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Evaluating the entrainment of the alpha rhythm during stroboscopic flash stimulation by means of coherence analysis
Medical Engineering & Physics 27 (2005) 167–173
Evaluating the entrainment of the alpha rhythm during stroboscopic flash stimulation by means of coherence analysis Antonio Mauricio F.L. Miranda de S´aa,∗ , Antonio F.C. Infantosib a
Federal University of S˜ao Jo˜ao del Rei, Electrical Engineering Department, (DEPEL), Universidade Federal de S˜ao Jo˜ao del Rei, UFSJ, Pra¸ca Frei Orlando, 170 Centro, S˜ao Jo˜ao del Rei, MG, CEP: 36307-352, Brazil b Federal University of Rio de Janeiro, Biomedical Engineering Program, P.O. Box 68510, 21945-970 Rio de Janeiro, RJ, Brazil Received 16 June 2004; received in revised form 9 September 2004; accepted 30 September 2004
Abstract Two major conflicting hypotheses propose that alpha rhythm activity should be either the output of a linear filter having a white noise as input or reflect the output of a nonlinear oscillator. External stimulation can be employed to test for nonlinearity in alpha genesis, since an entrainment of such rhythmic activity (shift in the alpha peak) could only be explained by nonlinear relationships. Flash photic stimulation has been used to investigate such entrainment. Nevertheless, only entrainments due to the second harmonic of the stimulation could be suitably measured. Aiming at overcoming this limitation, a coherence-based technique is proposed for evaluating the strength of responses due to rhythmic stimulation. It was applied to the occipital EEG derivations of 12 normal subjects during stroboscopic stimulation. Entrainment of alpha rhythm by the second harmonic of the stimulation occurred in 75% of the subjects, whilst no spectral shifts were observed for the remained that exhibited broadband alpha peak at rest. However, stimulating with fundamental frequency close to that peak led to entrainment in all subjects. These differences in the degree of synchronization due to stimulation at the first and second harmonics should reflect complex nonlinear mechanisms in alpha genesis. © 2004 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Alpha rhythm; Photic stimulation; Synchrony measure; Induced rhythm; Entrainment
1. Introduction The alpha rhythm is defined as the rhythm at 8–13 Hz occurring during wakefulness over the posterior regions of the head, generally with higher voltage over the occipital areas [1]. Some findings suggest a functional significance of such rhythm, since it can be induced (i.e. initiated by but not time-locked to a stimulus) or evoked by external stimulation [2]. According to Sch¨urmann and Basar [3], stimulus induced and/or endogenously induced brain rhythms are signs of higher-order neural operations intercalated between initial sensory processing and brain functions such as perception, storage in memory or execution of movement patterns. The knowledge of alpha rhythm dates from Berger’s pioneering work but its origin is still controversial. Although this ∗
Corresponding author. Tel.: +55 32 3379 2552; fax: +55 32 3379 2525. E-mail address: [email protected] (A.M.F.L. Miranda de S´a).
rhythmic activity should be generated in the cortex [4], the theory of a thalamic pacemaker function has surfaced and also been challenged since the beginning of the 1930s [5]. Investigating the relationship between thalamic and cortical EEG alpha rhythm, Lopes da Silva et al. [6] found a decrease within the alpha band of the intra-cortical coherence after the removal of the contribution from thalamus. This reduction could have been interpreted as the influence of the latter in the cortical alpha. However, since partial coherences were still high, they concluded that other factors should be involved in the generation of cortical alpha rhythm. More recent research [7,8] suggests feedback from cortex to thalamus to explain the cortically induced coherence of thalamic-generated oscillations. Besides this controversy of the thalamic pacemaker for the alpha rhythm, there is another regarding the fact that either alpha rhythm should be a stochastic signal reflecting the output of a linear filter [9] or reflect an output of
1350-4533/$ – see front matter © 2004 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2004.09.011
168
A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
non-linear oscillators. The latter was proposed by Wiener [10] and is based on the fact that such rhythm could be entrained by forced stimuli at near frequencies, which could only happen if the generating system for alpha rhythm were non-linear. According to Rombouts et al. [11], many researches were carried out since the middle of the 1980s to investigate whether the EEG could result from deterministic chaos. However, no conclusive hypothesis about the chaotic dynamics in EEG was established. Stam et al. [12] employed non-linear prediction statistics and phase-randomized surrogate data to test for non-linearity in the EEG at rest. The null hypothesis that alpha rhythm could result from linearly filtered noise was rejected only in 1.25% of the cases. These inconclusive results with many non-linear, sophisticated techniques, has led Gebber et al. [13] to investigate the Wiener’s model by measuring the phase locked activity within the alpha band due to photic stimulation. This has been carried out by obtaining time-series of the delays between peaks of the linearly filtered EEG within the alpha band and the stimulation signal. However, with this time-domain measuring methodology, only synchronization (i.e. phase-locked to the stimulation signal activities) with the second harmonic of the stimulation frequency could be measured. The approach used by Gebber et al. [13] imposes a limitation in the investigation, since there is some indication of physiological differences between
the first and second harmonic of the driving response [14–16]. In the present work, proceeding with the linear approach, we propose an alternative methodology based on the coherence function between EEG and the stimuli signals to investigate the phase lock in the activity within the alpha rhythm. This frequency domain technique allows overcoming the limitation of detecting synchronism even when the stimulation occurs near the alpha rhythm.
