Distinguishing the evoked response from phase reset: a comment to Mäkinen et al

Mäkinen et al. [Mäkinen, V., Tiitinen, H., May, P., 2005. Auditory event-related responses are generated independently of ongoing brain activity. Neuroimage 24, 961–968] suggest the use of amplitude variance to distinguish the evoked response from phase reset. Because their data do not exhibit a drop in amplitude variance, they conclude that ERPs are generated by ‘processes separate from and additive to ongoing brain activity.’ We argue that this conclusion is premature because of unrealistic assumptions about the processes underlying an event-related modulation of oscillations. A realistic phase reset model has to consider at least two parameters, degree of phase reset (or ‘phase concentration’) and amplitude change (event-related increase or decrease in amplitude). With simulated data, we show that a variable increase in amplitude size increases amplitude variance and masks the influence of a phase reset. On the other hand, an event-related decrease in amplitude without a phase reset leads to a sharp drop in variance. Furthermore, simulation of a frequency-specific phase reset shows a drop in variance that may be too small to be detected empirically. Thus, we conclude that amplitude variance is not capable of distinguishing the evoked response from phase reset.     

Modulation of spectral power and of phase resetting of EEG contributes differentially to the generation of auditory event-related potentials

Nowadays, the mechanisms involved in the genesis of event-related potentials (ERPs) are a matter of debate among neuroscientists. Specifically, the debate lies in whether ERPs arise due to the contribution of a fixed-polarity and fixed-latency superimposed neuronal activity to background electroencephalographic oscillations (evoked model) and/or due to a partial phase synchronization of the ongoing EEG (oscillatory model). The participation of the two mechanisms can be explored by the spectral power modulation and phase coherence of scalp EEG rhythms, respectively. However, an important limitation underlies their measurement: the fact that an added neural activity will be relatively phase-locked to stimulus, thus enhancing both spectral power and phase synchrony measures and making the contribution of each mechanism less clear-cut. This would not be relevant in the case that an increase in phase concentration was not accompanied by any concurrent spectral power modulation, thus opening the way to an oscillatory-based explanation. We computed event-related spectral power modulations and phase coherence to an auditory repeated-stimulus presentation paradigm with tone intensity far from threshold (90 dB SPL), in which N1 decreases its amplitude (N1 gating) as an attenuation brain process. Our data indicate that evoked and oscillatory activity could contribute together to the non-attenuated N1, while N1 to repeated stimuli could be explained by partial phase concentration of scalp EEG activity without concurrent power increase. Therefore, our results show that both increased spectral power and partial phase resetting contribute differentially to different ERPs. Moreover, they show that certain ERPs could arise through reorganization of the phase of ongoing scalp EEG activity only.     

Spectral spatiotemporal imaging of cortical oscillations and interactions in the human brain

This paper presents a computationally efficient source estimation algorithm that localizes cortical oscillations and their phase relationships. The proposed method employs wavelet-transformed magnetoencephalography (MEG) data and uses anatomical MRI to constrain the current locations to the cortical mantle. In addition, the locations of the sources can be further confined with the help of functional MRI (fMRI) data. As a result, we obtain spatiotemporal maps of spectral power and phase relationships. As an example, we show how the phase locking value (PLV), that is, the trial-by-trial phase relationship between the stimulus and response, can be imaged on the cortex. We apply the method to spontaneous, evoked, and driven cortical oscillations measured with MEG. We test the method of combining MEG, structural MRI, and fMRI using simulated cortical oscillations along Heschl's gyrus (HG). We also analyze sustained auditory gamma-band neuromagnetic fields from MEG and fMRI measurements. Our results show that combining the MEG recording with fMRI improves source localization for the non-noise-normalized wavelet power. In contrast, noise-normalized spectral power or PLV localization may not benefit from the fMRI constraint. We show that if the thresholds are not properly chosen, noise-normalized spectral power or PLV estimates may contain false (phantom) sources, independent of the inclusion of the fMRI prior information. The proposed algorithm can be used for evoked MEG/EEG and block-designed or event-related fMRI paradigms, or for spontaneous MEG data sets. Spectral spatiotemporal imaging of cortical oscillations and interactions in the human brain can provide further understanding of large-scale neural activity and communication between different brain regions.     

