Disentangling Event-Related Potential and Oscillatory Sources using Time- and Frequency-Domain Source Imaging

Highlights

• •Time- and frequency-domain source imaging provide distinct views of brain responses.
• •Additive and asymmetry mechanisms localize with both, unlike phase resetting.
• •P300 and N400 responses reflect both evoked and oscillatory neural sources.

Abstract

Objective

To determine whether event-related potentials (ERPs) and neural oscillations arise from common or distinct neural sources by combining two EEG source localization methods.

Methods

We applied eLORETA and DICS, which localize activity in the time and frequency domains respectively, to both simulated and real EEG data. Simulations assessed the spatial accuracy and specificity of each method. Real data analyses were used to examine the correspondence between ERP-related activity and oscillatory dynamics in relevant frequency bands.

Results

For the P300, eLORETA and DICS yielded overlapping source localizations, indicating a shared neural origin. Although alpha desynchronization temporally aligned with the P300, its sources were spatially distinct. In the case of the auditory N1, both methods revealed bilateral activation, with higher spatial precision observed using eLORETA. For the N400, DICS revealed sources that overlapped with eLORETA’s localization, suggesting a distributed semantic network engaged through amplitude asymmetry mechanisms.

Conclusions

ERP components may result from both shared and distinct oscillatory sources, varying by frequency band and cognitive function. The complementary use of eLORETA and DICS enhances interpretability of source dynamics.

Significance

This study underscores the value of integrating time- and frequency-domain source imaging to deepen our mechanistic understanding of stimulus-locked brain responses.

1. Introduction

Event-related potentials (ERPs) are a powerful tool for investigating the temporal dynamics of neural processing, offering millisecond-level resolution of brain activity. ERPs are time-locked responses to specific events, which can interact with oscillatory activity—both evoked and induced—and can be quantified using time–frequency analysis (TFA). The relationship between ERPs and oscillations remains debated: some researchers argue they reflect the same underlying neural processes (Hagoort et al., 2004, Roehm et al., 2007, Schneider et al., 2016), while others suggest they arise from distinct mechanisms (Bastiaansen and Hagoort, 2015, Wang et al., 2012).

Three prominent theoretical accounts have emerged to explain this relationship (Cohen, 2014). The additive model proposes that ERPs are generated by neural activity that is elicited by a stimulus and simply added to ongoing background oscillations, which are then attenuated through averaging. In contrast, the phase-resetting model suggests that ERPs arise when the phase of ongoing oscillations is reset by a stimulus, leading to a consistent phase alignment across trials without requiring an increase in overall power (Makeig et al., 2002). A third perspective highlights the role of amplitude asymmetry and baseline shifts. Although neural currents are theoretically balanced in polarity, outward-directed currents may be less detectable at the scalp surface (Mazaheri & Jensen, 2008). This detection bias can introduce asymmetries in the recorded oscillatory waveform, such that peaks and troughs are unequally represented. Such asymmetries, or subtle shifts in the oscillatory baseline, could generate ERP-like signals even in the absence of stimulus-locked activity (Nikulin et al., 2010). Fluctuations in oscillatory power, when averaged across trials, might therefore mimic slow ERP components through mechanisms unrelated to traditional evoked responses (Mazaheri and Jensen, 2010, van Dijk et al., 2010). Despite these differing accounts, conclusive evidence supporting one over the others remains limited, and the neural underpinnings of ERP generation are still not fully understood.

A major obstacle in resolving this debate lies in the ambiguity of scalp-level EEG data. Due to volume conduction and spatial smearing, it is often unclear which neural sources contribute to observed signals. Electrophysiological source imaging (ESI) has therefore become a crucial tool in disentangling these processes. By reconstructing the cortical origins of EEG activity, ESI can help identify whether the same or different sources give rise to ERPs and oscillatory dynamics.

Various source localization methods have been developed to address the inverse problem of estimating cortical sources from scalp-recorded potentials. Minimum-norm-based approaches like sLORETA, dSPM, and eLORETA estimate distributed source activity by minimizing the overall power of the source solution, typically under a smoothness constraint (Dale et al., 2000, Hämäläinen and Ilmoniemi, 1994, Pascual-Marqui et al., 2011). eLORETA (exact Low Resolution Electromagnetic Tomography), in particular, improves on earlier variants by providing zero localization error for single sources under ideal conditions and reducing depth bias, making it well-suited for time-domain analyses of event-related potentials (ERPs). It computes current density estimates assuming that neighboring neuronal populations exhibit highly correlated activity. This allows for a spatially smooth yet temporally precise reconstruction of source activity across time. In contrast, spatial filtering techniques such as LCMV (Linearly Constrained Minimum Variance) and DICS (Dynamic Imaging of Coherent Sources) take a beamforming approach (Gross et al., 2001, Van Veen et al., 1997). DICS operates in the frequency domain and constructs adaptive spatial filters based on the cross-spectral density (CSD) matrix of the EEG data to localize oscillatory sources at specific frequencies. Unlike distributed methods like eLORETA that tend to produce spatially extended solutions, DICS provides more focal source estimates by maximizing the signal-to-noise ratio for narrowband oscillatory activity. This makes it particularly suitable for analyzing sustained or transient oscillations and inter-regional coherence, allowing for detailed mapping of frequency-specific neural dynamics.

While several studies have compared these methods in terms of spatial accuracy, precision and resolution (e.g. Babajani-Feremi et al., 2023, Halder et al., 2019, Pellegrini et al., 2023), fewer have explored how their complementary strengths can be leveraged to clarify the relationship between ERPs and oscillations. Notably, minimum-norm-based inverse solutions have been used to localize ERP components such as the P300 (Bocquillon et al., 2011, Criel et al., 2024, Ehlers et al., 2015, van Dinteren et al., 2018) and N400 (Criel et al., 2025, Geukes et al., 2013, Khateb et al., 2010), while DICS has been applied to identify task-related alpha and beta oscillations in attention and language paradigms (Mazaheri et al., 2014, Wang et al., 2012). However, relatively few studies have used both methods in tandem to disentangle whether time-domain and frequency-domain activity stem from shared or distinct cortical generators.