2. Material and methods 2.1. Theoretical background The coherence estimate between a periodic signal, x[k], and a random one, y[k], may be obtained as [17]: 2 M Yi (f ) κˆ y2 (f ) = i=1 (1) M 2 M |Yi (f )| i=1
where Yi (f) is the T-length Fourier transform of the ith window of y[k] which has been divided into M disjoint segments. It is interesting to note that, contrary to the general case of two random signals, coherence between a periodic signal and
Fig. 1. Normalized power spectra estimates of the EEG, derivation O1 , from subject #4 before (dotted lines) and during (continuous lines) stroboscopic flash stimulation (SFS) at 4, 5 and 6 Hz. Coherence κˆ y2 (f ) (confidence limits for the harmonics of the stimulation frequency indicated with triangles) for the EEG data during SFS is also shown in the subplots bellow. The horizontal dotted lines in such subplots indicates the critical value of 0.2589 for κˆ y2 (f ).
A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
a random one can be estimated using only the latter. This constitutes an advantage for evoked potentials analysis, since the stimulation signal need not be recorded, avoiding the introduction of noise from a signal whose amplitude may vary too fast in cases such as in stimulation with flash. The estimate κˆ y2 (f ) has been derived by Dobie and Wilson [18] and used since then in the objective response detection [19,20]. Its statistical distribution for the case of lack of response (zero coherence) to periodic input is identical to the well established case when both signals are uncorrelated, Gaussian noise, as shown by Nuttall [21]. Hence, the threshold for the detection of evoked responses is readily obtained from the critical values of κˆ y2 (f ), which are given as [17]: 2 κˆ crit
F critα,2,2(M−1) = M − 1 + F critα,2,2(M−1)
(2)
where F critα,2,2(M−1) is the critical value of the F-distribution with 2 and 2(M − 1) degrees of freedom for a significance 2 , the null hypothesis (H ) of level ␣. Thus, for κˆ y2 (f ) < κˆ crit 0 no periodic component (i.e. no stimulus response) can be accepted. Miranda de S´a et al. [17] derived the sampling distribution of κˆ y2 (f ) for the alternative hypothesis (H1 ) of
169
presence of responses as: (M − 1)
κˆ y2 (f ) 1 − κˆ y2 (f )
(λ) ∼ F2,2(M−1)
(3)
where “∼” means “is distributed as” and F2,2(M−1) (λ) is the non-central F-distribution [22] with 2 and 2(M − 1) degrees of freedom and the non-centrality parameter λ, which may be expressed as a function of the number of windows used in the estimation, M, and the true value of κˆ y2 (f ), κy2 (f ), as:
λ = 2M
κy2 (f ) 1 − κy2 (f )
(4)
Knowing such distribution, the confidence limits of κˆ y2 (f ) can be obtained and thus the degree of synchronization due to stimulation can be measured. Nevertheless, the calculation of critical values of κˆ y2 (f ), under hypothesis H1 , is computationally expensive, since a closed-form inverse for its cumulative density function cannot be easily found. Approximate critical values of κˆ y2 (f ) may be easier estimated by using approximations to the non-central F distribution. Miranda de S´a et al. [17] used an approximation based on fitting a central to the non-central F-distribution, such that the first two moments
Fig. 2. Same as Fig. 1 but for a broad band alpha subject (#1).
