Biol. Cybern. 79, 49±57 (1998)
`
`Individual di€erences in brain dynamics: important implications
`for the calculation of event-related band power
`
`M. Doppelmayr, W. Klimesch, T. Pachinger, B. Ripper
`
`Department of Physiological Psychology, Institute of Psychology, University of Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria
`
`Received: 22 July 1997 / Accepted in revised form: 22 April 1998
`
`Abstract. Measures of event-related band power such as
`event-related desynchronization (ERD) are convention-
`ally analyzed within ®xed frequency bands, although it is
`known that EEG frequency varies as a function of a
`variety of factors. The question of how to determine
`these frequency bands for ERD analyses is discussed and
`a new method is proposed. The rationale of this new
`method is to adjust the frequency bands to the individ-
`ual alpha frequency (IAF) for each subject and to
`determine the bandwidth for the alpha and theta bands
`as a percentage of IAF. As an example, if IAF equals
`12 Hz, the widths of the alpha and theta bands are larger
`as compared to a subject with an IAF of, e.g., only 8 Hz.
`The results of an oddball paradigm show that the
`proposed method is superior to methods that are based
`on ®xed frequencies and ®xed bandwidths.
`
`1 Introduction
`
`Although it is well known that alpha (the dominant
`EEG frequency) varies as a function of age, EEG
`frequencies are conventionally subdivided into ®xed
`frequency bands such as theta (4±8 Hz), alpha (8±
`13 Hz), beta (14±30 Hz), and gamma (30±70 Hz). From
`childhood to puberty the mean EEG frequency increases
`with age (Epstein 1980), but then decreases for the
`remaining life span. After puberty the alpha frequency
`starts to decline with increasing age. As an example,
`KoÈ pruner et al. (1984) have found a linear relationship
`within the age range of adult subjects. They have shown
`that a young adult of, for example, 20 years has an
`expected alpha frequency of about 11 Hz, whereas a 70-
`year old subject shows a drop of 2.65 Hz down to a
`frequency of 8.24 Hz. In addition, data from our
`laboratory have indicated that even subjects of the same
`age show a considerable variability in alpha frequency,
`
`Correspondence to: M. Doppelmayr
`(e-mail: michael.doppelmayr@sbg.ac.at,
`Tel. +43-662-80445136 or -5100, Fax: +43-662-80445126)
`
`with a mean standard deviation of about 1 Hz (e.g., the
`reviews in Klimesch 1996, 1997). This means that even
`for age-matched subjects, an interindividual di€erence of
`about 2 Hz is quite a common case. Klimesch et al.
`(1990, 1993) have found evidence that these interindi-
`vidual di€erences in alpha frequency are largely due to
`interindividual di€erences in memory performance.
`Because of this large interindividual variability in al-
`pha frequency, signi®cant portions of alpha power will
`fall outside a ®xed frequency window when event-related
`desynchronization (ERD), a method originally proposed
`by Pfurtscheller and Aranibar (1977), or other types of
`band power measures are calculated. As an example, let
`us consider a subject with a low alpha frequency and let
`us assume that the lower alpha band falls below the
`frequency window of the ®xed band, which then covers
`only the upper alpha and some portions of the lower
`beta bands. In this case, event-related changes in the
`lower alpha band cannot be detected and changes in the
`upper alpha band will be misinterpreted if a ®xed band is
`used. This example demonstrates that frequency bands
`should be adjusted individually for each subject. One
`method that was applied in earlier studies (Klimesch
`et al. 1996a, 1996b, 1997a) in our laboratory was to use
`the individual alpha frequency (IAF) as an anchor point
`for distinguishing a lower from an upper alpha band.
`Although this method proved superior to the use of ®xed
`frequency bands (Schimke et al. 1990), the question still
`is whether the bandwidth may be considered a constant
`value that does not vary as a function of IAF. Before we
`consider this question in more detail, we want to show
`that besides the variation in IAF, the strikingly di€erent
`reactions of the lower and upper alpha bands and the
`transition from alpha desynchronization to theta syn-
`chronization provide additional arguments for an indi-
`vidual adjustment of frequency bands.
