Biol. Cybernetics34, 1-19 (1979) Biological Cybernetics by Springer-Verlag 1979 Combined Dynamics of EEG and Evoked Potentials* ** I. Studies of Simultaneously Recorded EEG-EPograms in the Auditory Pathway, Reticular Formation, and Hippocampus of the Cat Brain during the Waking Stage E. Ba~ar***, N. Demir, A. G6nder, and P. Ungan Institute of Biophysics, Brain ResearchLaboratories,HacenepeUniversity,Ankara,Turkey Abstract. This study is carried out on single (not averaged) recordings combining the spontaneous ac- tivity preceding the stimulus onset and the El' re- corded upon acoustical stimulation. These recordings, which we call EEG-El,ograms, are measured simul- taneously from different subdural brain structures, such as the auditory cortex, medial geniculate nucleus, inferior colliculus, reticular formation and the hip- pocampus of awake cats. Using a combined analysis procedure (C.A.P.), the relevant frequency components of spontaneous EEG and El,s, recorded simul- taneously from these brain nuclei, are analyzed accord- ing to the consistent selectivity bands depicted by the determined amplitude-frequency characteristics. These analyses provide us the following information: (1) there is an important congruency in the time courses of simultaneous response components in common fre- quency bands, especially in the ~ and /~ frequency ranges; (2) there exist significant coupling and synch- tony between the evoked amplitude enhancements in the simultaneously recorded single response com- ponents; (3) the inter-nuclei coherency in the brain's electrical activity is enormously increased upon stimulation; (4) the evoked response magnitude can be predicted, with reasonable accuracy, from the spontaneous activity preceding the stimulation. The strong dependence of the response magnitude on the stimulus-preceding EEG is explained by means of a model network consisting of a population of relaxation oscillators, which can be brought to different states of synchrony and asynchrony. Some suggestions and comments are also made for investigators working toward theories of signal transmission in the brain. * This studyis supportedby the Grant TAG-364of the Scientific and TechnicalResearchCouncilof Turkey ** Presented in part at the Ninth InternationalCongressof EEG and ClinicalNeurophysiology, Sept. 4-9, 1977, Amsterdam *** Present address: Institute of Physiology,University of Kiel, FRG 1. Introduction In our recent studies on dynamics of rhythmic and evoked potentials in auditory and visual pathways of the cat brain, we hypothetized three types of resonance phenomena which we called "strong resonances", "weak resonances" and "~ resonances". (Ba~ar et al., 1975b, c; Ba~ar, 1976: Ba~ar et al., 1976b, c). As strong resonance, we defined the responsiveness of the brain nucleus under study when the response signal (EP) contained frequency components which also existed in the spontaneous activity, but depicting stimulus- enhanced amplitudes in the time-locked single re- sponses. There exists an important relation between EEG and evoked potentials of the brain: in a given frequency band, upon stimulation, the spontaneous activity components are time-locked, enhanced and frequency-stabilized. In other words, frequency stabili- zation, time-lockin9 and amplification of the spon- taneous activity upon stimulation result in larger potential changes which we call "Evoked Potentials" (Ba~ar et al., 1976b, c). The degree of congruency in frequency and phase of the activities recorded simultaneously from different brain nuclei, and the degree of harmony in the va- riations of the enhancement factors evaluated from simultaneous single recordings are of major impor- tance in order to understand whether the strong resonance phenomena (or the increase in responsive- ness) occur simultaneously in various brain structures. In our previous time domain-studies of resonance phenomena in the brain, however, simultaneous single recordings from different brain structures were not included. Therefore, in the present study, the studies are carried out on combined single recordings of spontaneous EEG and El,s measured simultaneously from different centers of the cat brain, such as the auditory cortex, medial geniculate nucleus, inferior colliculus, reticular formation and the hippocampus, in 0340-1200/79/0034/0001/$03.80
Combined Dynamics of EEG and Evoked Potentials* ** I. Studies of Simultaneously Recorded EEG-EPograms in the Auditory Pathway, Reticular Formation, and Hippocampus of the Cat Brain during the Waking Stage
E. Ba~ar***, N. Demir, A. G6nder, and P. Ungan
Institute of Biophysics, Brain Research Laboratories, Hacenepe University, Ankara, Turkey
Abstract. This study is carried out on single (not averaged) recordings combining the spontaneous ac- tivity preceding the stimulus onset and the El' re- corded upon acoustical stimulation. These recordings, which we call EEG-El,ograms, are measured simul- taneously from different subdural brain structures, such as the auditory cortex, medial geniculate nucleus, inferior colliculus, reticular formation and the hip- pocampus of awake cats. Using a combined analysis procedure (C.A.P.), the relevant frequency components of spontaneous EEG and El,s, recorded simul- taneously from these brain nuclei, are analyzed accord- ing to the consistent selectivity bands depicted by the determined amplitude-frequency characteristics. These analyses provide us the following information: (1) there is an important congruency in the time courses of simultaneous response components in common fre- quency bands, especially in the ~ and /~ frequency ranges; (2) there exist significant coupling and synch- tony between the evoked amplitude enhancements in the simultaneously recorded single response com- ponents; (3) the inter-nuclei coherency in the brain's electrical activity is enormously increased upon stimulation; (4) the evoked response magnitude can be predicted, with reasonable accuracy, from the spontaneous activity preceding the stimulation. The strong dependence of the response magnitude on the stimulus-preceding EEG is explained by means of a model network consisting of a population of relaxation oscillators, which can be brought to different states of synchrony and asynchrony. Some suggestions and comments are also made for investigators working toward theories of signal transmission in the brain.
