Kolev, V., Demiralp, T., Yordanova, J., Ademoglu, A., Isoglu-Alkaç, Ü. (1997). Time-Frequency Analysis Reveals Multiple Functional Components During Oddball P300. NeuroReport, 8: 2061-2065.
Copyright © 1997 Rapid Science Publishers 

Time-Frequency Analysis Reveals Multiple Functional Components During Oddball P300



Vasil Kolev 2, Tamer Demiralp 1,3,CA, Juliana Yordanova 2, Ahmet Ademoglu 4, and Ümmühan Isoglu-Alkaç 1,3

1  Istanbul University, Electro-Neuro-Physiology Research and Application Center, 34390 Çapa-Istanbul, Turkey,
2  Institute of Physiology, Bulgarian Academy of  Sciences, Acad. G. Bonchev str. bl. 23, 1113 Sofia, Bulgaria,
3  Turkish Scientific and Technical Research Council (TÜBITAK), Brain Dynamics Research Unit, 06100
    Kavaklidere-Ankara, Turkey,
4  Bogaziçi University, Institute of Biomedical Engineering, Bebek-Istanbul, Turkey
 

CA Corresponding Author:
    Assoc. Prof. Dr. Tamer Demiralp
    Istanbul University
    Istanbul Faculty of Medicine
    Department of Physiology
    34390 Çapa-Istanbul, Turkey

    Tel (Fax):  90 212 533 94 68
    e-mail:  karamusa@hamlin.cc.boun.edu.tr



 
 
Abstract
 
A time-frequency decomposition was applied to rare target and frequent non-target event-related potentials (ERPs) elicited in an oddball condition to assess whether multiple functional components occur in the P300 latency range. The wavelet transform (WT) was used because it allows capture of simultaneous or partly overlapping components in ERPs without loosing their temporal relationships. The application of a four-octave quadratic B-spline wavelet transform at the level of single-sweep data allowed us to obtain new information and revealed the presence of separate events during P300 development. Several delta, theta, and alpha frequency components in the P300 latency range differed between target and non-target processing. These findings indicate that P300 is composed of multiple functional components and that the WT method is of use for the study of P300 functional correlates more precisely.

Key words:  Cognitive processes, Event-related brain potentials (ERPs), P300 (P3) wave, Time-frequency analysis, Wavelet transform (WT)



 
 
Introduction
 
Event-related brain potentials (ERPs) are time-varying signals which reflect the summated time-courses of underlying neural events during information processing. The processing mechanisms may operate on different time scales, from milliseconds to seconds, and may also be entirely or partly overlapping. To separate functionally meaningful events that occur simultaneously, different procedures or statistical methods have been applied to the ERP waveforms (e.g., Refs. 1-3), but the reliable component isolation remains problematic.

    Recently, an efficient time-frequency (time-scale) decomposition method, the wavelet transform (WT), was proposed as a tool to examine the multicomponent structure of ERPs [4-6]. The major advantage of the WT is its variable time resolution involving shorter effective time windows for higher frequencies reflecting fast and short-duration  processes and longer effective time windows for lower frequencies reflecting slow processes. The WT can therefore partition the ERP between several orthogonal functions (independent frequency components) with parallel time courses, thus respecting the overlapping component composition of ERPs [4,5,7]. These wavelet functions can be chosen such that they are well localized in time, which allows description of the time positions of events in different frequency ranges.
 
    According to many previous reports, a late positive wave P300 with a parieto-central distribution is consistently elicited by rare attended stimuli presented in an oddball task [8-10]. Similar late positive waves have been recorded in various other conditions where low probability, novel, or task-relevant (to-be-attended, to-be-memorized, or to-be-responded) stimuli are used [9,11]. P300 waves have shown condition-specific shapes, latencies, and scalp topographies [12]. In addition, different sites of P300 origin have been proposed. These observations  imply that even when P300 appears as a single wave, it is not a unitary phenomenon but may have a heterogeneous and multicomponent structure. For example, in the classical oddball condition, P300 is typically seen as a single wave or as a bifid wave in some cases [10].  However, stimulus probability, novelty, discriminability, task-relevance, etc. are all processed in the oddball condition. Each of these variables alone is known to affect P300 and may relate to several distinct subcomponents, but P300s with simple shapes are usually observed in the time domain ERP. In the frequency domain, delta (0.5-4 Hz) and theta (4-7 Hz) responses in the P300 latency range have been shown to differ between rare target and frequent non-target processing [13-15]. Given the advantages of the multiresolution time-frequency analysis provided by the wavelet transform, the present study was undertaken to examine whether multiple functional components can be disclosed within the oddball P300 and whether such components might correspond to those previously described.
 



