The oscillatory phase-resetting model predicts that event-related potential (ERP) components are generated by a superposition of evoked oscillations with different frequencies. We investigate this question in a memory task in which human subjects had to retrieve a verbal label in response to the presentation of a picture. The results show that (i) evoked oscillations in the delta, theta, alpha and beta range undergo a significant phase resetting and (ii) become synchronized in absolute phase during small time windows that (iii) coincide with the latencies of the P1–N1 complex. Our conclusion is that the latencies of ERP components can be predicted at least in part by phase synchronization between frequencies.
For a long time it has been suggested that event-related potentials (ERPs) are generated by a superposition of evoked oscillations (for extensive reviews, see Basar, 1999a,b). In line with this suggestion, several studies have been able to demonstrate that oscillations in the theta and alpha frequency range undergo a significant phase resetting in response to the presentation of a stimulus (Jansen and Brandt, 1991; Tallon-Baudry et al., 1996; Brandt, 1997; Tesche and Karhu, 2000; Makeig et al., 2002; Schack and Klimesch, 2002). Phase resetting per se, however, does not provide unambiguous evidence for evoked oscillations because a fixed-polarity, fixed-latency component superimposed on a (random) oscillation would also lead to a transient reduction in the inter-trial phase variability and, thus, mimic phase resetting. This latter assumption characterizes the evoked model of ERP generation. In contrast, the oscillatory phase-resetting model assumes that an ongoing oscillation (of a given frequency domain) undergoes (i) an event-related modulation of phase (i.e. exhibits phase resetting), and, in addition, may also undergo (ii) an event-related modulation in amplitude (Klimesch et al, 2004).
In the present study, we focus on the question of whether phase synchronization between different frequencies — in addition to resetting — is an important factor responsible for the generation of ERP components. This hypothesis, based on the oscillatory phase-resetting model, assumes that when oscillations with different frequencies undergo resetting, then these different oscillations must become synchronized (i.e. aligned) in absolute phase (within a certain time window poststimulus) in order to generate a prominent ERP component such as, for example, the P1 or N1. If this was not the case, evoked oscillations with different frequencies would largely cancel each other due to a lack of alignment in absolute phase. As an example, if we assume that the N1 is generated by evoked theta and alpha, we have to assume that both oscillations undergo a significant resetting, and, in addition, become aligned in absolute phase (i.e. show a negative peak with a phase angle of 180°) during the latency window of the N1. If in this latency window one of the two oscillations exhibited a negative peak (a phase angle of 180°) and the other a positive peak (a phase angle of 0°/360°), the two evoked oscillations would cancel each other, although both oscillations might exhibit a highly significant phase resetting. Thus, according to the proposed hypothesis, alignment in absolute phase between different frequencies will be an important factor for the generation of an ERP component.
In contrast to phase, amplitudes of different oscillations may contribute to the generation of ERP components in a differential way. As is well known from event-related desynchronization/synchronization (ERD/ERS) research (Klimesch, 1999; Lopes da Silva and Pfurtscheller, 1999), delta and theta power increase in response to a stimulus and/or task demands, whereas alpha power decreases (as compared to a pre-stimulus reference). If ERP components are generated by evoked oscillations with different frequencies, we have to assume that evoked theta amplitudes increase, whereas evoked alpha amplitudes decrease.
It should be noted that according to the evoked model, ‘phase resetting’ can occur only together with an increase in (evoked) amplitude and only during that time window where the evoked component appears. In the oscillatory model, phase resetting can occur independent of the type of amplitude modulation (i.e. increase, decrease or no change in amplitude). Furthermore, assumptions about the involvement of different frequencies and the type of amplitude modulation can be derived from ERD/ERS research but are meaningful only for the oscillatory model.