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were preserved. By applying this to expression (3), critical values under H1 are obtained as: 2 κˆ crit =
{1 + Mκy2 (f )/[1 − κy2 (f )]}F critα,ν ,2(M−1) M − 1 + {1 + Mκy2 (f )/[1 − κy2 (f )]}F critα,ν ,2(M−1) (5)
M ˆSyy (f ) = 1 |Yi (f )|2 MT
(6)
i=1
where 2
ν =
and digitised at 256 Hz. The spectrum of the signal (y[k]) from each subject was calculated before and during stimulation as the average of M windows (periodogram) of T = 2 s duration:
{2 + 2Mκy2 (f )/[1 − κy2 (f )]} 2 + 4Mκy2 (f )/[1 − κy2 (f )]
2.2. Data acquisition and processing The EEG signal of 12 normal young subjects (age range: 9–17 years) was recorded at O1 and O2 (reference at the ipsilateral earlobe) over a period of about 25–30 s before and during stroboscopic flash stimulation (SFS) at 4, 5, 6, 8, 10, 12 and 15 Hz. The signals were band-pass filtered (0.1–70 Hz)
In order to ensure steady state in the evoked responses, stretches of signals after at least 2 s from the beginning of the stimulation were selected. Thus, a total length of 22 s (M = 11) was used for estimating each spectrum. The spectra from each subject (before and during a given SFS) were normalised by the maximum spectral component. The synchronization of EEG signals with the stimulation was investigated with κˆ y2 (f ), obtained from (1), with critical value of the no-response case calculated according to (2). The confidence limits of κˆ y2 (f ) were determined by linear interpolation from values calculated using (5).
Fig. 3. Same as Fig. 1 (subject #4) but with stroboscopic flash stimulation (SFS) at 8, 10 and 12 Hz.
A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
3. Results From Fig. 1 it can be noted in the power spectrum estimates (O1 ) of subject #4 stimulated at 4 Hz that the peak within the alpha band before stimulation (around 10.5 Hz) is strongly attenuated, while new peaks appear at 4, 8, 12 and 16 Hz (1st, 2nd, 3rd and 4th harmonics). The κˆ y2 (f )-values indicate that these spectral peaks are synchronized with the stimulation, 2 = 0.2589). Further, since they exceed the critical value (ˆκcrit the degree of synchronization at 12 Hz is significantly greater than in these other frequencies (the inferior confidence limit of κˆ y2 (f ) at 12 Hz is higher than the superior ones of 4, 8 and 16 Hz). The stimulation at 6 Hz led to a similar spectral behaviour to that with SFS at 4 Hz, but with an overlap in the confidence limits of κˆ y2 (f ). On the other hand, with SFS at 5 Hz, a shift in the alpha peak to 10 Hz (2nd harmonic) occurs in the spectrum and κˆ y2 (f ) still indicates synchronization at 5, 10 and 15 Hz. Similar results were found for the contralateral derivation (O2 ) and for other eight subjects (#5, 6, 7, 8, 9, 10, 11, and 12, whose alpha peaks were also sharp and, respectively, at 10.0, 9.5, 10.5, 10.5, 10.0, 10.5, 11.0 and 10.5 Hz). A different behaviour is observed for subject #1 (Fig. 2), who has a broadband alpha activity at rest (peak at 10 Hz).
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With stimulation at 4 and 6 Hz, the spectra from this subject does not exhibit pronounced peaks at 8 and 12 Hz. Concerning the strength of the responses due to stimulation at 4 and 6 Hz, κˆ y2 (f ) is smaller than its critical value in the range 8–12 Hz, indicating the acceptance of H0 of no response. The spectral peaks at the harmonics of the stimulation frequencies that lie outside this frequency range are synchronized with the stimulation. For SFS at 5 Hz, the spectral peak at 10 Hz is maintained, but becomes sharper and synchronized with the 2nd harmonic of the stimulation frequency. Other two subjects (#2 and 3) also with broadband alpha at rest (peaks at 9.0 and 9.5 Hz, respectively) showed a similar behaviour. As the stimulation frequency is increased (8, 10 and 12 Hz), the power spectra and κˆ y2 (f ) at the first harmonic of the stimulation for the subjects #4, 5, 6, 7, 8, 9, 10, 11, and 12 behave similarly to the second harmonic of the stimulation at 4, 5 and 6 Hz. This is illustrated for subject # 4 (Fig. 3). However, for subject #1, stimulation at 8 Hz resulted in a deep spectral peak at this frequency, which is synchronized with the stimuli, since κˆ y2 (f ) is greater than its critical value (Fig. 4). This result was not observed for the second harmonic of stimulation at 4 Hz (see Fig. 2). Further, for this subject, stimulating at 12 Hz led to a sharp spectral peak, also synchronized with the frequency of stimulation, as confirmed by
Fig. 4. Same as Fig. 3 but for a broad band alpha subject (#1).
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Fig. 5. Histograms of the number of subjects for whom κˆ y2 (f ) in the harmonics of the stimulation frequency was greater than its critical value. The letters a, b, c, d, e, f, g, and h refer to stimulation at 3, 4, 5, 6, 8, 10, 12 and 15 Hz, respectively.
κˆ y2 (f ). Similar results were found for the remaining subjects with broadband alpha activity (#2 and 3). The stimulation at 15 Hz led to no significant spectral changes in the alpha band (result not shown). Fig. 5 displays the histogram, for each stimulation frequency, with the number of subjects for whom κˆ y2 (f ) is significant (α = 5%). As it can be noted, the detection rate in the harmonics of the stimulation frequency tends to be lower within the alpha band (Fig. 5a, b, c and d). On the other hand, when the fundamental frequency is within such band, the detection is higher (Fig. 5e, f and g).