`The results from principal component analyses have
`repeatedly shown that power values in the alpha band
`load on two di€erent and orthogonal components, with
`highest loadings in the lower and upper alpha bands. As
`an example, Mecklinger et al. (1992) found two or-
`thogonal components, one with highest loadings be-
`tween 7 and 11 Hz and a second with highest loadings
`
`Wave Neuroscience EX2003
`PeakLogic v. Wave Neuroscience
`IPR2022-01550
`
`

`

`50
`
`between 10 and 13 Hz. These data indicate that power
`values of the lower and upper alpha bands vary largely
`independently of each other. Experiments from our
`laboratory have shown that lower alpha ERD varies as a
`function of attentional demands whereas upper alpha
`ERD is associated with (semantic) memory demands
`(Klimesch 1996, 1997). Thus, the use of individually
`adjusted frequency bands is essential to prevent task-
`related band power changes in the lower and upper al-
`pha bands overlapping and cancelling each other.
`Another important ®nding that questions the use of
`®xed frequency bands is based on the fact that, with
`increasing task demands, alpha desynchronizes whereas
`theta synchronizes (see the reviews in Schacter 1977 and
`Klimesch 1996). These opposite changes in theta and
`alpha band power can be observed if a reference condi-
`tion in which subjects are in a state of alert wakefulness
`is compared with a test condition in which the subjects
`perform some type of task. In a recent study (Klimesch
`et al. 1996a) we were able to demonstrate that the
`transition between alpha desynchronization and theta
`synchronization occurs within a narrow frequency range
`that varies as a function of IAF. This frequency, where
`theta synchronization gives way to alpha desynchroni-
`zation, is called the transition frequency (TF). Conse-
`quently, if rather broad frequency bands are used which
`are not adjusted to IAF, these e€ects of an event-related
`increase (synchronization) and decrease (desynchroni-
`zation) in band power will tend to cancel each other.
`It is the purpose of the present paper to show the
`usefulness of a new method for determining frequency
`bands as well as the bandwidth individually for each
`subject. It is proposed to use IAF as cut-o€ frequency
`between the lower and upper alpha bands and to use a
`percentage of IAF to determine the width of frequency
`bands. When attempting to determine the bandwidth
`individually, the crucial question is: What criterion
`should be used? We proceed from the idea that TF
`marks the cut-o€ frequency between the theta and lower
`alpha bands. In previous research we have found that
`TF lies at about 4 Hz below IAF and is signi®cantly
`correlated with IAF (cf. Klimesch et al. 1996a). It should
`be noted, however, that TF shows a variation of about
`‹0.5 Hz between di€erent studies. In tasks where theta
`synchronization dominates, TF lies somewhat higher (at
`about 3.5 Hz below IAF) as compared to tasks where
`alpha desynchronization dominates. In the latter case,
`TF may be on average as low as about 4.5 Hz below
`IAF. Because a mean bandwidth of 4 Hz proved useful
`in previous studies, we suggest to uses steps of 20% IAF
`for an individual determination of the bandwidth. As an
`example, a subject with IAF ˆ 10 Hz would be ex-
`pected to show an individual bandwidth of 2 ´ 2 Hz for
`the lower alpha band. We have found (e.g., Klimesch
`et al. 1996a) that the width of the lower alpha band is
`about twice as wide as that of the upper band. Thus, for
`the analysis of ERD, we distinguish between three steps
`of 20% IAF, two steps below and 1 step above IAF. The
`two frequency bands below IAF are termed lower-1 and
`lower-2-alpha, respectively. Because we have found that
`the TF between alpha de- and theta synchronization lies
`
`at about 4 Hz below the IAF of about 10 Hz, and be-
`cause TF and IAF are signi®cantly correlated (cf.
`Klimesch et al. 1996a), we suggest to use steps of 20%
`IAF to cover the range of individual theta and alpha
`bands. Using individually determined frequency bands
`and bandwidths avoids a confusion between event-relat-
`ed changes in the lower and upper alpha band and pre-
`vents the desynchronizing and synchronizing responses
`of the alpha and theta bands cancelling each other.
`In order to show that the proposed method, which
`uses individually de®ned bands and widths (IBIW), is
`indeed superior to a method using ®xed bands and ®xed
`widths (FBFW) and also superior to a method using
`individually adjusted bands but ®xed widths (IBFW),
`control computations must be performed. For that
`purpose we use data from an oddball paradigm (in
`which subjects have to respond to rare target and ignore
`frequent nontarget stimuli) and distinguish two groups
`of subjects, one with high alpha frequency and another
`with low alpha frequency. Then, by applying the dif-
`ferent methods for de®ning frequency bands and band-
`widths, ERD is calculated for both groups of subjects.
