Theta EEG dynamics of the error-related negativity

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Abstract

Objective

The error-related negativity (ERN) is a response-locked brain potential (ERP) occurring 80–100 ms following response errors. This report contrasts three views of the genesis of the ERN, testing the classic view that time-locked phasic bursts give rise to the ERN against the view that the ERN arises from a pure phase-resetting of ongoing theta (4–7 Hz) EEG activity and the view that the ERN is generated – at least in part – by a phase-resetting and amplitude enhancement of ongoing theta EEG activity.

Methods

Time-domain ERP analyses were augmented with time–frequency investigations of phase-locked and non-phase-locked spectral power, and inter-trial phase coherence (ITPC) computed from individual EEG trials, examining time courses and scalp topographies. Simulations based on the assumptions of the classic, pure phase-resetting, and phase-resetting plus enhancement views, using parameters from each subject’s empirical data, were used to contrast the time–frequency findings that could be expected if one or more of these hypotheses adequately modeled the data.

Results

Error responses produced larger amplitude activity than correct responses in time–domain ERPs immediately following responses, as expected. Time–frequency analyses revealed that significant error-related post-response increases in total spectral power (phase- and non-phase-locked), phase-locked power, and ITPC were primarily restricted to the theta range, with this effect located over midfrontocentral sites, with a temporal distribution from ≈150–200 ms prior to the button press and persisting up to 400 ms post-button press. The increase in non-phase-locked power (total power minus phase-locked power) was larger than phase-locked power, indicating that the bulk of the theta event-related dynamics were not phase-locked to response. Results of the simulations revealed a good fit for data simulated according to the phase-locking with amplitude enhancement perspective, and a poor fit for data simulated according to the classic view and the pure phase-resetting view.

Conclusions

Error responses produce not only phase-locked increases in theta EEG activity, but also increases in non-phase-locked theta, both of which share a similar topography.

Significance

The findings are thus consistent with the notion advanced by Luu et al. [Luu P, Tucker DM, Makeig S. Frontal midline theta and the error-related negativity; neurophysiological mechanisms of action regulation. Clin Neurophysiol 2004;115:1821–35] that the ERN emerges, at least in part, from a phase-resetting and phase-locking of ongoing theta-band activity, in the context of a general increase in theta power following errors.

Introduction

The error-related negativity (ERN or Ne) is a negative response-locked frontal ERP component occurring ∼80–100 ms following commission of response errors (Falkenstein et al., 1991, Gehring et al., 1993), the putative generator of which (Dehaene et al., 1994, Luu and Tucker, 2001, Dikman and Allen, 2000) is the dorsal anterior cingulate cortex (ACC), a region implicated in executive control. The ERN is part of a class of “medial frontal negativities” (Gehring and Willoughby, 2004), which include other negative potentials evoked in response to error feedback stimuli (Miltner et al., 1997, Badgaiyan and Posner, 1998, Ruschow et al., 2002), response competition (Gehring et al., 1992, Falkenstein et al., 1999), and gambling task losses (Gehring and Willoughby, 2002). These findings have led to the interpretation that the ERN is indicative of error monitoring (Falkenstein et al., 1991, Falkenstein et al., 2000, Gehring et al., 1993) or response competition (Carter et al., 1998) processes.

The classic view of ERPs suggests that phasic bursts of activity in several brain regions are time locked to the stimulus or response, but such bursts are uncorrelated with the background oscillatory EEG activity (cf. Yeung et al., 2004). Challenges to this view propose instead that an ERP is the result of a reorganization and phase-resetting of oscillatory EEG activity following the event of interest (e.g., Basar, 1991, Basar-Eroglu et al., 1992, Makeig et al., 2002). Investigating the ERN specifically, Luu and Tucker (2001) observed the ERN as a theta-band midline oscillation with a source localized to centromedial frontal cortex, including the ACC, a region that exhibits task-related theta-band phase locking in patients with intracranial electrodes (Wang et al., 2005). The induction and maintenance of this theta rhythmic activity may arise from interactions between pyramidal cells and inhibitory interneurons, like those found in the rat hippocampus (Buzsáki et al., 1983, Freund and Buzaki, 1996).