* This study is supported by the Grant TAG-364 of the Scientific and Technical Research Council of Turkey ** Presented in part at the Ninth International Congress of EEG
and Clinical Neurophysiology, Sept. 4-9, 1977, Amsterdam *** Present address: Institute of Physiology, University of Kiel, FRG
1. Introduction
In our recent studies on dynamics of rhythmic and evoked potentials in auditory and visual pathways of the cat brain, we hypothetized three types of resonance phenomena which we called "strong resonances", "weak resonances" and "~ resonances". (Ba~ar et al., 1975b, c; Ba~ar, 1976: Ba~ar et al., 1976b, c). As strong resonance, we defined the responsiveness of the brain nucleus under study when the response signal (EP) contained frequency components which also existed in the spontaneous activity, but depicting stimulus- enhanced amplitudes in the time-locked single re- sponses. There exists an important relation between EEG and evoked potentials of the brain: in a given frequency band, upon stimulation, the spontaneous activity components are time-locked, enhanced and frequency-stabilized. In other words, frequency stabili- zation, time-lockin9 and amplification of the spon- taneous activity upon stimulation result in larger potential changes which we call "Evoked Potentials" (Ba~ar et al., 1976b, c).
The degree of congruency in frequency and phase of the activities recorded simultaneously from different brain nuclei, and the degree of harmony in the va- riations of the enhancement factors evaluated from simultaneous single recordings are of major impor- tance in order to understand whether the strong resonance phenomena (or the increase in responsive- ness) occur simultaneously in various brain structures. In our previous time domain-studies of resonance phenomena in the brain, however, simultaneous single recordings from different brain structures were not included. Therefore, in the present study, the studies are carried out on combined single recordings of spontaneous EEG and El,s measured simultaneously from different centers of the cat brain, such as the auditory cortex, medial geniculate nucleus, inferior colliculus, reticular formation and the hippocampus, in
0340-1200/79/0034/0001/$03.80
order to obtain the following information: a) The degree of congruency between the time
courses of the response components, which are simul- taneously recorded from these brain centers in com- mon selectivity bands, giving special emphasis on the c~ and fl frequency ranges.
b) The significance of the coupling and synchrony between the stimulus induced amplitude enhance- ments, in the simultaneously recorded single responses from these brain centers.
c) Coherence functions of spontaneous EEG and EPs recorded simultaneously from these brain centers.
d) The predictability of EPs from the spontaneous EEG preceding the stimulation and the accuracy in such a prediction, which seems possible according to our previous studies (Ba~ar et al., 1976b).
2. Material and Methods
2.1. Surgery
Our investigations were carried out using 11 cats with chronically implanted stainless steel electrodes of 0.2mm diameter (IVM. NEX-100 Electrodes) in the left inferior colliculus (Fr. P: 2.5, L: 5, H: 3.5), in the left medial geniculate nucleus (Fr. A : 3.5, L : 9, H : 1.5), in the left mesencephalic reticular formation (Fr. A: 3, L: 4, H : - 1), in the right dorsal hippocampus (Fr. A : 3.2, L: 6.2, H: 8.8) and at the gyrus ectosylvian anterior. The derivations were against a common reference which consisted of three stainless steel screws in different regions of the skull. A David Kopf 1404 Instrument was used for stereotaxic surgery. During the surgery the cats were anaesthetized with 36 mg/kg Nembutal and they were used in experiments not sooner than 2 weeks after the surgery. During the experiments the cats were freely moving in an echofree and sound proof room.
