Wavelet entropy analysis of event-related potentials indicatesmodality-independent theta dominance

Juliana Yordanova a,*, Vasil Kolev a, Osvaldo A. Rosso b, Martin Schurmann c,Oliver W. Sakowitz d, Murat Ozgoren e, Erol Basar e,f

a Institute of Physiology, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 23, 1113 Sofia, Bulgariab Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Buenos Aires,

Argentinac Institute of Physiology, Medical University Lubeck, Ratzeburger Allee 160, D-23538 Lubeck, Germany

d Department of Neurosurgery, Charite-Humboldt University Berlin, D-13353 Berlin, Germanye Department of Biophysics, Medical School, Dokuz Eylul University, Balcova, Izmir, Turkey

f Brain Dynamics Multidisciplinary Research Network, Ankara, Turkey

Received 11 February 2002; received in revised form 5 April 2002; accepted 8 April 2002

Abstract

Sensory/cognitive stimulation elicits multiple electroencephalogram (EEG)-oscillations that may be partly or fully overlapping

over the time axis. To evaluate co-existent multi-frequency oscillations, EEG responses to unimodal (auditory or visual) and

bimodal (combined auditory and visual) stimuli were analyzed by applying a new method called wavelet entropy (WE). The method

is based on the wavelet transform (WT) and quantifies entropy of short segments of the event-related brain potentials (ERPs). For

each modality, a significant transient decrease of WE emerged in the post-stimulus EEG epoch indicating a highly-ordered state in

the ERP. WE minimum was always determined by a prominent dominance of theta (4�/8 Hz) ERP components over other frequency

bands. Event-related ‘transition to order’ was most pronounced and stable at anterior electrodes, and after bimodal stimulation.

Being consistently observed across different modalities, a transient theta-dominated state may reflect a processing stage that is

obligatory for stimulus evaluation, during which interfering activations from other frequency networks are minimized. # 2002

Published by Elsevier Science B.V.

Keywords: Event-related potentials (ERPs); Bimodal stimulation; Time�/frequency analysis; Entropy; EEG

1. Introduction

Several reports have pointed out that the electroence-

phalogram (EEG) reflects the activity of ensembles of

generators producing spontaneous and event-related

oscillations in several frequency ranges. Upon stimula-

tion, functionally activated generators begin to act

together in a coherent way. This transition from a

disordered to an ordered state can be detected as

frequency stabilization, synchronization, and enhance-

ment of the ongoing EEG in the post-stimulus period

(Basar et al., 1976; Basar, 1980). In this way, exogenous

or endogenous inputs produce EEG responses from

different frequency bands (delta 0.1�/4 Hz, theta 4�/7

Hz, alpha 7�/14 Hz, beta 14�/30 Hz, and gamma 30�/70

Hz) defined as event-related EEG oscillations or fre-

quency components of the event-related potential (ERP)

(Basar, 1998; Basar et al., 2000). These multiple

frequencies are generated simultaneously in the event-

related EEG and their superposition has important

functional implications (Karakas et al., 2000a,b). How-

ever, although both global and local interactions among

different frequencies may reveal neuroelectric functional

involvement (Lisman and Idiart, 1995; Yordanova and

Kolev, 1997, 1998a,b; Haenschel et al., 2000; Kolev and

Yordanova, 2000; Bressler, 1995; Bressler and Kelso,

2001; Caplan et al., 2001), frequency-specific oscillations

are typically analyzed independently of each other.

Therefore, the aim of the present study was to evaluate

co-existent multi-frequency oscillations by applying a* Corresponding author. Tel./fax: �/359-2-979-3749.

E-mail address: jyord@iph.bio.bas.bg (J. Yordanova).

Journal of Neuroscience Methods 117 (2002) 99�/109

www.elsevier.com/locate/jneumeth

0165-0270/02/$ - see front matter # 2002 Published by Elsevier Science B.V.

PII: S 0 1 6 5 - 0 2 7 0 ( 0 2 ) 0 0 0 9 5 - X

new method quantifying the entropy of the event-related

EEG (Rosso et al., 2001; Quian Quiroga et al., 2001).

According to the information theory, entropy is a

relevant measure of order and disorder in a dynamicsystem (Shannon, 1948). For analysis of EEG order/

disorder the spectral entropy has been introduced by

Inouye et al. (1991, 1993). The Fourier spectral entropy

measures how concentrated or widespread the Fourier

power spectrum of a signal can be (Powell and Percival,

1979). Low entropy values correspond to a narrow-band

(mono-frequency) activity characterizing highly ordered

(regularized) bioelectrical states, and high entropyvalues reflect a wide-band (multi-frequency) activity

(Inouye et al., 1991). However, because of the low

time resolution of the conventional Fourier transform,

the spectral entropy cannot reliably assess fast changes

of EEG states. To overcome these limitations and

quantify more precisely transitions of the EEG from

short-lasting ordered to disordered states (or vice versa)

a new method has been recently developed and appliedto ERPs (Rosso et al., 2001; Quian Quiroga et al., 2001).