4. Discussion and conclusion In 75% of the subjects, the stimulation at 4, 5 and 6 Hz led to either a peak shift in alpha or its reduction followed by new spectral peaks in the harmonic frequencies. The values of κˆ y2 (f ) indicate that these shifted peaks or the new ones are synchronized with the stimulation. This finding (with stim-
ulation frequencies having the second harmonic close to the alpha rhythm at rest) agrees with that reported by Gebber et al. [13]. In our work, however, reduced changes in the spectral range of 8 to 12 Hz were observed in 25% of the subjects, who had broadband, alpha activity at rest. This result suggests that the entrainment of such rhythm by higher harmonics of the stimulations frequency depends on the alpha spectral width. Furthermore, the entrainment in alpha rhythm due to photic stimulation was investigated by Gebber et al. [13] only at frequencies whose second harmonic occurred near the alpha peak. In their paper, the subjects were stimulated with SFS at near half of the alpha peak frequency. The authors justified the use of such stimulation frequency based on inconclusive results of previous researches in which visual evoked potentials and entrained oscillations were not easily distinguishable. The method proposed here does not have such limitation. Thus, it allows investigating the changes within the alpha band due to the stimulation with fundamental frequency close to the alpha band. In our case, even the
A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
broadband alpha subjects showed spectral changes due to stimulation. The findings indicate physiological differences in the responses at the first and second harmonics and agree with some previous results reported about the driving reaction [14–16]. If the driving response depends on the harmonic of the stimulation, then it should reflect a complex nonlinear mechanism. Moreover, the lack of alpha rhythm entrainment when stimulating at 15 Hz can be explained by the nonlinear oscillators theory. According to it, only external stimulations with fundamental and/or harmonics close to the natural frequency of the system does lead to entrainment. In studies of event-related synchronization/desynchronization (ERS/ERD) [23], for which the blockage of alpha rhythm can occur as the effect of external stimulation in the ongoing EEG, the findings presented here should be taken into consideration. For subjects with broadband alpha rhythm, the stimulation may result in different patterns, depending on whether the fundamental frequency or one of its harmonics lies close to the alpha peak at rest. In this case, κˆ y2 (f ) can play an important role in ERS/ERD studies, since it allows investigating stimulation frequencies close to alpha peak. Moreover, the methodology proposed here can also be used to study the feedback from visual cortex to thalamus, provided visual stimulation is included in the experimental protocol. Acknowledgements The authors acknowledge the assistance of Dr. V. Lazarev and the Laboratory of Clinical Neurophysiology of the Instituto Fernandes Figueira (Rio de Janeiro, Brazil), in data collection. This work received financial support of the Brazilian agencies FAPEMIG, CNPq and CAPES.
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Basic Principles, Clinical Applications, and Related Fields. 4th ed. New York: Williams & Wilkins; 1998. p. 149–73. Lopes da Silva FH, van Lierop THMT, Schrijer CF, Storm van Leeuwen W. Organization of thalamic and cortical alpha rhythm: spectra and coherences. Electroencephal Clin Neurophysiol 1973;35:627–39. Lopes da Silva FH, Mooibroek J, Rotterdam A. Relative contributions of intracortical and thalamo-cortical processes in the generation of alpha rhythms revealed by partial coherence analysis. Electroenc Clin Neurophysiol 1980;50:449–56. Destexhe A, Contreras D, Steriade M. Cortically-induced coherence of thalamic-generated oscillation. Neuroscience 1999;92:427–43. Debay D, Destexhe A, Bal T. Cortical thalamic feedback can induce hypersynchronous low-frequency rhythms in the psychological intact thalamus. Neurocomputing 2001;38–40:529–38. Prast JW. An interpretation of certain EEG patterns as transient responses of a transmission system. Electroencephal Clin Neurophysiol 1949;16:290–4. Wiener N. Cybernetics: or control and communication in the animal and the machine. Cambridge: MIT Press; 1961. p. 212. Rombouts SARB, Keuen RWM, Stam CJ. Investigation of nonlinear structure in multichannel EEG. Phys Lett A 1995;202:352–8. Stam CJ, Pijn JPM, Suffczynski P, Lopes da Silva FH. Dynamics of the human alpha rhythm: evidence for non-linearity? Clin Neurophysiol 1999;110:1801–13. Gebber GL, Zhong S, Lewis C, Barman SM. Human brain alpha rhythm: nonlinear