2.2. Stimulation
The stimulation was in the form of auditory step functions which consisted of tone bursts of 2000Hz and 80 dB (SPL). The stimuli lasted 3 s following the onset and were applied randomly with intervals not less than 16s.
2.3. C.A.P. : Combined Analysis Procedure of EEG and EP
Our methodology for comparison of the brain's spon- taneous activity and the evoked potentials can be briefly described as follows:
1) A sample of the spontaneous activity of the studied brain structure just prior to stimulus is re- corded and stored in the disc-memory of the computer. (For the experimental set-up see Ba~ar et al., 1975a).
(In the case of a computer system without disc- memory, another peripheral unit can be used in order to provide this storage procedure.)
2) The stimulation signal described in Sect. 2.2 is applied to the experimental animal.
3) The single evoked response following the stimu- lation is also stored in the disc-memory. (The EEG just prior to stimulation and the resulting EP are stored together as a combined record. We call this record EEG-EPogram. For the definition see Appendix.)
4) The operations explained above (steps 1-3) are repeated about 100 times for one experimental session. (The number of trials depend on the nature of the experiments and the behavior of the experimental animal.)
5) The evoked potentials stored in the disc-memory of the computer are averaged using the selective averaging method (see Ba~ar et al., 1975a, b; Ba~ar, 1976; Ungan and Ba~ar, 1976).
6) The selectively averaged evoked potential (SAEP) is transformed to the frequency domain with the Fourier transform in order to obtain the amplitude frequency characteristic, IG(jc0)l, of the studied brain structure :
[G(jo~)] = S {dc(t)/dt} exp(-jo3t)dt. 0
c(t) is the step response of the system. (Here SAEP.) Details concerning this method, which we called TRFC-method (Transient Response-Frequency Characteristics method), are given in references (Ba~ar, 1976; Ba~ar, 1972).
7) The frequency band limits of the amplitude maxima in the plots of [G(jo))[ vs. frequency are determined, and theoretical pass-band filters are evalu- ated according to these band limits. For this purpose we use the response-adaptive filtering method described in our previous work (see Ba~ar and Ungan, 1973; Ba~ar, 1976).
We want to emphasize that the band limits of the digital filters are not arbitrarily chosen. These are response-adaptive filters and are depending on the nature of the experiments, they are especially adapted to the time-locked frequency selectivities detected in the evoked potentials of the subjects. The way how the band limits of these adaptive filteres are determined is exemplified as follows: The amplitude characteristics of the cat acoustical cortex shown in Fig. 1A depicts, between 1-100 Hz, four selectivity channels. Therefore we determine four pass-band filters with the following band limits for the acoustical cortex:
1 H z < f < 5Hz 7 H z < f < 1 8 H z
22 Hz < f < 40 Hz 50 Hz < f < 90 Hz.
Waking Stage 2olo st jw)l
0"
0-
/ 0"
0
l [ l I l l l l [ 1 I I I l i l l ~ ] I I I I I i l ~ I ]
2 34567 2 34567 2 34567 2 3 0.1 I 10 100
A Frequency (Hz) B
GEA
MG
20 lo~
0"
Is~jwll
~ GFA
0. MG
~ ~ IC
o ~ RF
1 I I I I . t . i | . , i i , . l , ~ I I I I ' l , i l , t ; 2 3 4 5 6 ' / 2 3 L, 5 6 1 2 3 4 5 6 1 2 3
0.1 I 10 100 Frequency (Hz)
Fig. 1A and B. Two sets of amplitude-frequency characteristics obtained by means of the TRFC-method and using the selectively averaged evoked potentials (SAEPs), which were simultaneously recorded from different brain nuclei of the cat during the waking stage. Direct computer plottings. Along the abscissa is the input frequency in logarithmic scale, along the ordinate is the potential amplitude, IG(jcg)l , in decibels. The curves are normalized in such a way that the amplitude at 0 Hz is equal to 1 (or 20 log 1 = 0)
8) The stored and selected epochs of EEG-EP sets (EEG-EPograms) are filtered with the adequately cho- sen filters described in step 7.
9) The rms-voltage of the filtered EEGs are com- pared with the maximal amplitudes of the filtered EPs, and the so-called enhancement factors for the given EEG-EPogram is evaluated.