Luu et al. (2004) performed a detailed analysis of error-related theta activity by separately examining the magnitude of phase-locked, non-phase-locked, and total theta (phase- plus non-phase-locked) EEG signal energy (a spectral measure in units of |μV|) elicited over midfrontal sites during a speeded reaction task. Phase-locked energy indexes oscillations demonstrating relative phase consistency with respect to a reference time point (stimulus or response onset) across trials; non-phase-locked energy indexes oscillations that are relatively inconsistent in phase across trials. Using a bandpass filtering rectification method, Luu et al. (2004) found theta-range increases over midfrontal regions for error and correct trials across all three types of energy (phase-locked, non-phase-locked, and total), but with a preferential increase for error trials. Luu et al.’s data are consistent with the hypothesis that the ERN is an oscillatory process that increases in phase-locking during the commission of errors.

In order to experimentally distinguish between the classic and phase-resetting hypotheses, it is necessary to distinguish between two sub-cases of the latter; pure phase-resetting and phase-resetting with enhancement (Yeung et al., 2004). During pure phase-resetting, ongoing oscillatory EEG signals reset phase to enter an increased state of phase-locking in response to stimulus or motor events; however the EEG signal does not increase in amplitude. During phase-resetting with enhancement, the phase of ongoing oscillatory EEG resets while simultaneously increasing in amplitude in response to a relevant event. Unfortunately these hypotheses of ERN genesis (classic, pure phase-resetting, phase-resetting with enhancement) cannot be unambiguously distinguished from one another by Luu et al.’s observations. This is because discrete event-related EEG signals that are uncorrelated to background physiological signals can mimic synchronized oscillatory signals in the time–frequency domain (Yeung et al., 2004).

For example, Luu et al.’s findings could be due to the induction of ringing artifact by the bandpass filtering of a phasic ERN response. Luu et al. (2004) show, however, that the theta oscillations are present without ringing artifact in the EEG single-trials (Figs. 2–4 of Luu et al., 2004), and that energy in the theta frequency extends well beyond the ERN window, which cannot be fully accounted for by filtering artifacts (Luu et al., personal communication, 2004). While this observation supports the interpretation of the ERN as an oscillatory process, it does not speak to whether or not an increase in overall EEG amplitude is involved. Luu et al. only examined theta-range signals. It turns out that the phase-reset of an EEG signal can induce total power increases in frequencies near the initial signal base frequency before the reset, while decreasing total power at base frequencies (as demonstrated in Section 1.3.2 below). These total power changes can occur in the absence of an amplitude increase (pure phase-resetting). To test this hypothesis, one would have to examine nearby frequency ranges for evidence of frequency shifts in spectral activity, something that Luu et al. did not do.

Thus distinguishing among these three hypotheses of ERN genesis might be better suited for modern time–frequency measures (such as wavelet transformations) that are less susceptible to bandpass filtering artifacts and that can assess multiple frequency ranges simultaneously. This latter characteristic affords a thorough way to investigate if the ERN arises primarily from theta-range signals, or if it additionally reflects signals within nearby frequency ranges (delta, alpha). Furthermore, these modern methods provide measures that directly assess the degree of phase-resetting and phase-locking of a signal across trials (see Section 2.6). Nonetheless, Yeung et al. (2004) have argued that these methods, when applied qualitatively, cannot differentiate unambiguously between the classic and phase-resetting views of the ERN.

Many studies have examined the differences in event-related phase synchronization predicted by the three views (classic, phase-resetting, phase-resetting with enhancement). Unfortunately, modern phase synchronization measures are beset by interpretational difficulties. Yeung et al. time–frequency analyzed ERN responses gathered during a standard flanker task and compared these with similar analyses of simulated data that modeled the ERN as a ‘phasic’ response. They examined whether spectral power (a measure in units of |μV|2) was present in the ERN evoked potential to a greater degree than expected on the classical interpretation. As the number of trials entering into the ERN average increases, the contribution of non-phase-locked activity to the spectral estimates should tend towards zero, assuming that the phases of this activity are randomly distributed across trials. Hence a greater degree of spectral power than expected in the evoked potential could be taken as evidence of a greater degree of phase-locked oscillations contributing to ERN genesis. Nonetheless, Yeung et al. showed that average ERN responses simulated according to the classic view exhibit a similar degree of phase-locked power as the empirical data.

They also showed that a phasic response can produce a qualitative pattern and degree of event-related phase synchronization (a measure of phase consistency across trials, see Section 2.6) similar to what is observed within their empirical ERN data. Other analyses, including examination of the correlation of ERN amplitude with EEG power and the scalp topography of spectral responses, showed similar difficulties in distinguishing between the classic and partial synchronization hypotheses of ERN genesis. Yeung et al. (2004) conclude that such qualitative time–frequency analyses are ambiguous tests of these two hypotheses.

