Annals of Biomedical Engineering, Vol. 28, pp. 691–698, 2000 Printed in the USA. All rights reserved.

0090-6964/2000/28共6兲/691/8/$15.00 Copyright © 2000 Biomedical Engineering Society

Objective Response Detection in an Electroencephalogram During Somatosensory Stimulation DAVID M. SIMPSON, CARLOS J. TIERRA-CRIOLLO, RENATO T. LEITE, EDUARDO J. B. ZAYEN, and ANTONIO F. C. INFANTOSI Biomedical Engineering Program, Federal University of Rio de Janeiro 共COPPE/UFRJ兲, P.O. Box 68510, 21945-970 Rio de Janeiro, RJ, Brazil (Received 1 April 1999; accepted 10 May 2000)

Abstract—Techniques for objective response detection aim to identify the presence of evoked potentials based purely on statistical principles. They have been shown to be potentially more sensitive than the conventional approach of subjective evaluation by experienced clinicians and could be of great clinical use. Three such techniques to detect changes in an electroencephalogram 共EEG兲 synchronous with the stimuli, namely, magnitude-squared coherence 共MSC兲, the phasesynchrony measure 共PSM兲 and the spectral F test 共SFT兲 were applied to EEG signals of 12 normal subjects under conventional somatosensory pulse stimulation to the tibial nerve. The SFT, which uses only the power spectrum, showed the poorest performance, while the PSM, based only on the phase spectrum, gave results almost as good as those of the MSC, which uses both phase and power spectra. With the latter two techniques, stimulus responses were evident in the frequency range of 20–80 Hz in all subjects after 200 stimuli 共5 Hz stimulus frequency兲, whereas for visual recognition at least 500 stimuli are usually applied. Based on these results and on simulations, the phase-based techniques appear promising for the automated detection and monitoring of somatosensory evoked potentials. © 2000 Biomedical Engineering Society. 关S0090-6964共00兲00606-8兴

These methods thus permit the false positive rate to be controlled and in some applications have shown the promise of greater sensitivity than human observers,10 with automated techniques having detected an auditory threshold about 10 dB lower than visual analysis of auditory evoked potentials.3,8,28 Thus the number of stimuli required and therefore the duration of the exam may be reduced, leading to the faster responses much sought after in order to reduce inconvenience to the patient and permit early detection of alterations in patient responses during monitoring tasks. The techniques are also able to identify evoked potentials that are severely distorted, such as those that may occur during surgery.14 There is additionally the prospect for a reduction in the workload of specialists and therefore in costs. To date, most work on ORD seems to have been carried out with auditory2,8,9,11,15 and visual stimulation,6,19,27,31 with few references to the somatosensory modality. Noss et al.24 employed electrical stimulation of the median nerve in the form of an amplitude modulated sine wave, which is not available on standard EP systems. The aim of the present study is to provide an indication of the potential of three ORD techniques in the detection of responses to conventional somatosensory pulse stimulation, using a sample of 12 normal adults stimulated at 5 Hz by electrical pulses applied to the tibial nerve. The efficiency of the techniques 共false positives and negatives兲, the number of stimuli required, the relevant signal bandwidth and which of the three techniques is most suitable are investigated. In the next section the ORD methods applied will be presented, followed by simulation studies to evaluate their performance in conditions under which signal parameters can be tightly controlled. Experimental results obtained in normal subjects during somatosensory stimulation are then presented, followed by a discussion of the results.

Keywords—Biological signal processing, Electroencephalography, Evoked potentials, Spectral estimation, Phase spectrum, Coherence.

INTRODUCTION Evoked potentials 共EPs兲 have become standard tools for the assessment of neurological function under visual, auditory and somatosensory stimulation. Whereas conventional interpretation of the signals is based on visual analysis, the techniques of objective response detection 共ORD兲 aim to automate the identification of the response of the nervous system based on some well-defined statistical criterion, rather than on subjective evaluation. Address all correspondence to Antonio F. C. Infantosi, Programa de Engenharia Biome´dica, COPPE/UFRJ, P.O. Box 68510, 21945-970, Rio de Janeiro, RJ, Brazil. Electronic mail: [email protected]

691

692

SIMPSON et al.