oscillation or filtered noise? Brain Research 1999; 818(2):556–560. Nyrke T, Lang AH. Spectral analysis of visual potentials evoked by sine wave modulated light in migraine. Electroencephal Clin Neurophysiol 1982;53:436–42. Takahashi T, Kataoka K, Tsukahara Y. Power spectral analysis of photic driving elicited by flickering dot pattern and red flicker stimuli in adult psychiatric outpatients—with special reference to age and gender. Tohoku J Exp Med 1998;156:165–73. Drake Jr ME, Shy KE, Liss L. Quantification of photic driving in dementia with normal EEG. Clin Electroencephal 1989;20:153–5. Miranda de S´a AMFL, Infantosi AFC, Simpson DM. Coherence between one random and one periodic signal for measuring the strength of responses in the EEG during sensory stimulation. Med Biol Comput 2002;40:99–104. Dobie RA, Wilson MJ. Analysis of auditory evoked potentials by magnitude-squared coherence. Ear Hearing 1989;10:2–13. Dobie RA, Wilson MJ. A comparison of t test, F test, and coherence methods of detecting steady-state auditory-evoked potentials, distortion-product otoacoustic emissions, or other sinusoids. J Acoust Soc Am 1996;100:12236–46. Simpson DM, Tierra-Criollo CJ, Leite RT, Zayen JB, Infantosi AFC. Objective response detection in an electroencephalogram during somatosensory stimulation. Ann Biomed Eng 2000;28:691–8. Nuttall AH. Invariance of distribution of coherence estimate to second-channel statistics. In: IEEE Trans Acoust, Speech, Signal Process, ASSP-29, 1981. pp. 120–122. Kay SM. Fundamentals of Statistical Signal Processing volume II detection theory. New Jersey: Prentice-Hall; 1998. p. 672. Pfurtscheller G, Lopes da Silva FH. Event-related EEG/MEG synchronization and desynchronization: basic principles. Clin Neurophysiol 1999;110:1842–57.
Evaluating the entrainment of the alpha rhythm during stroboscopic flash stimulation by means of coherence analysis Antonio Mauricio F.L. Miranda de S´aa,∗ , Antonio F.C. Infantosib a
Federal University of S˜ao Jo˜ao del Rei, Electrical Engineering Department, (DEPEL), Universidade Federal de S˜ao Jo˜ao del Rei, UFSJ, Pra¸ca Frei Orlando, 170 Centro, S˜ao Jo˜ao del Rei, MG, CEP: 36307-352, Brazil b Federal University of Rio de Janeiro, Biomedical Engineering Program, P.O. Box 68510, 21945-970 Rio de Janeiro, RJ, Brazil Received 16 June 2004; received in revised form 9 September 2004; accepted 30 September 2004
Abstract Two major conflicting hypotheses propose that alpha rhythm activity should be either the output of a linear filter having a white noise as input or reflect the output of a nonlinear oscillator. External stimulation can be employed to test for nonlinearity in alpha genesis, since an entrainment of such rhythmic activity (shift in the alpha peak) could only be explained by nonlinear relationships. Flash photic stimulation has been used to investigate such entrainment. Nevertheless, only entrainments due to the second harmonic of the stimulation could be suitably measured. Aiming at overcoming this limitation, a coherence-based technique is proposed for evaluating the strength of responses due to rhythmic stimulation. It was applied to the occipital EEG derivations of 12 normal subjects during stroboscopic stimulation. Entrainment of alpha rhythm by the second harmonic of the stimulation occurred in 75% of the subjects, whilst no spectral shifts were observed for the remained that exhibited broadband alpha peak at rest. However, stimulating with fundamental frequency close to that peak led to entrainment in all subjects. These differences in the degree of synchronization due to stimulation at the first and second harmonics should reflect complex nonlinear mechanisms in alpha genesis. © 2004 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Alpha rhythm; Photic stimulation; Synchrony measure; Induced rhythm; Entrainment
1. Introduction The alpha rhythm is defined as the rhythm at 8–13 Hz occurring during wakefulness over the posterior regions of the head, generally with higher voltage over the occipital areas [1]. Some findings suggest a functional significance of such rhythm, since it can be induced (i.e. initiated by but not time-locked to a stimulus) or evoked by external stimulation [2]. According to Sch¨urmann and Basar [3], stimulus induced and/or endogenously induced brain rhythms are signs of higher-order neural operations intercalated between initial sensory processing and brain functions such as perception, storage in memory or execution of movement patterns. The knowledge of alpha rhythm dates from Berger’s pioneering work but its origin is still controversial. Although this ∗
Corresponding author. Tel.: +55 32 3379 2552; fax: +55 32 3379 2525. E-mail address: [email protected] (A.M.F.L. Miranda de S´a).
