Intraindividual Specificity and Stability of Human EEG

Methods of Information in Medicine © F.K. Schattauer Verlagsgesellschaft mbH (2000)

R. M. D ünki1, G. B. Schmid2, H. H. Stassen3

1

Computer A ssisted Physics G roup, U niversity of Z ürich, 2 G eneral Psychiatry, Cantonal Psychiatric Clinic, R heinau, 3 Psychiatric U niversity H ospital, R esearch D ept., Z ürich, Switzerland

Intraindividual Specificity and Stability of Human EEG: Comparing a Linear vs a Nonlinear Approach Abstract: We have applied the so-called “ unfolding dim ension approach’’ to reanalyze an earlier longitudinal EEG study. Both linear and nonlinear approaches show that the EEG com prises a static, person-specific part upon w hich nonstatic and state-specific parts are superim posed. The intraindividual specificity and stability of the genetic part are sim ilar betw een m ethods. This is assessed by com paring the outcom e of a person to his ow n outcom es at later tim es (14 days and 5 years later). The nonlinear m ethod revealed a m edian correlation coefficient % = 0.55, w hereas advanced linear m ethods show ed a m edian % = 0.84. An apparent effect for the 5-year interval w as detected w ith the nonlinear m ethod and is discussed in term s of the different assum ptions of the tw o approaches concerning EEG signal generation. Keyw ords: Dim ension Analysis, Sim ilarity Approach, EEG Stability, Pow er Spectrum

1. Introduction 1.1 Scope of the A nalysis The dynamic behavior of human electroencephalogram (E E G ) activity can be studied on several different time scales (ts): (1) long-term or “trait” (ts: years), (2) functional or “state” (ts: minutes to hours), and (3) reactive or “transitory” (ts: seconds or less). This paper addresses the problem of the intraindividual long-term stability of E E G descriptors. The goal of this paper is to explore how much of the “trait” property (stable intraindividual specificity) that can be obtained by a nonlinear analysis might already be available from a linear description of the underlying E E G . By intraindividual specificity we mean the extent to which an E E G pattern uniquely belongs to a given person at a particular time point, compared to other persons. The term “stability” is used for the extent to which such a pattern remains invariant over time. In this regard, we have chosen to compare and contrast the so-called si78

milarity approach [1, 2] with the nonlinear unfolding dimension approach proposed recently [3, 4]. Some progress concerning the stable intraindividual specificity of E E G time series has already been made by advanced linear methods on healthy individuals between the ages of circa 25-35 years. Trait behavior was found to be particularly stable throughout this time span (see below). The contribution of nonlinear approaches in this domain seems scanty at best.

1.2 Characteriz ation of the E E G The linear view relies primarily upon a model of signal generation in the brain assuming cumulative stochastic processes. From this point of view, the E E G results from a complex Fourier-like sum of (infinitely?) many elementary “brain waves’’ superimposed upon a noisy background. H ence, the important quantity in Fourier analysis is the so-called power spectrum, which is – as known – insensitive to phase correlations.

E xperimental findings based on Fourier analysis show four major rhythmic activities: ! (0–3 H z), " (3–8 H z), # (8 –14 H z) and $ (14–30 H z).(O ther bands and approaches are also possible, cf., e.g., [5]). The proof of the intraindividual specificity of E E G time series has been established on healthy subjects in a resting state with eyes closed, by means of linear methods comparing the distributions of between-subject and withinsubject similarity coefficients [1]. The nonlinear view assumes the E E G to be a product of complex, nonlinear, dynamic processes with possible “deterministic-chaotic’’ movements within a corresponding phase or state space. In this point of view, an individual’s functional state is represented by a so-called attractor, that is, a geometric object within a limited region of the system’s phase space in which the abovementioned movements take place. In particular, it regards the time series not to be the algebraic sum of elementary parts. The number of degrees of Method Inform Med 2000; 39: 78–82

