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High frequency scalp potentials evoked by a reaction time task
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Electroencephalography and cfinical Neurophysiology, 1987, 67:222-230 Elsevier Scientific Publishers Ireland, Ltd.
EEG 03307
Experimental Section High frequency scalp potentials evoked by a reaction time task Don Krieger * and Michael Dillbeck * * • Department of Neurosurgery, Children's Hospital, Pittsburgh, PA 15213 (U.S.A.), and * * Department of Psychology, Maharishi International University, Fairfield, 1A 52556 (U.S.A.) (Accepted for publication: 12 January, 1987)
Summary
'Bursts' of high frequency (20-80 Hz) extracellular electrical activity are the signature of the brain mechanism mediating recognition of odors in rabbits and cats. To test the hypothesis that a similar mechanism may be functional in man outside the olfactory system, relationships were studied between bursts of 20-150 Hz scalp EEG and parameters of performance during visual reaction time tasks. Specific findings indicated that (1) muscle artifacts were not the primary source of identified EEG bursts, (2) the mechanism which produces the bursts may be similar in both rabbit olfactory bulb and human neocortex, (3) visual task peformance may be mediated by the brain areas which produced the bursts, and (4) burst activity varied with changes in performance which may be associated with attention and learning.
Key words: Evoked potential; Attention; Learning; Visual; Motor
In both the rabbit and cat, respiratory inspiration is accompanied by 'bursts' of synchronous 20-80 Hz electrical activity, observable throughout the olfactory system in extracellular recordings (Freeman 1975). Multi-dimensional analytic techniques applied to burst recordings from the olfactory bulb of the rabbit have shown that the differential response to presentation of one or the other of two expected odors could be predicted with greater than 80% accuracy (Freeman and Di Prisco 1986). In addition, Freeman and his coworkers have developed a physiological model of the underlying processes (Freeman 1975, 1979a, b, c) and have produced experimental verification of many of the model's features (Freeman 1975; Freeman and Schneider 1982; Freeman and Skarda 1985). The burst mechanism, apparently capable of mediating recognition of the pattern of sensory input corresponding to an odor, is an attractive
candidate as a mediator of pattern recognition in other processes. If it were generally functional outside the olfactory system, short duration bursts of high frequency activity would be occurring constantly during waking activity and might be evoked in stereotypic areas for selected tasks. In order to test this possibility the scalp EEG recorded between stimulus and response during visual-motor task performance was searched for sinusoidal bursts. Burst parameters, particularly latency, were then tested for their ability to predict reaction time (RT). Thus the primary hypothesis addressed by this work is: 'there is a relationship between parameters of high frequency activity and task performance parameters.' Because of resolution limitations obtainable with scalp recordings, spatial patterns were only interpreted in the context of burst source localization.
Methods Correspondence to: Don Krieger, Department of Neurosurgery, Children's Hospital, 125 Desoto Street, Pittsburgh, PA 15213 (U.S.A.).
Subjects were 8 right-handed men between ages 24 and 44. Each was thoroughly familiarized with the procedure during the week before the experi-
0013-4649/87/$03.50 © 1987 Elsevier Scientific Publishers Ireland, Ltd.
HIGH FREQUENCY SCALP POTENTIALS EVOKED BY RT TASK ment. Then on each of 2 consecutive days trials were presented in 2 sessions of twelve 1 min sets. These were separated by a 15 min eyes-closed period. Within each session, 1 min trial sets were separated by 15 sec eyes-closed rest periods. During trial presentation the subject sat with his eyes fixed to a marker on a computer monitor and with his index finger(s) positioned on response key(s). Response required a minimum weight of 65 g and a minimum motion of 2 mm. At random intervals ranging from 1.5 to 2.5 sec inter-trial interval, the fixation marker was replaced by an arrow pointing left or right to which response was required with the finger of the corresponding hand. Thus there were 20-25 trials/set. For the simple task (sRT), an entire trial set required response with a single hand, left or right. For the choice task (cRT), the arrow direction and responding hand changed from trial to trial in random order. The stimulus character subtended a visual angle of approximately 0.5 o × 0.5 o. The EEG was digitized at 600 Hz/channel from 10/20 system placements O1, 02, P3, P4, Pz, T3, T4, T5, T6, C3, C4, F3, F4, F7, F8. An additional digitized channel was used to monitor the voltage across a photo-resistor, positioned to detect the stimulus appearance at the terminal screen. This provided RT measurement resolution of 1.7 msec. Each EEG placement was referenced to the contralateral ear in order to maximize signal amplitude. The montage, shown in Fig. 3, was applied using an elastic cap with tin cup electrodes placed in it. Impedances were maintained below 5000 I2. Signals were amplified by a factor of 20,000 with high and low pass filters set at 0.3 and 100 Hz respectively. No line frequency notch filtering was used. Data acquisition began 0.5 sec prior to stimulus presentation and continued for a total of 1.06 sec for each trial. Trials in which eye blink or movement artifacts were evident in the polygraph record on visual examination were excluded from analysis. The EEG is typically on the order of tens of microvolts at the scalp while the amplitude of burst activity was expected to be at least an order of magnitude less. In order to enhance the ability to identify and study features of single-trial evoked potentials (sEPs), a procedure was used for identi-
223
fying and removing the ongoing background EEG (Krieger and Larimore 1986). For each trial, the technique was applied as follows. An optimal system identification technique (Larimore 1983), called CVA, was applied to the prestimulus data for 2 electrode placements at a time. CVA is a multivariate time series analysis technique formulated as a state space model whose fundamental assumption is that the error terms in the model are gaussian white noise. Each of the resulting bivariate models was used to forecast poststimulus activity at the corresponding pair of placements. For each pair of forecasts, the forecast errors, i.e., the differences between the forecasts and the observed signals, were taken as the sEPs for the corresponding channels. In tests with both constructed and pilot data we found CVA to be highly effective in detecting sinusoids in noise. Larimore (1986) has derived an expression for the lower bound on the expected integral of the relative squared error in computing spectral estimates and has found in Monte Carlo simulations (Larimore et al. 1984) that such estimates computed using CVA were near this bound. Therefore in addition to its use as described above for modeling the prestimulus data, CVA was also used to search for bursts, sEPs were searched one electrode placement at a time by repeated application of CVA to 100 msec epochs beginning with the stimulus presentation, stepping 50 msec at a time, and ending with the response. Resonances of the resultant models provided measures of burst frequencies while burst latency and amplitude were estimated using complex demodulation at the measured frequency (Hamming 1983) as follows. The peak of the amplitude ~emodulate was identified, its values used for the amplitude of the burst 1, and burst latency taken as the point preceding the peak at which the first difference was maximum. The sequence of steps in identifying and quantifying burst activity is summarized as follows: (a)
1 Equipment calibration showed that attenuation of signals above 55 Hz by analogue low pass filtering was closely approximated by the factor: frequency/55. As compensation, burst amplitudeestimates were multipliedby this factor.