Interesting though is that other works have tried to link the oscillatory dynamics and event-related responses in other ways. Schneider & Maguire (2018) for example, identified a significant relationship between the N400 and P600 ERPs and theta and beta oscillatory dynamics during respectively semantic and syntactic processing using Pearson's r correlation analyses. Based on these findings, they suggested that ERPs and neural oscillations measure similar neural processes. Similarly, Torrence et al. (2021) investigated the link between theta oscillations and N170 amplitudes in a dot-probe task, and found that greater N170 amplitudes were associated with greater theta oscillations, indicating that both are related to each other. Studenova et al. (2023) stated that the P300 evoked response and alpha oscillations (8–12 Hz) can be linked through the amplitude asymmetry model. They showed that the temporal evolution of the P300 and alpha amplitude is similar, and that their spatial localizations overlap. Additionally, they showed that the oscillations exhibit a non-zero mean, and both the P300 and alpha amplitude correlate with cognitive scores in a similar manner, further supporting the view that these two phenomena may share a common underlying neural mechanism.

While these studies offer valuable insights into the potential relationship between ERPs and oscillatory activity, they often infer this link indirectly, through correlations between ERP components and power in specific frequency bands, rather than explicitly examining whether these signals originate from common or distinct neural generators. As such, these associations do not clarify the mechanistic or spatial overlap between ERP and oscillatory sources. Without source-level analyses, it remains unclear whether these signals reflect shared cortical origins or merely co-occur due to parallel processes. Thus, a more integrated methodological approach is needed to directly test the extent of overlap between ERP and oscillatory sources.

We argue that combining different ESI methods offers a promising approach to address the open question of how ERPs and neural oscillations are related. In this study, we use both simulations to illustrate the strengths and limitations of eLORETA and DICS, and demonstrate how these tools can be applied to localize the sources of the P300 and N400 ERP components in real data. Through this, we aim to provide new insights into the interplay between phase-locked and non-phase-locked activity, and to assess whether distinct neural mechanisms contribute to each.

2. Materials and methods

2.1. Simulations

To illustrate how ESI can help us understand the relationship between ERPs and neural oscillations, we simulated the three prominent theoretical accounts. In short, our simulation approach consists of generating neural activity in distinct brain regions, adding realistic noise, and projecting the resulting signals to the scalp using a template head model.

This head model was based on Freesurfer’s standard template brain, fsaverage (Fischl, 2012). A three-layer boundary element model (BEM) was constructed, using the inner skull, outer skull, and scalp surfaces to define the compartments. Standard conductivity values were assigned to each layer: 0.3 S/m for both the brain and scalp, and 0.006 S/m for the skull. Dipoles were placed across the cortical surface with approximately 3 mm spacing, resulting in roughly 10,000 dipoles per hemisphere. Each dipole was constrained to be oriented normal to the cortical surface. The EEG leadfield matrix was then computed using the BEM approach.

Two different scenarios were simulated. In each scenario, we simulated a network involving two active brain regions: the left occipital pole and the left inferior temporal sulcus for the first scenario, and the right inferior frontal cortex (pars opercularis) and the left supramarginal gyrus in the second scenario. These regions were defined using the Destrieux cortical atlas (Destrieux et al., 2010), and for each region of interest (ROI), dipoles within a 10 mm radius of the parcellation center were selected. Additionally, we modeled a change in the amplitude of an ongoing oscillation. In Scenario 1, we included an increase in the amplitude of a 9 Hz oscillation in the frontal lobe between 400–800 ms, and in Scenario 2, a decrease in amplitude of a 22 Hz oscillation was modelled in the precentral gyrus, again between 400–800 ms.

In each simulation scenario, 80 epochs of 1600 ms were simulated, half of which contained the ERP as well as pink noise and ongoing oscillatory activity, while only the noise and ongoing oscillations were included in the other half. In each epoch, a pre-stimulus window of 300 ms was considered. By including epochs which only contain noise, and thus simulating two different conditions, it is possible to investigate the difference between the localizations obtained for both conditions. The noise amplitude was adjusted to achieve a signal-to-noise ratio (SNR) of −5 dB. The SNR was defined as the ratio of the peak amplitude of the ERP component to the peak-to-peak amplitude measured within the pre-stimulus window. This approach helps in reducing systematic biases in the source reconstruction process. If certain types of noise or non-specific activity consistently affect the EEG data, this might lead to similar localization errors across both conditions. By subtracting one condition from another, these systematic errors can be reduced, leading to a more accurate estimate of the neural sources.

2.1.1. The additive model

The additive model assumes that ERPs arise from stimulus-evoked neural activity that is linearly added to ongoing background oscillations, which are attenuated through trial averaging (Cohen, 2014). In this simulation, ERP waveforms were modeled using half-cycle sinusoidal signals.

As stated before, two different scenarios were simulated. In Scenario 1, we simulated a network involving the left occipital pole and the left inferior temporal sulcus. ERP activity was generated as a 4 Hz half-cycle sinusoidal waveform lasting 125 ms. To mimic a simple propagation pattern, a temporal delay was introduced: the ERP began in the first ROI at 200 ms post-stimulus and in the second ROI 10 ms later. Additionally, we modeled an increase in the amplitude of a 9 Hz ongoing oscillation in the frontal lobe between 400–800 ms.

In Scenario 2, a different network was simulated involving the right inferior frontal cortex (pars opercularis) and the left supramarginal gyrus. ERP activity here was modeled using a 6 Hz half-cycle sinusoid, and an amplitude decrease was applied to an ongoing 22 Hz oscillation in the precentral gyrus, again between 400–800 ms.