The present study implements the suggestion by Yeung et al. (2004) that the ambiguity of time–frequency measures may be removed through quantitative analysis of the spread of spectral activation across time and frequency under different hypotheses of ERN generation. Quantifying the time–frequency spread of spectral activity is important because the component processes predicted by each hypothesis may be identified by differentiable time–frequency patterns. The remainder of this section will briefly discuss some possible time–frequency patterns each hypothesis might predict.

Fig. 1A (left) shows a 5 Hz half-cycle cosine wave that had been used before to model single-trial ERN responses produced according to the classic hypothesis (Yeung et al., 2004). Fig. 1A (right) shows the associated wavelet-based total spectral power (see Sections 2.6 EEG time–frequency analysis, 2.7 ERN simulations for details about all simulations and wavelet transformations). Note that the spectral power has a distinctive triangular shape in time and frequency, with a wide base at lower frequencies and a narrow peak at high frequencies. Also note that there is significant power at frequencies outside of the base signal frequency (5 Hz); these portions of the spectrum are likely due to onset transients.

Although phase-locked power is equivalent to total power for a single-trial response (see Section 2.6), it is clear to see that if amplitude and/or phase-locking are high, the grand-average of many such classic responses should result in a pattern of phase-locked power similar to the basic triangular time–frequency shape of Fig. 1A (modulo any distorting effects due to noise). Measures of phase-locking, such as inter-trial phase coherence (ITPC; see Section 2.6), should also show a similar pattern. Low amplitude and/or phase-locking should produce classic power and ITPC responses of lower amplitude and a greater distortion of the basic triangular shape of the classic time–frequency pattern, as signal energies summate over a wider time–frequency interval.

The above considerations therefore predict that if the ERN arises according to the classic hypothesis, then empirical spectral power (total/phase-locked/non-phase-locked) and ITPC should increase in a manner resembling the basic triangular time–frequency shape of Fig. 1A.

Fig. 1B shows a 5 Hz ERN response (same amplitude and latency as Fig. 1A) simulated according to the pure phase-resetting hypothesis. It has been argued that pure phase-resetting can be empirically distinguished from either the classic or phase-resetting plus enhancement mechanisms by demonstrating event-related phase changes in the EEG without corresponding increases in the spectral power of the ERP (Makeig et al., 2002, Yeung et al., 2004; although see Klimesch et al., 2004). An absence of spectral power changes is not necessarily evidence for pure phase-resetting, however. The reason for this is that a change in phase of a signal necessitates a change in frequency of that signal, and the latter affects the frequency ranges in which event-related power changes will occur.

For example, let dϕ/dt be the change in phase ϕ with respect to time of some sinusoidal signal G defined over time t with amplitude A, base frequency f, and phase ϕ, i.e. G(t) = A · sin(2π · f · t + ϕ). To a first approximation, the argument of the sinusoid function describing the phase-changing signal is then 2π · f · t + ϕ =  · f · t + (dϕ/dt) · t =  · F · t. It follows that the signal frequency during the phase change given by the spectral transformation will be 2π · F =  · f + dϕ/dt, or F = f + (1/2π) · dϕ/dt; thus F < or > f, for dϕ/dt  0. This result indicates that in the case of phase-resetting without corresponding amplitude changes, the spectral power must decrease at the base frequency of the signal and increase in nearby frequencies.

Fig. 1B shows an example of a pure phase-reset signal (left column) and the associated total power spectrum. The latter confirms that total power of a phase-reset signal decreases in the base frequency range. The fact that previous studies claiming evidence of pure phase-resetting found event-related phase changes in the EEG without corresponding increases in spectral energy may indicate either that such phase-resetting was weak (i.e. dϕ/dt  0), or that signal amplitudes at base frequencies did in fact increase just enough to offset the power decrease due to the phase change (i.e. phase-resetting with enhancement; see below).1

These above considerations therefore predict that if the ERN arises from pure phase-resetting of ongoing oscillatory EEG signals, then total power should decrease in a manner resembling the pattern of decreases in Fig. 1B.

Fig. 1C shows a 5 Hz ERN response (same amplitude and latency as Fig. 1A and B) simulated according to the phase-resetting plus enhancement hypothesis. This hypothesis suggests that the time–domain ERN signal should be composed of a successive sequence of peaks and troughs characteristic of oscillatory activity with the amplitude increasing and then decreasing with respect to some base level over the duration of the ERN response (Fig. 1C, left). Such activity may onset substantially earlier than the ERP peak latency of the averaged ERN response and may persist for a significant time period afterward, as suggested by the data of Luu et al. (2004). Furthermore, this oscillatory activity must change or reset phase during the transition from the preceding background oscillations to onset of the ERN and then stay relatively phase-locked throughout the ERN peak response before the phase drifts back to background distributions (see dashed lines in Fig. 1C, left).