 
 
Materials and Methods
 
Ten healthy volunteers (age 18-27 years; six females) served as subjects. Electroencephalogram (EEG) was recorded at Fz, Cz, and Pz locations (10/20 system) with reference to linked mastoids. The cut-off frequencies of the EEG amplifiers were 0.5 and 70 Hz (-3 dB/oct.), and 1 s pre- and 1 s post-stimulus epochs were sampled with a frequency of 256 Hz (12 bit). The electro-oculogram was also recorded. Eighty tones with intensity of 60 dB SPL, duration of 1000 ms, and r/f 10 ms were presented binaurally in an oddball condition. Two types of auditory stimuli (frequent 2000 Hz and rare 1950 Hz) were mixed randomly with a probability of  0.2 for the rare tones. The rare tones were the targets and had to be counted silently. Interstimulus intervals varied randomly between 3.5 and 5.5 s. During the experimental session the subjects kept their eyes closed. After the experiment they reported the number of the counted target stimuli which was in all cases correct.
 
    After artifact rejection, only sweeps not exceeding ± 45 µV and free of ocular and muscular artifacts were accepted for further processing. In the averaged ERPs, P300 peak latency and base-to-peak amplitude values were measured and statistically analyzed.
 
    The wavelet transform was applied to both averaged and single-sweep ERPs (see bellow). A quadratic B-spline wavelet was used as having a basic waveshape especially applicable to single EEG data and providing for near optimal time-frequency localization [5,6,16,17]. A fast WT algorithm was employed in a standard pyramidal filter scheme to decompose average and single trial ERPs into the time-frequency plane [4,18]. The application of a four-octave wavelet transform yielded four sets of coefficients in 32-64 Hz (gamma), 16-32 Hz (beta), 8-16 Hz (alpha) and 4-8 Hz (theta) frequency ranges and residues in the 0.5-4 Hz (delta) frequency range. Each octave contained the number of coefficients appropriate to display the time resolution relevant for the respective frequency range (Fig. 1A). The interpolation of the coefficients by the quadratic spline functions can be used to reconstruct the analyzed signal and to represent the time course in each frequency band (Fig. 1B). In the present study, delta, theta, and alpha coefficients were evaluated. Eight delta, eight theta, and 16 alpha coefficients were obtained for each 1 s post-stimulus epoch, with the window size being 128 ms for delta and theta and 64 ms for the alpha scale. Only the coefficients in the P300 latency range (300-550 ms) were analyzed. These were coefficients 4 and 5 for delta and theta ranges, and coefficients 6, 7, and 8 for alpha range (Fig. 2). The wavelet coefficients are designated with a letter corresponding to each frequency band (D for delta, T for theta, and A for alpha) together with the coefficient number and two other numbers in brackets representing the approximate time window in ms. For example, D5(450-580) denotes the fifth delta coefficient obtained for the 450-580 ms epoch.
 
    The wavelet coefficients of single sweep and averaged ERPs were subjected to repeated measure analysis of variance (ANOVA) with two within-subjects factors, stimulus (target vs non-target) and lead (Fz, Cz, and Pz). Amplitude measures of the P300 ERP components were subjected to the same analysis.
 
 
FIG. 1.   One single-sweep recorded from the human scalp (frequency limits 0.1-70 Hz) after application of auditory target stimulus. (A) WT coefficient sets in the 8-16 Hz (alpha) and 4-8 Hz (theta) frequency ranges, and the residues in the 0.5-4 Hz (delta) frequency band. Each octave contains the number of coefficients which is appropriate to display the relevant time resolution for that frequency range. The interpolation of the coefficients by spline functions can be used (B) to visualize the single-sweep time course in each frequency band.
 