Definition of the enhancement factor, X: In a given experimental record of EEG-EP, the ratio of the maximal time-locked response amplitude to the rms value (root mean square value) of the spontaneous activity just prior to stimulus, both signals (spon- taneous and evoked activities) being filtered within the same band limits. (See also Fig. 2 for the definition of the enhancement factor.) We should further note that:
a) The enhancement factor is undefined for time- unlocked activities upon stimulation.
b) According to the consideration above, the filter- ing procedure used is adaptive filtering which is based on the time-locked frequency characteristics of the EP. The concept of the "enhancement" will be also un- certain if some other arbitrarily chosen filters should be used.
c) The procedure explained in step 9 is repeated for all the stored epochs.
The C.A.P. of EEG-EP, which is carried out with the help of the experimental setup given in detail by Ba~ar et al. (1975a), is schematized as follows:
C.A.P.
Recording of about 100 EEG-EPograms (EEG is for 1 s prior to stimulus)
Evaluation of the SAEP
Transform of the SAEP to the frequency domain : evaluation of the
amplitude frequency characteristics
1 Determination of the band limits of theoretical adaptive pass-band filters
1 Filtering the stored EEG-EPograms
by using the adaptive filters
1 Determination of the enhancement /
factors and time-locking r i
I Plotting the filtered EEG-EPograms ]
The maximal t ime-locked Enhancement factor, )~ - - amplitude of the filtered single EP
The rms value of the filtered EEG prior to stimulus (filtered in the same band )
El ...... ................................ ' R ,Y = -~- R
f stimulus
Fig. 2. Definition of the enhancement factor, X, on a sample component of EEG-EPogram. As it is shown in the illustration, the peak-to-peak value of the evoked response is compared with the peak-to-peak value of a sinusoidal signal having the same root- mean-square value with the spontaneous EEG preceding the sti- mulus onset
high frequencies (Ba~ar et al., 1975b, c; Ungan and Ba~ar 1976). Therefore, we had to find a compromise between an adequately short record length in order to take only the transient response into account and a record length as long as possible to improve the frequency resolution of the analysis. Due to these conflicting requirements, we chose a 330ms-analysis period, which provided a frequency resolution of ap- proximately 3 c/s, and which was a little more than enough for the transient EP components in the e - f l frequency range to die away practically. Since we intended to compare the coherence functions of spon- taneous and evoked activities, the same analysis period was used also for the spontaneous parts of the EEG- EPograms. In other words, only the 330 ms-sections of EEG-EPograms, which just preceded and followed the stimulus onset, were taken into account in the corn- potation of coherence functions of the spontaneous EEG and EP recordings, respectively.
2.4. Coherency Functions
The coherence functions were computed from both the spontaneous and evoked parts of the EEG-EPograms for all the possible pairings of the brain centers studied. This was done for the recordings of all the experiments, and the computed curves were directly plotted. In the computation of coherence functions, basically, the procedure described by Dumermuth and Fluhler (1967) was followed, except that we used Extended BASIC for programing our computer while recording and processing the data. The coherence function, Cxy(f), is defined as
[Sxy(f)l 2 C~y(f) = S~x(f)Syy(f ) ,
where, Sxy(f) is the cross spectrum of the two studied signals (x and y, functions of time). S ~ ( f ) and Syy(f) are the respective power spectra of these signals. The details of the mathematical manipulations and smoothing procedures, which can be found in the mentioned methodological report and also in a book by Glaser and Ruchkin (1976), are not repeated here for brevity. The following restriction was imposed, however, due to the nature of the data to be studied : as is well known, an EP recorded in response to a stimulation consists of a few oscillations and dies away in a certain time following the stimulus onset. After this limited period of time the EEG returns to its
spontaneous character. This period, where the tran- sient response occurs, may be extremely short es- pecially for the fast components of EPs with rather
2.5. Nomenclature
EP: Single Evoked Potential AEP : Averaged Evoked Potential
SAEP: Selectively Averaged Evoked Potential
GEA: Gyrus Ectosylvian Anterior MG: Medial Geniculate Nucleus RF: Mesencephalic Reticular Formation IC : Inferior Colliculus HI : Dorsal Hippocampus
IG(je~)l: Amplitude Frequency Characteristic
EEG-EPogram: A single EEG-EP-epoch, EEG being recorded immediately prior to stimulus
X: The enhancement factor
3. Results
3.1. Simultaneous Frequency-Characteristics
In this report we confine our attention to simul- taneously obtained responses from various structures of the cat brain, and we apply the methodology described to simultaneously recorded spontaneous ac- tivities and evoked potentials from these structures. These brain nuclei are chosen from the cortical area (GEA, gyrus ectosylvian anterior), thalamus (MG, medial geniculate nucleus), reticular formation (RF), midbrain (IC, inferior colliculus) and from the limbic system (HI, hippocampus).
