eeg alpha phase at stimulus onset significantly affects the amplitude of the p3 erp component

Intern. J . Neuroscience, Vol. 93(1-2), pp 101-1 16 Reprints available directly from the publisher Photocopying permitted by license only

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EEG ALPHA PHASE AT STIMULUS ONSET SIGNIFICANTLY AFFECTS THE AMPLITUDE

OF THE P3 ERP COMPONENT

ALBERT R. HAIG

University of Sydney, Australia

EVIAN GORDON

Cognitive Neuroscience Unit of Westmead Hospital, and Department of Psychological Medicine at the UniversiQ of Sydney, Australia

(Received injnal form 27August 1997)

Analysis of the relationship between prestimulus EEG alpha phase and the subsequent ERP has proved difficult because of the non-Euclidean nature of phase measurements. In this study, we employed a conventional P3 templating method of single-trial analysis to identify the P3 component in target auditory oddball data from 25 normals. As in previous studies, the absence or near absence of P3 from a subset of single-trials was clearly demonstrated. We investigated this phenomenon to determine whether those single-trials with a large P3 had a different prestimulus alpha phase from those with a small or no P3. Statistical analysis of phase required the use of circular statistical analysis and the development of a new form of topographic mapping, circular topography. The alpha phase at stimulus onset in single-trials with a large P3 was significantly different from that in single-trials with a small or no P3 ( p = .02).

Keywords: P3; alpha; phase; single-trial; pre-stimulus EEG; event-related potentials.

Traditional analysis of event-related potentials (ERPs) has been based on the method of averaging of single-trials devised by Dawson (195 1, 1954). However, there has also been longstanding interest in single-trial ERP analysis (see review by Childers, Perry, Fischler, Boaz, & Arroyo, 1987), because of the considerable variability among the single-trial ERP epochs which are conventionally averaged together (McGillem & Aunon, 1987). Recent studies have revealed that this vari-

Please address all correspondence to: Albert Haig, 41 Bridge St., Waratah, N.S.W., 2298. Australia.

We wish to thank Mr. Chris Rennie for the development of the acquisition system and Mr. John Tel.: 612 9845 6688. Fax: 612 9635 7734. E-mail: [email protected]

Anderson for his role in collecting the data which was analysed in this study.

101

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102 A. R. HAIG and E. GORDON

ability in single-trial ERPs may be of physiological (Stampfer & Basar, 198.5) and clinical (Anderson, Rennie. Gordon, Howson, & Meares, 1991; Ford, White, Lim, & Pfefferbaum, 1994) significance. In target auditory oddball data, it has been shown that traditional ERP components, particularly P3, which are readily identi- fiable in the average, may be absent or nearly absent from a considerable number of single-trials (Ford et al.. 1994; Haig, Gordon, Rogers, & Anderson, 199.5), even though all trials represent correct button-press responses by the subject to target stimuli.

A possible explanation for at least some of this variability is that differences in prestimulus brain state from trial to trial influence the subsequent response. It has been demonstrated in a number of studies, by subaveraging responses with different prestimulus EEG characteristics. that prestimulus cortical state, as reflected in specific EEG measures, influences the amplitude and latency of particular ERP components (Brandt. Jansen & Carbonari, 1991; Jansen & Brandt, 1991; Rahn & Baar, 1993). These prestimulus effects primarily concerned measures of power in certain frequency bands and the phase of alpha activity in the EEG.

Although analysis of the power in various frequency bands of the prestimulus EEG is uncomplicated, analysis of phase in relation to the ERP components has previously been hampered by two main problems, both due to the non-Euclidean nature of the measure. The first problem is that the standard subaveraging approach used for power cannot be employed for phase unless it is known in advance, in a given subject at a given site, how the phase should be divided up. For power measures, it is straightforward to divide single-trials for subaveraging, for example, into those with low power and those with high power. However, for phase, there is no such basis as to how the single-trials should be grouped, since there is no such thing as “high” phase and “low” phase. Neither is it possible to tell whether a particular phase difference represents a phase increase of xo or a phase decrease of (x-360)” for one single-trial compared to another. The most sys- tematic examination of prestimulus alpha phase to date was that carried out by Jansen and Brandt ( 1 99 I ) . Their approach to this problem was to divide the single-trials into eight different phase groupings, in order to reduce the arbitrariness of the division. However, they were able to do this because their data set consisted of 1000 stimulus presentations per subject (in a passive visual paradigm), which meant that they had a sufficient number of trials per division (125 on average) to form a subaverage waveform for each one. This would not be feasible in an oddball paradigm, which usually has only 20 to 40 target stimuli.

