusted R2 values show that 80% of electrodes exhibit greater R2 values when fit with the “knee” model relative to the “fixed” model. c, Spectral parameterization model fits for the grand-average power spectrum. Note that the knee model (blue) better captures the broadband shape of the spectrum than the fixed model (green). Download Figure 4-1, TIF file.
In order to disentangle oscillatory and aperiodic effects, we focused on task-modulated electrodes which exhibit modulation of total alpha and total gamma power. It is worth noting that a secondary analysis across all electrodes (N = 695) reproduces our findings that the aperiodic exponent is modulated during successful memory encoding. We performed a group-level contrast of the aperiodic exponent between the baseline and encoding period using a paired hierarchical bootstrap and Cohen's d to measure effect size and show that the aperiodic exponent decreases during both word encoding (p < 0.001, d = 0.145) and face encoding (p = 0.001, d = 0.125), although the effect size is smaller than that of the task-modulated electrodes.
We next assessed the statistical significance of observed differences in the aperiodic exponent at the level of individual electrodes. We applied a repeated measures t test, using Holm–Bonferroni correction for multiple comparisons, to single-trial spectral parameterization results. We found 21.15% (22/104) of task-modulated electrodes exhibit significant decreases in the aperiodic exponent during word encoding, while no electrodes show significant increases; similarly, we found 26.8% (26/97) of task-modulated electrodes exhibit significant decreases in the aperiodic exponent during face encoding, while 2.06% (2/97) electrodes show significant increases (Fig. 4f). These results demonstrate that task modulation is almost always in the direction of a flattening of the spectrum poststimulus, i.e., an increase in high-frequency power and decrease in low-frequency power. From the simple model of aperiodic activity reflecting the balance of excitation and inhibition, this suggests a task-related, dynamic shift toward excitation during the encoding phase of successfully retrieved memoranda.
The spectral parameterization method closely modeled the empirical power spectra for all electrodes, with an average R2 of 0.976 (Extended Data Fig. 4-1). We performed a multiverse analysis (Steegen et al., 2016) to confirm the robustness of our results across a range of spectral parameterization hyperparameters. We refit the dataset, systematically varying the maximum number of peaks (0, 2, 4, 6, and 8 peaks), the maximum peak width (4, 8, 12, 16, and 20 Hz), and the peak threshold (3, 4, and 5 standard deviations above the mean). Across all hyperparameters tested, we found that the aperiodic exponent is significantly modulated during encoding as assessed by the paired hierarchical bootstrap (p < 0.001).
Interdependence of oscillations and aperiodic activity
To assess the degree of interdependence between aperiodic activity and band power measurements, we estimated a linear regression model. We regressed alpha and gamma power on the aperiodic exponent to evaluate whether changes in the aperiodic exponent are related to changes in alpha and gamma band power. Here, we measured band power in two ways: in the first approach, consistent with most prior literature, we estimated total band power as the average power within a given frequency range, without accounting for aperiodic activity. In this scenario, the hypothesis is that a significant proportion of the task-related change in band power can be explained by task-related shifts in the aperiodic exponent. In the second approach, consistent with the other analyses in this paper that rely on spectral parameterization, we estimated aperiodic-adjusted power as the average PSD within a given frequency range relative to the aperiodic component of the power spectrum. In this case, we hypothesize that aperiodic activity will explain little to no task-related band power modulation.