The method is based on the time�/frequency decomposi-

tion of the EEG by means of the wavelet transform

(WT) and is called wavelet entropy (WE). The WT

provides for optimal time resolution for each frequency

(e.g. Schiff et al., 1994; Ademoglu et al., 1997; Blanco et

al., 1998; Demiralp et al., 1999; Samar et al., 1999) and

can accordingly extract in a reliable way superimposedevent-related oscillations from different frequencies

(Kolev et al., 1997; Demiralp et al., 1999; Yordanova

et al., 2000; Demiralp and Ademoglu, 2001). Therefore,

WE can quantify precisely time dynamics of order/

disorder states (defined here as microstates) in short-

duration signals such as the ERPs (Rosso et al., 2001;

Quian Quiroga et al., 2001).

In the present study, the WE method is applied tostudy complex ERP behavior and frequency ERP

components interaction in relation to sensory proces-

sing. Auditory and visual stimuli have been demon-

strated to generate multiple event-related oscillations in

delta, theta, alpha, gamma frequency ranges (rev. Basar,

1999; Basar et al., 2000). However, alpha and theta

oscillations have been shown to differ between auditory

and visual stimulus processing, with phase-locked alpharesponses dominating over the primary sensory areas of

each modality, and theta responses being more promi-

nent over nonspecific (associative) cortical regions

(Schurmann et al., 1997). Further, multisensory stimula-

tion is known to involve not only mechanisms specific

for each particular modality but also additional me-

chanisms underlying the integrative perception of the

complex stimulus, both at subcortical and cortical levels(Stein, 1998). Such differences have been described in

terms of specific frequency-domain characteristics of

auditory, visual, and bimodal (audio�/visual) evoked

potentials (AEPs, VEPs, BEPs) recorded at the scalp.

Amplitude-frequency characteristics (AFCs) of AEPs

manifest a compound peak (resonance) in the alpha and

theta ranges, VEPs display responsiveness in the upper

(12�/15 Hz) alpha band, and BEPs have highest peaks inthe theta band (Sakowitz et al., 2000).

Since differences in resonant frequencies have been

established between uni- and bisensory modalities, it is

important to study the interactions among coexistent

frequency responses and their possible associations with

modality-specific processing. With that aim, AEPs,

VEPs, and BEPs recorded in passive (no-task) condi-

tions were analyzed, and the minimal WE was evaluatedas a marker of oscillatory response ‘tuning’ in the ERP.

The following questions were addressed: (1) do states of

ERP ordering as reflected by WE minimum accompany

simple stimulus processing? (2) Do the amount and

temporal/spatial distribution of WE decrease depend on

the modality and complexity of the stimulation? (3)

Which oscillatory responses are affected in the process

of EEG-ordering?

2. Methods

2.1. Subjects

EEG was recorded from 15 right handed subjects(eight male, mean age of all subjects�/26 years, S.D.�/

3.2). Subjects were comfortably seated in a sound-proof

and dimly illuminated room. Personal data (handedness,

past medical history, medical family history, etc.) were

acquired with a standardized interview before record-

ings. None of the subjects reported on any neurological

disease in the past or had taken any drugs known to

affect the EEG.

2.2. Data recording

Raw data were recorded with Ag�/AgCl disc electro-

des placed at frontal, vertex, central, temporal, parietal

and occipital sites (F3, F4, Cz, C3, C4, T3, T4, P3, P4,

O1, O2) according to the international 10�/20 systemand referenced to linked earlobes. EEG signals were

amplified with frequency limits of 0.1 and 70 Hz by

means of a Schwarzer EEG machine. Additionally, a 50

Hz notch filter was used to avoid main interference.

EEG epochs (1 s pre- and 1 s post-stimulus) were

digitized at a rate of 250 Hz. During all sessions paper

recordings and video monitoring were used to control

for gross artifacts and subject’s behavior. Bipolarelectrooculogram (vertical�/horizontal) and surface

EMG of the frontal muscle were recorded for off-line

artifact rejection.

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109100

2.3. Experimental setup

The following sessions were included in each experi-

ment:

1) recording of AEPs in a passive condition. A total of

120 tone bursts (frequency 2 kHz, intensity 80 dBSPL, duration 1 s, r/f 5 ms, random inter-stimulus

intervals 1�/3 s) were presented binaurally.

2) Recording of VEPs in a passive condition. A total

of 120 rectangular light-stimuli centered in the

visual field at a distance of 1.5 m were delivered

for 1 s with inter-stimulus intervals varying between

1 and 3 s. Stimulus intensity exceeded surrounding

illumination by approximately 5 lx.3) Recording of BEPs: stimuli of (1) and (2) were

applied simultaneously. Subjects were instructed to

view and listen passively while maintaining focus on

a marker placed in the middle of the visual

stimulation field.

2.4. Data analysis

The first ten trials of each experiment were always

excluded to make sure that subjects were least affected

by the novelty of the situation. After further visual

inspection of the data, 64 artifact-free sweeps from eachmodality condition were selected for analysis, which

included the following procedures:

2.4.1. Time domain analysis

Artifact-free single sweeps were averaged. In theaveraged AEPs, VEPs, and BEPs, time-domain compo-

nents were identified and their amplitudes and latencies

were measured with a baseline of 200 ms before

stimulus.

2.4.2. Wavelet transform

The WT was used to represent the EEG signal in both

time and frequency (Daubechies, 1992; Mallat, 1999).