Figure 1 shows 2 sets of simultaneously obtained amplitude frequency characteristics of different centers
WAKING STAGE
GEA
MG
IC
RF
HI
2-8 Hz components
X':L9 51 rJV ~ i
I
123_pV I f ~ X=0.8
8-15 Hz components
29pV I . ^ X=2.8
65pV ^ ~ A X=2.6
15-25 Hz components
Ii =
81 ~v I
r
K'=3.2
28pV ^ ,/~ A X=3.7 = ~ 6
% VVw [
66 IJV I / ~ X=l.9 57pV X=l.2 30 pV ~ X=l.g
vvv vw 't r
{ I | I I I I I o e i i i I ' [ i i
2 msec 0 200 /.00 200 msec 200 400 2 0 msec 0 2 0 TIME (msec) TIME (msec) TIME (reset)
Fig. 3. Three components of a typical set of single EEG-EPograms with relatively high enhancement factors. These EEG-EPograms were simultaneously recorded from various brain structures of the cat during waking, and filtered without phase-shift. The pass-bands of the theoretical filters applied were chosen according to the shared band limits of the selectivities depicted in the amplitude characteristics presented in Fig. 1A. The exact frequency limits of the pass-bands, which are approximately quoted at the top, are as follows for different nuclei: GEA (1-6, 7-17, 20-30 Hz); MG (1-6, 8-18, 18-25 Hz) ; IC (2-8, 8-13, 15-26 Hz) ; RF (1-8, 8-17, 17-26 Hz) ; HI (2-7, 8-14, 15-26 Hz). The rms values of the spontaneous parts and the enhancement factors are also given above each filtered EEG-EPogram
of the cat brain. These amplitude characteristics were determined by applying the Fourier transform to selectively averaged evoked potentials of the above mentioned brain nuclei. As we reported earlier, during the waking stage, the amplitude maxima are seen mostly in the 0 (3-8 Hz), ~-/~ (10-25 Hz) and in some higher frequency ranges (40 Hz in GEA, and HI, 50 Hz in the MG and RF, 70 Hz in IC). Since we already described the resonance phenomena in these frequency channels (Ba~ar et al., 1975b) we now try to compare the synchrony in the occurrence of resonance pheno- mena through similar channels. We particularly em- phasize the c~-/? frequency range, i.e. the 8-25Hz range, since resonances in this frequency channel is common to all the studied nuclei (see Fig. 1). As we previously reported, it is not always possible to obtain two distinct and different peaks corresponding to these two frequency channels, namely c~ (8-15Hz) and fi (15-25 Hz) bands (Ba~ar et al., 1975b). This behaviour of c~-fi channel is further emphasized in the next section.
3.2. Simultaneously Recorded and Filtered EEG-EP Sets (Filtered EEG-EPograrns)
Figure 3 shows the three components of a typical set of EEG-EPograms which were simultaneously recorded from various brain structures and filtered without phase-shift within the band limits of about (2-8 Hz), (8-15 Hz), and (15-25 Hz). The band limits of these theoretical filters were chosen according to the shared band limits of the selectivities depicted in the ampli- tude characteristics of the brain structures illustrated in Fig. 1A. We should mention here that there are slight differences between the exact band-limits of filters applied to various nuclei, as it is described in the legends of Fig. 3. However, the band limits of the filters are roughly quoted at the top of the illustration. The computed values of the enhancement factor, which is defined in Sect. 2.3, are given besides each filtered EEG-EPogram in this figure. We should note here that the amplification factor which we introduced in our previous studies (Ba~ar et al., 1976a-c) described ap-
' ' i , I , I ] I i I I [ I 200 msec 0 200 400 200 msec 0 200
TIME (msec) TIME (msec)
Fig. 4. Three components of a typical set of single EEG-EPograms with relatively low enhancement factors. These EEG-EPograms were simultaneously recorded from various brain structures and filtered without phase-shift. For further description see the legend of Fig. 3
proximately the same relation. The enhancement fac- tor, however, reaches higher values than the amplifi- cation factor, for which the magnitude of the on-going activity was expressed in terms of its maximal ampli- tude prior to stimulus and not with its rms value.
Strong resonances : for a specific brain center and in a given frequency band, we define "Strong Resonance" as the occurrence of time-locked responses with en- hancement factors greater than 1.5. In Fig. 3 the rms values of the filtered EEG are also given together with the enhancement factors evaluated for the correspond- ing brain nuclei.