Wavelet transform:   The WT analysis provides an optimal mathematical solution for time-frequency representation of complex signals, which is achieved by using a wavelet basis function [4-7,16,17]. The WT includes the following principal operations:  (1) logarithmic scaling (or frequency decomposition) of the signal, which yields logarithmically ordered band-pass filters falling into different octaves. Thus, the ratio between the central frequency of the band-pass and the band-width is preserved constant, which improves the identification and discrimination of the time-scale components even if they are overlapped by other non-relevant signals [4].  (2) Linear shifting of the wavelet basis function in each scale (frequency band) where the scaled basis functions are used to obtain weighting coefficients resulting from the interaction of the wavelet basis function with the real signal. This allows for time localization of components in each frequency band in a manner that guarantees the separability of the captured component in time and frequency.
 
Spline basis functions:   The B-splines (Fig. 3) of order n are a basis of the subspace of all continuos piecewise polynomial functions of degree n with derivatives up to n-1 that are continuous everywhere on the real line [16,17]. For equally spaced integral knot points, any function  of this space can be expressed as:
                                                                                                                                 (1)
where  denotes the normalized B-spline function of order n with n + 2 equally spaced knots. The definition of  is
n + 1  times                                                        (2)
where  *   is the convolution operation and  is the indicator function in the interval [0,1] defined as
                                                                                                                      (3)
    The function  in (1) can be uniquely determined by its B-spline coefficients {c(i)}. For the B-spline interpolation, the essential point is to determine the coefficients of this expansion so that  matches the values of some discrete sequence {f(k)} at the knot points:  for . The discrete B-splines are obtained by sampling the corresponding continuos functions . Then, the interpolating function  is in the form
                                                                                                               (4)
    The B-spline filter coefficients {c(k)} can be computed for the case of second order (n = 2) using
    c+ (k) = f(k) + b1c+ (k-1)            (k = 2,....,K)                                                                                                     (5a)
    c- (k) = f(k) + b1c- (k+1)            (k = K-1,....,1)                                                                                                    (5b)
    c (k) = bo(c+(k) + c-(k) - f(k))                                                                                                                             (5c)
where b = -8/(1-2), b1  =  8 - 3  [16,17].
 
The fast wavelet transform algorithm:   The initial step for the wavelet decomposition up to a level I is to find the coefficients {c(k)} at the resolution level 0 (Eqns 6a-b). The wavelet coefficients {di(k)} are then computed iteratively for i = 0 to i = I-1 by filtering and decimating by factor of 2.
     c(i+1)(k) = [h*c(i)](k)                                                                                                                                         (6a)
     d(i+1)(k) = [g*c(i)](k)                                                                                                                                         (6b)
i = 0,1,2,.....I-1
where   indicates downsampling by 2 and where h and g are the low-pass and the high-pass filters for decomposition respectively.
 
 
FIG. 2.   Mean values of the analyzed delta, theta, and alpha wavelet coefficients of oddball target and non-target single responses at three electrode locations. The time windows of the multiresolution decomposition and the designation of the coefficients are presented at the bottom.
 
 
FIG. 3.   (a) Quadratic B-spline wavelet function  and (b) the associated spline wavelet 


 
 
Results

Grand average ERPs from oddball target and non-target stimuli are presented in Fig. 4 and illustrate that the P300 amplitude was significantly larger (stimulus, F(1/9) = 29.3; p < 0.001, mean 11.6 vs 3.2 µV) and P300 peak latency was longer (mean 410 ms vs 335 ms) for targets than for non-targets. P300 amplitude was maximal at Pz (lead, F(2/9) = 35.3; p < 0.001).
 