2.1.2. The phase-resetting model

The phase-resetting model, on the other hand, suggests that ERPs arise when the phase of ongoing oscillations is reset by a stimulus, leading to a consistent phase alignment across trials without requiring an increase in overall power (Makeig et al., 2002).

In this case, again two different scenarios were simulated. An ongoing oscillation of respectively 4 Hz (Scenario 1) and 6 Hz (Scenario 2) was simulated in the same ROIs as before, i.e. the left occipital pole and the left inferior temporal sulcus for Scenario 1 and the right inferior frontal cortex pars opercularis and the left supramarginal gyrus for Scenario 2. The phases of the oscillations were in both scenarios reset at 200 ms post stimulus onset, eliciting an ERP. As in the additive model scenarios, also here an increase in the amplitude of a 9 Hz ongoing oscillation at the frontal lobe was added between 400 ms and 800 ms in the first scenario, while a decrease in the amplitude of an ongoing oscillation in the precentral gyrus at 22 Hz was added in the second scenario.

2.1.3. The amplitude asymmetry model

The amplitude asymmetry model posits that ERPs can emerge from a stimulus-induced bias in the amplitude distribution of ongoing oscillations, without necessarily involving additive activity or phase resetting. In this account, even a symmetric oscillation can produce ERP-like components if it exhibits a non-zero mean, such that post-stimulus amplitude increases result in a consistent shift in the trial-averaged signal (Mazaheri & Jensen, 2008).

For these simulations, we used the same two ROIs as in the previous models. In both scenarios, we simulated ongoing oscillatory activity at either 4 Hz (Scenario 1) or 6 Hz (Scenario 2), using sinusoidal waveforms with a small positive baseline shift. This offset caused the oscillations to have a slightly positive mean, thereby introducing an asymmetry in the waveform. No explicit ERP waveform was added, and no phase resetting was applied.

A transient increase in the amplitude of the ongoing oscillation was introduced starting at 200 ms post-stimulus and lasting for 250 ms. Due to the baseline shift, this amplitude modulation led to a consistent deflection in the averaged signal, mimicking an ERP component while remaining purely oscillatory in origin.

In parallel with the other models, both scenarios included modulation of ongoing oscillations: an increase in amplitude of a 9 Hz oscillation in the frontal lobe between 400 ms and 800 ms in Scenario 1, and a decrease in amplitude of a 22 Hz oscillation in the precentral gyrus in the same time window in Scenario 2. This allowed consistent control over non-specific oscillatory activity across all simulation models.

2.2. Real data

2.2.1. Participants and data

To assess the complementarity of eLORETA and DICS, as well as if this approach allows us to get a better understanding of the link between the ERPs and the oscillations in real data, we incorporated datasets from our previous research exploring the cortical generators and functional connectivity associated with the P300 and N400 ERP components (Criel et al., 2024; Criel et al., 2025). The dataset includes 60 Dutch-speaking adults (30 men and 30 women), with an equal number of male and female participants represented in each of the following age brackets: 20–39 years, 40–59 years, and 60+ . Participants ranged in age from 23 to 80 years, with a mean age of 49.3 years (SD = 16.84). This balanced sample, stratified by age and sex, was designed to ensure the generalizability of the findings to the broader population. All participants were right-handed, as confirmed by a score of ≥ 8 on the Dutch Handedness Inventory (DHI; Van Strien, 1992). Cognitive status was screened using the Montreal Cognitive Assessment (MoCA; Nasreddine et al., 2005), with a minimum score of 26 required for inclusion (Thissen et al., 2010). General language functioning was evaluated using the Dutch version of the Comprehensive Aphasia Test (CAT-NL; Swinburn et al., 2014). Participants scoring below the cut-off on any test item were excluded. Additionally, participants self-reported no hearing impairments, normal or corrected-to-normal vision, and no history of neurological, psychiatric, or developmental disorders. The study was approved by the Ethics Committee of Ghent University Hospital (ONZ-2022–0127), and all participants provided written informed consent.

For each participant, high-density EEG was recorded from 128 electrodes using an EasyCap system (Brain Products, Germany). The ground electrode was placed at AFz, and the online reference at FCz. Impedances were maintained below 20 kΩ using an abrasive electrolyte gel (Abralyt 2000, EasyCap). EEG signals were acquired with a BrainVision BrainAmp amplifier (Brain Products, Germany) and digitized at a sampling rate of 500 Hz. Data collection was performed using the BrainVision Recorder software.

Participants completed two experimental tasks: an attentive auditory oddball paradigm designed to elicit a P300 response, and an auditory categorical priming task targeting the N400 component. In the oddball task, the standard stimulus [bə] was presented with a probability of 80%, while the deviant stimulus [gə] appeared in 20% of the trials. Both types stimuli lasted 250 ms. The main experiment consisted of 160 standard and 40 deviant trials, presented with a 2000 ms interstimulus interval (ISI), resulting in a total duration of 8 min. A brief practice block (16 standard and 4 deviant trials) preceded the main task. Participants were instructed to press a button on a Chronos response box (Psychology Software Tools, Pittsburgh, PA, USA) whenever they detected a deviant stimulus, allowing assessment of stimulus categorization.

The auditory categorical priming task was adapted from Hagoort et al. (1996) by Cocquyt et al. (2022). It consisted of 120 Dutch word pairs, each comprising a prime and a target word. Half of the pairs were semantically related (e.g., cat – horse), while the other half were unrelated (e.g., pink – coffee), with no pairs exhibiting thematic associations. Psycholinguistic properties of the target words were carefully matched across conditions for word frequency, phonological length, number of phonological neighbors, concreteness, imageability, age of acquisition, valence, arousal, dominance, and duration. For more details on stimulus selection, see Cocquyt et al. (2022). Word pairs were presented with a stimulus onset asynchrony (SOA) of 1800 ms. The interstimulus interval (ISI) between the prime and target words varied from 830 to 1520 ms to account for differences in word length. After the target word, participants were asked to judge the semantic relatedness of the word pair via button press. A delayed response design was employed to minimize movement artifacts and avoid contamination of the ERP by motor-related activity (Van Vliet et al., 2014). Responses were again collected using the Chronos response box, with participants pressing a green button for related word pairs and a red button for unrelated pairs.