`One obvious criterion for considering the proposed
`method superior to FBFW and IBFW is that the two
`groups of subjects with low and high alpha frequency do
`not show signi®cant di€erences when frequency bands
`are de®ned according to IBIW. Another criterion is based
`on physiological considerations and refers to that fre-
`quency band which is given by the di€erence between IAF
`and TF. Because TF de®nes the transition from the alpha
`to the theta band and because IAF de®nes the transition
`from the lower to the upper alpha band, the frequency
`window given by IAF ) TF equals the bandwidth of the
`lower alpha band. Thus, according to IBIW, the width of
`the lower alpha band IAF ) TF will always be equal to a
`certain percentage of IAF. To illustrate this idea, the
`three di€erent types of relationships between IAF and
`TF (corresponding to FBFW, IBFW, and IBIW) are
`plotted in Fig. 1. The dashed horizontal line character-
`izes FBFW and shows that TF remains constant
`regardless of variations in IAF. The dotted line exem-
`pli®es IBFW and illustrates a case where TF always is a
`constant value below IAF (re¯ecting a ®xed bandwidth).
`The bold line illustrates IBIW and shows that ± as
`compared to IBFW ± TF is smaller for large values of
`IAF but larger for small values of IAF. Thus, the crite-
`rion for accepting IBIW as the adequate way to deter-
`mine frequency bands is that the experimentally obtained
`relationship between IAF and TF ®ts the regression line
`predicted for IBIW. If IBIW is superior to FBFW and
`IBFW, and if IAF ) TF is equal to the bandwidth of the
`lower alpha band and proportional to IAF, then a sig-
`ni®cant correlation between IAF ) TF versus IAF
`(including also a signi®cant correlation between TF and
`IAF) will be expected. It should be noted that for both
`methods,
`IBIW and IBFW, a positive correlation
`between TF and IAF is expected. However, for IBFW
`this correlation is solely due to the variations in IAF.
`Thus, because the bandwidth IAF ) TF is a strictly
`constant value for IBFW, only for IBIW is a signi®cant
`correlation between IAF ) TF and IAF predicted.
`
`

`

`51
`
`Fig. 1. Hypothetical regression lines between the individual alpha frequency (IAF) and the transition frequency (TF) of theta synchronization
`and alpha desynchronization for three di€erent methods of frequency band de®nitions. While FBFW uses interindividually ®xed frequency bands
`with a bandwidth of 2 Hz for each frequency, for IBFW and IBIW the bands are adjusted to IAF. Whereas IBFW uses a ®xed width of 2 Hz,
`IBIW uses a percentage of 20% of the IAF as the width for the di€erent frequency bands. The hypothetical line for FBFW is a horizontal line
`with a equal to mean TF (5.9 Hz in this study). For IBFW the mean di€erence between IAF and TF (i.e., 4.6 Hz) was subtracted from each value
`of IAF. The regression line for IBIW was computed by subtracting the mean di€erence (IAF ) TF) as a percentage from IAF (i.e., 44%)
`
`In order to avoid confusion it is important to note
`that in Fig. 1 the actual mean values for TF and
`IAF)TF which were found in the present study were
`used for plotting the regression lines. For FBFW the
`regression line lies at 5.9 Hz, which is the actual mean
`value of TF. The regression line for IBFW is based on
`the actual mean value of IAF)TF, which is 4.6 Hz or
`44% and which is used for the regression line for IBIW.
`This was done to allow for a better comparison between
`the actual and predicted data.
`The reason that all of the ERD analyses reported
`below are based on a bandwidth of 4 Hz (or 40%) for
`IAF)TF instead of the actual 4.6 Hz (or 44% respec-
`tively) is that TF varies between studies, depending on
`the speci®c task, and that a value of 4 Hz has proved
`useful in previous research. Thus, proceeding with a
`bandwidth of 4 Hz for IAF)TF allows for a better and
`easier comparison with results from previous studies as
`well as with data from other laboratories.