The wavelet representations provide precise measure-

ments of when and to what degree transient events occur

in a neuroelectric waveform and of when and how the

frequency content of a neuroelectric wave-form changes

over time (Samar et al., 1999). This is achieved by usingfamilies of functions (wavelets) that are generated from

a single function (basic wavelet, which can be a smooth

and quickly vanishing oscillation) by operations of

scaling (stretching or shrinking the basic wavelet) and

translation (moving the basic wavelet to different time

positions at any scale without changing its shape).

In this way, as shown in Fig. 1 and described in Samar

et al. (1999), the WT performs a time�/frequencydecomposition of the signal, i.e. at each resolution level

(corresponding roughly to a given frequency band) and

each time position, the wavelet function is correlated

with the shape of the neuroelectric waveform at that

position. This correlation, known as a wavelet coeffi-

cient, measures how much of the wavelet at that

resolution level and position is included in the neuro-electric waveform. This process produces a sequence of

wavelet coefficients at each level. The sequences from

different levels of decomposition can be arranged in a

hierarchical scheme called multi-resolution decomposi-

tion (Mallat, 1999). Signals corresponding to different

levels can be reconstructed by applying an inverse

transform. More details of the multiresolution scheme

and its implementation can be found in previous works(Schiff et al., 1994; Ademoglu et al., 1997; Mallat, 1999).

In the present study, a multi-resolution decomposi-

tion (Mallat, 1999) was performed by applying a

decimated discrete WT (Blanco et al., 1998; Rosso et

al., 2001). In the discrete WT, the parameters of scaling

and translation have discrete values, which can also be

taken at logarithmic (dyadic) scales (Ademoglu et al.,

1997; Demiralp and Ademoglu, 2001; Rosso et al.,2001). Orthogonal cubic spline functions were used

here as mother wavelets and the time�/frequency in-

formation was organized in a hierarchical scheme

(Blanco et al., 1998; Rosso et al., 2001). Among several

alternatives, cubic spline functions were used as sym-

metric, orthogonal, and combining in a suitable propor-

tion smoothness with numerical advantages (for a

complete discussion, see Unser, 1999; Thevenaz et al.,2000).

Fig. 1 illustrates that after a five octave wavelet

decomposition, the coefficients for the following fre-

quency bands were obtained: 63�/125 Hz, 31�/63 Hz

(gamma), 16�/31 Hz (beta), 8�/16 Hz (alpha) and 4�/8 Hz

(theta), the residue was in the 0.1�/4 Hz band (delta).

The bottom of the figure also presents the number of

coefficients and the time resolution (length of consecu-tive non-overlapping time windows) for each scale

(frequency range). The number of coefficients and time

windows used for computing the residue (0.1�/4 Hz)

were the same as those used for the lowest resolution

level (4�/8 Hz). The highest frequency band (63�/125 Hz)

was not used further for analysis.

2.4.3. Wavelet energy

In case of dyadic WT, the number of coefficients fromall resolution levels is two times smaller than in the

previous level. Here, the shortest time length including

at least one coefficient from each resolution level was

128 ms. Hence, after the WT was performed, the

analyzed signal was divided into non-overlapping time

windows of 128 ms.

Since the coefficients from each resolution level j

correspond to different frequency bands, the energy Ej

for each frequency range in each time window of 128 ms

can be computed as the corresponding squared coeffi-

cients (Fig. 1). For resolution levels with more than one

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109 101

coefficient within 128 ms, Ej was computed as the mean

of squared coefficients within the respective 128 ms

epoch. Total energy Etot of the signal in each time

window was calculated as the sum of energies of all

resolution levels. Thereafter, the relative wavelet energy

Pj was computed as the ratio between the energy of each

level, Ej , and total energy of the signal, Etot, in therespective time window:

Pj �Ej

Etot

(1)

Relative energies were presented in percent to reflect

the probability distribution of energies at different

resolution levels.

2.4.4. Wavelet entropy

The Shannon entropy (Shannon, 1948) gives a useful

criterion for analyzing system’s order/disorder by com-

paring probability distributions. When derived from therelative wavelet energies of EEG/ERPs, entropy mea-

sures reflect the degree of order/disorder of the EEG

signal (Blanco et al., 1998; Quian Quiroga et al., 2001;

Rosso et al., 2001):

SWT��X

j

Pj ln Pj (2)

where SWT is the wavelet entropy designated as WE in

the text.

A very ordered EEG can be thought of as a periodic

mono-frequency signal with a narrow band spectrum

(Inouye et al., 1991, 1993). A wavelet representation of

such a signal will be greatly resolved in one unique

wavelet resolution level (scale). For this level, the

relative wavelet energy will be almost 100% and the

WE will be near zero or of a very low value. A signal

generated by white noise can be taken as representing a

very disordered behavior and will have a wavelet

representation with significant contributions from all

frequency bands. Moreover, these contributions can be

expected to be of the same order and consequently, the

relative wavelet energies will be almost equal for all

resolutions levels, thus producing WE with maximal

values.

In the present study, WE of averaged potentials was

evaluated to reflect the relationships among phase-

locked multiple frequency ERP components. The tem-

poral evolution of WE can be analyzed by computing

WE for non-overlapping temporal windows of 128 ms.

The obtained WE value was assigned to the central

point of the respective time window. As illustrated in

Fig. 1, the time window in the post-stimulus period, in

which the WE was minimal (WEmin), was identified.