2.2.2. ERP Preprocessing

The high-density EEG data recorded during an auditory oddball task (P300) and an auditory categorical priming task (N400) were processed using the MNE-python library (Gramfort et al., 2013). Bad electrode channels were automatically detected using the different noisy channel detection methods in the PREP pipeline (Bigdely-Shamlo et al., 2015). The electrodes indicated as bad were excluded from further analysis. The data was band-pass filtered using a zero-phase shift Butterworth filter with half-amplitude cut-off frequencies of 0.3 Hz and 100 Hz and a 12 dB/octave slope. The power line noise was then removed using a 50 Hz notch filter. Independent component analysis was applied for eye blink and horizontal eye movement artefact removal. In case bad electrode channels were identified and excluded in the first step, these channels were interpolated at this stage. Subsequently, data were re-referenced to an average common reference. In the next step, the data was segmented into epochs going from 200 ms before the stimulus onset to 1000 ms after. Finally, epochs containing artefacts were rejected using the following criteria: 75 µV maximum gradient criterion; 100 µV minimal/maximal amplitude criterion; 150 µV maximum difference criterion; 0.5 µV low activity criterion during 100 ms.

2.3. Time-Frequency analysis

To examine the spectral dynamics associated with both the simulated data and the experimental data, time–frequency analysis was performed using Morlet wavelet convolution. The analysis was applied to the epoched EEG data from the simulations as well as from all participants, separately for the different conditions. For each epoch, time–frequency representations (TFRs) of oscillatory power were computed using the MNE-Python package. A total of 75 logarithmically spaced frequencies were analyzed, ranging from 3 to 80 Hz. To balance temporal and spectral resolution across frequencies, the number of cycles per frequency increased linearly from 1.5 cycles at the lowest frequency to 15 cycles at the highest frequency. Wavelet transforms were computed using the fast Fourier transform (FFT) with downsampling (decimation factor = 3) to reduce computational load. The resulting TFRs were then cropped to a time window from −0.1 to 1.0 s relative to stimulus onset to remove edge artifacts.

The obtained TFRs were then averaged, over all trials and channels in the case of the simulations and over trials, channels and subjects for the experimental data, after which the data was baseline-corrected using a log-ratio transformation. To identify the time–frequency windows of interest, we applied a data-driven clustering approach to the grand-average TFR. Specifically, we selected the top 5% of absolute power values based on a percentile threshold. A binary mask was then created, marking these high-power values. Using connected component labeling, contiguous clusters of high activity were identified in the time–frequency plane. For each resulting cluster, we extracted the corresponding time and frequency boundaries. This allowed us to objectively define windows of interest that captured the most prominent task-related modulations in spectral power.

The percentile-based thresholding and clustering procedure was intended as a descriptive, data-driven approach to identify task-related modulations in the time–frequency domain and to guide the selection of windows of interest for subsequent source reconstruction. No statistical significance testing was performed at the time–frequency level, and the percentile threshold should not be interpreted as an inferential criterion. Because no mass-univariate statistical testing was conducted across time–frequency points, no correction for multiple or repeated comparisons was applied at this stage. The clustering procedure served to reduce the dimensionality of the data and to avoid point-wise comparisons across time and frequency.

2.4. Source reconstruction

Since individual MRI scans were not available for the real dataset, the same BEM head model used in the simulation setup—based on Freesurfer’s standard template subject fsaverage—was also applied for source localization in the real data (Fischl, 2012).

Two complementary inverse methods were applied for source reconstruction of both the real and the simulated EEG datasets: exact Low-Resolution Electromagnetic Tomography (eLORETA) and Dynamic Imaging of Coherent Sources (DICS). These methods target different aspects of the neural signal, with eLORETA focusing on time-locked evoked potentials and DICS estimating oscillatory power in specific frequency bands.

2.4.1. eLORETA

Source reconstruction was performed separately for each subject and condition (ERP vs. noise, standard vs. deviant, or related vs. unrelated) using the eLORETA algorithm (Pascual-Marqui et al., 2011). Given that the signal-to-noise ratio (SNR) is influenced by the number of epochs, an equal number of trials was used for both conditions before averaging and applying the inverse model.

Subsequent analyses focused on the absolute magnitude of the reconstructed dipoles, i.e. current source density (CSD), ignoring dipole orientation. As highlighted by (Fulham et al., 2014), CSD reflects both signal and noise components. To account for inter-subject differences in noise levels, CSD values were normalized using z-scores. This normalization was based on a noise estimate generated per subject: 50% of trials from each condition were randomly selected, and half of those were polarity-inverted to cancel out the ERP signal, yielding a noise-only signal with similar statistical characteristics. This synthetic noise signal was source-reconstructed, and the procedure was repeated 100 times to compute a mean and standard deviation for noise at each dipole location. The original CSD values were then z-transformed using these subject-specific noise estimates.

2.4.2. DICS

To investigate oscillatory activity in source space, Dynamic Imaging of Coherent Sources (DICS; Gross et al., 2001) was applied. This method was used to reconstruct frequency-specific power differences between conditions:ERP vs. noise for the simulations, standard vs. deviant for the P300 oddball paradigm, and related vs. unrelated for the N400 paradigm.

Cross-spectral density (CSD) matrices were computed using Morlet wavelet convolution, with the number of cycles and frequency ranges tailored to the frequencies of interest identified in the prior time–frequency analysis. For each subject, CSDs were estimated separately for each condition and for a pre-stimulus baseline period, providing both condition-specific and noise-related CSDs. Spatial filters were then computed using the forward model, the average CSD across all epochs, and the baseline CSD as the noise estimate. These filters were subsequently applied to the condition-specific CSDs to obtain source-level power estimates. To enable group-level comparisons and normalize for individual variability, the power difference between conditions (e.g., ERP minus noise, deviant minus standard, or unrelated minus related) was divided by the baseline power at each source location. The resulting normalized power changes were averaged across subjects to obtain a group-level source estimate for time–frequency window of interest.