TECHNIQUES FOR OBJECTIVE RESPONSE DETECTION In the literature many alternative approaches to ORD have been presented,16,30,31 each of which focuses on some specific aspect of the signal. The ones selected for this study have been chosen for their simplicity and for having well-defined statistics,18 which permits the accurate test of the null hypothesis, that the stimulus has no effect on the electroencephalogram 共EEG兲 signal. In the three methods, the EEG signal collected during stimulation is divided into epochs of equal duration, starting at a fixed latency after each stimulus. We have chosen each epoch to contain only one stimulus response, but longer windows can be used.9,14 An ensemble of epochs, x i (n), where i indicates the epoch (1⭐i⭐M ) and n the sample number (0⭐n⬍N), is thus formed. The discrete Fourier transform 共DFT兲 is then applied to each of the M epochs to give the complex spectra: x i (n)⇔X i ( f )⫽ 兩 X i ( f ) 兩 exp关 j␾i(f)兴, with f being the frequency, 兩 X i ( f ) 兩 the amplitude and ␾ i ( f ) the phase spectrum. The ORD technique magnitude-squared coherence 共MSC兲 is based on the coherence between the EEG and the stimuli 关s共n兲兴, the latter being represented by pulses at the instants of stimulation. Since these are identical in each data epoch i 关 s i (n)⫽s k (n), for all i and k兴, the MSC is given by7

冏兺 冏 M

MSC共 f 兲 ⫽

i⫽1

2

X i共 f 兲

.

M

M

兺 兩 X i共 f 兲兩

共1兲

2

i⫽1

In the absence of a consistent response to the stimuli, the numerator is low and the MSC approaches 0. If all responses to the stimuli are equal, i.e., all post-stimulus epochs are identical and X i ( f )⫽X k ( f ), then MSC共f兲⫽1. 2 ) sugBased on the similarity to a parameter (T circ 31 gested by Victor and Mast, it can readily be shown that for M independent epochs of a random Gaussian signal 共i.e., no response兲, the MSC is related to the F statistic by

The phase synchrony measure 共PSM兲, also known as the component synchrony measure 共CSM兲,3 tests for consistency in the phase of the DFT components obtained from consecutive data segments during stimulation:

PSM共 f 兲 ⫽

冋

1 M

册 冋

M

兺

i⫽1

2

cos ␾ i 共 f 兲 ⫹

1 M

册

M

兺

i⫽1

2

sin ␾ i 共 f 兲 . 共3兲

In the presence of a response, there is time- and phase-lock between the EEG and the stimulus, leading to values close to 1 for the PSM. In the absence of a stimulus response, the phase is random and a PSM approaching zero may be expected. This test parameter is also closely related to the phase coherence measure2 or the Rayleigh test.16,21 It may be noted that when all the amplitudes, 兩 X i ( f ) 兩 , are equal, the PSM and MSC are equivalent. We may therefore consider the PSM as a phase-only version of the MSC, i.e., one in which the amplitude is ignored. In the absence of phase-lock, to a first approximation we find that21

PSM共 f 兲 ⬇

␹ 22 , 2M

共4兲

where ␹ 22 is the chi-squared distribution with two degrees of freedom and M is the number of data segments. This is an approximation based on the central limit theorem, which improves with increasing M. According to Mardia,21 exact confidence limits can be obtained, however the chi-squared distribution provides a simpler alternative, giving almost identical results above M⫽100. The spectral F test 共SFT兲6 employs the ratio of the power spectra obtained from the EEG during ( ˜P xx ) and before or after stimulation ( ˜P y y ) obtained from X i ( f ) (M x epochs兲 and Y i ( f ) 共M y epochs兲, respectively. In the absence of spectral change, the ratio of averaged periodograms follows an F distribution: Mx

MSC共 f 兲 ⫽

F 2,2M ⫺2 , M ⫺1⫹F 2,2M ⫺2

共2兲

from which the critical values for a significance level of ␣ can be obtained in order to test the null hypothesis of no-stimulus response. In the presence of a 共linear兲 stimulus response, positive tests are expected at the stimulus frequency and its harmonics, although not at intermediate frequencies. In the absence of response or in the nostimulus condition, a false positive rate of ␣ is expected.

