Application of standard chaotic quantifiers for chemotherapy assessing by EEG-signal analysis Robert Stepien, Wlodzimierz Klonowski Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, 4 Trojdena St., 02-109 Warsaw, Poland; E-mail:
[email protected] Abstract: We computed standard chaotic quantifiers - time delay, embedding dimension, pointwise correlation dimension, the largest Lyapunov exponent - of EEG-signal for 4 healthy subjects before and after administration of Diazepam. It seems that these quantifiers are not suitable for chemotherapy assessment.
Introduction: EEG signal, which represents overall electric activity of the brain, shows feature characteristic of deterministic chaos [1]. So methods of non-linear dynamics and deterministic chaos theory may be used to analyse state of the brain, possible pathological changes in the brain, and assess the influence of applied therapy. Standard quantifiers of chaotic systems such as Lyapunov exponents has been used by some authors to show that diminishing chaos in the brain may lead to serious pathology, such as epileptic seizures [2]. However, calculation of some of these quantifiers requires long stationary EEG-signal epochs and needs relatively long time [3]. While looking for EEG characteristics which may help doctors in assessing therapy influence on the patient we calculated standard quantifiers of signal chaocity for 4 healthy subjects before and after administration of Diazepam (Valium), a drug which is known to influence brain activity.
Methods: We evaluated EEG-signals provided by the Institute of Psychiatry and Neurology in Warsaw. Files were extracted by the hospital staff from standard EEG-records, for each subject the first recording done before administration of Diazepam and the second one hour after oral administration of a single 5 mg dose of Diazepam. EEG Digitrack (ELMIKO) data-acquisition system with 16 channels (the International 10/20 Electrode Placement System) was used. EEG signals were filtered with a band pass filter (0.5 - 70 Hz) and sampled at 128 Hz. 12-bit ADC was used. IBM compatible PC with Intel Pentium 233 was used for data analysis.
Results: From each EEG-recording we computed several standard chaotic quantifiers for all 16 channels, but the most interesting results from a point of view of a neurologist we obtained for channels Fp2-F8, Fp1-F7, C4-P3, C4-P4, T5-O1, and T6-O2. We made full Taken’s attractor reconstruction for each channel before and after removing of artefacts.
Taking the signal on the given channel in a time series representation, x(n), where x is the signal amplitude at the discrete time moment n , we first construct vectors in the phase space by time delay method:
[
) )]
( (
r y(n ) = x(n ), x( n + τ), x(n + 2τ), K , x n + d E − 1 τ
where time delay, τ (Table 1) was calculated by the first zero crossing of the autocorrelation function:
()
2 Corr τ = ∑ xi xi+τ / ∑ xi i i
and embedding dimension dE (Table 2) was determined by saturation of correlation dimension:
() ()
log C ε D 2 = lim ε→0 log ε
Correlation integral C(ε) is defined C (ε) =
(
( )
( ))
N N r r ∑ ∑θ ε − y m − y n N N − 1 m =1 n =m +1
(
2
)
where ||...|| denotes Euclidean norm of the vector and θ(x) is the Heaviside step function; the autocorrelation function was calculated by inverse Fourier transformation of power spectrum of signal with zero padding. Table 1. Time delay for raw data and after removing artefacts (in units 1/128 sec) Raw data P. 642
P. 655 Channel
Diaz.
P. 655 Diaz.
Artefacts P. 642 Diaz.
Diaz.
Fp1-F7
115
89
66
5
92
140
90
67
Fp2-F8
499
102
59
104
976
138
89
19
C3-P3
57
204
49
5
57
26
4
4
C4-P4
90
35
5
5
101
26
5
5
T5-O1
15
4
5
5
5
4
5
5
T6-O2
2110
4
5
19
101
4
5
5
Table 2. Embedding dimension P. 655 Channel Fp1-F7 Fp2-F8 C3-P3 C4-P4 T5-O1 T6-O2
11 8 11 11 11 11
P. 642 Diaz. 8 8 11 11 10 10
11 9 10 10 9 10
P.638 Diaz. 10 10 9 10 9 10
N.C. 9 10 10 10 10
P. 623 Diaz. 8 8 11 11 11 9
11 7 11 N.C. 11 N.C.