2.5. Evaluation of the reconstructed activity

The evaluation of reconstructed neural activity was tailored to the nature of the data, distinguishing between simulated datasets with a known ground truth and experimental EEG data for which no such ground truth exists.

2.5.1. Simulated data

For the simulated datasets, ground truth was explicitly defined by the simulation design. Specifically, the spatial locations of the active sources, their temporal characteristics, and their frequency-specific modulations were known a priori for each scenario. Evaluation of the reconstructed activity therefore focused on the degree to which eLORETA and DICS recovered source activity in the predefined regions of interest (ROIs), as well as on the presence of activity outside these regions. Consistent with the aims of the study, this evaluation was qualitative and comparative in nature, emphasizing spatial correspondence, method-specific sensitivity, and differences in localization patterns across simulation models.

For ERP-related activity, reconstructed sources were examined within time windows derived from the time–frequency analysis and compared to the known ERP-generating ROIs. For oscillatory activity, evaluation additionally considered whether reconstructed power changes were confined to the simulated frequency bands and post-stimulus intervals. The simulation framework thus provided a controlled setting to assess the relative spatial specificity and interpretability of the two inverse methods under different generative assumptions.

2.5.2. Experimental data

For the experimental EEG data, no anatomical or physiological ground truth is available. Therefor, reconstructed source activity was evaluated using indirect criteria, such as the consistency of the source patterns across participants, the convergence between complementary inverse methods targeting different signal features (eLORETA for time-locked activity and DICS for oscillatory power), and the correspondence with cortical regions previously described in the generation of the P300 and N400 components. Importantly, source localization results for the experimental data are interpreted as physiologically plausible reconstructions rather than definitive localizations.

3. Results

3.1. Simulations

Fig. 1 displays the average ERP waveforms obtained from each of the three simulation models—additive, phase-resetting, and amplitude asymmetry—across both scenarios. As expected, all models produced clear ERP-like components, with peak amplitudes occurring around 265 ms in Scenario 1 and approximately 240 ms in Scenario 2. Each model exhibited distinct temporal profiles, consistent with their underlying generative mechanisms. In the phase-resetting model, oscillatory activity with similar frequency and spatial distribution persisted throughout the entire epoch, reflecting the continuous presence of the underlying rhythm. Due to the relatively small number of simulated epochs (n = 40), the non-phase-aligned oscillations were not fully averaged out, though a noticeable reduction in amplitude was observed outside the reset window. In the amplitude asymmetry model, the ERP component arose from transient amplitude modulations of an ongoing oscillation with a slight baseline shift. As a result, the evoked waveforms also exhibited lower-amplitude deflections at other time points, mirroring the same topographical distribution as the main component. Finally, subtle effects of the additional frontal oscillation modulations were visible in the waveforms for Scenario 1, where an amplitude increase was introduced. This was less evident in Scenario 2, where a decrease in oscillatory amplitude was simulated.

Fig. 1.

The average ERP waveforms for each simulation model and scenario, showing distinct temporal patterns linked to their underlying mechanisms.

The corresponding time–frequency representations are displayed in Fig. 2. In both the additive and amplitude asymmetry models, prominent transient increases in low-frequency power were observed around the time of the ERP component. Notably, these increases extended beyond the specifically simulated frequency band, affecting adjacent frequencies as well. This spread can be attributed to the inherent time–frequency trade-off associated with the spectral decomposition method, as well as the use of a finite time window that introduces spectral leakage. In contrast, the phase-resetting model did not exhibit a marked increase in power around the ERP component. This aligns with its theoretical basis, where ERP-like features emerge primarily through phase alignment across trials rather than changes in amplitude. As expected, across all simulation models, modulations were also detected in the ongoing oscillatory activity during the post-stimulus window (e.g., 400–800 ms), with peaks centered at 9 Hz and 22 Hz, depending on the scenario. These changes reflect the background oscillatory dynamics that were explicitly embedded into the simulated data.

Fig. 2.

The time–frequency plots corresponding to the simulated data, showing transient power increases in the additive and amplitude asymmetry models, with the phase-resetting model reflecting phase-based alignment.

To identify time–frequency windows of interest, we applied a percentile-based clustering procedure to the average time–frequency representations (TFRs). This revealed consistent clusters within the expected frequency bands and time windows for each model. In the additive model, the ERP-related cluster in Scenario 1 spanned 3–8.7 Hz and 146–392 ms, while in the amplitude asymmetry model it appeared between 3–7 Hz and 122–404 ms. In Scenario 2, the corresponding clusters were found between 3–15.5 Hz and 108–394 ms for the additive model, and 3–10 Hz and 150–344 ms for the amplitude asymmetry model. As expected, no ERP-related clusters were identified in the phase-resetting model for either scenario. For ongoing oscillations, power-related clusters were detected in Scenario 1 at 550–640 ms / 8.7–10.0 Hz (additive), 252–808 ms / 7.3–13.6 Hz (phase-resetting), and 526–664 ms / 8.3–10.4 Hz (amplitude asymmetry). In Scenario 2, the clusters were located at 456–746 ms / 19.3–25.2 Hz (additive), 474–732 ms / 20.2–24.1 Hz (phase-resetting), and 496–718 ms / 21.1–23.1 Hz (amplitude asymmetry).

Based on these results, we selected 130–400 ms as the time window for ERP source localization in Scenario 1, using eLORETA, and 130–400 ms / 3–8 Hz for DICS. For Scenario 2, we used 100–450 ms for eLORETA and 100–450 ms / 3–12 Hz for DICS. For localizing ongoing oscillations with power changes, we used 450–800 ms / 8–10 Hz in Scenario 1 and 480–750 ms / 21–23 Hz in Scenario 2 for DICS and used the same time windows for eLORETA.