F 2M x ,2M y ⫽

˜P xx 共 f 兲 ˜P y y 共 f 兲

My ⫽

兺 兩 X i共 f 兲兩 2

i⫽1 My

Mx

.

共5兲

兺 兩 Y i共 f 兲兩 2

i⫽1

It should also be pointed out that none of the above tests is valid for DC 共f⫽0兲 or the Nyquist frequency 共half the sampling rate兲, where the DFT components are real only.

Detection of Somatosensory Evoked Responses

FIGURE 1. Percentage of positive tests „detections… in simulation study with sinusoids in additive noise for a range of signal-to-noise ratios „in dB… and numbers of epochs „a… MSC „solid line… and PSM „dashed line… and „b… SFT.

Simulations In order to compare their relative performance, the three techniques given above for the objective identification of spectral changes were investigated in simulation studies. Responses to somatosensory stimulation were emulated as a sine wave with additive white Gaussian noise, such that at the frequency of oscillation, the signal-to-noise ratio 共SNR兲 of the DFT component ranged from ⫺30 to 0 dB. The ORD techniques were then applied to test for the presence of the oscillation using M⫽10, 30, 100, 500 and 1000 epochs. For the case of the SFT, M x ⫽M y , with the signal representing the EEG before stimulation 关 Y i ( f )兴 containing only noise and no oscillation. The ORD tests were applied to 500 such sets of data in order to determine, at each SNR, the fraction of cases in which the presence of the sine wave was detected. This was defined as occurring when the ORD test 共applied at the frequency of the sine wave兲 exceeded the ␣ ⫽5% critical value. In the presence of only noise and no signal, a 5% false positive rate is thus expected. Figure 1共a兲 presents the results for the MSC and PSM showing, as expected, that the ability to detect the ‘‘stimulus response’’ increases with increasing SNR and M. For small SNR, the detection rate converges to the ␣⫽5% false positive rate, as was separately confirmed in

693

FIGURE 2. Averaged evoked potential for one subject over „a… MÄ10, 50, 200 and 400 stimuli, together with „b… the MSC for MÄ50. For comparison, the MSC without stimulation „background EEG… is also shown „c…. The horizontal line in „b… and „c… indicates the critical value „ ␣ Ä5%… for the MSC „MÄ50…, and à indicates the harmonics at which this level is exceeded.

noise-only data. The detection rate of the MSC was best among the three techniques examined, with the PSM following very closely. The SFT shows much poorer results 关Fig. 1共b兲兴, requiring a far higher number of data epochs 共M兲 or SNR in order to achieve the same detection rate as the MSC or PSM. APPLICATION TO EEG SIGNALS DURING SOMATOSENSORY STIMULATION Methods Twelve volunteers, aged between 20 and 39 years, with no symptoms of neurological pathology and with normal somatosensory evoked potentials, were subjected to periodic stimulation of the right posterior tibial nerve at the ankle using a SapphireII 4ME 共Medelec, UK兲 system. Current pulses of 0.2 ms duration and of the minimum intensity necessary to provoke muscle twitch in the intrinsic foot muscle supplied by the tibial nerve 共5–19 mA兲 were employed. A ground electrode was placed proximal, close to the stimulation site. The recording electrodes were positioned at Cz⬘ 共2 cm behind the Cz electrode position of the 10–20 International System兲,

694

SIMPSON et al.

FIGURE 3. Mean „thick line… Ástandard deviation „thin lines… of „a…, „b… MSC and „c…, „d… SFT „a…, „c… during and „b…, „d… without stimulation calculated for the 12 subjects and for MÄ400. The horizontal lines indicate the critical values „ ␣ Ä5%…. Values of the confidence limits that fall below zero have been ignored.