We find that aperiodic exponent shifts strongly relate to total power modulation, while explaining far less of the variance in aperiodic-adjusted power. There is a strong positive relationship between modulation of the aperiodic exponent and total alpha power for the word-encoding (R2 = 0.177, F = 287.7, p < 10−57; Fig. 5a) and face-encoding blocks (R2 = 0.131, F = 99.7, p < 10−21; Fig. 5d). Similarly, there is a strong negative relationship between modulation of the aperiodic exponent and total gamma power for the word encoding (R2 = 0.229, F = 396.5, p < 10−76; Fig. 5g) and the face encoding (R2 = 0.174, F = 139.8, p < 10−29; Fig. 5j). This is consistent with the spectral “rotation” hypothesis where task-related changes in aperiodic activity can cause what looks like simultaneous decreases in low-frequency power with increases in high-frequency power, even if no oscillation is actually present in the data. In contrast, there is a weak or insignificant relationship between modulation of the aperiodic exponent and aperiodic-adjusted power. Exponent shifts only explained 0.3% of the variance in aperiodic-adjusted alpha power for the word-encoding block (R2 = 0.003, F = 4.434, p = 0.035; Fig. 5b) and 0.1% of the variance in aperiodic-adjusted alpha power for the face-encoding block (R2 = 0.001, F = 0.656, p = 0.418; Fig. 5e). Similarly, exponent shifts only explained 0.1% of the variance in aperiodic-adjusted gamma power for the word-encoding block (R2 = 0.001, F = 1.531, p = 0.216; Fig. 5h) and 0.5% of the variance in aperiodic-adjusted gamma power for the face-encoding block (R2 = 0.005, F = 3.403, p = 0.066; Fig. 5k). Additionally, we refit the model on data from each participant separately and show that aperiodic exponent shifts explain substantially more of the variance in total alpha (word encoding: T = 4.013, p = 0.002; face encoding: T = 3.405, p = 0.005; Fig. 5c,f) and gamma (word encoding: T = 3.315, p = 0.006; face encoding: T = 1.788, p = 0.099; Fig. 5i,l) power relative to aperiodic-adjusted power. For a few participants, aperiodic modulation only explained a small amount of variance in total alpha/gamma power; this is likely due to the presence of relatively strong oscillatory modulation on a subset of electrodes. These findings show that oscillations and aperiodic activity are only weakly correlated, while much more of the variance in total power can be explained by aperiodic activity alone. In other words, while stimulus-evoked modulation of periodic oscillations and aperiodic activity are related, they are mostly independent processes.
Aperiodic exponent shifts are conflated with total alpha/gamma power modulation. a, Scatterplot depicting the stimulus-evoked change in total alpha power versus the aperiodic exponent for the word-encoding block. b, Scatterplot depicting the stimulus-evoked change in aperiodic-adjusted alpha power versus the aperiodic exponent for the word-encoding block. c, Single participant regression results showing that aperiodic exponent shifts explain much more of the variance in total alpha power changes relative to aperiodic-adjusted power (N = 13). d–f, Same as a–c, except for gamma instead of alpha. g–l Same as a–f, except for the face-encoding block instead of the word-encoding block.
Spectral rotation effects on total power
To investigate how aperiodic dynamics can affect conventional power analyses, we next analyzed the intersection frequency, defined as the frequency at which power remains relatively stable during a rotation of the spectrum. This feature is of interest because the intersection frequency determines whether a change in the aperiodic exponent will result in total power increases or decreases (Fig. 6a,b). Specifically, a change in the aperiodic exponent will have inverse effects on power above and below the intersection frequency (Fig. 6b). Therefore, if aperiodic dynamics are contributing to previously reported alpha decreases and gamma increases, we expect the intersection frequency to be between the alpha and gamma bands. Previous research has demonstrated that power spectra generally rotate ∼20–60 Hz during working memory tasks, including in response to visual stimuli (∼30 Hz), auditory stimuli (∼40 Hz), and motor responses (∼60 Hz; Podvalny et al., 2015). Consistent with these previous results, we found the median intersection frequency to be 32.9 ± 20.9 Hz for the word-encoding block (Fig. 6c,d) and 37.9 ± 20.8 Hz for the face-encoding block (Fig. 6e,f). Critically, this intersection frequency is between the alpha and gamma bands. This finding suggests that decreases in the aperiodic exponent contribute to decreases in low-frequency and increases in high-frequency spectral power, which will confound total power measures within narrow frequency bands, regardless of any changes in oscillatory dynamics, if aperiodic influence is not properly corrected for. These results stand in contrast to the alternative hypothesis, where aperiodic flattening could result in uniform power increases across all frequencies, if the intersection point was at a very low frequency, or a uniform power decrease across all frequencies if the intersection point was at a very high frequency.
Power spectra rotate about central frequencies. Simulation (a, b) and empirical (c–f) analyses of the intersection frequency, i.e., the frequency at which power remains relatively stable during a rotation of the spectrum. a, A simulated neural power spectrum with no narrowband oscillatory peaks (black) is rotated at two example intersection frequencies. In both cases, the spectrum is rotated counterclockwise, i.e., the aperiodic exponent is decreased. Rotation at a low intersection frequency results in a broadband power increase (red), while rotation at a high intersection frequency results in a broadband power decrease (blue). b, Simulated rotations (decrease in the aperiodic exponent) across a range of intersection frequencies. When the intersection frequency is below both bands of interest, power in both bands decreases; when the intersection frequency is above both bands of interest, power in both bands increases; critically, when the intersection frequency is between the alpha and gamma bands, alpha power decreases and gamma power increases. c, d, Results for the word-encoding block. c, Grand-average power spectra for task-modulated electrodes (N = 104) for the baseline (gray) and encoding (black) periods. The intersection frequency is annotated with an orange circle. d, Histogram of the intersection frequency for all task-modulated electrodes, with a concentration at central frequencies. e, f, Same as c, d, except for the face-encoding block.