The center of the window was used as a measure of the

latency of WEmin, in which the stimulus induces the

highest degree of frequency ‘tuning’ in the brain

electrical activity (the highest degree of order in the

post-stimulus period). For appropriate evaluation of

Fig. 1. Schematic illustration of the method: the ERP is transformed to the time�/frequency domain by the WT. WT coefficients for each resolution

level (gamma, beta, alpha, theta, and residual delta) are obtained and used for calculation of the wavelet energy, from which the relative energy is

computed. Relative energies are further used for the calculation of WE. The minimum of WE in the post-stimulus epoch is identified (WEmin).

Parameters of WT for each resolution level are given in the table.

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109102

WEmin latency with the time resolution used here (128

ms), histograms were also constructed to reflect across-

individuals frequency of occurrence of WEmin in

different time windows.It is meaningful to validate whether the absolute value

of the so identified WEmin differs significantly from a

reference (pre-stimulus) epoch. Therefore, the WE

change was used as a measurable parameter (Rosso et

al., 2001). It reflects the ratio (in %) between WE of time

windows in the post-stimulus period and a common

reference time epoch from the pre-stimulus period. WE

decrease (increase) implies that post-stimulus signalshows a higher degree of order (disorder) than the

reference EEG signal.

2.4.5. Statistical analysis

WE change, WEmin latency, and relative waveletenergies from the delta, theta, alpha, beta, and gamma

ranges within the WEmin time window, were subjected

to repeated-measures analysis of variance (ANOVA). In

the ANOVA design, measures from F3, C3, P3 and T3

were used to form one level (left) of the laterality factor,

and F4, C4, P4, and T4 were used for the second level

(right) of the same factor. These electrodes were nested

under four levels of the anterior-to-posterior regionfactor (frontal, central, parietal, and temporal). Thus,

there were three within-subjects variables: modality

(auditory vs. visual vs. bimodal)�/laterality (right vs.

left)�/region (four levels). The Greenhouse�/Geisser

correction was applied to the repeated-measures factors

with more than two levels. The original degrees of

freedom df and the probability values from the reduced

df are reported in the results.

3. Results

3.1. Time-domain evoked potentials

Fig. 2 illustrates grand average AEPs, VEPs, and

BEPs at 11 electrodes. For AEPs, an N1�/P2 complex

was clearly observed with central maximum. In addi-

tion, a P3-like wave was seen at frontal, parietal, andcentral sites at around 330�/350 ms (P330), perhaps due

to the long and varying interstimulus intervals used here

(Polich, 1998). For VEPs, a clear P1 wave occurred at

occipital electrodes. A pronounced N1�/P2 complex

with central maximum characterized further VEP mor-

phology, with a P3-like wave being present at frontal

locations. Although larger in amplitude, waveforms of

BEPs at anterior sites were similar to those of AEPs.BEPs, like VEPs, manifested a well pronounced occipi-

tal P1, with the bimodal parieto�/occipital P2 compo-

nent being more prominent than after visual stimuli.

3.2. Characteristics of minimal WE

Fig. 3 illustrates time courses of group mean WE for

auditory, visual, and bimodal stimuli at 11 electrodes.

The figure shows that (1) the WE was lower in the post-stimulus than in the pre-stimulus time epochs, (2)

stimulus-related decrease in WE was strong at frontal,

central, and temporal locations and less evident at

occipital sites for all stimulus conditions, (3) WE

decrement was short-lasting and occurred with distinct

time localization, (4) WEmin time localization was less

specific, and WE decrease was less pronounced for

visual than for auditory and bimodal stimuli.

3.2.1. Time localization of WEmin

Fig. 4 presents the time localization of WEmin across

individuals. The figure demonstrates that WEmin oc-

curred within 128�/256 ms in most of the cases (up to

Fig. 2. Grand average (N�/15) auditory (AEP), visual (VEP), and

bimodal (BEP) evoked potentials at 11 electrodes.

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109 103

87%) for AEPs and BEPs. However, occipital ERPs did

not manifest a stable time localization of WEmin. Also,

a less stable time localization of WEmin was detected forVEPs, although frontal and central WEmin of VEPs

occurred again most frequently in the 128�/256 ms time

epoch.

3.2.2. WE decrease

Fig. 5 illustrates the WE decrease calculated in % for

the time epoch of its absolute minimum in the post-

stimulus period. The effect of stimulus modality was

significant (F (2,28)�/18.06, P B/0.001), resulting from

overall largest WE decrease for bimodal (mean �/70.7%)

as compared with auditory (�/65.3%) and visual (�/

52.8%) stimuli. The difference between the two uni-modal stimulus types (auditory vs. visual) was also

significant. As also seen in the figure, the WE decrease

was less expressed at occipital sites (region, F (4,56)�/

7.52, P B/0.001). The significant modality�/region in-

teraction (F (8,112)�/4.33, P B/0.01) resulted from a

most pronounced WE decrease to auditory and bimodal

stimuli at frontal, central, and parietal locations. Also,

the difference between VEP and AEP/BEP was mostly

expressed at the parietal electrodes.

3.3. Phase-locked frequency ERP components during

WEmin

Fig. 6 shows relative energies of different frequency

ranges at the time of WEmin. It is remarkable that for

Fig. 3. Group mean WE calculated from the averaged AEPs, VEPs

and BEPs.

Fig. 4. Frequency histograms of individual WEmin occurrence at

different time positions for AEPs, VEPs and BEPs.