rhythmic activity should be generated in the cortex [4], the theory of a thalamic pacemaker function has surfaced and also been challenged since the beginning of the 1930s [5]. Investigating the relationship between thalamic and cortical EEG alpha rhythm, Lopes da Silva et al. [6] found a decrease within the alpha band of the intra-cortical coherence after the removal of the contribution from thalamus. This reduction could have been interpreted as the influence of the latter in the cortical alpha. However, since partial coherences were still high, they concluded that other factors should be involved in the generation of cortical alpha rhythm. More recent research [7,8] suggests feedback from cortex to thalamus to explain the cortically induced coherence of thalamic-generated oscillations. Besides this controversy of the thalamic pacemaker for the alpha rhythm, there is another regarding the fact that either alpha rhythm should be a stochastic signal reflecting the output of a linear filter [9] or reflect an output of
1350-4533/$ – see front matter © 2004 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2004.09.011
168
A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
non-linear oscillators. The latter was proposed by Wiener [10] and is based on the fact that such rhythm could be entrained by forced stimuli at near frequencies, which could only happen if the generating system for alpha rhythm were non-linear. According to Rombouts et al. [11], many researches were carried out since the middle of the 1980s to investigate whether the EEG could result from deterministic chaos. However, no conclusive hypothesis about the chaotic dynamics in EEG was established. Stam et al. [12] employed non-linear prediction statistics and phase-randomized surrogate data to test for non-linearity in the EEG at rest. The null hypothesis that alpha rhythm could result from linearly filtered noise was rejected only in 1.25% of the cases. These inconclusive results with many non-linear, sophisticated techniques, has led Gebber et al. [13] to investigate the Wiener’s model by measuring the phase locked activity within the alpha band due to photic stimulation. This has been carried out by obtaining time-series of the delays between peaks of the linearly filtered EEG within the alpha band and the stimulation signal. However, with this time-domain measuring methodology, only synchronization (i.e. phase-locked to the stimulation signal activities) with the second harmonic of the stimulation frequency could be measured. The approach used by Gebber et al. [13] imposes a limitation in the investigation, since there is some indication of physiological differences between
the first and second harmonic of the driving response [14–16]. In the present work, proceeding with the linear approach, we propose an alternative methodology based on the coherence function between EEG and the stimuli signals to investigate the phase lock in the activity within the alpha rhythm. This frequency domain technique allows overcoming the limitation of detecting synchronism even when the stimulation occurs near the alpha rhythm.
2. Material and methods 2.1. Theoretical background The coherence estimate between a periodic signal, x[k], and a random one, y[k], may be obtained as [17]: 2 M Yi (f ) κˆ y2 (f ) = i=1 (1) M 2 M |Yi (f )| i=1
where Yi (f) is the T-length Fourier transform of the ith window of y[k] which has been divided into M disjoint segments. It is interesting to note that, contrary to the general case of two random signals, coherence between a periodic signal and
Fig. 1. Normalized power spectra estimates of the EEG, derivation O1 , from subject #4 before (dotted lines) and during (continuous lines) stroboscopic flash stimulation (SFS) at 4, 5 and 6 Hz. Coherence κˆ y2 (f ) (confidence limits for the harmonics of the stimulation frequency indicated with triangles) for the EEG data during SFS is also shown in the subplots bellow. The horizontal dotted lines in such subplots indicates the critical value of 0.2589 for κˆ y2 (f ).
A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
a random one can be estimated using only the latter. This constitutes an advantage for evoked potentials analysis, since the stimulation signal need not be recorded, avoiding the introduction of noise from a signal whose amplitude may vary too fast in cases such as in stimulation with flash. The estimate κˆ y2 (f ) has been derived by Dobie and Wilson [18] and used since then in the objective response detection [19,20]. Its statistical distribution for the case of lack of response (zero coherence) to periodic input is identical to the well established case when both signals are uncorrelated, Gaussian noise, as shown by Nuttall [21]. Hence, the threshold for the detection of evoked responses is readily obtained from the critical values of κˆ y2 (f ), which are given as [17]: 2 κˆ crit
F critα,2,2(M−1) = M − 1 + F critα,2,2(M−1)
(2)
where F critα,2,2(M−1) is the critical value of the F-distribution with 2 and 2(M − 1) degrees of freedom for a significance 2 , the null hypothesis (H ) of level ␣. Thus, for κˆ y2 (f ) < κˆ crit 0 no periodic component (i.e. no stimulus response) can be accepted. Miranda de S´a et al. [17] derived the sampling distribution of κˆ y2 (f ) for the alternative hypothesis (H1 ) of
169
presence of responses as: (M − 1)
κˆ y2 (f ) 1 − κˆ y2 (f )
(λ) ∼ F2,2(M−1)
(3)
where “∼” means “is distributed as” and F2,2(M−1) (λ) is the non-central F-distribution [22] with 2 and 2(M − 1) degrees of freedom and the non-centrality parameter λ, which may be expressed as a function of the number of windows used in the estimation, M, and the true value of κˆ y2 (f ), κy2 (f ), as:
λ = 2M
κy2 (f ) 1 − κy2 (f )
(4)
Knowing such distribution, the confidence limits of κˆ y2 (f ) can be obtained and thus the degree of synchronization due to stimulation can be measured. Nevertheless, the calculation of critical values of κˆ y2 (f ), under hypothesis H1 , is computationally expensive, since a closed-form inverse for its cumulative density function cannot be easily found. Approximate critical values of κˆ y2 (f ) may be easier estimated by using approximations to the non-central F distribution. Miranda de S´a et al. [17] used an approximation based on fitting a central to the non-central F-distribution, such that the first two moments
Fig. 2. Same as Fig. 1 but for a broad band alpha subject (#1).