The second problem with phase is the difficulty with statistical analysis of circular (phase angle) data. This is also because phase is non-Euclidean, for example, 0“ = 360” = 720” and so forth. It is consequently impossible to use any conventional linear statistical methods, including even simple measures like the mean and

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PRESTIMULUS ALPHA PHASE P3 103

standard deviation. Consider a simple example, the three angles 0", 30" and 330". The conventional arithmetic mean of 0, 30 and 330 is 120. However, the mean angle of 0", 30" and 330" is not 120°, as can be seen be plotting the points on a cir- cle (in fact, the correct angular mean is 0"). Such problems with angular data will occur irrespective of whether the data are expressed from -1 80" to 1 80", from 0" to 360", or in any other range. In fact, all standard linear statistical measures and tests for significance are inappropriate for angular data. The branch of statistics which deals with analysis of circular data is called circular statistics (Fisher, 1993). Circular statistics have been employed previously in studies of steady-state evoked potentials and response detection (Stapells, Makeig, & Galambos, 1987; Dobie &Wilson, 1993).

This study focuses on the relationship between alpha phase at stimulus onset and the P3 component of target auditory oddball data, as the relationship of prestimulus alpha phase to such a late component has never been previously examined. In order to overcome the first problem described above, we have adopted an alternative approach, based on a conventional method of single-trial analysis (P3 ternplating), which is the opposite of the usual subaveraging methodology. Instead of grouping the single-trials on the basis of prestimulus EEG characteristics, and then examining the poststimulus component structure of the subaverages, we have grouped the single-trials on the basis of poststimulus component structure derived from single-trial analysis, and then examined the prestimulus EEG characteristic of interest (alpha phase). This avoids having to group the single-trials based on phase. We have overcome the second problem by employing methods of circular statistical analysis. In addition, we introduce a new form of topography for circular data, which we call circular topography.

We analyzed ERPs evoked by target stimuli in a conventional auditory oddball paradigm in twenty-five normal subjects. The basis of grouping the single-trials was a P3 templating method described by Ford et al. (1994), which is a reliable method of P3 identification in single-trial ERPs. Those trials which passed the P3 screen were classed as having P3 "present" (large P3), and those which failed the screen were classed as P3 "absent" (small or no P3). We determined whether the presence or absence of the P3 component in single-trials was related to differences in prestimulus alpha phase.

METHODS AND MATERIALS

Subjects

Data from twenty-five normal subjects were examined in this study (17 males and 8 females). The males had a mean age of 25.2 yrs ( s d . = 7.5) and the females had

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a mean age of 30.5 yrs ( s d . = 7.2). The subjects were volunteers recruited from nondepartmental hospital staff and the surrounding community who disavowed any psychiatric history, neurological disorder or substance abuse. Written consent was obtained from all subjects prior to testing in accordance with National Health and Medical Research Council guidelines.