224
D. K R I E G E R , M. D I L L B E C K
the sEP for each trial at each electrode placement was computed, (b) each sEP was searched for sinusoids, (c) the latency, amplitude and frequency of each 'burst' were estimated, and (d) for each identified burst a record was made which included burst parameter estimates and RT for the trial in which it occurred. The analysis of this reduced data set was carried out as follows: (a) descriptive statistics were examined, (b) multiple regressions were computed to test for systematic relationships between burst parameters and RT, and (c) post-hoc tests were devised to explore possible changes in burst-RT relationships which might be associated with learning or attention.
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Descriptive statistics Mean sRT averaged over all subjects and trials was 276.4 msec; mean cRT was 412.0. The exclusion of artifact-contaminated trials from the burst search procedure resulted in (trials presented)/ (trials retained) ratios of 4014/2237 for sRT and 3838/1818 for cRT. For the sRT trials 3328 bursts were identified; for the cRT trials 6446 bursts were identified 2. Burst latency histograms decreased monotonically with maxima at short latencies. Amplitude histograms were unimodal and skewed, showing an extended tail towards the high end of the distribution. Frequency histograms, as shown in Fig. 1 (lower panels), were bimodal with major peak near 105 Hz and minor peak near 30 Hz. Frequency histograms compiled from rabbit olfactory bursts (Freeman and Di Prisco 1986), shown in Fig. 1 (upper panel), are similar in shape with minor peak near 30 Hz but with the major peak near 65 Hz. Because large numbers of bursts were identified in all electrodes, an attempt was made to determine (1) to what extent bursts with similar properties appeared in more than one electrode at a time, and (2) whether such multiple appearances
2 From visual examination of histograms for RT, burst latency and amplitude, cut-offs were established to exclude outlier observations which gave the curves a peaked tail
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Fig. 1. Number of bursts identified at each frequency. The upper panel shows burst frequency histograms compiled from epidural recordings in the rabbit. (From Freeman and Di Prisco 1986; courtesy of Springer Verlag.) The lower two panels are from h u m a n scalp EEG. All figures show a similar shape with minor peak near 30 Hz suggesting that the mechanism which produces the burst may be similar in both rabbit olfactory bulb and h u m a n neocortex. Note that h u m a n bursts peak near 105 Hz with rabbit burst peak near 65 Hz.
could be distinguished as volume conducted or propagated activity. (1) For a trial for which more than one burst was identified, bursts were defined as 'similar' if differences in both their latencies and their frequencies were less than set thresholds. These thresholds were varied from 10 to 60 msec for latency and from 6 to 30 Hz for frequency; for each combination of thresholds, the percentage of
H I G H F R E Q U E N C Y SCALP POTENTIALS EVOKED BY RT TASK
pairs for which the earlier burst had the greater amplitude was tabulated. The amplitude value used was normalized by dividing the measured amplitude by the average amplitude at that electrode placement. For both sRT and cRT bursts these percentages were ufiiformly greater than the value expected by chance, i.e., 50%. Moreover, there was a distinct peak for thresholds of 12 Hz and 30 msec for sRT bursts and 16 Hz and 25 msec for cRT bursts. These thresholds were therefore taken as criteria of 'similarity;' the fraction of bursts which were 'similar' to other bursts but longer in latency was 0.22 for sRT and 0.24 for cRT. 'Similar' bursts tended to occur in adjacent electrodes within the same hemisphere and across the midline for the homologous pairs F 3 / F 4 and O1/O2, indicating that volume conduction may be responsible for much of the observed 'similarity.' Increased occurrence of 'similar' bursts was also noted for T3/T4 and for several widely separated non-homologous electrode pairs: F3/O1, F4/O2,
225
F7/T4, T3/T4, and T3/T6, perhaps reflecting propagated activity via long-distance pathways. (2) For each electrode the question was asked: 'how often do bursts found at this electrode occur earlier than those to which they are similar?' The value which would be expected by chance is 50%; results of computation of X2 statistics for the observed percentages are shown in Fig. 2. These results suggest that medial frontal tissue tends to be a burst source, propagating activity which is observed elsewhere a short time later. It was anticipated that comparisons between sRT and cRT bursts might be useful if bursts could be identified for both task types which had the same functional relationship to the response. This expectation coupled with the observation that average cRT was approximately 140.0 msec greater than average sRT led to the following selection process: for cRT, bursts were divided into 2
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a,'ametervalue• grandmeanI Parametervalue< grandmeanF-~ Fig. 3. Topographic distribution of burst count deviations and burst amplitude deviations. Values shown are deviations at each placement from the grand mean for all bursts. Distributions are for LcRT; those for sRT and EcRT were nearly identical. Solid bars represent values higher than the grand mean; hollow bars represent values below it. The lack of covariance between burst counts and burst amplitude suggests that muscle activity was not the primary source of the observed signals.
226
D. KRIEGER, M. DILLBECK
TABLE i Summary statistics: RT and burst parameters. Mean RT was pooled over all trials. For cRT, bursts were divided into 2 groups: those whose latency was longer than the cut-off for sRT, i.e., late bursts (LcRT), and those whose latency was shorter, i.e., early bursts (EcRT). Mean burst parameters were computed for each subject; maxima and minima are shown. sRT
cRT
Trials presented Left hand Right hand Both hands
2032 1982 4014
1 982 1 856 3 838
Trials retained Left hand Right hand Both hands
1124 1 113 2237
907 911 1 818
Mean RT (msec) 276.4
Bursts identified Bursts/trial Bursts/sec
412.0
sRT
EcRT
LcRT
All cRT
3328 1.49 10.57
4126 2.27
2320 1.28
6446 3.55 12.43
sRT Mean burst parameters Latency (msec) Amplitude (~tV) Frequency (Hz)
EcRT
LcRT
Min
Max
Min
Max
Min
Max
80.8 2.2 80.3
107.8 4.5 93.9
93.9 2.5 79.0
106.0
202.0 2.7 83.6
241.7 5.9 94.1
groups: those whose latency was longer than the cut-off for sRT, i.e., late bursts (LcRT, n = 2320), and those whose latency was shorter, i.e., early bursts (EcRT, n = 4126). This p r o d u c e d groups of bursts (sRT and LcRT) which were comparable in latency with respect to the response, both having mean latency approximately 180 msec prior to the corresponding average R T (Table I). Burst parameter means pooled over all subjects and sessions were compiled for each combination of electrode placement and trial type. The topographic distributions of these parameters for L c R T are shown in Fig. 3. T3 and T4 are placements near likely sources of muscle activity. Although mean amplitude at these placements taken together was higher than at other locations (t = 11.69, P < 0.0001), the n u m b e r of bursts identified there was well below the average (t = - 6 . 6 4 , P < 0.001). Nearly identical distributions and P values were found for sRT. This marked lack of covariance between burst counts and burst ampli-
5.8 94.4
tude suggests that muscle activity is not primary source of the observed signals.