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109104

each modality and lead, a strong predominance of

relative theta power (up to 90%) was detected during

WEmin. Subsequent analyses of relative band powers

were performed to validate this observation and explore

finer differences in frequency bands distribution during

WEmin with respect to modality and topography.

3.3.1. Delta components

As seen in Fig. 6, delta power contribution to WEmin

was very small (mean 7, 16, and 11% for AEPs, VEPs,

and BEPs, respectively). It was more pronounced (12�/

20%) at occipital�/parietal electrodes (region, F (4,56)�/

3.04, P B/0.05), but this was valid only for VEPs and

BEPs (modality�/region, F (8,112)�/3.28, P B/0.05).

3.3.2. Theta components

Although theta power largely predominated during

WEmin for all stimulus conditions (Fig. 6), its contribu-

tion was significantly larger for bimodal (mean 76%)

and auditory (mean 73%) than for visual (mean 56%)

stimuli. Theta dominance was most pronounced at

anterior (frontal�/central�/temporal) sites (region, F (4,

56)�/13.74, P B/0.001), and less evident at parietal�/

occipital sites for visual, and at occipital sites for

bimodal stimuli (modality�/region, F (8,112)�/4.69,

P B/0.01).

3.3.3. Alpha components

Alpha power contribution to WEmin was larger for

VEPs (mean 20%) relative to AEPs (17%) and BEPs

(10%), and at occipital�/parietal (28�/30%) than at

frontal�/temporal (8�/9%) locations, but these effects

did not reach a level of significance.

3.3.4. Beta components

The relative power of beta WT components signifi-

cantly differentiated bimodal from visual condition

(modality, F (2, 28)�/5.47, P B/0.05) and was largerfor the visual stimuli, with this effect being most

prominent at right-side electrodes (modality�/laterality,

F (2, 28)�/3.67, P B/0.05). Since the contribution of

relative gamma WT power was less than 0.5%, gamma

components will not be considered.

3.3.5. Regression analysis

These analyses demonstrated that WEmin was deter-

mined by dominance of theta frequency components of

the evoked potentials. To determine to what extent the

theta power may have also influenced WEmin latency

(independently of modality and topography), a stepwisemultiple regression analysis was performed. The depen-

dent variable was the WEmin latency, and predictor

variables were the relative powers of delta, theta, alpha,

Fig. 5. Group mean (9/1 S.E.) of WE decrease calculated in percents for the time epoch of its minimum (WEmin) in the post-stimulus period relative

to a pre-stimulus reference. A, AEPs, V, VEPs, B, BEPs.

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109 105

and beta activities, and coded vectors of region and

modality. It was expected that variables that can affect

WEmin latency independently of each other would be

selected by the model. The model (R2 Total�/0.249;

F (3, 491)�/54.47, P B/0.001) selected relative theta

(B�/�/0.32, P B/0.001), alpha (B�/�/0.27, P B/0.001),

and beta (B�/�/0.55, P B/0.001) as independent pre-

dictors of WEmin latency. Fig. 7 illustrates that before

500 ms post-stimulus, and especially in the 128�/256 ms

epoch, theta dominance determines WE decrement.

4. Discussion

4.1. Wavelet entropy and frequency EEG responses

After external stimulation oscillatory EEG responses

from different frequency bands (gamma, beta, alpha,

theta, delta) are generated simultaneously (Stampfer and

Basar, 1985; Kolev et al., 1997; Demiralp et al., 1999;Basar, 1999; Karakas et al., 2000b). Oscillatory activity

from each frequency band is basically characterized with

its temporal dynamics (Basar et al., 2001). Typically, in

the first 250�/300 ms after external stimulus, oscillations

from various frequencies are most enhanced and phase-

locked (Basar, 1980, 1998), but in later post-stimulus

epochs, they may be prolonged or suppressed depending

on specific processing conditions (Basar-Eroglu et al.,1992; Krause et al., 1996; Yordanova et al., 2001; Kolev

et al., 1999; Klimesch, 1996, 1999; Karakas et al.,

2000a). Since the temporal dynamics of individual

frequencies has been previously related with various

aspects of stimulus evaluation and neural coding (Basar,

1999), it was important to establish if such dynamic

changes reflected independent or interactive behavior of

different frequencies.The present study demonstrates that during external

stimulus processing, the simultaneous frequency ERP

components interact in a specific way. The analysis of

Fig. 6. Relative energies of delta, theta, alpha, and beta frequency

ranges during WEmin. Note that for each modality, a strong

predominance of the relative theta power is clearly observed during

WEmin.

Fig. 7. Time dynamics of relative energies of delta, theta, alpha and

beta frequency ranges for six consecutive post-stimulus time windows.

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109106

the ERP WE (Rosso et al., 2001; Rosso et al., in press)

made it possible to confirm in an exact quantitative way

that after auditory, visual, and bimodal stimulation

there existed highly-ordered EEG microstates. For eachmodality, the decrease of entropy of multi-frequency

EEG response occurred for short-lasting periods. This

indicates that the ordering of event-related bioelectric

activity is transient and localized in time. Furthermore,

the highly-ordered microstates in each of the AEP, VEP,

and BEP conditions were always determined by a

regularity and dominance of synchronized theta re-

sponses (Fig. 6). Also, for each modality, ERP entropydecrease was most substantial and stable at anterior

(central, frontal) locations and much less expressed and

unstable at occipital sites (Fig. 5). The consistency of

these observations across modalities implies that a theta-

dominated ERP microstate may reflect a modality-

independent fronto�/central processing mechanism that

is basically involved in sensory/cognitive processing (see

also Kolev et al., 2001).