with the reference at Fpz⬘ 共midway between Fpz and Fz兲, as is usual for somatosensory evoked potentials.23 The stimulus rate was 5.13/s 共nominally 5 Hz兲, for which clearly defined evoked responses are expected.5 In each exam, stimuli were applied until 1024 valid responses 共i.e., those accepted by the Medelec system’s automatic artifact rejection algorithm兲 were obtained. Two sets of exams were carried out, with at least a 1 min interval between stimulation periods. The evoked potentials were visually checked by an experienced clinician. The band pass filter of the evoked potential system was set at 10 Hz–2 kHz and the electrode impedance kept below 2 k⍀. The raw EEG signal was collected throughout the session from the analog output of the SapphireII system. This was digitized on a personal computer at a sampling rate of 5 kHz and a resolution of 12 bits 共DAQPad-1200, National Instruments, US兲, using software developed in LabVIEW 共ver. 4.0, National Instruments, US兲. The trigger signal, showing the instant of each stimulus, was also acquired. The quality of the EEG signals was first visually checked and then the 105 ms epochs following each stimulus were extracted. The most significant components of the somatosensory evoked potentials occur within this period.25 The algorithm suggested by Chiappa5 for the automatic rejection of epochs showing strong artifacts was then applied. For this, first a 20 s segment of the EEG without stimulation was selected as a reference for signal levels, from which the standard deviation ( ␴ ) of the signal was estimated. A threshold

value of ⫾2.8 ␴ 共which includes 99.5% of samples for a normal distribution兲 was then defined and applied to the epochs of the EEG signal from 5 to 105 ms following each stimulus. Epochs in which a continuous segment of more than 5% of the samples, or a total of 10% of samples exceeded the threshold, were rejected as containing artifact. The first 5 ms after the stimuli was not included in the test as they contain a stimulus artifact.13 The ORD techniques require independent, identically distributed 共iid兲 DFT components from each epoch. This stationarity was checked with the run and reverse arrangements tests4 for the power of the frequency components later observed to be of main interest, those in the range from 20 to 80 Hz. The three methods of ORD were applied to the DFTs of the first M⫽50, 100, 200 and 400 epochs for each subject. No tapered data windows were employed, since the evoked response is not stationary within the epoch but a transient signal, and tapering could diminish, or even eliminate, important components. Since the epochs selected each refer to a single stimulus, all of the DFT components may be considered harmonics of the evoked potential and may therefore test positive for stimulus response. For the denominator of the SFT, artifact-free EEG 共as identified by the automated technique兲 from before the stimulus period was employed, with M y chosen as equal to M x . Results The results of the run and reverse arrangement tests indicate that the spectral components of interest may be

Detection of Somatosensory Evoked Responses

considered stationary 共p⬍0.05兲 over a period of 400 stimuli 共1 min, 18 s兲 in this group of subjects. In initial tests, the ORD techniques indicated response detection in the range up to approximately 80 Hz and then again above 250 Hz. The high-frequency responses were however almost entirely eliminated when the first 5 ms of each response, which contains the stimulus artifact, was skipped. As a result of these preliminary studies and in order to reduce the volume of data, all subsequent analysis was carried out after decimating the signal to a new sampling rate of 1000 Hz, following antialias filtering at 300 Hz, with the analysis window restricted to 5–105 ms after each stimulus. Figure 2 illustrates the results of the application of the MSC in one subject. The strong response to stimulation is clearly evident both in the averaged evoked potentials 关Fig. 2共a兲, M⫽10, 50, 200, 400兴 and the corresponding MSC 共M⫽50 stimuli兲, where the critical value, calculated according to Eq. 共2兲 and shown as a horizontal line, is exceeded at a number of harmonics 共indicated by ⫻), mainly in the low-frequency range. In the absence of stimulation 关background EEG, Fig. 2共c兲兴 the critical value is not attained at any of the harmonics. In Fig. 3, the mean ⫾ standard deviation of the MSC 关Figs. 3共a兲 and 3共b兲兴 and SFT 关Figs. 3共a兲 and 3共b兲 and 3共c兲 and 3共d兲, respectively兴 are shown during and without stimulation Figs. 3共a兲 and 3共b兲 and 3共b兲 and 3共d兲, respectively. The much higher values of MSC and SFT during stimulation are clearly evident, as is the greater consistency obtained with the MSC. The results for the PSM were found to be very similar to those of the MSC, just slightly lower. The histograms of Fig. 4 show at each frequency and for each ORD technique the number of subjects for whom a response was identified, with ␣ ⫽0.05. As in the simulation, the MSC gives very similar results to those of the PSM, and with M⫽400 both techniques detected a stimulus response at 20, 40 and 60 Hz in 11 of the 12 subjects 关Fig. 4共a兲兴. The detection rate drops off above 70 Hz, and as expected is somewhat worse with M⫽200 关Fig. 4共b兲兴 than M⫽400. Above 100 Hz, very few detections were recorded. The SFT performed poorly. Considering the ␣ ⫽5% false positive rate in the absence of stimulation, the probability of detecting a response at a given frequency in 3 or more of the 12 subjects is p⫽0.0196 and 4 or more p⫽0.0022 according to the binomial probability distribution. Thus the detection rate is highly significant at frequencies from 10 to 80 Hz, for both MSC and PSM, and M⫽200 and 400. Under the no-stimulus condition, the number of positive tests 共averaged over M⫽50, 100, 200, 400兲 obtained from the 12 subjects in the range of 10–300 Hz 共360 harmonics in total兲, were 15 for the MSC, 13.8 for the PSM and 130.3 for the SFT. Considering ␣ ⫽5%, the expected number of false positives is 18. There was no