the
Relationships between R T and burst parameters Multiple regressions of R T vs. burst parameters were c o m p u t e d for each combination of subject and task type (pooled over all electrodes) and for each combination of electrode and task type (pooled over all subjects). Prior to regression computation, RT, burst latency and burst amplitude were demeaned and detrended with respect to trial number. Trends in amplitude vs. frequency were also removed. Residual interdependence of R T observations was checked for each combination of subject, session, and trial type using the Q statistic (Ljung and Box 1978) and associated P value of the autocorrelation function (Bendat and Piersol 1980) c o m p u t e d to lag 12. For cRT, 4 out of 32 Qs were significant at P < 0.05 while for sRT, 13 out of 32 were significant. Thus bias due to correlated observations for regressions in which R T
H I G H F R E Q U E N C Y SCALP P O T E N T I A L S E V O K E D BY R T T A S K
was the dependent variable were negligible for c R T a n d modest for sRT. The dependence of RT on burst latency, RT(lat), was particularly robust, yielding positive parameter estimates and significant P values in all cases. Results for each task pooled over all subjects and electrodes were as follows. For sRT, regression parameter estimates with associated t statistics were 0.342 (t = 20.51, P < 0.0001) for burst latency, 1.66 (t = 4.02, P < 0.001) for amplitude, 1.03 (t = 0.84, P > 0.1) for 'side,' and 0.631 (t = 0.5, P > 0.1) for 'hand.' Estimates for LcRT were 0.343 (t = 17.13, P < 0.0001) for latency, 1.39 (t = 2.78, P < 0.01) for amplitude, 4.28 (t = 1.97, P (one-tailed) < 0.025) for 'side,' and -0.574 (t = -0.339, P > 0.1) for 'hand.' 'Hand' was defined as zero for bursts from trials requiring response with the right hand and one for the left. 'Side' was defined as zero for a burst if it occurred contralateral to the responding hand and one if not. The dependence of RT on 'side,' RT(side) 3, was as would be predicted if bursts were mediating the task, i.e., response was faster if the burst was on the same side as the motor cortex controlling the responding hand. Furthermore, the regression parameter estimate was near 12 msec for all individual electrode placements at which RT(side) was significant with P < 0.05 (P3, T4, F7 for sRT; F3 for cRT). This was the same delay as has been reported for response to a somatosensory stimulus delivered ipsilaterally vs. contrallaterally to the responding hand (Schieppati et al. 1984). The robust significance of RT(lat) coupled with the laterality finding represented by the significance of RT(side) supported the hypothesis that there is a relationship between parameters of high frequency activity and task performance. These findings, the analysis of bursts which occur in multiple electrodes (Fig. 2), and the topographic distributions of burst parameters (Fig. 3) are most parsimoniously interpretable as arising from neural activity, providing substantive evidence that
3 It is possible that this result was artifactually produced by referencing all EEG placements to the contralateral ear, i.e., muscle activity could be appearing consistently faster on the side ipsilateral to the responding hand and might be sensed by the ear electrodes.
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muscle activity was not the primary source of the observed signals.
Post-hoc analysis The positive sign of the dependence of RT on burst amplitude, RT(amp), indicating that RT was slower when burst amplitude was greater, was opposite to the simplest model of task mediation, i.e., greater activation, indicated by greater amplitude, produces faster response 4. To explore the unexpected positive value of RT(amp), it was computed for each day; results are shown in Table II. Note that cRT(amp) dropped markedly between days and there was a parallel, significant drop in mean cRT, suggesting that the betweendays change in cRT(amp) might be associated with learning. There was no drop, however, in sRT(amp), while there was a significant though modest improvement in performance. To test for a decrease in sRT(amp) comparable to that noted for cRT(amp), two subjects were recalled for a third testing session (60 days had passed) with sRT trials only. Table II shows that this subgroup was similar to the group as a whole for days 1 and 2 while for day 3, sRT(amp) felt to near zero accompanied by a marked improvement in performance, paralleling the findings for cRT. Although this raised questions regarding the influence of a 2 month delay between sessions as well as the change in protocol to sRT task presentation only, the result was consistent with the ' learning' interpretation. Encouraged by these results additional relationships were sought between burst parameters and changes in performance interpretable as learning. For purposes of comparison, trials were allocated to 2 groups according to operational definitions which have been used previously (Mackworth 4 It has been noted in direct recordings from the olfactory system (Freeman 1975; Bressler 1984) that burst amplitude increases with behavioral activation. The same was indicated here by consistent increases in amplitude with burst latency. This presumes that behavioral activation increases as the moment of response approaches. This relationship was marginally significant for EcRT (0.0011 # V / m s e c , df= 4125, t =1.35, P = 0.085) and LcRT (0.0009 /.tV/msec, df = 2321, t = 1.4, P = 0.08), but was robust when both were combined (0.0010 # V / m s e c , df = 6445, t = 3.42, P = 0.0006).
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D. K R I E G E R , M. D I L L B E C K
T A B L E 11
Changes between days in RT and RT(amp). sRT-8 refers to results for all sRT trials; sRT-2 refers to results for the subgroup of 2 subjects for which there were measurements on 3 days. The R T for each trial was converted to the difference from the mean RT for that subject. M e a n d e v i a t i o n s are shown for each day with t statistics and associated P values for changes. R T ( a m p ) refers to the t statistic and associated P value for the regression parameter relating RT and burst amplitude. Independent sample t tests were used rather than the more powerful dependent sample tests applicable to paired observations. Therefore the P values obtained were conservative. Days
1
2
3
1~2
2--*3
Deviation of R T (msec) from the mean with associated t statistics, P values cRT sRT-8 sRT-2
6.8 3.4 7.4
-7.1 0.1 6.6
4.07 * * *
1.98 * - 6.4
4.25 * * *
0.22
t statistics for R T(amp) with associated P values" cRT sRT-8 sRT-2
2.38 * 2.51 * 2.22 *
1.45 4.00 * * * 2.20 *
0.22
* P < 0.05, ** P < 0.01, * * * P < 0.001.