The pattern of total power contained within such a waveform (Fig. 1C, right) is strikingly different from the patterns associated with either classic or pure phase-resetting signals. Total power activation is restricted to a narrow range around the base frequency of the response, but remains extended in time; the qualitative appearance is almost circular, as opposed to the triangular shape seen for the classic responses (Fig. 1A). In addition the total power magnitude is much greater than for classic power, although less than pure phase-resetting power (note that each signal has equivalent peak amplitude and latency). This difference in power probably arises from the fact that an oscillatory signal possesses a larger temporal extension than a classic signal, and thus more signal energy is present over a given temporal duration. These considerations also suggest that, for an equal level of phase-locking, the non-phase-locked power should be greater for an oscillatory response than for a phasic response. The presence of phase-resetting, however, will also modify spectral activity by reducing total power responses at the base signal frequency, as seen in Section 1.3.2 above.

Therefore, if the ERN arises from the phase-resetting with enhancement of ongoing oscillatory EEG signals, then empirical spectral power (total/phase-locked/non-phase-locked) and ITPC should increase in a manner resembling the basic time–frequency pattern of Fig. 1C.

This paper tested the predictions discussed in Section 1.3 above using a wavelet-based time–frequency analysis applied to (1) error and correct trials gathered during a typical flanker task that varied in motivational incentive, and (2) ERN responses simulated according to the classic, pure phase-resetting, and phase-resetting with enhancement hypotheses. The three hypotheses of ERN genesis were then assessed by fitting the time–domain and time–frequency properties of the model data to the empirically gathered ERN signals (Sections 2.6 EEG time–frequency analysis, 2.7 ERN simulations). The present analysis was also refined by matching error and correct EEG trials for confounding factors (the total number of trials, reaction time, and degree of ocular activity; see Section 2.4.1) that almost always differ between conditions and thus potentially introduce additional variability into the EEG signals across accuracy conditions. Using these methods, it is quantitatively shown that phase-resetting plus enhancement provides a better model of the empirical data than either the classic view or the pure phase-resetting view; that is, the ERN indeed arises from an amplitude increase and phase-reset of theta-range oscillatory EEG activity. In this manner, the present report extends the approaches of Luu et al. (2004) and Yeung et al. (2004).

Section snippets

Methods

The present data were previously reported, as time–domain averaged ERPs, in an analysis of the effects of motivational incentive and participant socialization on the ERN evoked potential response (Dikman and Allen, 2000). Since these factors are not of interest in the present analysis of ERN genesis, the data were collapsed across them for all ERP and time–frequency analyses reported here (see Sections 2.5 ERP analysis, 2.6 EEG time–frequency analysis). Nonetheless, these factors did play roles

Behavioral results

Overall accuracy (before matching of trials for EEG analysis) under Punishment and Reward feedback conditions was 89% ± 1.0% and 88% ± 1.2%, respectively. There were no significant between-condition differences in accuracy (p > 0.42). Reaction times (before trial matching) for the Punishment Error and Correct trials were 422 ± 13 ms and 479 ± 13 ms, respectively; Reward Error and Correct reaction times were 417 ± 12 ms and 477 ± 11ms. There was a significant main effect of Accuracy, F(1, 20) = 122.1, p < 0.001, with

Evidence for the Phase-resetting with enhancement hypothesis of ERN generation

The empirical time–domain and time–frequency results (Sections 3.2 ERP analysis, 3.3 EEG analysis) support the hypothesis that the ERN emerges from the partial phase-locking of midfrontal theta-band EEG oscillatory activity. First, significant error-related post-response increases in spectral amplitude and ITPC were primarily restricted to the theta range for both Error and Correct trials. Second, a greater degree of activity was found for empirical Error versus Correct trials for the

Acknowledgements

This research was supported in part by a US Department of Education Jacob K. Javits Fellowship, a University of Arizona Institute for Collaborative Bioresearch (BIO5) Graduate Research Award, and an American Psychological Association Dissertation Research Award to L.T.T.; and a grant from the McDonnell-Pew Program in Cognitive Neuroscience to J.J.B.A. The authors are grateful to Ziya V. Dikman for assistance with data collection, data analysis, and helpful comments on drafts of this manuscript.

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