Spatial attention boosts short-latency neural responses in human visual cortex

In a previous study of visual-spatial attention, Martinez et al. (2007) replicated the well-known finding that stimuli at attended locations elicit enlarged early components in the averaged event-related potential (ERP), which were localized to extrastriate visual cortex. The mechanisms that underlie these attention-related ERP modulations in the latency range of 80-200 ms, however, remain unclear. The main question is whether attention produces increased ERP amplitudes in time-domain averages by augmenting stimulus-triggered neural activity, or alternatively, by increasing the phase-locking of ongoing EEG oscillations to the attended stimuli. We compared these alternative mechanisms using Morlet wavelet decompositions of event-related EEG changes. By analyzing single-trial spectral amplitudes in the theta (4-8 Hz) and alpha (8-12 Hz) bands, which were the dominant frequencies of the early ERP components, it was found that stimuli at attended locations elicited enhanced neural responses in the theta band in the P1 (88-120 ms) and N1 (148-184 ms) latency ranges that were additive with the ongoing EEG. In the alpha band there was evidence for both increased additive neural activity and increased phase-synchronization of the EEG following attended stimuli, but systematic correlations between pre- and post-stimulus alpha activity were more consistent with an additive mechanism. These findings provide the strongest evidence to date in humans that short-latency neural activity elicited by stimuli within the spotlight of spatial attention is boosted or amplified at early stages of processing in extrastriate visual cortex.     

The neuromagnetic response to spoken sentences: co-modulation of theta band amplitude and phase

Speech elicits a phase-locked response in the auditory cortex that is dominated by theta (3-7 Hz) frequencies when observed via magnetoencephalography (MEG). This phase-locked response is potentially explained as new phase-locked activity superimposed on the ongoing theta oscillation or, alternatively, as phase-resetting of the ongoing oscillation. The conventional method used to distinguish between the two hypotheses is the comparison of post- to prestimulus amplitude for the phase-locked frequency across a set of trials. In theory, increased amplitude indicates the presence of additive activity, while unchanged amplitude points to phase-resetting. However, this interpretation may not be valid if the amplitude of ongoing background activity also changes following the stimulus. In this study, we employ a new approach that circumvents this problem. Specifically, we utilize a fine-grained time-frequency analysis of MEG channel data to examine the co-modulation of amplitude change and phase coherence in the post-stimulus theta-band response. If the phase-locked response is attributable solely to phase-resetting of the ongoing theta oscillation, then amplitude and phase coherence should be uncorrelated. In contrast, additive activity should produce a positive correlation. We find significant positive correlation not only during the onset response but also throughout the response period. In fact, transient increases in phase coherence are accompanied by transient increases in amplitude in accordance with a "signal plus background" model of the evoked response. The results support the hypothesis that the theta-band phase-locked response to attended speech observed using MEG is dominated by additive phase-locked activity.     

Early, partly anticipatory, neural oscillations during identification set the stage for priming

Perceptual priming is a fundamental long-term memory capability by which exposure to a stimulus improves later perceptual processing of that stimulus. A widespread hypothesis is that priming is the later result of perceptual learning during stimulus identification. Testing this hypothesis involves isolating priming without explicit memory, and appropriately measuring brain activity during initial experimental exposure to assess whether brain activity related to identification differs as a function of later priming. Here, we show, using magnetoencephalography (MEG), that words primed in a later test are distinguished from unprimed words at initial exposure by (a) more specific responses in perceptual brain areas, indicated by an early (within 240 ms after word onset) decrease in amplitude but increase in phase alignment of beta and gamma oscillations, and (b) improved coordination of responses across perceptual and higher brain areas in the same time window, indicated by an increase in interareal phase synchrony of alpha oscillations. The increase in interareal phase synchrony partly started already in the pre-stimulus period, approximately 60-80 ms prior to word onset, showing that the improved coordination of responses across areas was partly anticipatory. The anatomy and early timing of these patterns reveal a neural link between identification and long-term memory. The pre-stimulus findings additionally show that priming is related to the stimulus-specific anticipatory state of visual identification areas at initial exposure.     