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A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
were preserved. By applying this to expression (3), critical values under H1 are obtained as: 2 κˆ crit =
{1 + Mκy2 (f )/[1 − κy2 (f )]}F critα,ν ,2(M−1) M − 1 + {1 + Mκy2 (f )/[1 − κy2 (f )]}F critα,ν ,2(M−1) (5)
M ˆSyy (f ) = 1 |Yi (f )|2 MT
(6)
i=1
where 2
ν =
and digitised at 256 Hz. The spectrum of the signal (y[k]) from each subject was calculated before and during stimulation as the average of M windows (periodogram) of T = 2 s duration:
{2 + 2Mκy2 (f )/[1 − κy2 (f )]} 2 + 4Mκy2 (f )/[1 − κy2 (f )]
2.2. Data acquisition and processing The EEG signal of 12 normal young subjects (age range: 9–17 years) was recorded at O1 and O2 (reference at the ipsilateral earlobe) over a period of about 25–30 s before and during stroboscopic flash stimulation (SFS) at 4, 5, 6, 8, 10, 12 and 15 Hz. The signals were band-pass filtered (0.1–70 Hz)
In order to ensure steady state in the evoked responses, stretches of signals after at least 2 s from the beginning of the stimulation were selected. Thus, a total length of 22 s (M = 11) was used for estimating each spectrum. The spectra from each subject (before and during a given SFS) were normalised by the maximum spectral component. The synchronization of EEG signals with the stimulation was investigated with κˆ y2 (f ), obtained from (1), with critical value of the no-response case calculated according to (2). The confidence limits of κˆ y2 (f ) were determined by linear interpolation from values calculated using (5).
Fig. 3. Same as Fig. 1 (subject #4) but with stroboscopic flash stimulation (SFS) at 8, 10 and 12 Hz.
A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
3. Results From Fig. 1 it can be noted in the power spectrum estimates (O1 ) of subject #4 stimulated at 4 Hz that the peak within the alpha band before stimulation (around 10.5 Hz) is strongly attenuated, while new peaks appear at 4, 8, 12 and 16 Hz (1st, 2nd, 3rd and 4th harmonics). The κˆ y2 (f )-values indicate that these spectral peaks are synchronized with the stimulation, 2 = 0.2589). Further, since they exceed the critical value (ˆκcrit the degree of synchronization at 12 Hz is significantly greater than in these other frequencies (the inferior confidence limit of κˆ y2 (f ) at 12 Hz is higher than the superior ones of 4, 8 and 16 Hz). The stimulation at 6 Hz led to a similar spectral behaviour to that with SFS at 4 Hz, but with an overlap in the confidence limits of κˆ y2 (f ). On the other hand, with SFS at 5 Hz, a shift in the alpha peak to 10 Hz (2nd harmonic) occurs in the spectrum and κˆ y2 (f ) still indicates synchronization at 5, 10 and 15 Hz. Similar results were found for the contralateral derivation (O2 ) and for other eight subjects (#5, 6, 7, 8, 9, 10, 11, and 12, whose alpha peaks were also sharp and, respectively, at 10.0, 9.5, 10.5, 10.5, 10.0, 10.5, 11.0 and 10.5 Hz). A different behaviour is observed for subject #1 (Fig. 2), who has a broadband alpha activity at rest (peak at 10 Hz).