695

FIGURE 4. Histograms showing the number of subjects giving positive responses with the MSC, PSM and SFT after „a… 400 and „b… 200 stimuli.

clear frequency range in which the false positives were more common. The significance of the results obtained with the three ORD techniques during stimulation was further evaluated by a comparison with those of the background EEG by applying the Wilcoxon signed rank test 共S-Plus 4.0, MathSoft, USA, with continuity correction as recommended by Lehmann17兲 on the MSC values at each harmonic. As shown in Fig. 5 共M⫽400兲, the difference was highly significant 共p⬍10⫺3 ) in the band from 20 to 70 Hz for the MSC and PSM. With the SFT, however, none of the harmonics showed significant differences between the periods with or without stimulation. In this test, the SFT of background activity was calculated using two periods of M⫽400 epochs: the first forming the numerator of Eq. 共5兲, the second the denominator. Table 1 shows, for the group of subjects, the mean and median number of frequencies in the 20–80 Hz range 共seven harmonics兲 at which a response was detected, both with and without stimulation. This frequency range was selected based on the results of Figs. 4 and 5. It is again evident that generally the MSC produces slightly higher rates of detection than those of the PSM, and considerably better ones than those of the SFT. The SFT also produces a far higher number of false positives.

696

SIMPSON et al.

FIGURE 5. Significance „p… values for the Wilcoxon test comparing the MSC, PSM and SFT „MÄ400… values during stimulation with those from background EEG.

Comparing the periods with and without stimulation, the Wilcoxon test applied to the number of harmonics at which a response was detected again showed highly significant differences both for MSC and PSM and for all M examined. For the SFT, however, there was no significant difference between these periods. Table 1 also shows that with M⫽200 and 400, in all 12 subjects, both MSC and PSM detected the response in at least three of the seven harmonics examined; during background EEG, this occurred in none of the cases. With fewer stimuli, detection rates were lower, but even with M⫽50, equivalent to only 9.2 s of stimulation, the MSC showed clear evidence of stimulus response 共positive tests in ⭓3 harmonics兲 in 10 of the 12 subjects. DISCUSSION AND CONCLUSION In the simulation study, the MSC clearly gave the best performance in the detection of additive components in the signals, and was closely followed by the PSM. The

MSC uses both the amplitude and phase spectrum, and therefore may be expected to be better at detecting the deterministic component in the signal than either PSM 共which neglects the amplitude spectrum兲 or SFT 共which neglects phase兲. What is notable, however, is that without the amplitude spectrum performance is only very slightly degraded, whereas neglect of the phase has a very strong effect on the results. In work on auditory evoked potentials, it had previously been noted that a wide range of techniques based on signal phase is more effective in identifying evoked potentials than those using the amplitude spectrum,14,16,29 and that the MSC is slightly superior to phase coherence 共the square root of the PSM兲.9 Based on the observation that phase appears to be more strongly affected by stimulation than the amplitude spectrum, Sayers et al.29 suggested that auditory evoked potentials may be the result of phase reordering in response to stimulation, rather than additive components. This question does not appear to have been settled

TABLE 1. Detection rates for each of the ORD methods. Mean and median number of harmonics in the range of 20–80 Hz „seven harmonics… giving positive tests during stimulation and background EEG „in parentheses…, together with the significance of their difference „Wilcoxon matched pairs…. Number of cases „of a total of 12 subjects… giving Ð K harmonics with positive tests at the ␣ Ä0.05 level.