Procedure

Subjects were seated in a sound- and light-attenuated room. An electrode cap (Bloni & Anneveldt, 1982) was used to acquire data from the Fz, F3. F4, F7, F8, C r . C3, C4. T3. T4. Pz. P3. P4. 01 and 0 2 scalp sites. Linked earlobes served as the reference. Electrodes placed 1 cni above the outer canthus of the left eye and below the outer canthus of the right eye served as the EOG bipolar recording. EOG contaminated epochs (exceeding k 100 pV) were automatically rejected. Skin resistance at each site was <5 kR. The ERP data were collected according to a standard auditory “oddball” paradigm. Stereo headphones conveyed regular tones of 1000 Hz at an interval of 1.3 s to both ears. The subjects were instructed to ignore these tones (task-irrelevant). A second target (task-relevant) tone of 1500 Hz was presented. randomly intermixed with the lower tone, the only con- straint being that two high tones were never presented in succession. Eighty-five percent of the tones were task-irrelevant and 15% were targets. The subjects were instructed to respond to the target tones by pressing two reaction-time buttons “as fast and accurately as possible” with the middle finger of each hand (to counter- balance motor effects). All tones were presented at 60 dB above the subject’s auditory threshold (determined prior to recording). Only correctly identified target epochs for which a button press response were obtained within one second of the target tone were analysed. The recording session was continued until 30 correctly identified target epochs uncontaminated by eye movements were acquired. Subjects had their eyes open and were instructed to look at a colored dot in the center of a screen, in order to minimize eye movements. The sampling rate was 256 Hz and the duration of each epoch analyzed was one second, from 300 ms prestimulus to 700 ms post-stimulus. A 70 Hz low-pass filter was applied to the signals prior to digitization.

Single-trial ERP Analysis

The method of Ford et al. (1994) was employed as closely as possible, with minor alterations necessary due to differences in the epoch length and sampling rate in this study. The data were digitally filtered with a bandpass of 0.5 to 4.5 Hz and then subsampled to reduce the sampling rate to 128 Hz. A half-cycle 2 Hz sine-

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wave template was moved in 7.8 ms (one sample) increments across the single- trial ERP epoch. The fit between the single-trial and the sine-wave template (EEG:Template) was estimated at each increment by calculating correlation, cross-product, and covariance. The ERP was divided into two epochs: the signal epoch (280 to 460 ms) was defined as the window where P3 was expected, and the (prestimulus) noise epoch (-180 to 0 ms) was defined as the window in which P3 was not expected. To pass the P3-screen, the maximum EEG:Template covariance had to be greater during the signal epoch than during the noise epoch and the correlation had to be statistically significant (I- 2 .301, p 5 .05, one-tailed). Trials not passing the P3-screen could be considered to have at least as much P3-like activity in the noise epoch as in the signal epoch. The trials passing the P3-screen were considered to have P3 present (called “ons”) and the trials not passing the P3-screen were considered to have P3 absent (called “offs”).

Alpha Phase at Stimulus Onset

For each single-trial, a narrow band-pass filter centered at 10 Hz was applied to the -250 ms to 0 ms prestimulus signal segment. The filter function was a Gaussian centerd (maximal amplitude) at 10 Hz and with the half-amplitude (-6 dB) points at 10 k 3.33 Hz. This was designed to filter the signal leaving only the alpha component present. The next step was to determine the positive and negative peaks in the filtered signal, which represented phases of 0” and 1 80” respectively. Changes in gradient from positive to negative were marked as positive peaks, and changes in gradient from negative to positive were marked as negative peaks. Because of the extreme smoothing of the waveforms that had been pro- duced by means of the filter, changes in the sign of the gradient always represented genuine peaks and troughs in the alpha signal.

Having marked the positive and negative peaks in the alpha signal over the 250 ms, the next step involved calculating the mean interpeak interval, i ms. The mean wavelength of the alpha activity was therefore 2i ms. The time interval t from the last peak (whether positive or negative) before the stimulus onset until the stimulus onset was computed. If the last peak prior to stimulus onset was positive, then the alpha phase p in degrees was given by the following equation:

t 1

p = 180:

If the last peak prior to stimulus onset was negative, then the alpha phasep was given by:

t p = 180 + 180: ( 2 )

2

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This provided a measure of alpha phase at stimulus onset. This method is illus- trated with an example single-trial in Figure 1.