Diaz. 11 10 9 N.C. 8 9
An average pointwise correlation dimension, PD2, was calculated for reconstructed attractors (Table 3, cp. [4]). The PD2 algorithm in contrast to D2 algorithm is counted for every point in the phase space for a stationary epoch of the signal (algorithm detects nonstationarity in the signal). Table 3. Pointwise correlation dimension (PD2) for raw data P. 655 Channel Fp1-F7 Fp2-F8 C3-P3 C4-P4 T5-O1 T6-O2
7.0 3.7 9.5 9.1 9.3 9.2
P. 642 Diaz. 6.6 6.2 9.2 9.1 8.7 8.9
8.3 7.8 8.7 8.3 7.6 8.0
P. 638 Diaz. 8.0 8.4 7.6 8.4 7.8 9.0
N.C. 7.4 8.3 8.7 8.3 7.0
P. 623 Diaz. 6.3 6.1 9.3 9.4 9.0 7.6
9.2 5.1 9.0 N.C. 8.9 N.C.
Diaz. 9.5 8.7 7.5 N.C. 6.6 7.8
The largest Lyapunov exponent was positive in all cases (Table 4). Algorithm for estimation of Lyapunov exponents was based on Eckmann method [5]. Table 4. Largest Lyapunov exponent P. 655 Channel Fp1-F7 Fp2-F8 C3-P3 C4-P4 T5-O1 T6-O2
13.0 8.5 34.8 34.6 40.6 34.7
P. 642 Diaz. 13.9 8.9 32.4 33.2 25.7 24.2
20.6 25.8 37.3 13.1 9.1 9.6
P. 638 Diaz. 20.3 39.7 13.1 12.5 8.7 23.8
N.C. 24.8 28.1 17.9 16.3 18.5
P. 623 Diaz. 20.6 9.0 36.0 23.7 32.7 16.7
16.9 6.8 28.7 N.C. 36.5 N.C.
Diaz. 54.6 25.0 16.1 N.C. 15.7 17.1
Conclusion: Standard chaotic quantifiers seem to show no consistent pattern of changes when EEG-signals before and after therapy are compared. This is because of tremendous variability between individual subjects and no statistical elaboration of the results will give more plausible conclusion. So these quantifiers are not suitable for therapy assessment and it is necessary to look for other EEG-signal quantifiers which could be more suitable for this purpose. One of such promissing quantifiers on which we work in our Lab seems to be fractal dimension of EEG-signal.
Acknowledgements: The authors wish to thank Dr. W.Jernajczyk and Dr. K.Niedzielska from the Institute of Psychiatry and Neurology, Warsaw, for supplying EEG-data for analysis. We also thank P.I.M. ELMIKO (Warsaw) for supplying us with their EEG-data acquisition system. This work was partially supported by the State Committee for Scientific Research (K.B.N.) grant No. 8T11 F01112 and SIERRA-APPLE (PHARE) grant No. 0039.
References: [1] King C.C. (1991) Fractal and Chaotic Dynamics in Nervous Systems Progress in Neurobiology 36: 279-308; [2] Babloyantz A., Destexhe A. (1986) Low Dimensional chaos in an instance of epilepsy. PNAS 83: 3513-3517; [3] Schuster H.G. (1988) Deterministic Chaos. An Introduction. VCH Verlagsgesellschaft, Weinheim; [4] Skinner J.E., Carpeggiani C., Landisman C.E., Fulton K.W. (1991) Correlation dimension of heartbeat intervals is reduced in conscious pigs by myocardial ischemia. Circ. Res. 4/68: 966-976; [5] Eckmann J.-P. et al, (1986) Lyapunov exponents from time series. Phys. Rev. A 34, 4971.