4.2. Selectively distributed entropy changes in the

framework of brain dynamics

Standard measures of theta response amplitude have

demonstrated that enhanced and phase-locked theta

responses are generated at central�/frontal locations

upon visual and auditory stimuli (Sakowitz et al.,

2000; Schurmann and Basar, 1994; Yordanova andKolev, 1997, 1998a,b). Following bimodal (combined

visual and auditory) stimulation, absolute amplitudes of

frontal theta responses have been observed to be

significantly larger than unimodal ones (Sakowitz et

al., 2000). Notably, the theta dominance (largest relative

theta energy) leading to ERP entropy minimum eval-

uated here also was maximal after bimodal stimuli and

depended on the electrode such that entropy decreasedmostly at anterior sites (Figs. 5 and 6). In view of these

present and previous findings, it may seem that absolute

rather than relative theta amplitudes have contributed

substantially to entropy minimum.

However, despite these signs of similarity, it has been

previously shown that the most enhanced frequency

ERP components vary with modality (Sakowitz et al.,

2000). Only for BEPs, was the dominant peak of theAFCs in the theta range, indicating that theta ERP

components were mostly amplified. In contrast, domi-

nant AFC peaks for AEPs and VEPs occupied higher-

frequency bands (slow and fast alpha, respectively). Yet,

contrary to AFC results, the present study shows that

for each modality (auditory, visual, bisensory), synchro-

nized theta oscillations contribute to entropy decrease.

Also, there is a remarkable difference between thespatial distribution of entropy and the spatial distribu-

tion of those oscillatory responses that are most

enhanced in the modality-specific ERPs. For example,

upon visual stimulation, alpha responses are most

enhanced in comparison to other frequencies, and they

are primarily distributed at central, parietal and occipi-

tal sites (Schurmann et al., 1997). However, the presentresults demonstrate that even with visual stimulation,

entropy decrease is maximal at anterior locations and is

determined by theta dominance. Furthermore, the

spatial distribution of entropy decrease is similar across

the three modalities.

Possibly, a most important inference from these

observations is that entropy decrements in distributed

oscillatory responses are not necessarily linked toenhancements of oscillations and/or to the selectively

distributed evoked coherences (Basar, 1980). Rather, the

short-duration entropy decreases appear as complemen-

tary manifestations of oscillations and may act as

additional operators for sensory and cognitive pro-

cesses. It is not yet possible to make exact statements

about the functional associations of ERP entropy and

discussions have to be only limited to some theoreticalimplications in the framework of brain dynamics (Basar

et al., 2001).

In this regard, the present study provides evidence

that the cooperative and integrative activity of multiple

oscillations can specifically account for information

processing mechanisms. The functional integration of

multiple frequency oscillations acting in parallel can be

conceptualized as reflecting basic properties of neuraloscillatory systems: (1) collectivity, and (2) connectivity.

Further, multiple neural oscillatory systems can be

proposed to subserve brain information functions by

the specific time localization and the specific spatial

distribution of their interactions, which can be intro-

duced as (1) time-coding and (2) space-coding opera-

tional principles of multiple oscillatory systems. Thus,

time dynamics of individual frequency’s power may beinterpreted as resulting from interactive rather than

independent behavior of oscillatory systems.

4.3. Theta dominance and cognitive processes:

perspectives

Synchronized event-related theta activity has been

typically correlated with neural mechanisms related to

higher brain functions including associative integration(Basar, 1998; Sakowitz et al., 2000), memory (Klimesch

et al., 1997; Yordanova and Kolev, 1998a; Yordanova et

al., 2000; Sarnthein et al., 1998; Burgess and Gruzelier,

2000), or focused attention (Basar-Eroglu et al., 1992;

Karakas et al., 2000a). In the present study, task-related

paradigms were not used. Accordingly, whether and

how a prolongation of theta oscillations observed in

task conditions (Stampfer and Basar, 1985; Basar-Eroglu et al., 1992; Kolev and Schurmann, 1992) would

affect the spatio-temporal distribution of the ERP

entropy decrease is a matter of interest. Further, Quian

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109 107

Quiroga et al. (2001) have shown that the maximal

entropy decrease occurs after target stimuli, possibly in

relation with the so called P300-wave. Since P300 power

comes from the delta frequency range, it is possible thata delta-dominated entropy may emerge during P300.

Therefore, it is a matter of future investigation to

establish if temporal-spatial distribution of entropy

would show a specificity in relation to cognitive-specific

processing and long distance space coherence.

5. Conclusion

Entropy is a quantity describing the amount of order/disorder in a system (Shannon, 1948). By summarizing a

large amount of results on oscillatory brain dynamics,

Basar (1980, 1999) made a statement on the basis of a

semi-quantitative evaluation: Upon stimulation the

brain oscillations (from delta to gamma frequency

ranges) shift from disordered states to ordered states.