Statistical Analysis of Alpha Phase

As mentioned previously, the branch of statistics concerned with analysis of angular (or circular) measures is known as circular sraristics. All of the circular statistical measures employed in this study were obtained from Fisher (1993). It is necessary to define the circular equivalent of the mean, standard deviation and variance. These are called the angular (or circular) mean, the circular standard deviation (or angular deviation) and the circular (or angular) variance, respectively. Measures of the circular variance of phase are sometimes called phase coherence measures (Stapells et al., 1987).

Take a sample of angular measurements 0,. 0?. . . . O,l. Then the elements x and J of the mean vector (centroid vector) V are given by:

From this the length of the mean vector r can be computed as:

I f x > 0 then the mean angle $ is given by (see equation 2.9 in Fisher, 1993):

Q = arctan( f)

If x < 0 then $ (in radians) is given by:

$ = x + arctan 2 (3 The definitions of angular variance and angular deviation are as follows. Note

that the angular standard deviation is not the square root of the angular variance. The angular deviation s is defined by (Equation 2.12 in Fisher):

s = %1-2 ln(r) (7)

The angular variance Vis given by (equation 2.1 1 in Fisher):

V = l - r

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108 A. R . HAIG and E. GORDON

The next step involves deriving a paired. univariate two-sample test for the significance of a difference in means. akin to the paired Student's t-test in linear statistics, In linear statistics. a paired two-sample Student's t-test is equivalent to the following procedure. Form the difference between the two paired measures for each subject (for paired data sets p , , p 2 . . . p,, and q l . q2 . . . q,l, this means deriving the differences d , = p , - q,, d2 = p 2 - q. . . . ci,, = p, , - q,,), and then use a one-sample Student's t-test to test if the mean of these differences (d , , d2 . . . (I,,) is significantly d rent from 0. The same procedure can be followed with circular statistics, given a one-sample test of whether the mean angle of a set of angular measures is significantly different from 0". For sample sizes greater than or equal to 25, as in this study, the standard test statistic (which is nonparamet- ric) was devised by Watson and will be referred to here as the Watson S-test (Fisher, 1993. pp. 79). The test statistic S is given by equation 4.23 in Fisher, along with the method for computing the corresponding significance estimate. In this study it was necessary to reduce all multivariate circular statistical problems to a univariate comparison because (except in the two dimensional case, known as spherical statisfics [Fisher, Lewis, & Embleton, 1987]), there does not appear to be a method available for multivariate analysis of circular data. It is also worth pointing out. at this point, a peculiar property of the angular mean (compared to the arithmetic mean). This is that the mean of a set of differences between two data sets does not necessarily equal the difference of the means of the two data sets.

For each site in each subject, the angular mean of the alpha phase in the P3 "ons" and the angular mean alpha phase in the P3 "offs" was computed for that site. Then the difference between these two values was computed. We then formed the global angular mean of the 15 phase difference values (from the 15 electrode sites in that subject). This gave us a single value for each subject, the global angular mean phase difference between "ons" and "offs." The global angular mean phase differences from the 25 subjects were then tested to see if their angular mean was significantly different from 0". The test employed was the Watson S-test. This procedure tested whether overall a significant alpha phase difference existed between the P3 "ons" and the P3 "offs."

Topographic mapping was also employed for phase angle measures. However, topographic mapping of circular data requires a different interpolation procedure from topographic mapping of linear measures. For example, suppose that there are two nearby electrode sites x and y, and that there is a phase of 355" at site x and of 5" at site y. If a conventional linear interpolation is used, the interpolation over the intervening scalp will have to decrease from 355" down through 350", 345" and so forth until 5". However, in reality 355" and 5" are only 10" apart. The interpolation should increase from 355" to 360" (identical to 0") and then from 0" to 5".

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The correct method of interpolation for circular measures is as follows (which we will refer to as circular topography). Instead of interpolating the measure 8 as a function of position on the scalp, two interpolations are employed. One interpolates sine(8) as a function of position on the scalp, and the other interpolates cosine(€)) as a function of position on the scalp. Then, in order to determine the interpolated angle at a particular location, the sine and the cosine of the angle are obtained from these two interpolations, and then the interpolated angle is computed in the same way as the angular mean in (5) and (6) above (if y = sine(€)) and x = cosine(€))). In addition, a circular color map has to be employed that “wraps around” so that the colour scale at 360” merges into the color scale at 0”, other- wise there will be a sharp boundary on the map whenever this transition occurs. Circular topography cannot be performed using a grey scale. Examples of circular topography are shown in Figure 3.