Time-resolved spectral parameterization
To assess the temporal dynamics of aperiodic and oscillatory measures on a more fine-grained scale, we performed time-resolved spectral parameterization. We computed the trial-average spectrogram for each electrode using the multitaper method (time bandwidth: 500 ms) and then applied spectral parameterization to each spectrogram time bin. The average spectrogram for all task-modulated electrodes is plotted for the word-encoding block (Fig. 7a; N = 104) and the face-encoding block (Fig. 7d; N = 97). Canonical decreases in low-frequency and increases in high-frequency power are clearly evident in the spectrograms. Consistent with previous reports, the time-course of total power within the alpha and gamma bands show significant decreases and increases, respectively (Fig. 7b,e). In contrast, aperiodic-adjusted power fails to show these same dynamics (Extended Data Fig. 7-1). Aperiodic-adjusted alpha is transiently modulated during word encoding (Fig. 7c) but not face encoding (Fig. 7f). While aperiodic-adjusted gamma is not significantly modulated during either task block (Fig. 7c,f). These findings add further evidence that modulation of the aperiodic exponent contributes to traditionally observed alpha and gamma power changes.
The aperiodic exponent is rapidly modulated following stimulus onset. a–c, Results for the word-encoding block. a, Baseline-subtracted group average spectrogram (N = 104). Normalized power values represent the across-time z-score, computed individually for each electrode and frequency bin. The vertical dashed line (time = 0 s) represents the time of stimulus onset. See Extended Data Figure 7-1 for aperiodic-corrected spectrograms. b, Time-resolved estimates of total power within the alpha (purple) and gamma (green) ranges. c, Time-resolved estimates of the aperiodic exponent (orange) and aperiodic-adjusted power in the alpha (purple) and gamma (green) ranges. Shaded regions represent 95% confidence intervals. Horizontal lines indicate significant modulation at a given time point, as assessed by a one-sample t test, using Holm–Bonferroni correction for multiple comparison. d–f, Same as a–c, except for the face-encoding block (N = 97). Extended Data Figure 7-2 provides evidence that the observed aperiodic modulation is independent of event-related potentials.
Figure 7-1
Aperiodic-corrected spectrograms. a, Aperiodic-corrected, baseline-subtracted group average spectrogram for the word-encoding block (N = 104). Normalized power values represent the across-time z-score, computed individually for each electrode and frequency bin. The vertical dashed line (time = 0 s) represents the time of stimulus onset. b, Same as a, except for the face-encoding block (N = 97). While the uncorrected spectrograms in 7a,b show clear rotational dynamics characterized by broadband changes in power, the aperiodic-corrected spectrograms instead show more transient and moderate power modulation with no clear broadband effects. Download Figure 7-1, TIF file.
Figure 7-2
Aperiodic modulation is independent of event-related potentials. Dissociation between event-related potentials (ERP) and exponent shifts. a,b, Empirical results from two contrasting electrodes are shown: one electrode with a clear ERP and another with a strong exponent decrease. Note that “electrode 1” exhibits a strong exponent shift but no detectable ERP, suggesting that this effect is not due to the presence of an ERP. Also note that “electrode 2” exhibits a strong ERP but only a weak exponent increase. This further suggests that the reported exponent decreases are not due to the presence of an ERP. c,d, Simulation of ERPs with similar waveforms to those observed in the empirical data. Increasing ERP amplitude is associated with increased aperiodic exponent, suggesting that empirically observed exponent decreases are not driven by the presence of ERPs. Download Figure 7-2, TIF file.
These task-related aperiodic effects are distinct from event-related potentials (ERPs). We illustrate a dissociation between ERPs and exponent shifts in empirical and simulated data (Extended Data Fig. 7-2). This dissociation is evident in two example electrodes: electrode 1 has no discernable ERP, while electrode 2 displays a clear ERP (Extended Data Fig. 7-2a). For electrode 1, there is a strong exponent decrease despite the absent ERP, suggesting that this effect is not due to the presence of an ERP; for electrode 2, there is a slight exponent increase, possibly due to the low-frequency spectral content of the ERP (Extended Data Fig. 7-2b). In simulation, we verify that ERP amplitude is positively correlated with the aperiodic exponent, suggesting that empirically observed exponent decreases are likely not driven by the presence of ERPs (Extended Data Fig. 7-2c,d).