    Figure 2 shows group mean values of single-sweep delta, theta, and alpha wavelet coefficients. D4(320-450) did not depend on the lead and was significantly larger for targets only at the fronto-central sites (stimulus x lead, F(2/1366) = 11; p < 0.001; simple stimulus effects at Fz and Cz, F(1/683) > 3.8; p < 0.05). A most remarkable stimulus type effect was obtained for the parietally predominant fifth positive delta coefficient D5(450-580) (lead, F(2/1366) = 198.8; p < 0.001), which was significantly larger for targets at all electrodes (stimulus, F(1/683) = 156.9; p < 0.001), with this difference being most pronounced at Pz (stimulus x lead, F(2/1366) = 26.6; p < 0.001). As also illustrated in Fig. 2, targets produced a significantly larger T4(320-450) at the three locations (stimulus, F(1/683) = 16.7; p < 0.001). This coefficient was maximal at the centro-frontal locations (lead, F(2/1366) = 11.3; p < 0.001). The alpha coefficients  A6(290-350) and  A7(350-420) were smaller for the targets (stimulus, F(1/683) > 8; p < 0.001) and did not manifest any dependence on the electrode location. In the averaged ERPs, similar statistical results were obtained for delta and theta coefficients, and no significant effects were found for the alpha coefficients.
 

 
FIG. 4.   Grand average ERPs from oddball non-target and target stimuli and the reconstructed delta (0.5-4 Hz), theta (4-8 Hz), and alpha (8-16 Hz) frequency components. Stimulus onset occured at 0 ms.


 
 
Discussion
 
The present results confirmed previous reports and demonstrated that the amplitude of the late positive wave P300 was significantly larger to oddball targets than to frequent non-targets and was maximal at the parietal location [8-10]. In the averaged potentials, the P300 appeared as a pronounced single ERP wave. However, the wavelet analysis revealed that during the oddball task multiple functional components were present in the P300 latency range. First, the WT partitioned the ERPs among independent time-frequency components that also manifested specific scalp topography patterns. Therefore, it is likely that the time-frequency components from the P300 latency range reflect distinct functional subprocesses that occur during P300 development. Because these subprocesses are simultaneous or partly overlapping, they cannot be distinguished in the oddball P300 potential obtained by means of time domain analysis. Second, the time-frequency components differed significantly between oddball targets and frequent non-targets, which indicates that they are functionally meaningful and relevant to oddball task processing. Hence, separate functional mechanisms appear to be involved in the early and late stages of P300 expression.
 
    Previous results have shown that a P300 with a relatively short latency and frontal predominance, called P3a, can be elicited when the oddball stimuli are extremely rare, surprising, or novel [8,19,20]. It is likely that similar processes are activated during the classical oddball condition, but P3a could not be distinguished in the averaged ERP. With regard to the present WT findings it may be assumed that these processes are reflected by the fronto-central theta components T4(320-450) and by the simultaneous delta D4(320-450) component that was significantly larger for the oddball targets at fronto-central sites. It is noteworthy that these early target vs non-target differences were accompanied by a wide-spread decrease in alpha (A6 and A7) components to targets, which is in accordance with previous studies, in which alpha desynchronization was described for less precisely localized time windows [21].
 
    The rare stimuli in the present study were also task-relevant. Task-related P300 is recognized typically as a parietal wave with longer latency (P3b) or as a late positive complex [9,11,22,23]. The WT analysis yielded a later delta coefficient D5(450-580) with a parietal predominance, which differed most markedly between targets and non-targets. Given also the findings of the contribution of delta activity to P3b expression [18,24,25], this delta component is most probably associated with P3b.
 
 
Conclusion
 
By applying the wavelet analysis, the present results reveal the presence of several functional components in the P300 latency range during an oddball condition. Further research on the specific responsiveness of  the time-frequency components to cognitive variables known to modulate P300 might lead to a more precise evaluation of the functional correlates of this endogenous potential.
 

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Acknowledgements. Supported by the DOPROG Program and project TBAG Ü 17-3 of the Turkish Scientific and Technical Research Council (TÜBITAK), Ankara, Turkey, and the National Research Fund at the Ministry of Science, Education and Technologies, Sofia, Bulgaria.

Received 6 February 1997;
accepted 26 March 1997