The use of stationarity and nonstationarity in the detection and analysis of neural oscillations

Using available signal (i.e., spectral and time-frequency) analysis methods, it can be difficult to detect neural oscillations because of their continuously changing properties (i.e., nonstationarities) and the noise in which they are embedded. Here, we introduce fractally scaled envelope modulation (FSEM) estimation which is sensitive specifically to the changing properties of oscillatory activity. FSEM utilizes the fractal characteristic of wavelet transforms to produce a compact, two-dimensional representation of time series data where signal components at each frequency are made directly comparable according to the spectral distribution of their envelope modulations. This allows the straightforward identification of neural oscillations and other signal components with an envelope structure different from noise. For stable oscillations, we demonstrate how partition-referenced spectral estimation (PRSE) removes the noise slope from spectral estimates, yielding a level estimate where only peaks signifying the presence of oscillatory activity remain. The functionality of these methods is demonstrated with simulations and by analyzing MEG data from human auditory brain areas. FSEM uncovered oscillations in the 9- to 12-Hz and 15- to 18-Hz ranges whereas traditional spectral estimates were able to detect oscillations only in the former range. FSEM further showed that the oscillations exhibited envelope modulations spanning 3-7 s. Thus, FSEM effectively reveals oscillations undetectable with spectral estimates and allows the use of EEG and MEG for studying cognitive processes when the common approach of stimulus time-locked averaging of the measured signal is unfeasible.     

A wavelet-based method for measuring the oscillatory dynamics of resting-state functional connectivity in MEG

Determining the dynamics of functional connectivity is critical for understanding the brain. Recent functional magnetic resonance imaging (fMRI) studies demonstrate that measuring correlations between brain regions in resting-state activity can be used to reveal intrinsic neural networks. To study the oscillatory dynamics that underlie intrinsic functional connectivity between regions requires high temporal resolution measures of electrophysiological brain activity, such as magnetoencephalography (MEG). However, there is a lack of consensus as to the best method for examining connectivity in resting-state MEG data. Here we adapted a wavelet-based method for measuring phase-locking with respect to the frequency of neural oscillations. This method employs anatomical MRI information combined with MEG data using the minimum norm estimate inverse solution to produce functional connectivity maps from a "seed" region to all other locations on the cortical surface at any and all frequencies of interest. We test this method by simulating phase-locked oscillations at various points on the cortical surface, which illustrates a substantial artifact that results from imperfections in the inverse solution. We demonstrate that normalizing resting-state MEG data using phase-locking values computed on empty room data reduces much of the effects of this artifact. We then use this method with eight subjects to reveal intrinsic interhemispheric connectivity in the auditory network in the alpha frequency band in a silent environment. This spectral resting-state functional connectivity imaging method may allow us to better understand the oscillatory dynamics underlying intrinsic functional connectivity in the human brain.     

Changes in the amplitude and timing of the hemodynamic response associated with prepulse inhibition of acoustic startle

Disruption of the early stages of information processing in limbic brain circuits may underlie symptoms of severe neuropsychiatric disorders. Prepulse inhibition of acoustic startle (PPI) is diminished in many of these disorders and may reflect the disruption of this CNS function. PPI is associated with brain activity in many of the same regions in humans as it is in laboratory animals, suggesting that neuroimaging studies in humans may help localize deficits that can then be elucidated in animal models. In this article, we employed a rapid presentation event-related design during continuous EPI BOLD scanning to examine hemodynamic response functions (HRFs) associated with PPI. Fourteen healthy participants listened to 100 pulse alone and 100 prepulse combined with pulse (prepulse-pulse) trials. PPI is the normalized difference in the startle response to the two trial types. Following the prepulse-pulse trials, the amplitudes of the HRFs in auditory cortices and in the anterior insula were increased, while in the cerebellum, thalamus and anterior cingulate, they were decreased, relative to the pulse alone trials. In addition, the timing of the prepulse-pulse responses was delayed in the auditory cortices, anterior insula and cerebellum. Finally, PPI measured outside the scanner was predicted by the difference in BOLD responses between trial types in the anterior insula and in the cerebellum. The results suggest that prepulse inhibition, and by extension early stages of information processing, modulate both the amplitude as well as timing of neural activity.     