`
`2 Method
`
`2.1 Subjects
`
`EEG data were recorded from 19 right-handed subjects
`(6 male and 13 female students) who participated
`voluntarily in the experiment. The mean age was 21.6
`years (with a range of 20±31 years). Handedness was
`determined by asking subjects about the hand they use
`in ten di€erent tasks such as handwriting, throwing a
`ball, etc. A subject was considered right-handed if he/she
`indicated to use the right hand for all of these di€erent
`tasks and if none of the parents was left-handed.
`
`2.2 Stimuli and procedure
`
`A visual oddball paradigm was used in which targets
`and nontargets were presented randomly but with the
`restriction that no more than three targets or nontargets
`may occur in a row. A total of 200 stimuli were
`presented. Targets consisted of a row of ®ve X's
`(XXXXX) and were presented at a probability of 0.30.
`Nontargets consisted of ®ve O's (OOOOO) and were
`presented at a probability of 0.70. Subjects were
`instructed to press a response key with the right hand
`if a target occurs and to silently count the targets but to
`ignore nontargets. At
`the end of
`the experimental
`session, subjects had to report how many targets
`they had counted. The percentage of correct responses
`(pressing the response key) to targets was 99.2%.
`Targets and nontargets appeared for 1 second at the
`center of a computer monitor (see Fig. 2). They were
`0.7 cm in height and 3 cm in length. Subjects were
`placed at a distance of about 90 cm from the monitor in
`a comfortable armchair.
`
`Fig. 2. A single trial comprises a total of 7 s and is composed of a
`reference interval (250±1250 ms), the presentation of a warning signal
`(1875±2125 ms), and an imperative stimulus (3000±4000 ms). The
`intervals t1 and t2 (500 ms duration each) mark the time intervals for
`which ERD was calculated
`
`

`

`52
`
`A brief acoustic warning signal (3000 Hz, lasting for
`250 ms) appeared 1125 ms before a stimulus was pre-
`sented. The length of a single trial was 7 s and the length
`of the whole session was 23 min and 20 s for each sub-
`ject. In an attempt to avoid artifacts, subjects were asked
`to maintain ®xation by looking at the middle of the
`screen and to prevent eyeblinking as soon as the warning
`signal appeared.
`
`2.3 Recording and analysis of EEG data
`
`EEG activity was recorded with a set of 12 silver
`electrodes (F3, F4, C3, Cz, C4, T3, T4, P3, Pz, P4, O1
`and O2) according to the International Electrode (10±
`20) Placement system. For simplicity, only the data for
`Pz were analyzed. Furthermore, the electrooculogram
`(EOG) was recorded from two pairs of leads in order to
`record horizontal and vertical eye movements. All
`electrodes were attached with a Nihon Khoden glue
`paste to the scalp.
`Data were recorded monopolarly against a common
`reference placed on the nose. In order to eliminate the
`e€ects of the nose reference as well as other types of
`artifacts, the EEG recordings were corrected by sub-
`tracting the arithmetically averaged ear
`recordings
`[(A1 + A2)/2] from all of the monopolar recordings.
`EEG signals were ampli®ed by a 32-channel biosignal
`ampli®er system (frequency response: 0.16 to 30 Hz),
`subjected to an anti-aliasing ®lterbank (cut-o€ frequen-
`cy: 30 Hz, 110 dB/octave) and were then converted to a
`digital format via a 32-channel A/D converter. Sampling
`rate was 128 Hz. During data acquisition, EEG signals
`were displayed online on a monitor and stored on disk
`for later analyses.
`By visual inspection, all of the epochs were checked
`individually for artifacts (e.g., eye blinks, muscle arti-
`facts). After rejecting artifacts, an average of 35 out of
`the 60 attended stimuli remained for further analyses;
`only targets were analyzed.
`
`2.4 Calculation of ERD
`
`ERD represents the percentage of a change in band
`power during a test interval with respect to a reference
`within a de®ned frequency band. When calculating ERD,
`in a ®rst step the EEG data for each epoch and each
`channel are digitally band-pass ®ltered (in speci®c bands
`and with either ®xed or varied bandwidths as described
`below in Sect. 2.5), squared (in order to obtain simple
`power estimates) and averaged separately for each
`experimental condition and for each subject. Based on
`these data, the percentage of event-related changes in
`band power are calculated in using the ERD procedure
`proposed by Pfurtscheller and Aranibar (1977), who
`have coined the term event-related desynchronization or
`ERD. Thus, ERD is de®ned as the percentage of decrease
`or increase in band power during a speci®c interval as
`compared to a reference interval: ERD% ˆ {[(band
`power, reference interval) ) (band power, test interval)]/
`
`(band power, reference interval)} ´ 100. For a more
`detailed description see, for example, Pfurtscheller and
`Klimesch (1992). It is important to note that positive
`values indicate a power suppression, while negative ERD
`values (also termed ERS for event-related synchroniza-
`tion, cf. Pfurtscheller 1992; Pfurtscheller et al. 1996)
`re¯ect an increase in power.