Mean No. of harmonics

M 400

200

100

50

MSC PSM SFT MSC PSM SFT MSC PSM SFT MSC PSM SFT

5.8 5.6 1.6 5 4.9 1.5 4.7 4.6 2.5 3.8 3.8 2.4

(0.2) (0.3) (1.9) (0.2) (0.2) (2.1) (0.5) (0.5) (1.8) (0.4) (0.2) (0.9)

Median No. of harmonics

p (Wilcoxon)

6 (0) 6 (0) 0.5 (1) 5 (0) 5 (0) 0 (0) 5 (0) 5 (0) 2 (1) 4 (0) 4 (0) 2 (0)

0.0023 0.0024 0.9682 0.0023 0.0024 0.7784 0.0024 0.0023 0.7172 0.0024 0.0024 0.0913

Cases with detection in ⭓ K harmonics

K ⫽2

K ⫽3

12 12 5 12 12 4 11 12 6 10 11 6

12 12 3 12 12 3 10 9 6 10 9 6

(0) (0) (4) (0) (0) (4) (1) (2) (4) (1) (0) (2)

(0) (0) (4) (0) (0) (4) (1) (0) (4) (0) (0) (2)

Detection of Somatosensory Evoked Responses

yet,9,20 although additive components have been clearly identified in auditory evoked responses.16 Our results show that even in simulations using a purely additive model of stimulus response, the MSC and PSM are more effective than the SFT 共Fig. 1兲, suggesting that these techniques are intrinsically more sensitive. The fact that alterations in phase of the EEG signals under stimulation are more readily evident should therefore primarily be taken as further evidence of the fundamental role of the phase spectrum in transient signals, rather than necessarily pointing towards the physiological process involved in generating evoked potentials. Considering the paramount importance of phase in determining signal shape,26 this conclusion is not surprising. The SFT requires the collection of reference data from before 共or after兲 stimulation. This makes it highly sensitive to nonstationarities of the EEG, which may be difficult to distinguish from genuine stimulus responses. The low sensitivity of the SFT 共Figs. 4 and 5兲, together with the larger number of false positives in the nostimulus condition observed here and by Ramos et al.27 with visual stimuli, provide a strong argument against its use in ORD. The results in Fig. 2 and Table 1 show that, even after only M⫽50 stimuli, the MSC and PSM techniques can clearly distinguish 共p⬍0.003兲 between background EEG and stimulus responses. A simple criterion for identifying that, in a given subject, a response has occurred that may be based on the number of harmonics 共K兲 giving positive ORD tests. Thus with the MSC, for example, by selecting K⫽3 as the threshold in Table 1 it is found that in 10 of the 12 subjects M⫽50 stimuli were sufficient to identify the responses. Applying the same criterion in the absence of stimulation, no false positives were obtained in the 12 subjects. With 200 stimuli, all subjects showed the response, and there were no false positives. Under the null hypothesis of stationary signals without responses and for ␣ ⫽0.05, three or more harmonics with positive tests may be expected in less than 1% of experiments 共binomial distribution兲. Nonstationarities in some parts of the signals could increase this figure, and this may have occurred with M⫽100. A simple criterion such as the one employed above for the detection of responses could certainly be improved upon, since some of the harmonics in the band analyzed are evidently 共Figs. 4 and 5兲 more sensitive to the presence of a stimulus responses than others. However, the identification of a more suitable criterion that optimizes sensitivity and specificity must be based on data from a target patient population, and not just normal subjects. A comparison of such a technique with conventional, visual detection of the evoked potentials and some of the alternative ORD methods implemented in the time domain1,12,22 is beyond the scope of this article.