freedom underlying the attractor dynamics are bounded by the topological dimension of this geometric object. The attractor dimension thus provides a lower bound to the minimum number of degrees of freedom inherent to the behavior of the E E G time series generator. O ne such measure of attractor dimension is the so-called G rassbergerProcaccia correlation dimension D 2 [6]. A n improved variant [3] seems particularly promising with regard to physiological time series analysis. This variant provides two parameters, an asymptotic dimension estimate b0 (associated with D 2) and the unfolding dimension m*, the initial rate at which an attractor unfolds. This biparametric representation of dynamical analysis applied to human E E G has been shown to: (1) successfully discriminate so-called surrogate data [7, 8] from raw E E G in cases where traditional dimensional analysis lacks this capability, and (2) indicate some evidence that certain human E E G functional states are both intraindividually specific and stable over time [4]. These observations were not visible from the correlation dimension by itself. The choice of the method i. e., linear vs. nonlinear, thus seems to depend on assumptions about the E E G generating process. If one expects a signal with information only in a limited frequency range, linear analysis may be favorable. In contrast, if a complex signal with broad frequency range and phase relations between bands are expected, the non-linear view seems appropriate. In the case of a signal possessing a limited frequency range but having phase relations between frequency bands, it is not a priori clear which measure is more favorable and the answer may depend on the context. This situation could occur in E E G analysis, where information may be found within certain frequency bands but the role of phase correlations seems unclear. This suggests three major questions with respect to our longitudinal study: (1) D o we see an individually specific and stable component in both approaches? (2) If so, how comparable is this stability between approaches? (3) D oes the nonlinear approach reveal properties not seen with the linear approach? Method Inform Med

The rest of this paper is organized as follows: We present a description of our data set and recapitulate the two algorithms applied. The results are then presented for each method and put in relation to one another. These findings are then discussed and our conclusions presented.

ed by a 50 H z notch filter eliminating contributions from the power supply. This somewhat unfortunate situation was unavoidable due to a hardware renewal of the recording instrument between t2 and t3.

3. Methods 2. Proband Sample and EEG D ata The E E G normative study group used here involves 30 healthy individuals (mean age: 28 years; range: 19–33) recorded at rest with eyes closed at four different times: t1, t2 = t1 + 14 days, t3 = t2 + 5 years and t4 = t3 + 14 days (for t1 and t2 only, the linear analysis could be carried out with 91 individuals, 30 of whom formed a subset). These recording days allowed for the definition of 14 day (t1/t2 and t3/t4)and 5 year (t1/t3 and t2/t4) intervals. E ach individual was screened through the Z urich G eneral H ealth (Z G F) questionnaire which comprises 80 items concerning lifetime consumption behavior, somatic disorders, psychosomatic disturbances and psychocological impairment. The E E G s were visually scrutinized by a physician and the outcome of the Z G F was analyzed by a psychiatrist. The opportunity to consult a physician/psychiatrist and to discuss the matter with him was offered to those persons whose E E G or Z G F might have indicated a possible problem. With respect to our study, any person with abnormalities in the E E G was not accepted as a proband. The screening procedure was applied again after the 5-year interval. No proband showed a significant status change after that time span (the reduction to 30 probands correlates with the probands’ willingness to participate again). R esting E E G s were processed, i.e., recordings were carried out with the proband at rest with eyes closed, and in the absence of external activation or induced sensory information processing. R ecordings were made from two bipolar E E G channels (T3-T5 and T5-O 1, international 10-20 scheme) with a sampling rate of 256 H z. A low-pass filter of 32 H z (-3 dB) was used at t1/t2, and of 26 H z at t3/t4. The former was support-

Linear analysis was carried out according to the similarity approach [1, 5] and nonlinear analysis according to the unfolding dimension approach [3, 4], both summarized below. Four artifact-free E E G epochs were taken into account (from up to nine 20second epochs per channel and recording day).