`In the present study, an interval of 2750 to 1750 ms
`before the onset of the target was used as reference. Test
`intervals are the time periods of 500 ms preceding and
`following onset of the imperative stimulus. It is a well-
`established ®nding that during a variety of di€erent
`tasks changes in band power can be observed with res-
`pect to a `baseline' which usually is an interval preceding
`the onset of a task or stimulus by a few seconds (e.g., the
`reviews in Pfurtscheller 1992; Pfurtscheller and Klimesch
`1992; Klimesch 1996).
`
`2.5 The determination of frequency bands
`
`Three di€erent methods for determining the frequency
`windows were applied and according to this method,
`frequency windows for each of the delta, theta, lower-1-
`alpha, lower-2-alpha and upper-alpha bands were spec-
`i®ed. Table 1 shows the mean frequency windows
`averaged over the entire sample of 19 subjects as well
`as the values for the subject with the highest and the
`lowest IAF.
`
`2.5.1 Determination of FBFW
`
`The frequency windows had a standard bandwidth of
`2 Hz and were the same for all of the subjects. The delta
`band ranged from 2 to 4 Hz, the theta band from 4 to
`6 Hz, the lower-1-alpha from 6 to 8 Hz, the lower-2-
`alpha from 8 to 10 Hz, and the upper-alpha band from
`10 to 12 Hz.
`
`2.5.2 Determination of IBFW
`
`For each subject the peak frequency of the dominant
`EEG frequency in the alpha band for all recording sites
`was used as an anchor point. This mean IAF was
`calculated over the entire epoch of 7 s. Again, ®ve
`di€erent frequency bands with a bandwidth of 2 Hz
`each were de®ned by using IAF as the individual anchor
`point: (IAF-8) to (IAF-6), (IAF-6) to (IAF-4), (IAF-4)
`to (IAF-2), (IAF-2) to IAF, and IAF to (IAF+2),
`termed delta, theta, lower-1-alpha, lower-2-alpha, and
`upper-alpha, respectively. Averaged over the entire
`sample of subjects, IAF was 10.6 Hz (see Table 1).
`
`2.5.3 Determination of IBIW of EEG frequencies
`
`As for IBFW, IAF was used as the cut-o€ frequency
`between the lower and upper alpha bands. However, the
`bandwidth was calculated as a percentage of the IAF:
`
`

`

`53
`
`Table 1 Frequency bands for three di€erent methods of de®nition. The respective frequency values and the transition frequencies (TFs) are
`presented for the subject with the highest and the lowest individual alpha frequency (IAF ) as well as for the mean of the whole 19 subject
`sample
`
`IAF
`
`Delta
`
`Theta
`
`Lower-1-alpha
`
`Lower-2-alpha Upper-alpha
`
`TF
`
`From To
`
`From To
`
`From To
`
`From To
`
`From To
`
`FBFW lowest IAF
`highest IAF
`IAF of 19 subs.
`
`IBFW lowest IAF
`highest IAF
`IAF of 19 subs.
`
`IBIW lowest IAF
`highest IAF
`IAF of 19 subs.