697

Considering that clinically at least 500 stimuli are generally employed,24 the performance of the techniques after only 50 stimuli 共9.2 s兲 is encouraging for applications in the monitoring of somatosensory evoked potentials. It was noted that in some cases the response was hardly evident in the averaged evoked response, even after 400 stimuli, but clearly identified by the MSC after only 50. Noss et al.24 found that in 20 s stimulus periods, they could detect 共p⬍1%兲 stimulus responses in at least 94% of tests carried out in three subjects after optimizing the stimulus frequency. After 10 s of stimulation, they identified the response in 50% of epochs tested. They 2 statistic, which is mathematically closely used the T circ related to the MSC. However, they employed amplitudemodulated electrical stimuli, which are not normally available on EP equipment, rather than the standard pulses in the present work. In addition, the intensity of stimulation was higher, at the pain threshold, hardly acceptable in conscious patients. It is well known5 that stronger somatosensory stimulation causes larger responses in the EEG. In conclusion, the techniques of magnitude-squared coherence and phase synchrony measure have been found effective in the objective detection of somatosensory evoked potentials. The initial results presented here have shown the potential of the methods and are encouraging for the application of the techniques in monitoring patients, for example, during surgery. ACKNOWLEDGMENTS The authors are grateful for assistance from the Brazilian Agencies CNPq and CAPES, and to PRONEX/ MCT for financial support of this work.

REFERENCES 1

Achim, A. Signal detection in averaged evoked potentials: Monte Carlo comparison of the sensitivity of different methods. Electroencephalogr. Clin. Neurophysiol. 96:574–584, 1995. 2 Ali, A. A., and J. Jerger. Phase coherence of the middlelatency response in the elderly. Scand. Audiol. 21:187–194, 1992. 3 Aoyagi, M., T. Fuse, T. Suzuki, Y. Kim, and Y. Koike. An application of phase spectral analysis to amplitudemodulation following response. Acta Oto-Laryngol. Suppl. 504:82–88, 1993. 4 Bendat, J. S., and A. G. Piersol. Random Data: Analysis and Measurement Procedures. New York: Wiley, 1986, p. 586. 5 Chiappa, K. H. Evoked Potentials in Clinical Medicine. Philadelphia: Lippincott–Raven, 1997, p. 719. 6 Coelho, F. C., D. M. Simpson, and A. F. C. Infantosi. Testing recruitment in the EEG under repetitive photo stimulation using frequency-domain approaches. Conference Proceedings of IEEE Engineering in Medicine and Biology Society 共CDROM, 2 pp.兲, Montreal, Canada, 20–23 September 1995.

698 7

SIMPSON et al.

Dobie, R. A., and M. J. Wilson. Analysis of auditory evoked potentials by magnitude-squared coherence. Ear Hear. 10:2– 13, 1989. 8 Dobie, R. A., and M. J. Wilson. Optimal smoothing of coherence estimates. Electroencephalogr. Clin. Neurophysiol. 80:194–200, 1991. 9 Dobie, R. A., and M. J. Wilson. Objective detection of 40 Hz auditory evoked potentials: Phase coherence vs. magnitude squared coherence. Electroencephalogr. Clin. Neurophysiol. 92:405–413, 1994. 10 Dobie, R. A., and M. J. Wilson. Objective versus human observer detection of 40 Hz auditory-evoked potentials. J. Acoust. Soc. Am. 97:3042–3050, 1995. 11 Dobie, R. A., and M. J. Wilson. 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. 100:2236– 2246, 1996. 12 Doyle, K. J., S. Fujikawa, P. Rogers, and E. Newman. Comparison of newborn hearing screening by transient otoacoustic emissions and auditory brainstem response using ALGO-2. Int. J. Pediatr. Otorhinolaryngol. 43:207–211 共1998兲. 13 Erwin, C. W., M. P. Rozear, R. A. Radtke, and A. C. Erwin. Somatosensory evoked potentials and surgical monitoring. In: Electroencephalography: Basic Principles, Clinical Applications, and Related Fields, edited by E. Niedermeyer, and F. Lopes da Silva. Baltimore: Williams and Wilkins, 1993, pp. 957–974. 14 Greenblatt, E., R. A. Zappulla, S. Kaye, and J. Fridman. Response threshold determination of the brain stem auditory evoked response: A comparison of the phase versus magnitude derived from the Fast Fourier Transform. Audiology 24:288–296, 1985. 15 Harada, J., M. Aoyagi, T. Suzuki, T. Kiren, and Y. Koike. A study on the phase spectral analysis of middle latency response and 40-Hz event-related potential in central nervous system disorders. Acta Oto-Laryngol. Suppl. 511:34–39, 1994. 16 Jervis, B. W., M. J. Nichols, T. E. Johnson, E. Allen, and N. R. Hudson. A fundamental investigation of auditory evoked potentials. IEEE Trans. Biomed. Eng. 30:43–50, 1983. 17 Lehmann, E. L. Nonparametrics: Statistical Methods Based on Ranks. San Francisco: Holden and Day, 1975, p. 473. 18 Leite, R. T., D. M. Simpson, and A. F. C. Infantosi. Comparison of techniques for the objective identification of EEG responses to somatosensory stimulation. Conference Proceedings of IEEE Engineering in Medicine and Biology Society 共CDROM, 2 pp.兲, Amsterdam, Netherlands, 31 October– 3 November 1996.