For the evaluation of the proposed hypotheses, four different measures (explained in the Materials and Methods) — one for phase resetting [termed phase locking index or PLI hereafter (Schack and Klimesch, 2002; Schack and Weiss, 2003)], one for phase alignment between frequencies, one for amplitude changes in single trials (termed whole power hereafter) and another for the amplitudes of the evoked potential (termed evoked power hereafter) — will be used. PLI reflects the degree of phase variation between trials. [For very similar measures see, for example, the ‘inter-trial coherence’ suggested by Makeig et al. (2002), the ‘phase locking factor’ used by Tallon-Baudry et al. (1996) and the phase-locking value of Rodriguez et al. (1999).] PLI is a normalized measure with a PLI = 0 reflecting maximal and a PLI = 1 reflecting no phase variability (Schack and Klimesch, 2002). Phase alignment is calculated for those frequencies exhibiting significant phase locking (cf. Materials and Methods). Whole power (a measure similar but not identical to traditional band power) and evoked power will be determined for each frequency band (in the theta and alpha range) on the basis of Gabor wavelet analyses (Schack and Weiss, 2003) in order to achieve adequate time–frequency resolution and direct amplitude estimates. Evoked power will be calculated on the basis of individual ERPs, and reflects amplitude estimates of evoked theta and alpha oscillations respectively. To calculate whole power, single trial power estimates will be obtained, and then averaged over trials.
We analyze the data of a memory task in which subjects had to retrieve a learned label to an abstract picture to test the predictions of the oscillatory phase resetting model. Because recent findings indicate that evoked theta and alpha play an important role during retrieval (Schack and Klimesch, 2002; Rizzuto et al., 2003; Klimesch et al., 2004) we predict phase alignment within and between these frequency ranges.
Materials and Methods
After giving written informed consent, a sample of 18 subjects participated in the present experiment. The sample consisted of 15 females and 3 males (mean age 21.5 ± 2.5 years).
Materials and Design
The experiment consisted of two parts: a paired associate learning task and a recognition task. In the first part subjects had to learn a label (a number between 1 and 8) for each of eight abstract two-dimensional patterns constructed from a varying number of black bars (on a white background) that differed in length, width and orientation. In the second part of the experiment the patterns (4.3° × 3.4° visual angle) were presented in random order (each of the eight patterns was shown six times) without a label and subjects had to retrieve the corresponding label from their memory. A single trial consisted of 1000 ms visual presentation of a pattern after which a mask was shown for 2000 ms to prevent after-images. Subjects were told to report the label of the pattern during the presentation of the mask. The inter-trial interval was 3000 ms.
Electrophysiological Recordings and Analyses
Brain electric activity was recorded referentially against a linked earlobe reference by a 32-channel amplifier (SynAmps, Neuroscan Inc.) with a sampling frequency of 250 Hz. Data were acquired between 0.15 and 50 Hz using 30 Ag–AgCl electrodes at the scalp, placed according to the international 10–20 system, and two additional electro-oculogram (EOG) channels. After ocular artefact reduction, any remaining artefacts were rejected by visual inspection of the data. Data were then epoched in 2 s time intervals ranging from 1000 ms preceding to 1000 ms following stimulus onset. For all subjects, at least 40 artefact-free epochs remained for statistical analysis. For the present study, data for recording sites O1, O2, P3, P4, T5 and T6 were analyzed.
P1–N1 Amplitude and Latencies
Time windows for detecting peak amplitudes and their latencies (determined with Neuroscan standard ERP-analysis software) were 60–130 ms for the P1 and 120–180 ms for the N1. For one subject a large positivity not peaking in the P1 time window was found. This participant was not included in further analyses involving the P1 and N1 ERP components.
Whole Power and Evoked Power
Whole power (a measure similar but not identical to traditional band power) and evoked power was determined for frequency bins of 0.5 Hz on the basis of the Gabor expansion (see below) in order to achieve adequate time–frequency resolution and frequency-specific amplitude estimates for ERPs (Schack and Klimesch, 2002). Evoked power was calculated on the basis of individual ERPs. For whole power, single trial power estimates were obtained which were then averaged over trials.
Instantaneous Phase Alignment (IPA) between Frequencies
Data processing described in this section is based on the Gabor expansion (Gabor, 1946; Lachaux et al., 1999; Schack et al., 2001) which transforms a signal x(t) into a complex time–frequency signal y(fn,t). The components of y(fn,t) — the Gabor coefficients — form a matrix of size (m × n) where m is frequency (with a resolution of 0.5 Hz in the present case) and n time (with a resolution of 4 ms in the present case). Information about the phase angle for each frequency–time pair can be extracted from the complex coefficients of the matrix (Schack et al., 2001).