`
`9.0
`12.5
`10.57
`
`9.0
`12.5
`10.57
`
`9.0
`12.5
`10.57
`
`2.0
`2.0
`2.00
`
`1.0
`4.5
`2.57
`
`1.8
`2.5
`2.11
`
`4.0
`4.0
`4.00
`
`3.0
`6.5
`4.57
`
`3.6
`5.0
`4.23
`
`4.0
`4.0
`4.00
`
`3.0
`6.5
`4.57
`
`3.6
`5.0
`4.23
`
`6.0
`6.0
`6.00
`
`5.0
`8.5
`6.57
`
`5.4
`7.5
`6.34
`
`6.0
`6.0
`6.00
`
`5.0
`8.5
`6.57
`
`5.4
`7.5
`6.34
`
`8.0
`8.0
`8.00
`
`7.0
`10.5
`8.57
`
`7.2
`10.0
`8.46
`
`8.0
`8.0
`8.00
`
`7.0
`10.5
`8.57
`
`7.2
`10.0
`8.46
`
`10.0
`10.0
`10.00
`
`9.0
`12.5
`10.57
`
`9.0
`12.5
`10.57
`
`10.0
`10.0
`10.00
`
`9.0
`12.5
`10.57
`
`9.0
`12.5
`10.57
`
`12.0
`12.0
`12.00
`
`11.0
`14.5
`12.57
`
`10.8
`15.0
`12.68
`
`4.3
`6.5
`5.93
`
`4.3
`6.5
`5.93
`
`4.3
`6.5
`5.93
`
`(IAF ´ 0.2) to (IAF ´ 0.4), (IAF ´ 0.4) to (IAF ´ 0.6),
`(IAF ´ 0.6) to (IAF ´ 0.8), (IAF ´ 0.8) to IAF, and
`IAF to (IAF ´ 1.2).
`
`2.6 Determination of TF between synchronization
`and desynchronization
`
`As suggested by Klimesch et al. (1996a), each individual
`TF was determined by comparing the power spectra for
`the reference and test intervals. First, power spectra for
`the reference and test intervals were calculated for each
`subject and averaged over all trials. Then, the frequency
`of the transition region between the theta and alpha
`bands was determined within a ®xed frequency window
`of 4±10 Hz. This was done by determining that frequen-
`cy for each subject where the lines of the two power
`spectra intersected. This point was used as the indicator
`for the TF between theta and alpha. The idea behind this
`simple procedure is that during the test interval and in
`comparison the reference interval alpha power decreases
`whereas the theta power increases. Table 1 indicates the
`mean TF as well as the TF values for the subject with the
`highest and the lowest IAF.
`
`2.7 Statistical analyses
`
`First, a correlation was calculated between IAF and TF;
`it should be noted that a positive coecient simply
`would show that TF increases with increasing IAF.
`Thus, in a second step, the di€erence between TF and
`IAF (representing the bandwidth of the two lower alpha
`bands) was correlated with the IAF.
`Three di€erent predictions can be distinguished:
`
`(1) If TF is a constant value, TF and IAF would be not
`signi®cantly correlated; in this case, FBFW can be
`assumed.
`(2) If TF is signi®cantly correlated with IAF (cf. Fig. 1),
`IBFW or IBIW can be assumed.
`(3) In order to distinguish between the latter two cases
`the bandwidth IAF)TF is correlated with IAF. Only
`if this correlation is positive can IBIW be assumed.
`
`In order to compare the results of the three di€erent
`methods for determining frequency bands, subjects with
`a high versus low IAF were distinguished. Group IAF)
`comprises 10 subjects (6 female, 4 male) falling below the
`median; group IAF+, on the other hand, included 9
`subjects (7 female, 2 male) with an IAF above the
`median. For each of the ®ve frequency bands (delta,
`theta, lower-1-alpha, lower-2-alpha and upper-alpha) a
`three-factorial ANOVA with Sche€eÂ
`tests on the 5%
`level for pairwise comparisons of means was performed.
`The factors and their levels are Method (FBFW, IBFW,
`IBIW), Time (t1, t2;
`i.e., two 500 ms intervals, one
`preceding, the other following the onset of a target) as a
`repeated measure, and Group (IAF+, IAF)) as a
`between-subjects factor. The levels for factor TIME are
`the two 500 ms epochs preceding and following the
`onset of the imperative stimulus. These intervals were
`selected because t1 (prestimulus) represents a time
`interval with high attention so that a strong desynchro-
`nization in the lower-1-alpha and the lower-2-alpha can
`be expected. On the other hand,
`t2 (poststimulus)
`represents an interval with a simple cognitive demand
`which is characterized by a synchronization in the theta
`and delta band (Klimesch et al. 1997b). Because these
`ANOVAs were performed to test the hypothesis whether
`subjects with high and low IAF respond in a similar
`way, the interaction Group ´ Method is of particular
`interest.
`
`3 Results
`
`3.1 Correlations
`
`The correlation between IAF and TF shows a signi®-
`cant positive coecient (r ˆ 0.467, P < 0.05),
`indi-
`cating that a high IAF occurs together with a high TF.