Cholinergic modulation of preattentive auditory processing in aging

Auditory event-related potential (ERP) components P50 and N100 are thought to index preattentive auditory processing underlying stimulus detection, whereas a subsequent component termed mismatch negativity (MMN) has been proposed to reflect comparison of incoming stimuli to a short-lived sensory memory trace of preceding sounds. Existing evidence suggests impairment of preattentive auditory processing in aging, which appears to be accompanied by decline of cholinergic activity. Previous studies indicate that scopolamine, which is a centrally acting muscarinic receptor antagonist, modulates preattentive auditory processing in young subjects. It has remained elusive, however, to which extent scopolamine affects preattentive auditory processing in aged subjects. We measured auditory responses simultaneously with electroencephalogram (EEG) and magnetoencephalogram (MEG) from nine non-demented elderly subjects after intravenous injection of scopolamine or glycopyrrolate, the latter being a peripherally acting cholinergic antagonist, using a double blind protocol. Scopolamine significantly delayed electric P50, both electric and magnetic N100 responses, whereas subsequent MMN and P200 responses were not altered by scopolamine. Our results indicate that the cholinergic system modulates auditory processing underlying stimulus detection in aging. In addition, auditory evoked responses appear to have different age-related sensitivity to cholinergic modulation. The combined MEG/EEG measurements using particularly auditory N100 response might offer an objective tool to monitor cholinergic activity in aging and Alzheimer's disease (AD).     

A neural mass model for MEG/EEG: coupling and neuronal dynamics

Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequency-specific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their functional significance remains a matter of debate. Some of the mechanisms that generate these signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. The kinetics of the ensuing population dynamics determine the frequency of oscillations. In this work we extended the classical nonlinear lumped-parameter model of alpha rhythms, initially developed by Lopes da Silva and colleagues [Kybernetik 15 (1974) 27], to generate more complex dynamics. We show that the whole spectrum of MEG/EEG signals can be reproduced within the oscillatory regime of this model by simply changing the population kinetics. We used the model to examine the influence of coupling strength and propagation delay on the rhythms generated by coupled cortical areas. The main findings were that (1) coupling induces phase-locked activity, with a phase shift of 0 or pi when the coupling is bidirectional, and (2) both coupling and propagation delay are critical determinants of the MEG/EEG spectrum. In forthcoming articles, we will use this model to (1) estimate how neuronal interactions are expressed in MEG/EEG oscillations and establish the construct validity of various indices of nonlinear coupling, and (2) generate event-related transients to derive physiologically informed basis functions for statistical modelling of average evoked responses.     

Magnetoencephalography: From SQUIDs to neuroscience. Neuroimage 20th anniversary special edition

Magnetoencephalography (MEG), with its direct view to the cortex through the magnetically transparent skull, has developed from its conception in physics laboratories to a powerful tool of basic and clinical neuroscience. MEG provides millisecond time resolution and allows real-time tracking of brain activation sequences during sensory processing, motor planning and action, cognition, language perception and production, social interaction, and various brain disorders. Current-day neuromagnetometers house hundreds of SQUIDs, superconducting quantum interference devices, to pick up signals generated by concerted action of cortical neurons. Complementary MEG measures of neuronal involvement include evoked responses, modulation of cortical rhythms, properties of the on-going neural activity, and interareal connectivity. Future MEG breakthroughs in understanding brain dynamics are expected through advanced signal analysis and combined use of MEG with hemodynamic imaging (fMRI). Methodological development progresses most efficiently when linked with insightful neuroscientific questions.     

Gamma band pitch responses in human auditory cortex measured with magnetoencephalography

We have previously used direct electrode recordings in two human subjects to identify neural correlates of the perception of pitch (Griffiths, Kumar, Sedley et al., Direct recordings of pitch responses from human auditory cortex, Curr. Biol. 22 (2010), pp. 1128-1132). The present study was carried out to assess virtual-electrode measures of pitch perception based on non-invasive magnetoencephalography (MEG). We recorded pitch responses in 13 healthy volunteers using a passive listening paradigm and the same pitch-evoking stimuli (regular interval noise; RIN) as in the previous study. Source activity was reconstructed using a beamformer approach, which was used to place virtual electrodes in auditory cortex. Time-frequency decomposition of these data revealed oscillatory responses to pitch in the gamma frequency band to occur, in Heschl's gyrus, from 60 Hz upwards. Direct comparison of these pitch responses to the previous depth electrode recordings shows a striking congruence in terms of spectrotemporal profile and anatomical distribution. These findings provide further support that auditory high gamma oscillations occur in association with RIN pitch stimuli, and validate the use of MEG to assess neural correlates of normal and abnormal pitch perception.     