3.1 L inear A nalysis: R ecapitulation of the Sim ilarity A pproach The basis of linear analysis is the digital Fourier transform (D FT) of the E E G time series. In contrast to standard frequency-band conventions [9], a tonal scheme was applied [5]. The D FTs of four consecutive artifact-free E E G epochs are overlaid to construct an E E G feature vector, that is, a spectral pattern (see below). In the case of more than four consecutive epochs, the package providing the best four consecutive epochs was taken. In the case that less than four such epochs were available, the analysis was not performed. These spectral patterns are used to investigate how similar a given spectral pattern of an individual is to the spectral pattern of the same individual constructed earlier. For the so-called similarity analysis, this “self-similarity” is compared to the similarity of the given spectral pattern to other individuals. In detail, the construction of an individual spectral pattern [5] is carried out with a combination of n separate pairs of frequency curves. E ach such pair of curves defines an envelope E (f) as a function of frequency f. E (f) consists of the maximum and minimum intensity bounds as obtained from spectral analysis of the four consecutive E E G segments. This spectral analysis encompasses a set of frequency distribution curves for each of n parallel E E G recording channels originating from the same registration. Such patterns meas79

Table 1 Correlations am ong scalar frequency param eters as obtained from 14-day and 5-year intervals (91 probands for the t1 and t2 and 30 probands for all other intervals). Correlations not m arked w ith N are significant on at least the 99% level.

ure a variety of individual E E G characteristics while also being relatively stable over time. E ach spectral pattern is regarded as a kind of feature vector associated with an (n+1)-dimensional bounded volume. The coincidence between spectral patterns is measured with a set-theoretically defined similarity coefficient. This coefficient depends on certain free parameters (frequency bands and associated weights). The discrimination between distributions of between-subject and within-subject similarity coefficients can be used as a criterion function to be optimized upon these parameters. For the construction of scalar parameters, the E E G s of the four consecutive segments from a single location could be used. These allow for the estimation of several frequency parameters, i.e., absolute power, relative power (measured in percent of the total power in the range between 0 and 20 H z), centroid (determined by the energy distribution around the fundamental frequency and measured in H z), symmetry (a dimensionless quantity measuring the energy distribution around the center frequency of a frequency band), peak frequency and peak amplitude for – preferably – a tonal frequency band selection [5], but also for any other selected frequency range. To be compatible with a major portion of the literature, we selected the frequency bands 0–2 H z, 2–5 H z ( !), 5–8 H z ( (), 8 –12 H z ( #_1), and 12–16 H z ( #_2). For a more detailed description of the linear approach, we refer the reader to [1, 5] and the references therein. 80

the relative unfolding at 2b0 + 1. To become acceptable for the (b0-m *) assessment, no time series yielding two successive, not well-resolved dimension estimates in the range m = 9 to 12 was accepted. Segments failing this requirement were excluded from further analysis [4]. To be in accordance with the linear treatment, the average of b0, m * and & of four segments entered the statistical analysis. If less than four segments provided acceptable outcomes, the recording of this channel and day was excluded from further analysis. A detailed description of all these concepts and the algorithm used are given in [3, 4].

3.2 N onlinear A nalysis: T he Unfolding D im ension A pproach The basis for nonlinear analysis is the reconstruction of a topological equivalent of the original state space as derived from the E E G time series. This reconstruction may be achieved by a socalled delay-time embedding [10] where an m -dimensional vector X m (t) is defined as: X m (t)=x(t),x(t+T), x(t+2T),.., x(t+(m –1)T). (1) H ere, x(t) denotes the scalar signal at time t. T is a particular delay time. O ur biparametric variant of dimensional analysis, i. e., the unfolding dimension approach, also includes a scheme for estimating T for the embedding [4]. O ur automatic algorithm mostly suggested delay 1 to be the optimum for our data. We carried out our analysis by varying the embedding dimension m from 2 to 12. G iven the correlation integral for the actual embedding dimension, this algorithm also includes a strategy for the automatic and reliable assessment of the associated scaling region [3]. From this region, the dimension D 2(m ) is extracted from the correlation integral as usual, i.e., from the slope of a log-log plot [6]. D imensional estimates are assessed by a biparametric model: D 2(m ) = b0 · 1-exp(-(m /m *) ')),

(2)

with ' fixed to 1. For theoretical considerations we also estimate:

4. Results 4.1 L inear A pproach To test for age effects, an analysis of variance (A NO VA /MA NO VA ) with channel as repeated assessments was performed and yielded no age effects in the frequency range considered. The model is formulated as: E E G = proband + age + day + channel + channel*day, (4) where “day” stands for recording day (t1 to t4) and channel for repeated measurement. This model explained 50 to 90% of the variability in the dependent variables and only the variable “proband” showed a significant effect (p < 0.01). The correlation of scalar frequency parameters is shown in Table 1. D epending on the interval, frequency band and spectral parameter, correlations between 0.31 (peak frequency in the ! band from the 14-day interval) and 0.94 (centroid and symmetry in the #_1 band from the 14-day interval) with a median of 0.841 were found when comparing the outcomes of the same person on two different days. We note, however, that only one value was as low as the minimum, while for all frequency bands the five most important parameters correlated with at least 0.62. The lowest correlation of 0.31 for the peak frequency in the ! band 1

& = D 2(2b0 + 1)/b0,

(3)

This number is slightly higher than that in [4] which was derived from a subset, only. Method Inform Med

possibly indicates that this band carries “state’’ rather than “trait’’ properties. With respect to frequency parameters, we find average contributions (i.e., median) of more than 80% except for the peak frequencies which perform with 51% . The highest contributions, namely, 91% , come from the #_1 band and the 14-day interval. With respect to frequency bands, we similarly find performances of more than 80% except for the !-band which performs at about 70% . This holds for both the 14-day interval and the 5-year interval.

Table 2 Correlations am ong nonlinear analysis as obtained from 14-day and 5-year intervals (30 probands on each interval). Correlations not m arked w ith N are significant on at least the 99% level.

4.2 N onlinear A pproach

rather low specificity. A n example is shown in Figure 1.

Method Inform Med

5.1 L inear A pproach

5. D iscussion and Comparison of Results O ur results with both approaches reveal significant correlations for a given person over a time span of up to five years, thereby indicating intraindividual specificity and longitudinal stability of the human E E G over periods of time at least this long. To best understand the

The only relevant variable found in the E E G model as presented in formula (4) is “proband”. O ne might therefore expect rather high correlations between a person’s E E G outcomes assessed on different days. D epending on the spectral parameter, correlation coefficients between 0.31 and 0.94 occurred with a median of 0.84. The deviations found mainly concern the parameter “peak frequency“, which may contain specific information pertaining to functional state. This allows one to interpret the E E G as being made up of a static, person-specific part (“trait”) upon

& (reference day + 14 days)

A nalysis of variance was also carried out again using the model as represented in formula (4). This model explained 50 to 60% of the variability of the dependent variables where the variables “proband” and “day” revealed a nonrandom contribution (p < 0.01). A ccordingly, the correlation coefficients between different days were present, but lower than in the linear case (Table 2). In particular, the range is narrower (0.22 to 0.60) with a median of 0.55. We noted that the most stable contributions come from &, while the correlation dimension b0 provides the highest but also the lowest correlation and seems to be most sensitive for the 5-year interval. This is in agreement with the findings of variance analysis where &, in contrast to b0 and m *, showed no effect on the time parameter “day”. A closer inspection of the influence of day on b0 and m * seemed to reveal the effect on the 5-year, but not on the 14-day interval. Comparing the outcome of a person on a certain day with its equivalent on a later day is a test for longitudinal stability. A visual impression of the range of interindividual differences as well as of the stability of individual outcomes over time may be seen in a scatter plot. A ll points lying along the diagonal indicate perfect reproducibility, whereas a cloud of points reveals a less perfect reproducibility.The angle between the regression lines r1(y) = x and r2(x) = y is inversely proportional to the correlation between the two recordings under comparison. Furthermore, a cloud distribution of points stretched along the diagonal indicates high specificity whereas a ball-like cloud indicates

pros and cons of the similarity versus the unfolding dimension approaches to the intraindividual specificity and stability of E E G analysis, it is important to recall some of the above-mentioned details about the way in which these two approaches process the data. The linear approach regards the signal as a sum of independent elementary waves whereas the nonlinear approach treats it as a whole.