1964) for learning vs. vigilance decrement (inattentiveness), viz., negative vs. positive trends in RT. Regression of RT vs. trial number, RT(trial), was computed for each combination of subject, session, and task type. A negative value for RT(trial) was assumed to indicate learning while a positive value indicated vigilance decrement. Only those sessions were included for which the t statistic for RT(trial) was greater than 2.0 or less than -1.0. The more liberal threshold for negative values was used to obtain comparable numbers of bursts for both groups. For each group, RT(lat) and RT(amp) were computed for bursts at each electrode placement and then normalized into an effect size independent of sample size by dividing the t statistic of the parameter estimate by the square root of the number of bursts at that electrode. Results are shown in Fig. 4. Note that RT(lat) appears more widespread or homogeneous in the inattentive condition for both sRT and cRT. In support of this observation, the variability across electrode placements for both RT(lat) and RT(amp) increased from the distracted to the learn condition for both task types. This coupled with the subsequent finding, detailed below, that burst rate was significantly lower in the 'learn' vs. the 'vigilance decrement' group for both trial types suggested that cortical reactivity may be locally inhibited during' learning.'
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decrement' indicate sessions for which decreasing or increasing trend respeceach bar indicates how well R T was predicted by the latency of bursts at that electrode (effect size independent of sample size); the width indicates the associated P value.
HIGH FREQUENCY SCALP POTENTIALS EVOKED BY RT TASK
sRT: 11.3 vs. 12.7 bursts/sec; X2 (df: 2) = 26.9; P << 0.001. cRT: 9.7 vs. 12.2 bursts/sec; X2 (df: 2) = 23.5; P << 0.001. An alternative explanation of reduced burst rate during 'learning' is suggested in a recent review of olfactory burst dynamics (Freeman and Skarda 1985). They note that 'disorderly' bursts, i.e., bursts which show a broad rather than a sharp spectral peak, are produced in response to novel stimuli and are consistently followed by orienting for several additional presentations. Because the identification algorithm which we used is less efficient when applied to 'disorderly' bursts (unpublished data), and because increased attentiveness induced by orienting might be expected to produce the performance improvements which we found, an apparent reduction in burst rate might be expected to accompany 'learning.' This explanation is also consistent with the delay in performance improvement for sRT (third testing session) compared with cRT (second testing session): one subject reported that during the first two testing sessions, he was more attentive to the choice task. However, he paid close attention during the third session, when he was tested with sRT trials only.
Discussion The results of this study support the hypothesis that neural cell populations which produce high frequency scalp potentials also mediate visual task performance. Key findings included (a) similarity between burst frequency histograms of rabbit olfactory bulb and human scalp, (b) robust dependence of reaction time (RT) on burst latency, (c) a significant delay in choice RT when bursts occurred ipsilateral vs. contralateral to the responding hand, and (d) an unexpected positive covariance of RT and burst amplitude (RT(amp)). Exploration of result (d) produced additional findings, viz. (e) a marked reduction in RT(amp) from one day to the next accompanied by a significant improvement in task performance and (f) a significant reduction in burst rate during 'learn' vs. 'vigilance decrement' sessions. Although the inter-
229
pretability of these latter findings is limited by their post-hoc nature, results of this report suggest that further study of high frequency EEG with interpretation in the context of known olfactory bulb dynamics may elucidate not only brain mechanisms mediating task performance but also changes in performance associated with both attention and learning. We gratefully acknowledge the direction and criticism of Alan Gevins at the early stages, the help with the manuscript of Ken Walton and David Orme-Johnson, and particularly the cooperation of the MIU computing center staff, without which this work would have been impossible.
References Bendat, J. and Piersol, A. Engineering Applications of Correlation and Spectral Analysis. Wiley, New York, 1980. Bressler, S. Spatial organization of EEGs from olfactory bulb and cortex. Eiectroenceph. clin. Neurophysiol., 1984, 57: 270-276. Freeman, W. Mass Action in the Nervous System. Academic Press, New York, 1975. Freeman, W. Non-linear gain mediating cortical stimulus-response relations. Biol. Cybernet., 1979a, 33: 237-247. Freeman, W. Nonlinear dynamics of paleocortex manifested in the olfactory EEG. Biol. Cybernet., 1979b, 35: 21-37. Freeman, W. EEG analysis gives model of neuronal templatematching mechanism for sensory search with olfactory bulb. Biol. Cybernet., 1979c, 35: 221-235. Freeman, W. and Di Prisco, G. EEG spatial pattern differences with discriminated odors manifest chaotic and limit cycle attractors in olfactory bulb of rabbits. In: Proc. Conf. on Brain Theory, Trieste, Italy, 11/84. Springer, Berlin, 1986: 97-119. Freeman, W. and Schneider, W. Changes in spatial patterns of rabbit olfactory EEG with conditioning to odors. Psychophysiology, 1982, 19: 44-56. Freeman, W. and Skarda, C. Spatial EEG patterns, non-linear dynamics and perception: the neo-sherringtonian view. Brain Res. Rev., 1985, 10: 147-175. Hamming, R.W. Digital Filters. Prentice Hall, Englewood Cliffs, NJ, 1983. Krieger, D. and Larimore W. Automatic enhancement of single evoked potentials. Electroenceph. clin. Neurophysiol., 1986, 64: 568-572. Larimore, W. System identification, reduced-order filtering and modeling via canonical variate analysis. In: Proc. 1983 American Control Conference. IEEE, New York, 1983. Larimore, W. Simultaneous confidence bands for efficient parametric multivariate spectral estimation. Biometrika, 1986, in press. Larimore, W., Mahmood, S. and Mehra, R. Multivariable
230 adaptive model algorithmic control. In: Proc. 23rd Conf. on Decision and Control. IEEE, New York, 1984. Ljung, G. and Box, G. On a measure of lack of fit in time series models. Biometrika, 1978, 65: 297-304. Mackworth, J.F. Performance decrement in vigilance, threshold,
D. KRIEGER, M. D1LLBECK and high-speed perceptual motor tasks. Canad. J. Psychol.. 1964, 18: 209-223. Schieppati, M., Musazm, M., Nardone, A. and Seveso, (3. Interhemispheric transfer of voluntary motor commands in man. Electroenceph. clin. Neurophysiol, 1984, 57: 441-447.