Fig. 3 presents the source localization results for the ERP time window using both eLORETA and DICS. For all three simulation models, eLORETA successfully localized source activity to the two simulated ROIs (i.e. the left occipital pole and left inferior temporal sulcus in Scenario 1, and the right inferior frontal cortex (pars opercularis) and left supramarginal gyrus in Scenario 2) closely matching the ground truth. In contrast, DICS yielded more variable results. In Scenario 1, both the additive and amplitude asymmetry models showed source activity in the simulated ROIs, but also exhibited spurious activations outside these regions. For the phase-resetting model, no clear or consistent source localization was observed. A similar pattern emerged in Scenario 2: while DICS captured activity near the simulated sources for the additive and amplitude asymmetry models, localization was less accurate and more spatially diffuse compared to eLORETA. Again, no meaningful localization was achieved for the phase-resetting model.

Fig. 3.

The source localization results for the simulated ERP components using both eLORETA and DICS. In the first column, the ground truth of the simulated sources is shown. In Scenario 1, a 130–400 ms / 3–8 Hz time–frequency window was used for the localization using DICS, and a 100–450 ms / 3–12 Hz time–frequency window in Scenario 2. The same time windows were also used for the localizations using eLORETA.

Fig. 4 shows the source localization results for the ongoing oscillations using both eLORETA and DICS. In this case, DICS successfully identified the simulated ROIs, accurately localizing the amplitude changes in the ongoing oscillations across all models. In contrast, eLORETA did not yield clear localization results for the additive model. Interestingly, for the phase-resetting and amplitude asymmetry models, eLORETA localized some of the same regions involved in the ERP simulation. This is not entirely unexpected, as in these models, the oscillations underlying the ERP are not confined to the ERP time window but persist throughout the trial.

Fig. 4.

The source localization results for the simulated ongoing oscillations using both eLORETA and DICS. In the first column,the ground truth of the simulated sources is shown. In Scenario 1, a 450–800 ms / 8–10 Hz time–frequency window was used for the localization using DICS, and a 480–750 ms / 21–23 Hz time–frequency window in Scenario 2. The same time windows were also used for the localizations using eLORETA.

3.2. Real data

Grand-average ERP waveforms for the oddball (P300) and semantic priming (N400) tasks are shown in Fig. 5. As expected, the P300 was characterized by a positive deflection between approximately 300–800 ms post-stimulus at parietal electrodes, while the N400 showed a negative deflection between 400–800 ms at central-posterior sites.

Fig. 5.

Grand-average evoked potentials for the P300 and N400 paradigms, showing characteristic stimulus-locked components.

Fig. 6 displays the average time–frequency representations (TFRs) across participants for both the standard and deviant trials in the P300 paradigm, as well as the related and unrelated trials in the N400 paradigm. In both tasks, stimulus-related spectral modulations were evident. The P300 task revealed post-stimulus increases in low-frequency power (3–8 Hz), along with modulations in the alpha (8–12 Hz) and beta (15–30 Hz) bands. In the N400 task, broader frequency changes were observed, extending across delta, theta, alpha, and beta ranges.

Fig. 6.

Time-frequency representations for the P300 and N400 tasks, revealing distinct patterns of low- and high-frequency modulations following stimulus onset.

Cluster analysis of the TFRs revealed distinct time–frequency windows of interest for each condition. For the P300, a prominent cluster was identified in standard trials between 3 and 6.3 Hz and 96–900 ms. In the deviant trials, three clusters were found: a low-frequency cluster between 3 and 5.8 Hz from 228 to 552 ms, an alpha-band cluster between 7.6 and 11.4 Hz from 408 to 948 ms, and a beta-band cluster between 17.7 and 25.2 Hz from 354 to 594 ms. In the N400 paradigm, both the related and unrelated trials showed an early theta cluster between 3 and 5.8 Hz from 132 to 336 ms, as well as a broader cluster from 6.1 to 19.3 Hz between 330 and 1002 ms. Also a smaller cluster from 3 to 3.9 Hz between 600 and 756 ms was found in both conditions.

These cluster results were used to guide the selection of time–frequency windows for source localization using DICS. For the P300 task, we localized delta/ theta power (3–7 Hz) between 200 and 400 ms across both conditions. We also examined alpha desynchronization (6–13 Hz) between 300 and 1000 ms and beta desynchronization (20–22 Hz) between 400 and 500 ms, both derived from the deviant-minus-standard contrast. In parallel, we applied eLORETA to localize temporally defined ERP components, i.e. the P300 was localized between 300 and 800 ms. This dual approach allowed us to separately capture the spatial patterns of both evoked and induced activity.

For the N400 dataset, we adopted a similar approach. DICS windows were again based on the cluster findings, while eLORETA was informed by the timing of components in the grand-average evoked potentials. DICS was used to localize delta power between 600 and 1000 ms (3–4 Hz), theta power between 100 and 300 ms (4–6 Hz), alpha desynchronization between 300 and 1000 ms (6–12 Hz), and beta desynchronization between 300 and 1000 ms (15–20 Hz). The N1 and N400 were localized using eLORETA within the 120–180 ms and 400–800 ms windows, respectively.

The results of the source localization analyses for both the P300 and N400 paradigms are summarized in Fig. 7, Fig. 8. In the P300 paradigm, eLORETA localized the P300 component to the left and right cingulate cortex, with additional activity observed in the left superior premotor cortex. The DICS results revealed condition-specific power changes across frequency bands. Delta/Theta-band activity (3–7 Hz) between 200 and 400 ms was localized to the left superior premotor and frontal cortex. Alpha desynchronization (6–13 Hz) between 300 and 1000 ms was observed in the left superior parietal lobe, while beta desynchronization (20–22 Hz) between 400 and 500 ms was primarily localized to the left motor cortex.

Fig. 7.