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With stimulation at 4 and 6 Hz, the spectra from this subject does not exhibit pronounced peaks at 8 and 12 Hz. Concerning the strength of the responses due to stimulation at 4 and 6 Hz, κˆ y2 (f ) is smaller than its critical value in the range 8–12 Hz, indicating the acceptance of H0 of no response. The spectral peaks at the harmonics of the stimulation frequencies that lie outside this frequency range are synchronized with the stimulation. For SFS at 5 Hz, the spectral peak at 10 Hz is maintained, but becomes sharper and synchronized with the 2nd harmonic of the stimulation frequency. Other two subjects (#2 and 3) also with broadband alpha at rest (peaks at 9.0 and 9.5 Hz, respectively) showed a similar behaviour. As the stimulation frequency is increased (8, 10 and 12 Hz), the power spectra and κˆ y2 (f ) at the first harmonic of the stimulation for the subjects #4, 5, 6, 7, 8, 9, 10, 11, and 12 behave similarly to the second harmonic of the stimulation at 4, 5 and 6 Hz. This is illustrated for subject # 4 (Fig. 3). However, for subject #1, stimulation at 8 Hz resulted in a deep spectral peak at this frequency, which is synchronized with the stimuli, since κˆ y2 (f ) is greater than its critical value (Fig. 4). This result was not observed for the second harmonic of stimulation at 4 Hz (see Fig. 2). Further, for this subject, stimulating at 12 Hz led to a sharp spectral peak, also synchronized with the frequency of stimulation, as confirmed by
Fig. 4. Same as Fig. 3 but for a broad band alpha subject (#1).
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Fig. 5. Histograms of the number of subjects for whom κˆ y2 (f ) in the harmonics of the stimulation frequency was greater than its critical value. The letters a, b, c, d, e, f, g, and h refer to stimulation at 3, 4, 5, 6, 8, 10, 12 and 15 Hz, respectively.
κˆ y2 (f ). Similar results were found for the remaining subjects with broadband alpha activity (#2 and 3). The stimulation at 15 Hz led to no significant spectral changes in the alpha band (result not shown). Fig. 5 displays the histogram, for each stimulation frequency, with the number of subjects for whom κˆ y2 (f ) is significant (α = 5%). As it can be noted, the detection rate in the harmonics of the stimulation frequency tends to be lower within the alpha band (Fig. 5a, b, c and d). On the other hand, when the fundamental frequency is within such band, the detection is higher (Fig. 5e, f and g).
4. Discussion and conclusion In 75% of the subjects, the stimulation at 4, 5 and 6 Hz led to either a peak shift in alpha or its reduction followed by new spectral peaks in the harmonic frequencies. The values of κˆ y2 (f ) indicate that these shifted peaks or the new ones are synchronized with the stimulation. This finding (with stim-
ulation frequencies having the second harmonic close to the alpha rhythm at rest) agrees with that reported by Gebber et al. [13]. In our work, however, reduced changes in the spectral range of 8 to 12 Hz were observed in 25% of the subjects, who had broadband, alpha activity at rest. This result suggests that the entrainment of such rhythm by higher harmonics of the stimulations frequency depends on the alpha spectral width. Furthermore, the entrainment in alpha rhythm due to photic stimulation was investigated by Gebber et al. [13] only at frequencies whose second harmonic occurred near the alpha peak. In their paper, the subjects were stimulated with SFS at near half of the alpha peak frequency. The authors justified the use of such stimulation frequency based on inconclusive results of previous researches in which visual evoked potentials and entrained oscillations were not easily distinguishable. The method proposed here does not have such limitation. Thus, it allows investigating the changes within the alpha band due to the stimulation with fundamental frequency close to the alpha band. In our case, even the
A.M.F.L. Miranda de S´a, A.F.C. Infantosi / Medical Engineering & Physics 27 (2005) 167–173
broadband alpha subjects showed spectral changes due to stimulation. The findings indicate physiological differences in the responses at the first and second harmonics and agree with some previous results reported about the driving reaction [14–16]. If the driving response depends on the harmonic of the stimulation, then it should reflect a complex nonlinear mechanism. Moreover, the lack of alpha rhythm entrainment when stimulating at 15 Hz can be explained by the nonlinear oscillators theory. According to it, only external stimulations with fundamental and/or harmonics close to the natural frequency of the system does lead to entrainment. In studies of event-related synchronization/desynchronization (ERS/ERD) [23], for which the blockage of alpha rhythm can occur as the effect of external stimulation in the ongoing EEG, the findings presented here should be taken into consideration. For subjects with broadband alpha rhythm, the stimulation may result in different patterns, depending on whether the fundamental frequency or one of its harmonics lies close to the alpha peak at rest. In this case, κˆ y2 (f ) can play an important role in ERS/ERD studies, since it allows investigating stimulation frequencies close to alpha peak. Moreover, the methodology proposed here can also be used to study the feedback from visual cortex to thalamus, provided visual stimulation is included in the experimental protocol. Acknowledgements The authors acknowledge the assistance of Dr. V. Lazarev and the Laboratory of Clinical Neurophysiology of the Instituto Fernandes Figueira (Rio de Janeiro, Brazil), in data collection. This work received financial support of the Brazilian agencies FAPEMIG, CNPq and CAPES.
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