Electroencephalography and cfinical Neurophysiology, 1987, 67:222-230 Elsevier Scientific Publishers Ireland, Ltd.
EEG 03307
Experimental Section High frequency scalp potentials evoked by a reaction time task Don Krieger * and Michael Dillbeck * * • Department of Neurosurgery, Children's Hospital, Pittsburgh, PA 15213 (U.S.A.), and * * Department of Psychology, Maharishi International University, Fairfield, 1A 52556 (U.S.A.) (Accepted for publication: 12 January, 1987)
Summary
'Bursts' of high frequency (20-80 Hz) extracellular electrical activity are the signature of the brain mechanism mediating recognition of odors in rabbits and cats. To test the hypothesis that a similar mechanism may be functional in man outside the olfactory system, relationships were studied between bursts of 20-150 Hz scalp EEG and parameters of performance during visual reaction time tasks. Specific findings indicated that (1) muscle artifacts were not the primary source of identified EEG bursts, (2) the mechanism which produces the bursts may be similar in both rabbit olfactory bulb and human neocortex, (3) visual task peformance may be mediated by the brain areas which produced the bursts, and (4) burst activity varied with changes in performance which may be associated with attention and learning.
Key words: Evoked potential; Attention; Learning; Visual; Motor
In both the rabbit and cat, respiratory inspiration is accompanied by 'bursts' of synchronous 20-80 Hz electrical activity, observable throughout the olfactory system in extracellular recordings (Freeman 1975). Multi-dimensional analytic techniques applied to burst recordings from the olfactory bulb of the rabbit have shown that the differential response to presentation of one or the other of two expected odors could be predicted with greater than 80% accuracy (Freeman and Di Prisco 1986). In addition, Freeman and his coworkers have developed a physiological model of the underlying processes (Freeman 1975, 1979a, b, c) and have produced experimental verification of many of the model's features (Freeman 1975; Freeman and Schneider 1982; Freeman and Skarda 1985). The burst mechanism, apparently capable of mediating recognition of the pattern of sensory input corresponding to an odor, is an attractive
candidate as a mediator of pattern recognition in other processes. If it were generally functional outside the olfactory system, short duration bursts of high frequency activity would be occurring constantly during waking activity and might be evoked in stereotypic areas for selected tasks. In order to test this possibility the scalp EEG recorded between stimulus and response during visual-motor task performance was searched for sinusoidal bursts. Burst parameters, particularly latency, were then tested for their ability to predict reaction time (RT). Thus the primary hypothesis addressed by this work is: 'there is a relationship between parameters of high frequency activity and task performance parameters.' Because of resolution limitations obtainable with scalp recordings, spatial patterns were only interpreted in the context of burst source localization.
Methods Correspondence to: Don Krieger, Department of Neurosurgery, Children's Hospital, 125 Desoto Street, Pittsburgh, PA 15213 (U.S.A.).
Subjects were 8 right-handed men between ages 24 and 44. Each was thoroughly familiarized with the procedure during the week before the experi-
0013-4649/87/$03.50 © 1987 Elsevier Scientific Publishers Ireland, Ltd.
HIGH FREQUENCY SCALP POTENTIALS EVOKED BY RT TASK ment. Then on each of 2 consecutive days trials were presented in 2 sessions of twelve 1 min sets. These were separated by a 15 min eyes-closed period. Within each session, 1 min trial sets were separated by 15 sec eyes-closed rest periods. During trial presentation the subject sat with his eyes fixed to a marker on a computer monitor and with his index finger(s) positioned on response key(s). Response required a minimum weight of 65 g and a minimum motion of 2 mm. At random intervals ranging from 1.5 to 2.5 sec inter-trial interval, the fixation marker was replaced by an arrow pointing left or right to which response was required with the finger of the corresponding hand. Thus there were 20-25 trials/set. For the simple task (sRT), an entire trial set required response with a single hand, left or right. For the choice task (cRT), the arrow direction and responding hand changed from trial to trial in random order. The stimulus character subtended a visual angle of approximately 0.5 o × 0.5 o. The EEG was digitized at 600 Hz/channel from 10/20 system placements O1, 02, P3, P4, Pz, T3, T4, T5, T6, C3, C4, F3, F4, F7, F8. An additional digitized channel was used to monitor the voltage across a photo-resistor, positioned to detect the stimulus appearance at the terminal screen. This provided RT measurement resolution of 1.7 msec. Each EEG placement was referenced to the contralateral ear in order to maximize signal amplitude. The montage, shown in Fig. 3, was applied using an elastic cap with tin cup electrodes placed in it. Impedances were maintained below 5000 I2. Signals were amplified by a factor of 20,000 with high and low pass filters set at 0.3 and 100 Hz respectively. No line frequency notch filtering was used. Data acquisition began 0.5 sec prior to stimulus presentation and continued for a total of 1.06 sec for each trial. Trials in which eye blink or movement artifacts were evident in the polygraph record on visual examination were excluded from analysis. The EEG is typically on the order of tens of microvolts at the scalp while the amplitude of burst activity was expected to be at least an order of magnitude less. In order to enhance the ability to identify and study features of single-trial evoked potentials (sEPs), a procedure was used for identi-
223
fying and removing the ongoing background EEG (Krieger and Larimore 1986). For each trial, the technique was applied as follows. An optimal system identification technique (Larimore 1983), called CVA, was applied to the prestimulus data for 2 electrode placements at a time. CVA is a multivariate time series analysis technique formulated as a state space model whose fundamental assumption is that the error terms in the model are gaussian white noise. Each of the resulting bivariate models was used to forecast poststimulus activity at the corresponding pair of placements. For each pair of forecasts, the forecast errors, i.e., the differences between the forecasts and the observed signals, were taken as the sEPs for the corresponding channels. In tests with both constructed and pilot data we found CVA to be highly effective in detecting sinusoids in noise. Larimore (1986) has derived an expression for the lower bound on the expected integral of the relative squared error in computing spectral estimates and has found in Monte Carlo simulations (Larimore et al. 1984) that such estimates computed using CVA were near this bound. Therefore in addition to its use as described above for modeling the prestimulus data, CVA was also used to search for bursts, sEPs were searched one electrode placement at a time by repeated application of CVA to 100 msec epochs beginning with the stimulus presentation, stepping 50 msec at a time, and ending with the response. Resonances of the resultant models provided measures of burst frequencies while burst latency and amplitude were estimated using complex demodulation at the measured frequency (Hamming 1983) as follows. The peak of the amplitude ~emodulate was identified, its values used for the amplitude of the burst 1, and burst latency taken as the point preceding the peak at which the first difference was maximum. The sequence of steps in identifying and quantifying burst activity is summarized as follows: (a)
1 Equipment calibration showed that attenuation of signals above 55 Hz by analogue low pass filtering was closely approximated by the factor: frequency/55. As compensation, burst amplitudeestimates were multipliedby this factor.