Source localization results for the P300 paradigm using eLORETA and DICS, showing distinct regions involved in evoked responses and frequency-specific activity. All results were obtained by comparing the localizations obtained for both conditions.

Fig. 8.

Source localization results for the N400 paradigm using eLORETA and DICS, highlighting frontal and temporal contributions to semantic processing. Note that the early components—the N1 and theta activity—were analyzed by combining both conditions and comparing them to baseline, based on the expectation that they reflect shared auditory processing mechanisms present in both conditions. In contrast, the N400 effect, delta synchronization, alpha desynchronization and beta desynchronization were analyzed by comparing the two conditions directly.

In the N400 paradigm, eLORETA localized the N1 component to the bilateral auditory cortices. The N400 component was primarily found in the left frontal cortex, with additional activation in the right frontal and right middle temporal regions, and weaker involvement of the left temporal cortex. DICS analysis revealed theta-band power changes (4–6 Hz, 100–300 ms) in the left and right auditory cortices, extending toward the supramarginal gyrus. These early components—the N1 and theta activity—were analyzed by combining both conditions and comparing them to baseline, based on the expectation that they reflect shared auditory processing mechanisms present in both conditions. In contrast, delta synchronization (3–4 Hz, 600–1000 ms) and alpha desynchronization (6–12 Hz, 300–1000 ms), primarily observed in the left frontal cortex with some extension to the left middle temporal gyrus, and beta desynchronization (15–20 Hz, 300– 1000 ms), localized bilaterally to the posterior temporal poles, were analyzed by comparing the two conditions directly. This approach was taken to capture condition-specific neural dynamics associated with the N400 time window.

4. Discussion

In this work, we combined simulation-based and empirical approaches to explore how different neurophysiological mechanisms underlying event-related potentials can be disentangled using two complementary source localization methods: eLORETA and DICS. By systematically simulating ERPs based on three models, namely the additive, phase-resetting, and amplitude asymmetry models, and applying these source reconstruction methods to both simulated and real EEG data, we gained novel insights into how each method captures different facets of brain activity, and how they can be jointly used to better infer the origins of observed ERPs.

4.1. Complementarity of eLORETA and DICS in ERP localization

Our simulations demonstrated a clear dissociation in the localization performance of eLORETA and DICS depending on the underlying mechanism. eLORETA, which localizes activity based on evoked signals, reliably recovered the known sources of ERP components across all three models, regardless of whether the ERP was generated through additive, phase-resetting, or amplitude asymmetry mechanisms. In contrast, DICS, which localizes sources based on oscillatory power changes in the frequency domain, was particularly sensitive to amplitude-related changes, showing accurate localization only in the additive and amplitude asymmetry models. Notably, DICS failed to recover meaningful sources in the phase-resetting model, aligning with the theoretical understanding that phase-resetting does not necessarily produce power changes detectable by spectral methods. These results are consistent with, and expected from, the patterns observed in our time–frequency analysis, which likewise showed no power changes in the phase-resetting condition, underscoring this limitation of DICS.

This divergence underscores the methodological complementarity of eLORETA and DICS. Whereas eLORETA is well-suited to identify sources of time-locked ERP components, DICS is more sensitive to stimulus-induced modulations in oscillatory power, even when they are not strictly phase-locked. Therefore, interpreting ERP components solely through one method may lead to incomplete conclusions about their neural generators. When used together, these methods provide a more nuanced picture: eLORETA highlights the evoked, time-locked responses, while DICS reveals the induced, frequency-specific dynamics that may underlie or accompany ERP generation.

4.2. ERP mechanisms in Light of source localization

The different localization patterns observed across simulation models also inform the longstanding debate on what generates ERPs. While simulations cannot confirm any single model of ERP generation, they offer a controlled framework for probing how different mechanisms, such as additive activity or amplitude asymmetry, interact with different source localization techniques. The additive model, which assumes that ERPs result from the addition of transient activity to ongoing background oscillations, led both eLORETA and DICS to localize activity to the simulated sources within the ERP time window and during ongoing oscillation. Similarly, in the amplitude asymmetry model, which assumes transient amplitude increases in ongoing oscillations, both methods again identified meaningful source patterns, with DICS accurately capturing power changes and eLORETA detecting the consistent topography of the evoked component.

In contrast, the phase-resetting model, where ERPs emerge through trial-wise realignment of ongoing oscillatory phase, showed a clear dissociation: only eLORETA captured the simulated sources, while DICS yielded no consistent results. This reflects a fundamental limitation of DICS, which relies on changes in spectral power and is insensitive to phase-based dynamics. Since phase-resetting does not necessarily produce measurable power changes, DICS is unable to detect such activity. Interestingly, eLORETA also identified some of the ERP-related sources in the later (post-ERP) time windows, particularly in the phase-resetting and amplitude asymmetry models, suggesting that these mechanisms involve more sustained spatially-specific dynamics, even beyond the ERP time window.

Taken together, these findings suggest that the additive and amplitude asymmetry models are more readily detectable using both evoked and induced measures, while the phase-resetting model cannot be adequately assessed using frequency-based source localization methods like DICS, due to their insensitivity to phase dynamics. Therefore, multimethod source reconstruction provides critical leverage for adjudicating between competing mechanistic accounts of ERP generation.

4.3. Insights from real data: the P300

In the P300 oddball paradigm, we observed partial convergence between the source localization results obtained with eLORETA and DICS, particularly in the delta/theta band. While the peak time windows of these effects were not identical, they nonetheless point to potentially overlapping neural sources. This discrepancy in timing is likely due to the intrinsic trade-off in frequency-based methods—lower frequency components such as delta inherently suffer from reduced temporal resolution due to time–frequency smearing. Despite this, the spatial overlap between eLORETA's evoked activity and DICS's delta-band power increase suggests that both methods may be tapping into the same underlying neural process that supports the generation of the P300.