If a significant alpha phase difference existed overall, then the group angular mean alpha phase for the “ons” and the “offs” were topographically mapped. In addition, the angular means of the difference values at each site were mapped topographically. All topographic mapping was performed using a closed (spherical) spline interpolation, with interpolated values being mapped onto a three- dimensional head shape derived from an MlU scan.

RESULTS

Number of “Ons” and “Offs”

Overall, 73.5% of trials in normals passed the P3-screen and were therefore classed as P3 present or “ons.” The group average waveforms for all 25 normals at sites Fz, Cz and Pz are shown in Figure 2. The group average waveforms of the conventional average ERPs are shown on the left of the figure. Additionally, for each site in each subject two subaverage waveforms were formed, one of single- trials with P3 present (“ons”) and one of single-trials with P3 absent (“offs”). The group average waveforms of these “on” and “off’ subaverages are also shown in Figure 2, on the middle and right of the figure respectively. The conventional average ERPs show the typical morphology. The averages of the “ons” show a promi- nent P3 component of slightly larger amplitude than in the conventional averages. The averages of the “offs” show no unambiguous P3 component. This demon- strates that the P3-screen is working effectively in discriminating those trials which contain a P3 from those which do not.

Alpha Phase

Alpha phase was significantly different between P3 “ons” and “offs” overall ( p = . O l & S = 2.37). The group angular mean of global alpha phase was 281.3” in the

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Circular topography of alpha phase in P3 "ons" and P3 "offs"

P3 "ons" P3 "offs"

Differences Scale 90"

270"

FIGURE 3 Figure 3 shows the circular topography of group mean alpha phase in the single-trials with P3 present ("ens"-upper left), in the single-trials with P3 absent ("offs"-upper right), and the group mean alpha phase differences between "ons" and "offs" (lower left). The scale, in degrees, is shown on the lower right.

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Circular topography of alpha phase in P3 "ons" and P3 "offs"

P3 "ons" P3 "offs"

Differences Scale 90"

180" 0"

270"

FIGURE 3 Haig and Gordon

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“ons” and 227.5’ in the “offs.” The group angular mean of the global phase difference between “ons” and “offs” was 99.5’. This figure is not just the difference between the previous two but provides additional information, because, as mentioned previously, the mean of a set of differences does not equal the difference of the means for circular measures.

The topographic distributions of group angular mean alpha phase in the “ons” and the “offs” are shown in Figure 3, together with the distribution of group angular mean phase difference between the “ons” and “offs.” These maps show that the significant overall difference in alpha phase between “ons” and “offs” reflects widespread topographical differences in alpha phase. Alpha phase in the “ons” tends to be roughly around 270” across the scalp, while phase in the “offs” is markedly different to the “ons” and is more spatially variable. The difference map shows: (a) that phase differences of around 1 SO”, the maximum possible, exist at a number of sites (Cz, C4. P4. P3); (b) that phase differences of around 90” exist at all frontal sites; and (c) that non-zero phase differences are evident across the whole scalp.

DISCUSSION

This study sought to examine the relationship between alpha phase at stimulus onset and the P3 ERP component evoked in response to target stimuli. The results demonstrate that alpha phase at stimulus onset does significantly affect the P3 component in the subsequent evoked response, in that some prestimulus alpha phases are associated with the presence of a large P3 and others with its absence or near-absence. This finding provides support for the importance of prestimulus EEG characteristics in relation to late component ERPs.

Although previous studies have determined that the amplitude and latency of some ERP components are affected by prestimulus EEG characteristics, especially measures of power in particular frequency bands (Brandt et al., 1991; Jansen & Brandt, 1991; Rahn & B a a . 1993), this is the first study to examine this issue by means of single-trial analysis, and the first to address alpha phase sys- tematically in relation to the P3 component. We employed methods of circular statistical analysis which are uncommon in the ERP literature, and introduced a new form of topographic mapping, circular topography, for topographical display of phase angle data.