19

Liavas, A. P., G. V. Moustakides, G. Henning, E. Z. Psarakis, and P. Husar. A periodogram-based method for the detection of steady-state visually evoked potentials. IEEE Trans. Biomed. Eng. 45:242–248, 1998. 20 Lopes da Silva, F. Event-related potentials: Methodology and quantification. In: Electroencephalography: Basic Principles, Clinical Applications, and Related Fields, edited by E. Niedermeyer and F. Lopes da Silva. Baltimore: Lippincott Williams and Wilkins, 1998, pp. 947–957. 21 Mardia, K. V. Statistics of Directional Data. London: Academic, 1972, p. 377. 22 Mason, S. M. Automated system for screening hearing using the auditory brainstem response. Brit. J. Audiol. 22:211–213, 1988. 23 Misulis, K. E. Espehlmann’s Evoked Potential Primer: Visual, Auditory and Somatosensory Evoked Potentials in Clinical Diagnosis. Boston: Butterworth–Heinemann, 1994, p. 255. 24 Noss, R. S., C. D. Boles, and C. D. Yingling. Steady-state analysis of somatosensory evoked potentials. Electroencephalogr. Clin. Neurophysiol. 100:453–461, 1996. 25 Nuwer, M. R., M. Aminoff, J. Desmedt, A. A. Eisen, D. Goodin, S. Matsuoka, F. Mauguie`re, H. Shibasaki, W. Sutherling, and J. F. Vibert. IFCN recommended standards for short latency somatosensory evoked potentials. Report of an IFCN committee. Electroencephalogr. Clin. Neurophysiol. 91:6–11, 1994. 26 Oppenheim, A. V., and J. S. Lim. The importance of phase in signals. Proc. IEEE 69:529–541, 1981. 27 Ramos, E. G., R. T. Leite, F. C. Coelho, D. M. Simpson, and A. F. C. Infantosi. Identificac¸˜ao objetiva no domı´nio da frequeˆncia de resposta a fotoestimulac¸˜ao repetitiva. In: Anais do III Fo´rum Nac. Cieˆn. Tecn. Sau´de-XV Cong. Bras. Eng. ˜o 共SP兲: Brazil, Biom., Vol. 2, pp. 539–540, Campos do Jorda 13–17 October 1996. 28 Ross, J. A., H. A. Beagley, and B. McA. Sayers. Signal statistics in objective auditory evoked potential 共AEP兲 detection by the phase spectral method. J. Biomed. Eng. 2:310– 314, 1980. 29 Sayers, B. McA., H. A. Beagley, and W. R. Henshall, The mechanism of auditory evoked EEG responses. Nature (London) 247:481–483, 1974. 30 Sayers, B. McA., H. A. Beagley, and J. Riha. Pattern analysis of auditory evoked EEG potentials. Audiology 18:1–16, 1979. 31 Victor, J. D., and J. Mast. A new statistic for steady-state evoked potentials. Electroencephalogr. Clin. Neurophysiol. 78:378–388, 1991.