`On the basis of
`this correlation, FBFW can be
`excluded. The highly signi®cant and positive correla-
`tion (r ˆ 0.580, P < 0.01) between IAF and the
`bandwidth (IAF)TF) rules out IBFW and supports
`IBIW. The respective regression lines are depicted in
`Fig. 3a and b.
`
`

`

`54
`
`Fig. 3. a Regression lines and the respective
`correlations between TF and IAF and b
`between the di€erence (IAF ) TF) and IAF a
`shows the signi®cant positive correlation be-
`tween TF and IAF. Most importantly, the
`highest correlation was obtained between the
`di€erence (IAF ) TF) and IAF as b reveals.
`This supports the hypothesis that the frequency
`bandwidths also vary as a function of IAF, as
`explained in the Introduction
`
`3.2 ANOVAs
`
`For the delta band, only factor Time reached signi®-
`cance at the 1% level (F ˆ 60.08, P < 0.01), showing a
`strong synchronization during t2.
`For the theta band, signi®cant e€ects were found for
`Method (F ˆ 13.86, P < 0.01), Time (F ˆ 18.11,
`P < 0.01), Group ´ Method (F ˆ 16.62, P < 0.01),
`and Group ´ Method ´ Time (F ˆ 7.45, P < 0.01).
`With respect to factor Method, the respective means
`indicate that synchronization is strongest for FBFW and
`weakest for IBFW. The means for factor Time reveal
`that, in contrast to t1, a pronounced synchronization
`was found during t2. For the means of interaction
`Group ´ Method, Sche€e tests for pairwise comparisons
`yield a critical di€erence of 10.65 ERD%. Inspection of
`Fig. 4a shows that signi®cant di€erences at the 5% level
`between IAF+ and IAF) (marked with asterisks) were
`found for FBFW during t2 and for IBFW during t1 and
`t2 but not for IBIW.
`The results for the lower-1-alpha bands show signi-
`®cant e€ects for Method (F ˆ 8.39, P < 0.01) and for
`Group ´ Method (F ˆ 8.44, P < 0.01). Here a mod-
`erate amount of desynchronization during t1 and t2
`was found. The ®ndings for factor Method reveal that
`the
`strongest desynchronization was obtained for
`
`IBFW and the smallest for FBFW. The Sche€e test for
`testing signi®cance of di€erences on the 5% level be-
`tween the means of interaction Group ´ Method re-
`veals a critical value of 12.55 ERD%. As depicted in
`Fig. 4b,
`signi®cant di€erences between IAF+ and
`IAF) can only be observed for FBFW during t2 and
`for IBFW during t1. Again no such e€ects can be ob-
`served for IBIW.
`In the lower-2-alpha band, signi®cant results were
`obtained for factor Time (F ˆ 15.09, P < 0.01) and the
`interaction Method ´ Time (F ˆ 6.43, P < 0.01). The
`respective means for TIME show a strong desynchro-
`nization that increases from t1 to t2. As Fig. 4c reveals,
`the signi®cant interaction is largely due to the higher
`level of ERD for group IAF) during t2 which was found
`for FBFW.
`In the upper-alpha band the only signi®cant e€ect
`was found for Time (F ˆ 16.73, P < 0.01), which
`shows an increase in desynchronization from t1 to t2.
`
`4 Discussion
`
`The results show that only for the proposed method
`(IBIW) were no signi®cant di€erences obtained between
`the two groups of high and low alpha frequency (IAF+
`
`

`

`55
`
`Fig. 4. The means of interaction Group ´ Time ´ Method are shown for the theta, lower-1-alpha, and lower-2-alpha bands. Factor Group
`comprises IAF+ and IAF) (n for IAF+ ˆ 9, n for IAF) ˆ 10), factor Time includes the two time intervals t1 and t2 (see Fig. 2), and Method
`comprises IBIW, IBFW, and FBFW. Signi®cant di€erences as determined by Sche€e tests on the 5% level between group IAF+ and IAF) are
`marked with asterisks. In the theta and lower-1-alpha bands, signi®cant di€erences between IAF+ and IAF) were observed only for FBFW and
`IBFW. Because no signi®cant di€erences were found for IBIW, the assumption is supported that IBIW is superior to FBFW and IBFW
`
`and IAF)). In sharp contrast to IBIW, large di€erences
`between these two groups were particularly obtained
`for the conventional method that uses FBFW, as Fig. 4
`indicates. These ®ndings demonstrate that interindivid-
`ual di€erences in alpha frequency and bandwidth can
`be adequately treated when applying the proposed
`method.