Moreover, time–frequency analysis and DICS revealed additional frequency-specific changes: an alpha-band desynchronization localized to the superior parietal cortex, and a beta-band desynchronization localized to the left motor cortex. These findings align with the cognitive and motor demands of the task. Alpha desynchronization in the parietal cortex has been robustly associated with attentional allocation (Capotosto et al., 2016, van Winsun et al., 1984, Woodman et al., 2022), which is expected to be enhanced in response to deviant stimuli in an oddball paradigm. The beta desynchronization observed in the motor cortex during deviant trials also fits this model: beta suppression is classically linked to motor preparation and execution (Engel and Fries, 2010, Gross et al., 2005, Heinrichs-Graham and Wilson, 2016; Stancák Jr & Pfurtscheller, 1996). Given that participants were required to press a button only in response to deviant tones, the beta decrease in these trials likely reflects the engagement of motor systems, again through transient amplitude modulations of ongoing oscillations.

These real data observations provide evidence for both additive and amplitude asymmetry mechanisms in the generation of the P300. The convergence of eLORETA and DICS in the delta range supports the additive model, where evoked components are superimposed on ongoing oscillations and lead to both increased ERP amplitude and low-frequency power. More surprisingly though is that while the time-course of the alpha desynchronization aligns closely with that of the P300, the obtained localizations do not overlap. It is however not possible to rule out the amplitude asymmetry model in this case, as it is possible that both models are involved in the P300 component generation and that the obtained amplitude shift gets lost in the combination with the additive model.

4.4. Insights from real data: the N400

In the N400 paradigm, eLORETA localized the early N1 component to the bilateral auditory cortices, in line with its well-established role in early auditory processing (Bertrand et al., 1991, Giard et al., 1994). The N400 component was primarily found in the left frontal cortex, with additional activation in the right frontal and right middle temporal regions, and weaker involvement of the left temporal cortex. This spatial pattern is consistent with prior studies implicating a predominantly left-lateralized frontotemporal network in semantic processing and integration (Kutas and Federmeier, 2011, Lau et al., 2008).

DICS analysis revealed theta-band power changes (4–6 Hz, 100–300 ms) localized to the left and right auditory cortices, extending toward the supramarginal gyrus. These results closely align with the N1 findings from eLORETA and were similarly analyzed by collapsing across conditions and comparing them to baseline. This approach was based on the expectation that these early components reflect shared auditory and early context-processing mechanisms that are not specific to semantic deviation (Bastiaansen et al., 2005).

In contrast, delta synchronization (3–4 Hz, 600–1000 ms), alpha desynchronization (6–12 Hz, 300–1000 ms) and beta desynchronization (15–20 Hz, 300–1000 ms) were evaluated by directly contrasting the deviant and standard conditions, aiming to isolate neural dynamics specific to the semantic deviation captured by the N400. Alpha desynchronization was predominantly observed in the left frontal cortex, with some spread to the left middle temporal gyrus—regions associated with semantic control and attentional engagement (Klimesch, 2012). This suggests that increased semantic or cognitive demands in deviant trials may drive greater alpha suppression, consistent with theories linking alpha decreases to active information processing. Interestingly is that the same cortical generators were found for the delta synchronization (3–4 Hz, 600–1000 ms).

The convergence of neural sources for both delta and alpha activity strongly supports the amplitude asymmetry model. In this framework, fluctuations in alpha amplitude can modulate the phase or amplitude of delta oscillations in the same regions, reflecting a cross-frequency coupling mechanism. This interdependence suggests that high-frequency alpha and low-frequency delta oscillations interact nonlinearly, providing a shared neural mechanism for cognitive processes. These findings align with existing literature, such as the work of Varga & Manns (2021) on delta-modulated alpha oscillations in memory integration, where delta-phase modulation of alpha amplitude contributes to the synchronization of distributed cortical networks. A similar interaction may also apply to the N400 component during semantic processing.

Beta desynchronization was found bilaterally in the posterior temporal poles, a region increasingly implicated in conceptual integration and context updating during language comprehension (Lam et al., 2016, Lewis and Bastiaansen, 2015). The observed beta suppression may reflect a mismatch between predicted and incoming semantic content or the need to reconfigure the current context, both of which are heightened during deviant trials.

Together, the eLORETA and DICS results converge on a view of the N400 as a product of both evoked potentials and induced oscillatory dynamics within a distributed semantic network. The N1 evoked component seems to correspond to additive neural activity, as we find an increase in theta power in the corresponding window, while the alpha and beta desynchronizations in the N400 time window point toward amplitude asymmetry mechanisms responsive to task demands.

4.5. Implications and Future Directions

This study highlights the value of multimodal source localization for disentangling the neural basis of ERPs. While eLORETA provides reliable localization of phase-locked responses, DICS offers complementary insights into frequency-specific, non-phase-locked processes. The divergence in performance across different simulation models further illustrates that observed ERP components could arise from distinct and overlapping mechanisms, each with unique implications for how brain dynamics are temporally organized.

Moreover, the interaction between different frequency bands, such as cross-frequency coupling, emerges as a critical factor in understanding ERP components. Specifically, the interplay between higher-frequency oscillations (e.g., alpha desynchronization) and lower-frequency rhythms (e.g., delta synchronization) may help explain the dynamic coordination of brain networks engaged in cognitive processing. This cross-frequency coupling provides insight into the neural mechanisms underlying complex ERP components like the N400, highlighting the importance of studying both spectral and temporal dynamics in tandem.

Moving forward, this dual-method approach can be used to characterize ERPs in clinical or cognitive populations, helping to identify whether atypical ERP responses arise from altered evoked activity, disrupted oscillatory dynamics, or both. Moreover, combining these tools with techniques like dynamic causal modeling or intracranial recordings may further deepen our understanding of the causal architecture underlying ERP phenomena.

In sum, this study provides empirical and conceptual evidence for the complementary use of eLORETA and DICS in ERP research. By harnessing the strengths of both methods, we gain a richer, more mechanistic understanding of the temporal and spectral processes that give rise to stimulus-locked brain responses.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.