MEG imaging of sensorimotor areas using inter-trial coherence in vibrotactile steady-state responses

We utilized a novel analysis technique to identify brain areas that activate synchronously during the steady-state interval of responses to vibrotactile stimulation of the right index finger. The inter-trial coherence at the stimulation rate (23 Hz) was determined for whole-brain neural activity estimates based on a linearly-constrained minimum variance beamformer applied to the MEG data. Neural activity coherent with the stimulus occurred in the contralateral primary somatosensory cortex in all subjects, and matched well with equivalent dipole modeling of the same data. Subsets of subjects exhibited additional loci of strongly coherent activity in the contralateral primary motor cortex, posterior parietal cortex, and supplementary motor area, as well as in deeper brain structures above the brainstem. An activation delay of 7 ms from deep structures to cortical areas was estimated based on the mean phase at each coherent neural source within a single subject. This new approach - volumetric mapping of the statistical parameter of inter-trial coherence in steady-state oscillations - broadens the range of MEG beamformer applications specifically for identifying brain areas that are synchronized to repetitive stimuli.     

Gamma Power Is Phase-Locked to Posterior Alpha Activity

Neuronal oscillations in various frequency bands have been reported in numerous studies in both humans and animals. While it is obvious that these oscillations play an important role in cognitive processing, it remains unclear how oscillations in various frequency bands interact. In this study we have investigated phase to power locking in MEG activity of healthy human subjects at rest with their eyes closed. To examine cross-frequency coupling, we have computed coherence between the time course of the power in a given frequency band and the signal itself within every channel. The time-course of the power was calculated using a sliding tapered time window followed by a Fourier transform. Our findings show that high-frequency gamma power (30–70 Hz) is phase-locked to alpha oscillations (8–13 Hz) in the ongoing MEG signals. The topography of the coupling was similar to the topography of the alpha power and was strongest over occipital areas. Interestingly, gamma activity per se was not evident in the power spectra and only became detectable when studied in relation to the alpha phase. Intracranial data from an epileptic subject confirmed these findings albeit there was slowing in both the alpha and gamma band. A tentative explanation for this phenomenon is that the visual system is inhibited during most of the alpha cycle whereas a burst of gamma activity at a specific alpha phase (e.g. at troughs) reflects a window of excitability.     

Reduced phase locking to slow amplitude modulation in adults with dyslexia: an MEG study

Perception of speech at multiple temporal scales is important for the efficient extraction of meaningful phonological elements. Individuals with developmental dyslexia have difficulty in the accurate neural representation of phonological aspects of speech, across languages. Recently, it was proposed that these difficulties might arise in part because of impaired phase locking to the slower modulations in the speech signal (< 10 Hz), which would affect syllabic parsing and segmentation of the speech stream (the “temporal sampling” hypothesis, Goswami, 2011). Here we measured MEG responses to different rates of amplitude modulated white noise in adults with and without dyslexia. In line with the temporal sampling hypothesis, different patterns of phase locking to amplitude modulation at the delta rate of 2 Hz were found when comparing participants with dyslexia to typically-reading participants. Typical readers exhibited better phase locking to slow modulations in right auditory cortex, whereas adults with dyslexia showed more bilateral phase locking. The results suggest that oscillatory phase locking mechanisms for slower temporal modulations are atypical in developmental dyslexia.     

Changes in brain network activity during working memory tasks: a magnetoencephalography study

In this study, we elucidate the changes in neural oscillatory processes that are induced by simple working memory tasks. A group of eight subjects took part in modified versions of the N-back and Sternberg working memory paradigms. Magnetoencephalography (MEG) data were recorded, and subsequently processed using beamformer based source imaging methodology. Our study shows statistically significant increases in θ oscillations during both N-back and Sternberg tasks. These oscillations were shown to originate in the medial frontal cortex, and further to scale with memory load. We have also shown that increases in θ oscillations are accompanied by decreases in β and γ band oscillations at the same spatial coordinate. These decreases were most prominent in the 20-40 Hz frequency range, although spectral analysis showed that γ band power decrease extends up to at least 80 Hz. β/γ Power decrease also scales with memory load. Whilst θ increases were predominately observed in the medial frontal cortex, β/γ decreases were associated with other brain areas, including nodes of the default mode network (for the N-back task) and areas associated with language processing (for the Sternberg task). These observations are in agreement with intracranial EEG and fMRI studies. Finally, we have shown an intimate relationship between changes in β/γ band oscillatory power at spatially separate network nodes, implying that activity in these nodes is not reflective of uni-modal task driven changes in spatially separate brain regions, but rather represents correlated network activity. The utility of MEG as a non-invasive means to measure neural oscillatory modulation has been demonstrated and future studies employing this technology have the potential to gain a better understanding of neural oscillatory processes, their relationship to functional and effective connectivity, and their correspondence to BOLD fMRI.     