The calculation of a significant phase alignment between different frequencies is based on the following analysis steps (done for each subject separately). First, we determined those frequencies that showed a significant phase locking. The PLI for a time period of 1000 ms preceding and following the presentation of a stimulus was calculated. Then, the average PLI for a 120 ms pre-stimulus period (ranging from −840 to −720 ms) for each frequency bin was computed. The resulting vector of averaged PLIs was tested for normal distribution (Lillie's test, α = 1%). By using the mean and standard deviation of these values for each frequency bin, a 90% confidence interval was determined. Only those frequencies and time periods poststimulus, in which the PLI exceeded the upper confidence limit (e.g. Fig. 1c) were considered for further analyses.
Second, in using the same (m × n) data matrix, the phase angle was calculated for each frequency and time point. Inspection of Figure 1e shows straight vertical bands reflecting phase alignment between frequencies ranging from theta to slow beta. At ∼100 ms a vertical red band reflecting a positive peak followed by a blue band (reflecting a negative peak at ∼150 ms) can be observed. The statistical procedure for determining a significant phase alignment between frequencies is the following. (i) For each time point we tested (at the α = 10% level) over all frequency bins for circular unimodal distribution of the phase angle, using the Hodges–Ajne test (Hodges, 1955; Ajne, 1968; Upton and Fingelton, 1989). Time bins not showing a unimodal distribution were excluded for further analysis. (ii) For each time bin with unimodal distribution a 95% confidence interval (Hodges, 1955; Ajne, 1968; Fisher and Lewis, 1987; Upton and Fingelton, 1989) was computed. Frequencies with values falling outside the confidence interval were also excluded from further analyses. (iii) Furthermore, after these two selection steps only those frequencies and time points with a significant PLI were considered. The result shows significant phase alignments at certain frequencies and latencies (cf. Fig. 1d).
For the prediction of ERP latencies, for each of the selected frequency ranges and time points the difference between the measured angle and 180° or 0°/360° was calculated to determine how far the measured values deviate from a negative or positive peak. If the measured angle was between 90° and 270°, the distance to 180° was calculated. If the measured angle was between 270° and 90° the distance to 0°/360° was calculated. These distances were averaged over frequencies for each time point. From all of these data, two final values were selected, one closest to 180° (reflecting a negative peak), and another closest to 0°/ 360° (reflecting a positive peak). The latencies of these two values were selected within the broad time interval of 60–180 ms poststimulus but ‘blind’ with respect to the specific latency windows of the P1 and N1 used for peak detection in ERP analyses. An example for a circular histogram of the selected phase angles for each bin of the obtained frequencies at exactly the predicted P1 and N1 latency is shown in Figure 1f.
It should be noted that the prediction of the P1 and N1 latency can be based on the respective values of one or more frequencies. In an attempt to check for inconsistent findings, only those final values were considered for predicting P1 and N1 latency and amplitude, for which at least two frequency bins were obtained. This means that the number of cases (n) for the correlations between the obtained and predicted values can be <18. The last row in Table 1 shows the number of cases that remained for data analyses.
|r a (alpha)||0.46b||0.09||0.42||0.43||0.29||0.62b||0.48b||0.57b||−0.21||0.17||0.10||0.47b|
|r a (alpha)||0.46b||0.09||0.42||0.43||0.29||0.62b||0.48b||0.57b||−0.21||0.17||0.10||0.47b|
1% level of significance, one-tailed.
5% level of significance, one-tailed.