& (reference day)

Fig. 1 Scatter Plot (nonlinear approach). Reproducibility and specificity of the estim ates of & for a given proband and day against the sam e m easure 14 days later. The angle betw een the tw o regression lines is inversely proportional to the correlation betw een the tw o m easurem ents (y = r (x): solid line; x = r (y): dash-dotted line; x = y: dotted line; a zero angle betw een the tw o m eans perfect m atch). The correlation coefficient is % = 0.59.

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which nonstatic and non trait-specific parts are superimposed. The differences found between parameters and bands indicate a preference for certain frequency ranges. H ence, the linear view may optimally serve the analysis. The similarity approach has been shown to provide an accurate one-toone correspondence between individual patterns with a reliability of over 90% [2, 5]. E vidence from the similarity approach based upon a resolution of E E G spectral patterns into a static and a dynamic component suggests that the static (trait) component of E E G spectral patterns encompasses more than 70% of the entire information with reactive variation superimposed upon it [1]. The hereby established view, static vs functional, also offers a clinically interesting perspective. Investigations of functional state-related E E G asymmetries, which look for subtle differences between spectral patterns corresponding to different functional states biased by a high common coincidence, could be carried out with this approach by first subtracting the static component (the intersection of a sequence of individual E E G spectral patterns extending in time over both states). For the assessment of this static component, the linear approach seems appropriate.

5.2 N onlinear A pproach Intraindividual comparisons returned correlation coefficients with a median of 0.55. A closer look at Table 2 suggests the stability to be less than that found with the linear approach and to be in the order of that of the peak frequency. H ence, the outcome does not really prove that the longitudinal information found in the human E E G is not exclusively inherent to (thus, completely deducible from) the linear properties.The possible influence of functional contributions to the E E G cannot be overlooked, because the nonlinear approach processes the signal as a whole. O n the one hand, lower correlations than those obtained from the optimal frequency bands do not seem unreasonable and may indicate that the linear view of the E E G is valid to a good approximation. O n the other hand, the non-visible influence of the variable “day” in the linear approach 82

points to an incompleteness of the linear view. A closer inspection of this influence showed the five-year interval to be relevant; this is also reflected in the correlations (Table 2). Furthermore, the highest contributions (% > 0.85, T5-O 1) were found between the days t1 and t2. This apparent incompleteness is in accordance with surrogate-data tests, which already revealed small but significant differences between an E E G segment and its linear equivalents (i.e., phase correlations) [3]. This 5-year behavior may thus point to a longitudinal effect of altering phase correlations rather than that of intensities. The latter are expected for frequency ranges not considered in the linear analysis only, if present at all. The fact that & displayed the most stable correlations seems remarkable and also conforms to earlier results [4] where explicit relations m * = s·b0 + i were considered. These relations where based on at least five segments on days t1, t2 and t3 and revealed slightly higher correlations than those found here. O ur results, therefore, confirm the previously made conjectures, namely, that the E E G is not fully describable by linear methods and that b0-m * relationships considerably improve nonlinear analysis.

6. Conclusion We have investigated the problem of individual specificity and longitudinal stability of the human E E G using both a linear and a nonlinear approach. With regard to our three questions concerning the E E G assessed from the functional state of rest with eyes closed we found: (1) the outcomes of both approaches suggest distinguishing a static/ generic, individually specific component (trait) from a fluctuating or random component of the human E E G ; (2) The goodness of differentiation, based upon correlation coefficients, is higher with frequency parameters; (3) The apparent 5-year effect, as seen with the nonlinear approach, suggests the existence of nonlinear changes in the E E G generation not visible with linear methods. These findings favor the view of individually specific information, being

mainly found within certain frequency bands rather than being inherent to the signal as a whole. Furthermore, the apparent nonlinear effect seems to disturb the person-specific relations. Taking this into account, we may conclude that on the one hand the linear approach seems preferable when analyzing longitudinal stability and specificity. O n the other hand, the nonlinear approach seems to harbor advantages for analyzing problems of functional states, involving broad frequency ranges whereby the relations between frequency bands are important.

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A ddress of the A uthors: D r. R udolf M. D ünki, Computer A ssisted Physics G roup, Winterthurer Str. 190, CH -8057 Z ürich, Switzerland E -mail: rmd@physik_unizh.ch Method Inform Med