Cortical source estimates of gamma band amplitude and phase are different in schizophrenia

Reductions in gamma band phase synchrony and evoked power have been reported in schizophrenic subjects in response to auditory stimuli. These results have been observed in the EEG at one or two electrode sites. We wished to extend these results using magnetic field data to estimate the responses at the neural generators themselves in each hemisphere. Whole head magnetoencephalographic (MEG) recordings were used to estimate the phase and amplitude behavior of sources in primary auditory cortex in both hemispheres of schizophrenic and comparison subjects. Both ipsi- and contralateral cases were evaluated using a driving (40 Hz modulated 1 kHz carrier) and a non-driving (1 kHz tone) stimulus. We used source space projection (SSP) to collapse the magnetic field data into estimates of the time course of source strengths in individual trials. Complex wavelet based time–frequency decomposition was used to compute inter-trial phase locking factor (PLF), and mean evoked and induced amplitude for each cortical generator. Schizophrenic subjects showed reduced SSP PLF and evoked source strength for contralateral generators responding to the driving stimulus in both hemispheres. For the pure tone stimulus, only the left hemisphere PLF's in the transient window were reduced. In contrast, subjects with schizophrenia exhibited higher induced 40 Hz power to both stimulus types, consistent with the reduced PLF findings. The method of SSP combined with wavelet based complex demodulation produces a significant improvement in signal-to-noise ratio, and directly estimates the activity of the cortical generators responsible for gamma band auditory MEG evoked fields. Schizophrenic subjects exhibit significant impairment of generation and phase locking of this activity in auditory cortex, suggesting an impairment of GABA-ergic inhibitory interneuronal modulation of pyramidal cell activity.     

Modelling event-related responses in the brain

The aim of this work was to investigate the mechanisms that shape evoked electroencephalographic (EEG) and magneto-encephalographic (MEG) responses. We used a neuronally plausible model to characterise the dependency of response components on the models parameters. This generative model was a neural mass model of hierarchically arranged areas using three kinds of inter-area connections (forward, backward and lateral). We investigated how responses, at each level of a cortical hierarchy, depended on the strength of connections or coupling. Our strategy was to systematically add connections and examine the responses of each successive architecture. We did this in the context of deterministic responses and then with stochastic spontaneous activity. Our aim was to show, in a simple way, how event-related dynamics depend on extrinsic connectivity. To emphasise the importance of nonlinear interactions, we tried to disambiguate the components of event-related potentials (ERPs) or event-related fields (ERFs) that can be explained by a linear superposition of trial-specific responses and those engendered nonlinearly (e.g., by phase-resetting). Our key conclusions were; (i) when forward connections, mediating bottom-up or extrinsic inputs, are sufficiently strong, nonlinear mechanisms cause a saturation of excitatory interneuron responses. This endows the system with an inherent stability that precludes nondissipative population dynamics. (ii) The duration of evoked transients increases with the hierarchical depth or level of processing. (iii) When backward connections are added, evoked transients become more protracted, exhibiting damped oscillations. These are formally identical to late or endogenous components seen empirically. This suggests that late components are mediated by reentrant dynamics within cortical hierarchies. (iv) Bilateral connections produce similar effects to backward connections but can also mediate zero-lag phase-locking among areas. (v) Finally, with spontaneous activity, ERPs/ERFs can arise from two distinct mechanisms: For low levels of (stimulus related and ongoing) activity, the systems response conforms to a quasi-linear superposition of separable responses to the fixed and stochastic inputs. This is consistent with classical assumptions that motivate trial averaging to suppress spontaneous activity and disclose the ERP/ERF. However, when activity is sufficiently high, there are nonlinear interactions between the fixed and stochastic inputs. This interaction is expressed as a phase-resetting and represents a qualitatively different explanation for the ERP/ERF.