224
D. K R I E G E R , M. D I L L B E C K
the sEP for each trial at each electrode placement was computed, (b) each sEP was searched for sinusoids, (c) the latency, amplitude and frequency of each 'burst' were estimated, and (d) for each identified burst a record was made which included burst parameter estimates and RT for the trial in which it occurred. The analysis of this reduced data set was carried out as follows: (a) descriptive statistics were examined, (b) multiple regressions were computed to test for systematic relationships between burst parameters and RT, and (c) post-hoc tests were devised to explore possible changes in burst-RT relationships which might be associated with learning or attention.
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Descriptive statistics Mean sRT averaged over all subjects and trials was 276.4 msec; mean cRT was 412.0. The exclusion of artifact-contaminated trials from the burst search procedure resulted in (trials presented)/ (trials retained) ratios of 4014/2237 for sRT and 3838/1818 for cRT. For the sRT trials 3328 bursts were identified; for the cRT trials 6446 bursts were identified 2. Burst latency histograms decreased monotonically with maxima at short latencies. Amplitude histograms were unimodal and skewed, showing an extended tail towards the high end of the distribution. Frequency histograms, as shown in Fig. 1 (lower panels), were bimodal with major peak near 105 Hz and minor peak near 30 Hz. Frequency histograms compiled from rabbit olfactory bursts (Freeman and Di Prisco 1986), shown in Fig. 1 (upper panel), are similar in shape with minor peak near 30 Hz but with the major peak near 65 Hz. Because large numbers of bursts were identified in all electrodes, an attempt was made to determine (1) to what extent bursts with similar properties appeared in more than one electrode at a time, and (2) whether such multiple appearances
2 From visual examination of histograms for RT, burst latency and amplitude, cut-offs were established to exclude outlier observations which gave the curves a peaked tail
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could be distinguished as volume conducted or propagated activity. (1) For a trial for which more than one burst was identified, bursts were defined as 'similar' if differences in both their latencies and their frequencies were less than set thresholds. These thresholds were varied from 10 to 60 msec for latency and from 6 to 30 Hz for frequency; for each combination of thresholds, the percentage of
H I G H F R E Q U E N C Y SCALP POTENTIALS EVOKED BY RT TASK
pairs for which the earlier burst had the greater amplitude was tabulated. The amplitude value used was normalized by dividing the measured amplitude by the average amplitude at that electrode placement. For both sRT and cRT bursts these percentages were ufiiformly greater than the value expected by chance, i.e., 50%. Moreover, there was a distinct peak for thresholds of 12 Hz and 30 msec for sRT bursts and 16 Hz and 25 msec for cRT bursts. These thresholds were therefore taken as criteria of 'similarity;' the fraction of bursts which were 'similar' to other bursts but longer in latency was 0.22 for sRT and 0.24 for cRT. 'Similar' bursts tended to occur in adjacent electrodes within the same hemisphere and across the midline for the homologous pairs F 3 / F 4 and O1/O2, indicating that volume conduction may be responsible for much of the observed 'similarity.' Increased occurrence of 'similar' bursts was also noted for T3/T4 and for several widely separated non-homologous electrode pairs: F3/O1, F4/O2,
225
F7/T4, T3/T4, and T3/T6, perhaps reflecting propagated activity via long-distance pathways. (2) For each electrode the question was asked: 'how often do bursts found at this electrode occur earlier than those to which they are similar?' The value which would be expected by chance is 50%; results of computation of X2 statistics for the observed percentages are shown in Fig. 2. These results suggest that medial frontal tissue tends to be a burst source, propagating activity which is observed elsewhere a short time later. It was anticipated that comparisons between sRT and cRT bursts might be useful if bursts could be identified for both task types which had the same functional relationship to the response. This expectation coupled with the observation that average cRT was approximately 140.0 msec greater than average sRT led to the following selection process: for cRT, bursts were divided into 2
Burst P a r a m e t e r s - L c R T Counts
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a,'ametervalue• grandmeanI Parametervalue< grandmeanF-~ Fig. 3. Topographic distribution of burst count deviations and burst amplitude deviations. Values shown are deviations at each placement from the grand mean for all bursts. Distributions are for LcRT; those for sRT and EcRT were nearly identical. Solid bars represent values higher than the grand mean; hollow bars represent values below it. The lack of covariance between burst counts and burst amplitude suggests that muscle activity was not the primary source of the observed signals.
226
D. KRIEGER, M. DILLBECK
TABLE i Summary statistics: RT and burst parameters. Mean RT was pooled over all trials. For cRT, bursts were divided into 2 groups: those whose latency was longer than the cut-off for sRT, i.e., late bursts (LcRT), and those whose latency was shorter, i.e., early bursts (EcRT). Mean burst parameters were computed for each subject; maxima and minima are shown. sRT
cRT
Trials presented Left hand Right hand Both hands
2032 1982 4014
1 982 1 856 3 838
Trials retained Left hand Right hand Both hands
1124 1 113 2237
907 911 1 818
Mean RT (msec) 276.4
Bursts identified Bursts/trial Bursts/sec
412.0
sRT
EcRT
LcRT
All cRT
3328 1.49 10.57
4126 2.27
2320 1.28
6446 3.55 12.43
sRT Mean burst parameters Latency (msec) Amplitude (~tV) Frequency (Hz)
EcRT
LcRT
Min
Max
Min
Max
Min
Max
80.8 2.2 80.3
107.8 4.5 93.9
93.9 2.5 79.0
106.0
202.0 2.7 83.6
241.7 5.9 94.1
groups: those whose latency was longer than the cut-off for sRT, i.e., late bursts (LcRT, n = 2320), and those whose latency was shorter, i.e., early bursts (EcRT, n = 4126). This p r o d u c e d groups of bursts (sRT and LcRT) which were comparable in latency with respect to the response, both having mean latency approximately 180 msec prior to the corresponding average R T (Table I). Burst parameter means pooled over all subjects and sessions were compiled for each combination of electrode placement and trial type. The topographic distributions of these parameters for L c R T are shown in Fig. 3. T3 and T4 are placements near likely sources of muscle activity. Although mean amplitude at these placements taken together was higher than at other locations (t = 11.69, P < 0.0001), the n u m b e r of bursts identified there was well below the average (t = - 6 . 6 4 , P < 0.001). Nearly identical distributions and P values were found for sRT. This marked lack of covariance between burst counts and burst ampli-
5.8 94.4
tude suggests that muscle activity is not primary source of the observed signals.