By means of the WE method, this statement is verified in

an exact quantitative way. Broad applications of thisnew metric of transient order/disorder EEG processes

may gain new insights to the integrative sensory-

cognitive processing in the brain. In the present study,

it is demonstrated that external stimulus processing

produces a transient highly-ordered microstate in the

ERPs reflected by WE minimum. The emergence of this

ordered microstate (1) does not depend on stimulus

modality, (2) is consistently determined by synchronizedtheta oscillations, (3) has a specific anterior distribution.

This indicates that a transient dominance of stimulus-

locked theta components may reflect a processing stage

that is obligatory for stimulus evaluation, during which

interfering activations from other frequency networks

are minimized.

Acknowledgements

Work was supported by the James S. McDonnell

Foundation, USA (98-66 EE-GLO-04), the Deutsche

Forschungsgemeinschaft, Germany (436-BUL-113/105),

the International Office of BMBF, Germany (ARG-4-

G0A-6A), National Research Fund at the Ministry of

Science and Education, Bulgaria (B-703/97, B-812/98),

Consejo Nacional de Investigaciones Cientıficas y Tec-nicas (CONICET), Argentina (PIP 0029/98), and Fun-

dacion Alberto J. Roemmers, Argentina.

References

Ademoglu A, Micheli-Tzanakou E, Istefanopulos Y. Analysis of

pattern reversal visual evoked potentials (PRVEP’s) by spline

wavelets. IEEE Trans Biomed Eng 1997;44:881�/90.

Basar E. EEG Brain Dynamics. Relation between EEG and Brain

Evoked Potentials. Amsterdam: Elsevier, 1980.

Basar E. Brain function and oscillations. vol. I. Brain Oscillations,

Principles and Approaches. Berlin: Springer, 1998.

Basar E. Brain function and oscillations. vol. II. Integrative Brain

Function. Neurophysiology and Cognitive Processes. Berlin:

Springer, 1999.

Basar E, Gonder A, Ungan P. Important relation between EEG and

brain evoked potentials. II. A systems analysis of electrical signals

from the human brain. Biol Cybern 1976;25:41�/8.

Basar E, Basar-Eroglu C, Karakas S, Schurmann M. Brain oscillations

in perception and memory. Int J Psychophysiol 2000;35:95�/124.

Basar E, Schurmann M, Demiralp T, Basar-Eroglu C, Ademoglu A.

Event-related oscillations are ‘real brain responses’*/wavelet

analysis and new strategies. Int J Psychophysiol 2001;39:91�/127.

Basar-Eroglu C, Basar E, Demiralp T, Schurmann M. P300-response:

possible psychophysiological correlates in delta and theta fre-

quency channels. A review. Int J Psychophysiol 1992;13:161�/79.

Blanco S, Figliola A, Quian Quiroga R, Rosso OA, Serrano E. Time�/

frequency analysis of electroencephalogram series. III. Wavelet

packets and information cost function. Phys Rev E 1998;57:932�/

40.

Bressler S. Large-scale cortical networks and cognition. Brain Res Rev

1995;20:288�/304.

Bressler SL, Kelso JA. Cortical coordination dynamics and cognition.

Trends Cogn Sci 2001;5:26�/36.

Burgess AP, Gruzelier JH. Short duration power changes in the EEG

during recognition memory for words and faces. Psychophysiology

2000;37:596�/606.

Caplan JB, Madsen JR, Raghavachari S, Kahana MJ. Distinct

patterns of brain oscillations underline two basic parameters of

human maze learning. J Neurophysiol 2001;86:368�/80.

Daubechies I. Ten Lectures on Wavelets. Philadelphia: SIAM, 1992.

Demiralp T, Ademoglu A. Decomposition of event-related brain

potentials into multiple functional components using wavelet

transform. Clin Electroencephalogr 2001;32:122�/38.

Demiralp T, Yordanova J, Kolev V, Ademoglu A, Devrim M, Samar

VJ. Time�/frequency analysis of single-sweep event-related poten-

tials by means of fast wavelet transform. Brain Lang 1999;66:129�/

45.

Haenschel C, Baldeweg T, Croft RJ, Whittington M, Gruzelier J.

Gamma and beta frequency oscillations in response to novel

auditory stimuli: a comparison of human electroencephalogram

(EEG) data with in vitro models. Proc Natl Acad Sci USA

2000;97:7645�/50.

Inouye T, Shinosaki K, Sakamoto H, Toi S, Ukai S, Iyama A,

Katsuda Y, Hirano M. Quantification of EEG irregularity by use

of the entropy of the power spectrum. Electroencephalogr Clin

Neurophysiol 1991;79:204�/10.

Inouye T, Shinosaki K, Imaya A, Matsumoto Y. Localization of

activated areas and directional EEG patterns during mental

arithmetic. Electroencephalogr Clin Neurophysiol 1993;86:224�/30.

Karakas S, Erzengin O, Basar E. A new strategy involving multiple

cognitive paradigms demonstrates that ERP components are

determined by the superposition of oscillatory responses. Clin

Neurophysiol 2000a;111:1719�/32.

Karakas S, Erzengin O, Basar E. The genesis of human event-related

responses explained through the theory of oscillatory neural

assemblies. Neurosci Lett 2000b;285:45�/8.

Klimesch W. Memory processes, brain oscillations and EEG synchro-

nization. Int J Psychophysiol 1996;24:61�/100.