The results of this study confirm that prestimulus cortical state as measured by the EEG does significantly influence the poststimulus ERP. There are two possible models to explain how such an interaction could occur, which are not mutu- ally exclusive. The more traditional model postulates that ERP components are

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manifested at the scalp by means of volume conduction from a localized genera- tor site or sites. Differences in prestimulus cortical state are either a cause or an effect (more likely an effect, given current models of EEG generation as described below) of differences in activity at localized (primarily subcortical) regions involved in stimulus processing events and directly relate to differences in either the speed, mode or nature of stimulus processing. The alternative model postulates that late ERP components are primarily a widespread cortical phenom- ena, and that if (as seems likely for some components at least) they reflect neural events in deeper structures such as the hippocampus, cingulate and/or basal gan- glia, they probably do so by neural transmission rather than by volume conduction. In this case, the component as manifested by widespread cortical activity could be influenced by the dynamics of local cortical activity quite independently of any differences in underlying stimulus processing events. Either of these models is compatible with current models of the generation of the EEG (Nunez, 1989, 1995; Wright, 1990; Wright & Liley, 1995, 1996; Jansen & Rit, 1995) which tend to regard ongoing EEG activity as a cortical phenomenon driven by input without much significance at the output side. However, alternative conceptions of the EEG also have been proposed which place more emphasis on output (Freeman, 1983, 1994). The findings in this study are compatible with either model.

It is important to address two possible counter arguments to the findings in this study. The first is due to the fact that the P3 screen we employed used a segment of prestimulus EEG as the latency window in which P3 was not expected (the noise epoch), and we also derived alpha phase estimates from the same prestimulus EEG. Some interaction between these might be suggested as an explanation for the findings of this study. However, there are two reasons for rejecting such an explanation. First, for the P3 screen the EEG was filtered from 0.5 to 4.5 Hz, well below the alpha bandwidth employed. Secondly, such an interaction presupposes that trials are failing the P3 screen not because they have little or no P3-like activity in the signal epoch, but because they have spurious P3-like activity in the noise epoch. In other words, it is being asserted that the P3 screen is not working properly and is falsely classifying trials on the basis of features of the noise epoch. This suggestion is refuted by the waveforms in Figure 2, which show that the method works well in discriminating between trials with and without a P3.

A second possible counter argument is that the results could be due to an over- lap of continuing alpha activity with the P3 component. If this ongoing alpha signal is in phase with the P3 component, the P3 amplitude would be increased and vice versa. This presupposes that the alpha activity measured at stimulus onset is large amplitude and sustained until around 300 ms when P3 occurs. However, this hypothesis is readily refuted also from Figure 2. If this were true, the other three components N1, P2, and N2 would have to be affected on a large scale as well.

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The P3 “on” subaverages would have to have a very different N1, P2 and N2 structure to the P3 “off” subaverages. This is not the case. Some difference in the amplitude of the other components is to be expected, especially in those components close to P3, since the components are not completely independent but reflect processes which are functionally related to each other. Although we see some reduction of N 2 amplitude in the P3 “offs,” which is as expected, we see only slight reduction in N1 and P2 amplitude. While this fits in with the idea that the components are functionally related, it is not compatible with the alpha over- lap hypothesis, which could not result in huge differences in P3 amplitude, without similarly affecting the other components.

There are potentially important implications of the findings of this study for the clinical and psychological aspects of ERPs, since differences in prestimulus EEG state may be a confounding variable in all such studies. Any reduction in the amount of unexplained variability in ERPs is potentially important for improving these measures in a clinical context. The results of this study emphasize the importance of this area of research in order to yield greater understanding of the physiology of ERPs, and to improve model development and clinical interpreta- tion concerning these signals as measures of psychobiological function and dys- function.

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eeg alpha phase at stimulus onset significantly affects the amplitude of the p3 erp component

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