According to the definition above, most of the EEG-EP epochs of various nuclei illustrated in Fig. 3 present strong resonance phenomena in the 0, ~, and fl frequency ranges : the enhancement factors have values v.arying between 0.8 and 4.7 ; the time-locking is perfect in most of the evoked responses. The congruency in responses of various nuclei in the ~ and fl frequency channels are, leaving aside the absolute values, almost perfect.
Another set of filtered EEG-EP records is illus- trated in Fig. 4. In this set of EEG-EPograms, which were obtained from the same cat during the same
experimental session, the responsiveness after stimu- lation does not have the same magnitude of enhance- ment as in the event illustrated in Fig. 3. Almost all of the enhancement factors are smaller than those in Fig. 3 ; perfect time-locking upon stimulation is not observ- ed in all the potentials.
We should emphasize here that in the 0 frequency range, where the spontaneous activities of the medial geniculate nucleus and the hippocampus usually show high amplitude regular activities, the enhancement factors are usually less than 1.5 (Weak Resonance Phenomena explained in detail by Ba~ar et al., 1976b). Although the enhancement factor in the 0 band can increase when the spontaneous 0 activity is desynchro- nized with relatively low voltages, this increase in the recordings of medial geniculate nucleus and hippoc- ampus is not as significant as can be obtained from the recordings of the other nuclei studied. (Compare, for example, the hippocampal activities in Figs. 3 and 4; see also Table 4 in Sect. 3.5.)
In the examples of Figs. 3 and 4 the frequency characteristics do not always depict distinct maxima in both the c~ and fl frequency ranges, although in some of the experiments the differentiation between c~ and fl
acoustical cortex INSTANTANEOUS FREQUENCY CHARACTERISTICS
Table 1o Five sets of enhancement factors in the c~ frequency range obtained from the EEG-EPograms recorded during the same experi- mental session of approximately 30 rain with one cat. The figures in each of the five columns are the simultaneous enhancement factors of different brain nuclei for each of the five identical stimulation trials (events) during the waking stage
Fig. 5. For the waking stage, examples of acoustical cortex- frequency characteristics computed from single (not averaged) EP recordings by means of the TRFC-method. Note that there are often two separate peaks with alternating dominance in the c~ and /~ frequency ranges, respectively
peaks is considerably important. We have described this fact in detail, in our earlier studies (Ba~ar et al., 1975b); Ba~ar, 1976). However, we usually use two different and adjacent pass-band filters which, togeth- er, cover the frequency range between approximately 7 and 30 Hz, as we have done after the experiments given in Figs. 3 and 4. Since the procedure of averaging the EPs disturbs the obtaining of two distinct peaks in the
- / ? frequency range, we performed also the analysis of amplitude-characteristics computed from single
evoked potentials. Although it is not the aim of this study to compare these instantaneous amplitude fre- quency characteristics, in Fig. 5, we give an example of a set of single amplitude characteristics for the acousti- cal cortex. Such experiments and evaluations were performed for all the nuclei and cats for which the averaged curves could not allow us to define precise band limits for the adaptive filters to choose. In Fig. 5, it is shown that, often, separate peaks in the e and/3 frequencies do exist in single recordings. However, after the averaging, one may often obtain a common ~- /3 maximum (see Fig. 1B).
Figures 3 and 4 show further, that in the ~ and/~ frequency channels the enhancement factors are in- versely proportional to the magnitude of the spon- taneous activity prior to stimulus. This fact, which will also be mentioned in Sect. 3.6, can be seen in an illustrative manner in Figs. 3 and 4.
3.3. Couplin 9 and Synchrony in the Response of Various Brain Struetures in the ~ and ~ Ranges
a) Similarity in Time Courses, and Enhancement Factors. One of our major questions in this study is, whether the resonance phenomena ought to occur synchronously in various structures of the brain, and whether the enhancement factors in various nuclei have mutual influences. In this study we confine our attention mostly to the c~ and /~ frequency channels. From Fig. 3 one recognizes immediately that in the frequency range between 8-25 Hz (e-/~ channels) the filtered EPs of all the studied nuclei are almost cong- ruent in time. There is almost no phase difference between the EPs of various nuclei during the first 150 ms after the stimulation. We consider further, as an example, five sets of simultaneous enhancement factors in the e frequency channel of a cat during the same experimental session. The figures in each column of Table 1 are the simultaneous enhancement factors of various brain nuclei for the corresponding trial (event).