Klimesch W. EEG alpha and theta oscillations reflect cognitive and

memory performance: a review and analysis. Brain Res Rev

1999;29:169�/95.

Klimesch W, Doppelmayr M, Schimke H, Ripper B. Theta synchro-

nization and alpha desynchronization in a memory task. Psycho-

physiology 1997;34:169�/76.

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109108

Kolev V, Schurmann M. Event-related prolongation of induced EEG

rhythmicities in experiments with a cognitive task. Int J Neurosci

1992;67:199�/213.

Kolev V, Yordanova J. The position of event-related EEG activity in

the local/global theory. Behav Brain Sci 2000;23:407.

Kolev V, Demiralp T, Yordanova J, Ademoglu A, Isoglu-Alkac U.

Time�/frequency analysis reveals multiple functional components

during oddball P300. NeuroReport 1997;8:2061�/5.

Kolev V, Yordanova J, Schurmann M, Basar E. Event-related alpha

oscillations in task processing. Clin Neurophysiol 1999;110:1784�/

92.

Kolev V, Rosso OA, Yordanova J. A transient dominance of theta

ERP component characterizes passive auditory processing:

evidence from a developmental study. NeuroReport

2001;12:2791�/6.

Krause CM, Lang AH, Laine M, Kuusisto M, Porn B. Event-related

EEG desynchronization and synchronization during an auditory

memory task. Electroencephalogr Clin Neurophysiol 1996;98:319�/

26.

Lisman JE, Idiart MA. Storage of 79/2 short-term memories in

oscillatory subcycles. Science 1995;267:1512�/5.

Mallat S. A Wavelet Tour of Signal Processing, 2nd Ed. San Diego:

Academic Press, 1999.

Polich J. P300 clinical utility and control of variability. J Clin

Neurophysiol 1998;15:14�/33.

Powell GE, Percival IC. A spectral entropy method for distinguishing

regular and irregular motion of Hamiltonian systems. J Phys A:

Math Gen 1979;12:2053�/71.

Quian Quiroga R, Rosso OA, Basar E, Schurmann M. Wavelet

entropy in event-related potentials: a new method shows ordering

of EEG oscillations. Biol Cybern 2001;84:291�/9.

Rosso OA, Blanco S, Yordanova J, Kolev V, Figliola A, Schurmann

M, Basar E. Wavelet Entropy: a new tool for analysis of short time

brain electrical signals. J Neurosci Meth 2001;105:65�/75.

Rosso OA, Yordanova J, Kolev V, Blanco S, Figliola A, Schurmann

M, Basar E. Time�/frequency analysis of sensorial brain activity,

Clin Neurophysiol. Special issue, in press.

Sakowitz OW, Schurmann M, Basar E. Oscillatory frontal theta

responses are increased upon bisensory stimulation. Clin Neuro-

physiol 2000;111:884�/93.

Samar VJ, Bopardikar A, Rao R, Swartz K. Wavelet analysis of

neuroelectric waveforms: a conceptual tutorial. Brain Lang

1999;66:7�/60.

Sarnthein J, Petsche H, Rappelsberger P, Shaw GL, von Stein A.

Synchronization between prefrontal and posterior association

cortex during human working memory. Proc Natl Acad Sci USA

1998;95:7092�/6.

Schiff SJ, Aldroubi A, Unser M, Sato S. Fast wavelet transformation

of EEG. Electroencephalogr Clin Neurophysiol 1994;91:442�/55.

Schurmann M, Basar E. Topography of alpha and theta oscillatory

responses upon auditory and visual stimuli in humans. Biol Cybern

1994;72:161�/74.

Schurmann M, Basar-Eroglu C, Basar E. A possible role of evoked

alpha in primary sensory processing: common properties of cat

intracranial recordings and human EEG and MEG. Int J

Psychophysiol 1997;26:149�/70.

Shannon CE. A mathematical theory of communication. Bell Syst

Technol J 1948;27:379�/423; 623�/56.

Stampfer HG, Basar E. Does frequency analysis lead to better

understanding of human event related potentials. Int J Neurosci

1985;26:181�/96.

Stein BE. Neural mechanisms for synthesizing sensory information

and producing adaptive behaviors. Exp Brain Res 1998;123:124�/

35.

Thevenaz P, Blue T, Unser M. Interpolation revisited. IEEE Trans

Med Imaging 2000;19:739�/58.

Unser M. Splines: a perfect fit for signal and image processing. IEEE

Sig Porc Mag 1999;16:22�/38.

Yordanova J, Kolev V. Developmental changes in the event-related

EEG theta response and P300. Electroencephalogr Clin Neuro-

physiol 1997;104:418�/30.

Yordanova J, Kolev V. A single-sweep analysis of the theta frequency

band during an auditory oddball task. Psychophysiology

1998a;35:116�/26.

Yordanova J, Kolev V. Developmental changes in the theta response

system: a single sweep analysis. J Psychophysiol 1998b;12:113�/26.

Yordanova J, Devrim M, Kolev V, Ademoglu A, Demiralp T.

Multiple time�/frequency components account for the complex

functional reactivity of P300. NeuroReport 2000;11:1097�/103.

Yordanova J, Kolev V, Polich J. P300 and alpha event-related

desynchronization (ERD). Psychophysiology 2001;38:143�/52.

J. Yordanova et al. / Journal of Neuroscience Methods 117 (2002) 99�/109 109