All of the statistical analyses reported below were carried out for the entire sample of subjects (or selected subsamples for correlational analyses). First, in order to test whether the selected frequency bins (underlying the prediction of the P1 and N1) are consistent across subjects within the traditional frequency bands (delta: 0–4 Hz, theta: 4–8 Hz, alpha: 8–12 Hz, beta1: 12–16 Hz, beta2: 16–20 Hz) χ2 tests were calculated for each frequency band, topography and ERP component (P1 and N1). The data used for the χ2 test are the number of subjects showing 0, 1, 2,…, k frequency bins in the respective frequency band. A significant χ2 indicates inconsistency of bins across subjects, whereas a non-significant value indicates consistency. Second, in order to test whether ERP components can be predicted by phase alignment across frequencies, correlations were calculated between the predicted and obtained P1 and N1 latencies. In addition, correlations were calculated between P1 and N1 amplitude size and the number of frequency bins underlying the prediction of latencies. Third, ANOVAs were calculated to check whether an increase in PLI is paralleled by an increase in whole power. The following time intervals were used, a reference interval ranging from 700 to 300 ms pre-stimulus and four consecutive time windows of 100 ms (0–400 ms poststimulus). For each subject, the respective PLI and whole power values were averaged within the selected intervals and for 10 frequency bands with a width of 1 Hz (ranging from 3 to 13 Hz). Two-way ANOVAs with factor TIME (reference and four poststimulus time-windows) and FREQUENCY (10 frequency bands) were calculated separately for each of the six recording sites (O1, O2, P3, P4, T5 and T6) and the two dependent measures: PLI and whole power. The Greenhouse–Geisser corrected results are reported.
Subjects reported the correct label in 86.1% of all presentations. ERPs of all but one subject show a typical P1–N1 complex. Mean latencies and standard deviations (P1: mean = 108.5; SD = 9.4; N1: mean = 150.4; SD = 15.0) indicate larger variability for the N1. Similar findings were obtained for amplitudes (P1: mean = 9.7; SD = 3.4; N1: mean = −4.2; SD = 5.4).
The results of the χ2 tests are summarized in Table 1 and indicate that particularly within the alpha and beta1 band the findings are consistent across subjects. In contrast, the findings for the delta band show a very large variability between subjects.
The ERP of a typical subject is shown in Figure 1a. Inspection of evoked power (Fig. 1b) of the same subject indicates a prominent contribution of the alpha frequency range. Significant phase locking (as indicated by PLI) can be observed over a wide frequency range including the delta, theta, alpha and slow beta range (cf. Fig. 1c). As indicated by Figure 1g, pronounced alpha activity in the upper alpha frequency range (between 10 and 13 Hz) can be observed during the prestimulus period. Most interestingly, despite a large decrease in power (alpha desynchronization) at ∼250 ms poststimulus, phase locking in the upper alpha band reaches significance (cf. Fig.1e).
Representation of absolute phase in Figure 1e documents phase alignment (indicated by straight vertical red and blue bands within the white rectangle) particularly in the time window of the P1–N1 complex (see Fig. 1a for an illustration). In these intervals, significant phase alignment (as depicted in Fig.1d) can be observed during the P1 and N1 peak in the alpha range (cf. red and yellow colors around the P1, and blue and purple colors around the N1). In order to demonstrate the differential contribution of theta and alpha for phase alignment, the phase angle for 6 and 13 Hz are plotted for all trials in Figure 2.
Whereas the data in Figure 1a–g stem from one subject (subject ‘L’, recording site O1), Figure 1h gives an overview of those frequencies (within the traditional frequency bands) that were involved for predicting P1 and N1 latencies. This figure does not contain data from the entire sample but for a subsample of subjects showing phase alignment at O1 between at least two frequencies during P1 (n = 16) and N1 (n = 14).
Correlations between obtained and predicted ERP latencies and amplitudes are summarized in Table 1. The results show that — with a single exception — significant correlations for latency measures were obtained for all of the six recording sites and both ERP components. This indicates that the latency of the P1 and N1 vary significantly as a function of phase alignment between frequencies. The correlations between the number of involved frequency bins and amplitude size exhibit significant findings only for the alpha band. Table 1 indicates that 5 out of the 12 possible cases reached significance. The latter finding shows that the number of frequency bins with significant phase alignment in the alpha band has a significant influence on amplitude size for the P1 amplitude at O1, the N1 at P3, the P1 and N1 at P4, and the N1 at T6.