the
Relationships between R T and burst parameters Multiple regressions of R T vs. burst parameters were c o m p u t e d for each combination of subject and task type (pooled over all electrodes) and for each combination of electrode and task type (pooled over all subjects). Prior to regression computation, RT, burst latency and burst amplitude were demeaned and detrended with respect to trial number. Trends in amplitude vs. frequency were also removed. Residual interdependence of R T observations was checked for each combination of subject, session, and trial type using the Q statistic (Ljung and Box 1978) and associated P value of the autocorrelation function (Bendat and Piersol 1980) c o m p u t e d to lag 12. For cRT, 4 out of 32 Qs were significant at P < 0.05 while for sRT, 13 out of 32 were significant. Thus bias due to correlated observations for regressions in which R T
H I G H F R E Q U E N C Y SCALP P O T E N T I A L S E V O K E D BY R T T A S K
was the dependent variable were negligible for c R T a n d modest for sRT. The dependence of RT on burst latency, RT(lat), was particularly robust, yielding positive parameter estimates and significant P values in all cases. Results for each task pooled over all subjects and electrodes were as follows. For sRT, regression parameter estimates with associated t statistics were 0.342 (t = 20.51, P < 0.0001) for burst latency, 1.66 (t = 4.02, P < 0.001) for amplitude, 1.03 (t = 0.84, P > 0.1) for 'side,' and 0.631 (t = 0.5, P > 0.1) for 'hand.' Estimates for LcRT were 0.343 (t = 17.13, P < 0.0001) for latency, 1.39 (t = 2.78, P < 0.01) for amplitude, 4.28 (t = 1.97, P (one-tailed) < 0.025) for 'side,' and -0.574 (t = -0.339, P > 0.1) for 'hand.' 'Hand' was defined as zero for bursts from trials requiring response with the right hand and one for the left. 'Side' was defined as zero for a burst if it occurred contralateral to the responding hand and one if not. The dependence of RT on 'side,' RT(side) 3, was as would be predicted if bursts were mediating the task, i.e., response was faster if the burst was on the same side as the motor cortex controlling the responding hand. Furthermore, the regression parameter estimate was near 12 msec for all individual electrode placements at which RT(side) was significant with P < 0.05 (P3, T4, F7 for sRT; F3 for cRT). This was the same delay as has been reported for response to a somatosensory stimulus delivered ipsilaterally vs. contrallaterally to the responding hand (Schieppati et al. 1984). The robust significance of RT(lat) coupled with the laterality finding represented by the significance of RT(side) supported the hypothesis that there is a relationship between parameters of high frequency activity and task performance. These findings, the analysis of bursts which occur in multiple electrodes (Fig. 2), and the topographic distributions of burst parameters (Fig. 3) are most parsimoniously interpretable as arising from neural activity, providing substantive evidence that
3 It is possible that this result was artifactually produced by referencing all EEG placements to the contralateral ear, i.e., muscle activity could be appearing consistently faster on the side ipsilateral to the responding hand and might be sensed by the ear electrodes.
227
muscle activity was not the primary source of the observed signals.
Post-hoc analysis The positive sign of the dependence of RT on burst amplitude, RT(amp), indicating that RT was slower when burst amplitude was greater, was opposite to the simplest model of task mediation, i.e., greater activation, indicated by greater amplitude, produces faster response 4. To explore the unexpected positive value of RT(amp), it was computed for each day; results are shown in Table II. Note that cRT(amp) dropped markedly between days and there was a parallel, significant drop in mean cRT, suggesting that the betweendays change in cRT(amp) might be associated with learning. There was no drop, however, in sRT(amp), while there was a significant though modest improvement in performance. To test for a decrease in sRT(amp) comparable to that noted for cRT(amp), two subjects were recalled for a third testing session (60 days had passed) with sRT trials only. Table II shows that this subgroup was similar to the group as a whole for days 1 and 2 while for day 3, sRT(amp) felt to near zero accompanied by a marked improvement in performance, paralleling the findings for cRT. Although this raised questions regarding the influence of a 2 month delay between sessions as well as the change in protocol to sRT task presentation only, the result was consistent with the ' learning' interpretation. Encouraged by these results additional relationships were sought between burst parameters and changes in performance interpretable as learning. For purposes of comparison, trials were allocated to 2 groups according to operational definitions which have been used previously (Mackworth 4 It has been noted in direct recordings from the olfactory system (Freeman 1975; Bressler 1984) that burst amplitude increases with behavioral activation. The same was indicated here by consistent increases in amplitude with burst latency. This presumes that behavioral activation increases as the moment of response approaches. This relationship was marginally significant for EcRT (0.0011 # V / m s e c , df= 4125, t =1.35, P = 0.085) and LcRT (0.0009 /.tV/msec, df = 2321, t = 1.4, P = 0.08), but was robust when both were combined (0.0010 # V / m s e c , df = 6445, t = 3.42, P = 0.0006).
228
D. K R I E G E R , M. D I L L B E C K
T A B L E 11
Changes between days in RT and RT(amp). sRT-8 refers to results for all sRT trials; sRT-2 refers to results for the subgroup of 2 subjects for which there were measurements on 3 days. The R T for each trial was converted to the difference from the mean RT for that subject. M e a n d e v i a t i o n s are shown for each day with t statistics and associated P values for changes. R T ( a m p ) refers to the t statistic and associated P value for the regression parameter relating RT and burst amplitude. Independent sample t tests were used rather than the more powerful dependent sample tests applicable to paired observations. Therefore the P values obtained were conservative. Days
1
2
3
1~2
2--*3
Deviation of R T (msec) from the mean with associated t statistics, P values cRT sRT-8 sRT-2
6.8 3.4 7.4
-7.1 0.1 6.6
4.07 * * *
1.98 * - 6.4
4.25 * * *
0.22
t statistics for R T(amp) with associated P values" cRT sRT-8 sRT-2
2.38 * 2.51 * 2.22 *
1.45 4.00 * * * 2.20 *
0.22
* P < 0.05, ** P < 0.01, * * * P < 0.001.