Trial-by-trial aperiodic and oscillatory dynamics in working memory performance
Finally, we sought to assess the functional significance of the observed spectral effects on a trial-by-trial basis. To do this we performed a logistic regression for each electrode, regressing binary trial-by-trial memory performance on the change in aperiodic exponent and aperiodic-adjusted alpha and gamma power between the baseline and encoding period. We used fivefold cross-validation on an 80–20 train–test split to estimate prediction accuracy and used a one-sample t test to compare model accuracy to chance performance (i.e., 0.5: “remembered” vs “forgotten”). There was a notable class imbalance in that there were far more remembered than forgotten items (61% remembered vs 39% forgotten, on average). When we performed weighted logistic regression to account for this imbalance, performance was at chance level. Including the rotation frequency as an additional predictor did not improve model performance. Additionally, we examined whether task-active electrodes showed better prediction accuracy and whether there were topographic differences in model performance, but none of those analyses were significant.
Discussion
The present results support the hypothesis that both oscillations and the aperiodic exponent are modulated during memory encoding. Our reanalysis of the Fellner iEEG dataset (Fellner et al., 2019) leverages a novel, time-resolved spectral parameterization approach that explicitly quantifies aperiodic activity distinct from oscillations. Our findings demonstrate that the aperiodic exponent dynamically decreases—or flattens out—concurrently with changes in narrowband, oscillatory power. This aperiodic modulation was observed during both word and face encoding suggesting that it is a general feature of memory encoding that occurs in conjunction, both in time and space, with more traditional oscillatory changes during visual memory encoding.
These findings stand in contrast to dichotomous oscillations versus aperiodic models that argue against an aperiodic interpretation. This dichotomy has been drawn between two models of memory formation, which are variously referred to as oscillations or “spectral fingerprints” versus aperiodic activity or “spectral tilts” (Fellner et al., 2019). The oscillations model posits that decreases in lower-frequency theta/alpha/beta power and increases in higher frequency gamma power during memory encoding reflect multiple distinct processes and are dynamically interlinked such that reductions in low-frequency oscillations operate in a push–pull manner to high-frequency, or high gamma, activity (Miller et al., 2018; Fig. 1a). In contrast, the aperiodic model posits that these yoked changes in power across multiple frequency bands instead reflect dynamic changes in a singular aperiodic process that only look like coupled changes in different frequency bands due to the standard practice of discretizing the full spectrum into a priori bands (Fig. 1b,c). This broadband spectral shift will modulate power in a priori bands even in the absence of any oscillatory peaks (Fig. 1c). There is recent evidence that different frequency bands exhibit dissociable characteristics with respect to time, space, and stimulus response, arguing against the aperiodic perspective (Fellner et al., 2019); however, further consideration of a third mixed model (Fig. 1d) wherein both processes are dynamically altered during memory encoding is warranted.
One important theoretical aspect regarding aperiodic changes is that it is entirely plausible for event-related aperiodic flattening to result in broadband power increases or decreases, depending on the intersection frequency. For that reason, we examined the nature of this spectral flattening and found robust evidence for a “rotation” about an intersection frequency in the 30–40 Hz frequency range. This is consistent with prior reports that show opposite direction task-related dynamics in low (<30 Hz) and high (>50 Hz) frequency ranges. While these opposite direction effects are often presumed to be oscillatory in nature, suggestive of push–pull dynamics between theta/alpha/beta oscillations and gamma oscillations, our alternative hypothesis, supported by the data, is that these dynamics are aperiodic in nature, with no oscillatory changes required.
These clear, even-related aperiodic dynamics occur simultaneously with more well-described decreases in alpha oscillatory activity. From a physiological standpoint, the fact that slower oscillations and aperiodic activity are comodulated in human cortex may not be surprising due to the importance of inhibitory dynamics in oscillatory formation (Haegens et al., 2011; Snyder et al., 2015; Halgren et al., 2019) and the suggestive evidence that the aperiodic exponent may partially index excitation/inhibition balance (Gao et al., 2017; Chini et al., 2022). In the context of high gamma activity, the task-related “flattening” of the spectrum that we observe here—which has also been observed in human iEEG in the context of visual perception (Podvalny et al., 2015)—is particularly striking. While prior work has argued that broadband spectral shifts track population spiking (Mukamel et al., 2005; Manning et al., 2009; Miller et al., 2009), our spectral tilt results offer a related, but slightly different, interpretation: instead of population spikes altering total broadband power, task-related shifts in cortical excitation/inhibition balance—driven by excitatory inputs—shift the aperiodic signal to be flatter. This spectral flattening also results in an increase in high gamma power, along with a simultaneous decrease in lower-frequency power, regardless of the presence of oscillations. Each of these phenomena: oscillatory power changes, broadband power shifts, high gamma activity, and spectral tilts, all have different—but likely interrelated—interpretations.