8
3 SETS OF SIMULTANEOUS E P s IN THE ALPHA --REQUENCY RANGE
Fig. 6. A graphical representation of the coupling and synchrony in the responses of various brain structures in the c~ frequency range. In the upper part, three sets of EP-components are given in a three dimensional form. All the EP sets were recorded from the same cat in a single experimental session. The EPs in each set were recorded simultaneously from different brain nuclei and in response to a single stimulation. Below, the magnitudes of the EP-components and the enhancement factors are represented by hatched and full vertical bars, respectively, together with the empty bars standing for the rms values of the spontaneous EEG-components preceding the stimulation. Note the synchrony in the responsiveness levels of different nuclei as quite clearly displayed by the harmony in waxing and waning of the enhancement factors
Five sets of enhancement factors, X, in this table were evaluated from EEG-EPograms recorded in response to five stimulation trials. The X-values present typical results chosen from an experimental session of approx- imately 30 min. One can recognize immediately that all the enhancement factors belonging to various nuclei (element groups in columns) are increasing or decreas- ing almost proportionally throughout the experiment : in the first even (first column) all the X-values are in the vicinity of 1-1.5, whereas all the enhancement factors in the fifth event have values higher than 3.5.
Figure 6 shows this effect more markedly in an illustrative manner. The three sets of EP-components from various nuclei presented in this figure were again recorded during the same experimental session. In the first set of responses the magnitude of components in the e frequency range have largest values, whereas the second set of responses depict a case with considerably low responsiveness: the enhancement factors and EP- components are very small, there is no perfect time locking. The third set of evoked potential components and the corresponding enhancement factors present an intermediary stage with moderate values. Figure 6 illustrates further, graphically, that in case of low EEG voltages the enhancement factors and EP components are large; and vice versa.
b) The Coherence Functions Computed from all the Possible Pairings of Recording Electrodes. The coupl- ing (and/or synchronization) of resonant responses from various nuclei in the ~ and fi frequency ranges can also be demonstrated by using the coherence functions between all possible pairings of spontaneous and
evoked activities in the studied brain structures. In Fig. 7, which presents results of a typical experiment, the coherencies in a frequency range of 3-60 Hz for spon- taneous activities and evoked potentials of all possible parings of the studied brain structures are illustrated. Due to the reasonably large number of single sweeps included in the averaging process of the computations and to the spectral window used, the auto- and cross- spectral amplitudes have been adequately smoothed and a significance level of 0.2 has been attained for all the curves. Therefore, the area under the coherence function is darkened only if the curve is ranging over this value, in order to give emphasis to those parts of the curves above the significance level. One recognizes immediately, that in the ~ (8-14 Hz) and/7 (14-25 Hz) frequency ranges the coherency has usually high values between 0.5 and 0.9 for evoked responses. However, the coherency between spontaneous activities of the same pairings of nuclei has definetely lower values. In the c~ and /7 frequency ranges, the coherency of the spontaneous activity can hardly reach 0.3 in a very few cases. In other words, there exists an important coher- ency increase upon stimulation.
Table 2 represents averaged coherencies for e and/7 frequencies from 11 experiments performed with 11 cats. As averaged coherency, we mean the mean value of the respective coherencies obtained from the results of 11 experimental sessions. We also evaluated a mean value of the coherencies over all possible pairings of nuclei. We call this value the overall coherency of all the studied nuclei. In the c~ frequency range the overall coherency increases from 0.075 to 0.50. In the/7 band the overall coherency increases from 0.08 to 0.35.