1964) for learning vs. vigilance decrement (inattentiveness), viz., negative vs. positive trends in RT. Regression of RT vs. trial number, RT(trial), was computed for each combination of subject, session, and task type. A negative value for RT(trial) was assumed to indicate learning while a positive value indicated vigilance decrement. Only those sessions were included for which the t statistic for RT(trial) was greater than 2.0 or less than -1.0. The more liberal threshold for negative values was used to obtain comparable numbers of bursts for both groups. For each group, RT(lat) and RT(amp) were computed for bursts at each electrode placement and then normalized into an effect size independent of sample size by dividing the t statistic of the parameter estimate by the square root of the number of bursts at that electrode. Results are shown in Fig. 4. Note that RT(lat) appears more widespread or homogeneous in the inattentive condition for both sRT and cRT. In support of this observation, the variability across electrode placements for both RT(lat) and RT(amp) increased from the distracted to the learn condition for both task types. This coupled with the subsequent finding, detailed below, that burst rate was significantly lower in the 'learn' vs. the 'vigilance decrement' group for both trial types suggested that cortical reactivity may be locally inhibited during' learning.'
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decrement' indicate sessions for which decreasing or increasing trend respeceach bar indicates how well R T was predicted by the latency of bursts at that electrode (effect size independent of sample size); the width indicates the associated P value.
HIGH FREQUENCY SCALP POTENTIALS EVOKED BY RT TASK
sRT: 11.3 vs. 12.7 bursts/sec; X2 (df: 2) = 26.9; P << 0.001. cRT: 9.7 vs. 12.2 bursts/sec; X2 (df: 2) = 23.5; P << 0.001. An alternative explanation of reduced burst rate during 'learning' is suggested in a recent review of olfactory burst dynamics (Freeman and Skarda 1985). They note that 'disorderly' bursts, i.e., bursts which show a broad rather than a sharp spectral peak, are produced in response to novel stimuli and are consistently followed by orienting for several additional presentations. Because the identification algorithm which we used is less efficient when applied to 'disorderly' bursts (unpublished data), and because increased attentiveness induced by orienting might be expected to produce the performance improvements which we found, an apparent reduction in burst rate might be expected to accompany 'learning.' This explanation is also consistent with the delay in performance improvement for sRT (third testing session) compared with cRT (second testing session): one subject reported that during the first two testing sessions, he was more attentive to the choice task. However, he paid close attention during the third session, when he was tested with sRT trials only.
Discussion The results of this study support the hypothesis that neural cell populations which produce high frequency scalp potentials also mediate visual task performance. Key findings included (a) similarity between burst frequency histograms of rabbit olfactory bulb and human scalp, (b) robust dependence of reaction time (RT) on burst latency, (c) a significant delay in choice RT when bursts occurred ipsilateral vs. contralateral to the responding hand, and (d) an unexpected positive covariance of RT and burst amplitude (RT(amp)). Exploration of result (d) produced additional findings, viz. (e) a marked reduction in RT(amp) from one day to the next accompanied by a significant improvement in task performance and (f) a significant reduction in burst rate during 'learn' vs. 'vigilance decrement' sessions. Although the inter-
229
pretability of these latter findings is limited by their post-hoc nature, results of this report suggest that further study of high frequency EEG with interpretation in the context of known olfactory bulb dynamics may elucidate not only brain mechanisms mediating task performance but also changes in performance associated with both attention and learning. We gratefully acknowledge the direction and criticism of Alan Gevins at the early stages, the help with the manuscript of Ken Walton and David Orme-Johnson, and particularly the cooperation of the MIU computing center staff, without which this work would have been impossible.
References Bendat, J. and Piersol, A. Engineering Applications of Correlation and Spectral Analysis. Wiley, New York, 1980. Bressler, S. Spatial organization of EEGs from olfactory bulb and cortex. Eiectroenceph. clin. Neurophysiol., 1984, 57: 270-276. Freeman, W. Mass Action in the Nervous System. Academic Press, New York, 1975. Freeman, W. Non-linear gain mediating cortical stimulus-response relations. Biol. Cybernet., 1979a, 33: 237-247. Freeman, W. Nonlinear dynamics of paleocortex manifested in the olfactory EEG. Biol. Cybernet., 1979b, 35: 21-37. Freeman, W. EEG analysis gives model of neuronal templatematching mechanism for sensory search with olfactory bulb. Biol. Cybernet., 1979c, 35: 221-235. Freeman, W. and Di Prisco, G. EEG spatial pattern differences with discriminated odors manifest chaotic and limit cycle attractors in olfactory bulb of rabbits. In: Proc. Conf. on Brain Theory, Trieste, Italy, 11/84. Springer, Berlin, 1986: 97-119. Freeman, W. and Schneider, W. Changes in spatial patterns of rabbit olfactory EEG with conditioning to odors. Psychophysiology, 1982, 19: 44-56. Freeman, W. and Skarda, C. Spatial EEG patterns, non-linear dynamics and perception: the neo-sherringtonian view. Brain Res. Rev., 1985, 10: 147-175. Hamming, R.W. Digital Filters. Prentice Hall, Englewood Cliffs, NJ, 1983. Krieger, D. and Larimore W. Automatic enhancement of single evoked potentials. Electroenceph. clin. Neurophysiol., 1986, 64: 568-572. Larimore, W. System identification, reduced-order filtering and modeling via canonical variate analysis. In: Proc. 1983 American Control Conference. IEEE, New York, 1983. Larimore, W. Simultaneous confidence bands for efficient parametric multivariate spectral estimation. Biometrika, 1986, in press. Larimore, W., Mahmood, S. and Mehra, R. Multivariable
230 adaptive model algorithmic control. In: Proc. 23rd Conf. on Decision and Control. IEEE, New York, 1984. Ljung, G. and Box, G. On a measure of lack of fit in time series models. Biometrika, 1978, 65: 297-304. Mackworth, J.F. Performance decrement in vigilance, threshold,
D. KRIEGER, M. D1LLBECK and high-speed perceptual motor tasks. Canad. J. Psychol.. 1964, 18: 209-223. Schieppati, M., Musazm, M., Nardone, A. and Seveso, (3. Interhemispheric transfer of voluntary motor commands in man. Electroenceph. clin. Neurophysiol, 1984, 57: 441-447.