`The superiority of the proposed method can be do-
`cumented by referring to the following two examples.
`First,
`let us consider the ®nding that the traditional
`method, FBFW, shows no desynchronization for IAF+
`during t2 in the lower-1-alpha band (cf. Fig. 4b). In
`earlier experiments we have found consistently that,
`particularly in the lower alpha band, the presentation of
`a visual stimulus leads to a pronounced desynchroniza-
`tion with a very early onset that even precedes the pre-
`sentation of a stimulus and most
`likely re¯ects
`expectancy (e.g., Klimesch et al. 1992). This lack of
`desynchronization which was found for FBFW can
`easily be explained by considering the fact that group
`IAF+ comprises subjects with comparatively high alpha
`frequency. Thus, the ®xed lower-1-alpha band of group
`IAF+ already falls to a considerable extent below the
`lower boundary of the individual lower-1-alpha band.
`Consequently, either no or only a rudimentary lower
`alpha desynchronization can be detected. Another ex-
`ample well in line with this interpretation shows up in
`the theta band, where FBFW yields the largest amount
`of synchronization (cf. Fig. 4a). In a similar way as for
`the lower-1-alpha band, the ®xed theta band of group
`IAF+ already falls in part outside the theta frequency
`range if individual bands with ®xed widths are used.
`This ®nding is illustrated by Fig. 5, which shows that
`
`people with high IAF also have higher theta frequency
`and if ®xed bands are not adjusted individually, theta
`synchronization already is confused with the much
`larger delta synchronization.
`The transition frequency TF marks the upper fre-
`quency limit of the theta band. Thus, the positive cor-
`relation between IAF and TF clearly indicates that the
`theta band also varies interindividually and that about
`22% of the variance of theta frequency can be ex-
`plained by variations in alpha frequency. In addition,
`the correlation between IAF and the di€erence between
`TF and IAF demonstrates a close covariation between
`the bandwidth (i.e., the di€erence IAF)TF) and alpha
`frequency (IAF), which explains about 34% of the
`variance. Based on the results of the correlation anaysis
`and the predictions discussed in Sect. 2.7, IBIW (which
`is superior to FBFW and IBFW) can be accepted.
`Comparing the predicted relationship between IAF and
`TF with the actual data in Fig. 6 reveals that IBIW
`gives the best estimates. The regression line for the
`actual data is highly similar with the predicted regres-
`sion line for the proposed method but quite di€erent
`from the predicted regression lines for FBFW and
`IBFW.
`Taken together, the reported results argue for the
`use of
`individually adjusted frequency bands when
`event-related band power measures of di€erent types
`are used (Petsche and Rappelsberger 1992; Dujardin et
`al. 1995; Neubauer et al. 1995; Krause et al. 1996;
`Weiss and Rappelsberger 1996). It also appears likely
`that the individual determination of EEG frequencies
`may even prove useful for the analysis of ERPs (Basar
`et al. 1992; Basar-Eroglu et al. 1992; Basar and
`
`

`

`56
`
`Fig. 5. Hypothetical power spectra for a subject with a comparably high IAF of 12.5 Hz. The three di€erent methods (FBFW, IBFW, and IBIW
`as discussed in the text) yield di€erent frequency bands, as shown in the lower part of the ®gure. Note that only IBIW covers the entire spectrum.
`The bold line (representing the reference interval) and the dashed line [representing period t2 (see Fig. 2)] intersect at TF, which marks a transition
`between theta synchronization and alpha desynchronization
`
`SchuÈ rmann 1994). Basar and his research group have
`provided convincing evidence that event-related po-
`tentials (ERPs) under certain conditions are composed
`at least in part of phase-locked alpha activity (e.g.,
`Basar and SchuÈ rmann 1994; SchuÈ rmann and Basar
`1994). According to Basar (1972), phase-locked EEG
`activity as re¯ected by certain ERP components can be
`considered a resonance phenomenon that plays an
`important role in biological cybernetics. For future
`
`research in the increasingly important ®eld of alpha
`oscillations (Basar e