The percentage of frequency bins (within traditional frequency bands) that underlie the prediction of ERP components is listed in Table 1. The data reveal an interesting association between alpha and theta and their contribution to the P1 and N1. Whereas for alpha the influence on the P1 is consistently larger than for the N1, for theta the influence on the N1 is consistently larger than for the P1. Calculation of a non-parametric measure of correlation, the contingency coefficient (C) reveals that the association between alpha and the P1 and theta and the N1 is significant for five of the six recording sites (C = 0.24, P < 0.05; C = 0.45, P < 0.01; C = 0.50, P < 0.01; C = 0.52, P < 0.01; C = 0.14, NS and C = .30, P < 0.01 for O1, O2, P3, P4, T5 and T6 respectively).
The results of the two-way ANOVAs with PLI as dependent measure showed a significant main effect for factor TIME at all recording sites [F(4/68) = 73.1, 69.5, 43.2, 37.2, 59.7 and 88.9 at O1, O2 P3, P4, T5 and T6 respectively; P < 0.01 in all cases], indicating a strong increase of phase locking across all frequencies between 3 and 13 Hz. In addition, at O2, the factor FREQUENCY reached significance [F(9/153) = 3.0; P < 0.05], showing that the increase in PLI is much larger for alpha as compared to the slower frequencies (theta and delta in particular). At P4 a significant TIME × FREQUENCY interaction [F(36/612) = 2.4, P < 0.05] was obtained. This finding shows that the increase in PLI over time is more pronounced for alpha as compared to slower frequencies. For whole power, in addition to a significant main effect for TIME [F(4/68) = 5.9, 6.7, 6.4, 4.4, 12.2 and 8.8 at O1, O2 P3, P4, T5 and T6 respectively; P < 0.05 in all cases with the exception of T5 and T6 which were significant at the 1% level], a significant TIME × FREQUENCY interaction was found for all recording sites [F(36/612) = 7.5, 10.2, 11.7, 10.4, 11.3 and 10.4 at O1, O2 P3, P4, T5 and T6 respectively; P < 0.01]. As depicted in Figure 3 for recording site O1, this interaction reveals that frequencies in the theta and slow alpha frequency range show an event-related increase in power, whereas frequencies at and beyond 10 Hz exhibit an event-related decrease in power. Finally for P3, P4, T5 and T6, the factor FREQUENCY reached significance [F(9/153) = 10.0, 7.1, 3.7 and 3.1 respectively; P < 0.01 for P3 and P4; P < 0.05 for T5 and T6]. The latter finding demonstrates that power in the slow frequencies (theta and delta in particular) is significantly larger than for alpha and beta.
Our findings provide strong support for the hypothesis that ERP components are generated at least in part by a superposition of evoked oscillations (Basar, 1999a,b). The results demonstrate that P1 and N1 peak latency, and in some cases peak amplitude, can be predicted by referring to phase measures and the number of frequency bins involved during a significant and transient phase alignment (cf. Table 1). Because all of these measures are independent of the amplitude of the analyzed oscillations, the conclusion is that phase alignment between frequencies has a significant influence on the generation of the P1–N1 complex.
In contrast to the P1, which is generated primarily by frequencies in the alpha range, the N1 is generated primarily in frequencies in the theta range (see Table 1, Figs 1h and 2) although the influence of alpha on the N1 is still considerable. It is important to emphasize that phase alignment between frequencies necessarily is a transient event, occurring after resetting. Consequently, from those frequencies that were aligned in absolute phase at the P1 peak, only that frequency will be realigned at the N1 peak whose half period equals the P1–N1 inter-peak latency. Because in our example (cf. Fig. 1) inter-peak latency is ∼50 ms, only a frequency of ∼10 Hz will have the potential to realign at the N1 peak (see Fig. 2b).
Our results demonstrate that phase resetting and phase alignment between frequencies have a statistically significant effect on the amplitudes and latencies of early ERP components. However, the influence of phase does not explain the entire variance of ERP components. Consequently our findings cannot exclude the possibility that ERPs are generated by a combination of transient evoked potentials, phase resetting and phase alignment between frequencies.