Understanding these interrelations across frequencies requires precise analytical techniques that can separate oscillations and aperiodic activity. Although spectral parameterization is able to achieve this, this method still relies on Fourier analyses that assume a sinusoidal basis, which could be too simplifying for neural data with respect to its interpretation. There are emerging new methods such as autoregressive modeling that sidestep this assumption by analyzing aperiodic activity in the time-domain. Future directions should leverage such techniques to investigate the link between aperiodic activity and memory performance.
Previous EEG and iEEG work using subsequent memory paradigms have shown a variety of band-limited decoders can successfully predict whether an item is remembered or not in free recall tasks that are conceptually similar to the task analyzed here (Rubinstein et al., 2023; Li et al., 2024). These approaches show that successful decoding/prediction is related to decreases in low-frequency activity and increases in high-frequency activity but drops to chance levels for power in the ∼30 Hz range. Given our observations in this report, we believe that these kinds of effects are likely best explained from the perspective that aperiodic activity dynamically “rotates” about an intersection frequency that happens to be at ∼30 Hz. While the mechanistic significance of this particular intersection frequency is still an open question, computational modeling provides some clues (Gao et al., 2017). If we simplistically assume that the aperiodic iEEG signal were driven entirely by asynchronous excitation or entirely by asynchronous inhibition, those two modes represent the extremes between which the cortical iEEG signal can shift, where the power spectra of those extremes reflect the shape of excitatory and inhibitory postsynaptic currents. As the balance between those two extremes shifts from relatively inhibited (such as at rest) to increased excitatory drive (such as with coding inputs), the aperiodic exponent happens to cross at ∼30 Hz between those two modes.
These results have broad implications in light of contemporary oscillatory theories of memory. The observation of band-limited changes in neural activity has led to the widespread assumption that those changes are oscillatory in nature. Despite the persistence of this view, it has long been known to be an incorrect inference, referred to in 1948 as the “Fourier fallacy” where “one assumes ad hoc that all of the necessary frequencies actually occur as periodic phenomena in cell groups within the brain” (Jasper, 1948). This fallacy has guided assumptions that the neural code for memory must be oscillatory, where the nesting of fast oscillations inside slower ones limits memory capacity (Lisman and Jensen, 2013) with interregional oscillatory synchronization being the mechanism by which brain regions coordinate spiking in the service of memory, in a highly influential theory for neural communication known as communication through (oscillatory) coherence (Fries, 2015). Our observation of widespread, rapid, event-related aperiodic dynamics stands in stark contrast to the assumption that all band-limited changes are oscillatory. While visual cortical oscillatory alpha changes are evident during memory encoding, so too are nonoscillatory aperiodic dynamics.
Based on our observations, we posit a speculative role for aperiodic activity in cognition, complementary to that of neural oscillations, in a form of neural communication through aperiodic dynamics. Such a model is predicated on two facts: the first is that visual cortical oscillatory alpha power drops after stimulus onset, thought to reflect a state of disinhibition (Jasper and Penfield, 1949; Klimesch, 2012). We clearly observe this oscillatory alpha power decrease in our data in conjunction with changes in aperiodic activity. The second is the fact that aperiodic activity is at least partially driven by the timescales of the underlying neural population (Gao et al., 2020), which is reflected in the relative contributions of excitatory and inhibitory drive (Gao et al., 2017; Ahmad et al., 2022; Chini et al., 2022). Given the link between aperiodic activity and local excitation/inhibition, in conjunction with the fact that flatter spectra are less autocorrelated, our observation that stimulus onset results in a rapid “flattening” of the power spectrum and a drop in oscillatory alpha power suggests that the visual cortex shifts to a more excited state that is less driven by local correlations and more driven by the broad excitatory drive from the thalamus. What remains unclear is how this excitatory drive gets transduced into a delay period memory trace along the cortical hierarchy, that is protected from interference by alpha oscillatory power resurgence.
Footnotes
This work was supported by the NIH National Institute of General Medical Sciences (https://www.nigms.nih.gov/) grant R01GM134363-01 to B.V. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. We thank Fellner and colleagues for sharing their original data (Fellner et al., 2019) and Simon Hanslmayr and colleagues for fun, constructive discussions.
The authors declare no competing financial interests.
- Correspondence should be addressed to Michael Preston Jr. at mpreston{at}ucsd.edu.