In a recent study (Klimesch et al., 2004), we have found that theta phase locking is larger during encoding than recognition and that good memory performers show a larger increase in theta and alpha phase locking during recognition in the time window of the N1. On the basis of these and other findings (Klimesch, 1999) we concluded that the P1–N1 complex is generated primarily by evoked alpha and theta oscillations, reflecting the synchronous activation of the different neural networks that are important for memory. It would be an interesting question for future research to investigate whether phase alignment between theta and alpha frequencies (as observed in the positive going slope of the present study) also is related to memory performance.
In using ICA to find spatially fixed but temporally maximally independent sources during the P1–N1 time window, Makeig et al. (2002) found a cluster of frontocentral components that exhibited phase locking in the theta and alpha ranges. These components accounted for half of the N1 variance at anterior channels and their source was located in or near the left dorsal anterior cingulate cortex, a brain region belonging to the Papez circuit. Rizzuto et al. (2003) analyzed the intracranial EEG and observed significant phase locking in the extended theta and alpha frequency range during the retrieval of a probe item in a memory scanning task and in a time window that included the typical N1 latency range. Thus, these findings agree with our results of a transient phase alignment between theta and alpha frequencies in the time window of the N1 component.
With respect to the functional meaning of our findings, we proceed from the assumption that distributed processes in a neural network can be functionally and transiently tied together by coherent (‘correlated’) synchronous neuronal activity (Fell et al., 2001; Salinas and Sejnowski, 2001; Varela et al., 2001; Wagner, 2001). If we assume that different neural networks operate in different frequency domains (e.g. in the theta and alpha frequency), the analysis of m:n phase synchronization (i.e. phase synchronization between frequencies, e.g. between theta and alpha) offers a good way to analyze the co-activity between different networks (Varela et al., 2001). Phase alignment between frequencies — as analyzed in the present study — may be considered a special case of m:n phase synchronization. Our findings showing a transient phase alignment of theta and alpha may, thus, be interpreted in terms of different networks becoming transiently co-activated during the P1–N1 time window.
The results obtained demonstrate that ongoing oscillations may exhibit three different types of event-related modulations. In response to a stimulus and/or task demands, (i) the phase may be modulated as reflected by a significant phase locking (increase in PLI; cf. Fig. 1c) over a broad frequency range; (ii) the phase between different frequencies may become aligned (cf. Figs 1e,d and 2); and (iii) amplitudes may be modulated as reflected by an increase, decrease (see Fig. 3) or no change in amplitude size (as measured by whole power). In addition we found that event-related changes in whole power are frequency specific (cf. Fig. 3a and 3b) and can be observed independent of phase locking. The fact that amplitudes of fast alpha oscillations exhibit an event-related decrease in power despite a significant phase locking clearly supports the phase reset model and is inconsistent with the evoked model.
Finally it should be noted that the prestimulus EEG is another factor that contributes to the generation of the ERP. This is important because in the traditional view the EEG is considered ‘background noise’ that does not have any influence on the generation of ERPs. A variety of findings, well reviewed recently by Barry et al. (2003), however, suggest that the momentary state of the brain, reflected by the ‘background’ EEG, determines the response to a stimulus. As an example, it has been demonstrated that the amplitude of particular EEG frequencies in the prestimulus period has a strong influence on the amplitude of ERP components [see the work of Basar and co-workers (e.g. Basar and Stampfer, 1985)]. The impact of prestimulus alpha amplitude (Barry et al. 2000) and phase has been thoroughly investigated. Most interestingly, the phase of alpha at stimulus onset determines the amplitude and topography of poststimulus alpha activity (Remond, 1969). Jansen and Brandt (1991) and Brandt (1997) found evidence that stimuli presented during the alpha cycle associated with a positive-going zero crossing tended to enhance poststimulus alpha activity. In extending these findings, Barry et al. (2003) reports that the N1 amplitude is increased if stimuli were presented during the positive-going alpha cycle. Taken together, these findings too are inconsistent with the traditional evoked model but well in line with the oscillatory model for ERP generation.
This research was supported by the Austrian Science Fund, P-13047.