Waking stage (acoustical stimulation)
, - - s p o n t . EEG-- , EP , , - s p o n t . E E G ~ , ~ E P ,
Fig. 7. A typical set of coherence functions computed from the spontaneous activities and EPs of all possible pairings of the studied brain structures during waking. The scale is indicated at the bottom. Along the abscissa is the frequency from 0 to 60 Hz, along the ordinate is the coherency between 0-1. The horizontal broken lines indicate the significance level, which is 0.2 for all the plots. The area under the coherence function is darkened only if the curve is ranging over this level. In order to facilitate a comparison between the coherence values computed from spontaneous and evoked parts of the EEG-EPograms, the respective coherence functions are presented adjacently as couples for all the pairings of recording electrodes
Table 2. Averaged magnitudes of coherences in pairings of spon- taneous EEG and evoked potentials recorded from the respective brain structures of 11 cats during the waking stage. The mean values of the averaged coherences in all possible pairings of nuclei are also given, in the e and/3 frequency ranges, as the overall coherency, which may represent to coherence state of the brain as a whole. Note that the overall coherency is significantly increased, in these frequency channels, upon auditory stimulation
Table 3. As averaged over the results of the experiments with 11 cats, the mean values of the correlation coefficients computed from the pairings of time courses of the enhancement factors recorded from different brain nuclei, each time course consisting of the results of 40 successive stimulation trials with one cat
c) Correlation of the Enhancement Factors Between all Pairings of Electrodes. T h e c o u p l i n g ( a n d / o r s y n c h r o -
n i z a t i o n ) o f r e s o n a n t r e s p o n s e s f r o m v a r i o u s nuc le i in
t he 1 0 - 2 5 H z f r e q u e n c y r a n g e c a n a l so b e d e m o n s t r a t -
ed b y u s i n g t he c o r r e l a t i o n coef f ic ien ts b e t w e e n t he
t i m e c o u r s e s o f t he e n h a n c e m e n t f a c t o r s r e c o r d e d f r o m
t h e s e c e n t e r s to success ive s t imul i . F o r th i s p u r p o s e we
e v a l u a t e d t he c o r r e l a t i o n coef f ic ien ts b e t w e e n t he X-
v a l u e s of al l p a i r i n g s of e l e c t r o d e s for al l t h e
e x p e r i m e n t s : T a b l e 3 r e p r e s e n t s t he m e a n v a l u e s of t h e
c o r r e l a t i o n coef f ic ien ts o b t a i n e d f r o m 11 cats , e v a l u a t -
10
WAKING STAGE
higher than 2-8 Hz 8-15 Hz 15-25 Hz 30 Hz
^ \ / ^ \ ~ I ^ \
G E A '
I I I
,c L : CA)
GEA
big
IC
RF
HI q i i [ i I ' I ' "~ I ' I ' I I ' I ' I i I I i 0 2 0 0 zOO 6 0 0 0 2 0 0 4 0 0 0 2 0 0 0 2 0 0 0
TIME (msec) TIME (msec) TIME (msec) TII4E (msec)
(B)
Fig. 8. Response components of two single EP sets, each recorded simultaneously from the brain structures studied. Approximate frequency limits of the components are given at the top
ing 40 evoked potentials for each cat. In other words, each figure in this table is the mean value of 11 correlation coefficients, each being computed from the two simultaneous time courses (40 successive stimu- lation trials with one cat) of the enhancement factors recorded from the corresponding pairs of brain centers.
From Table 3 one recognizes immediately, that the mean values of the correlation coefficients between the time courses of enhancement factors of various nuclei have positive values, except the one between the inferior colliculus and the hippocampus. The cor- relation coefficients can reach values (as mean) up to 0.5 between the medial geniculate nucleus reticular
formation and inferior colliculus. It is to remark, that the resonant response of the hippocampus is less correlated with responses of other brain centers in- cluded in this study. We should note that the coheren- cies between the responses of hippocampus and of other brain centers are also relatively small (see Table 2).
3.4. Higher Frequency Components in Single Evoked Potentials
In the previous sections we have considered only the frequency components covering a frequency region of about 1-25 Hz. Figure 8, however, illustrates the corn-
11
Table 4. As averaged over the results of 11 experiments, each consisting of 40 successive stimulation trials with one cat during the waking stage, are given the mean values of the rms-EEG-components and of the EP-components in various frequency channels. The mean values are specified by their band limits and center frequencies at the top, together with the mean values of the corresponding enhancement factors obtained for the brain nuclei studied. Standard deviations around the mean values are also given
ponents of two sets of single evoked potentials, cover- ing a frequency range between 2 and approximately 200 Hz. In other words, this figure presents all the t ime-locked EP-components up to frequencies of 200 Hz. F r o m this illustration one can recognize that, in the higher frequencies too, there also exist com- ponents with ample magnitudes as is the case on lower frequency channels. Also a propor t ional i ty between high frequency and low frequency components can be marked by compar ing the respective curves in two sets. Similar illustrations, which can not all be given in this report, indicated that in high frequency channels there also exist couplings between the studied nuclei. These couplings will be illustrated in Sect. 4.1, where the evaluations of a greater number of cases is graphically presented (see Fig. 10).
3.5. Mean Values of rms-EEG, EP-Components, and Enhancement Factors in Various Frequency Ranges of the Studied Brain Structures
Table 4 shows the mean values of rms -EEG com- ponents recorded from various brain structures and in given frequency ranges. The frequency ranges were determined by using the band limits of the adaptive filters described in the Sect. 2.3. We also want to recall that these frequency channels do also correspond to the "consistent selectivity" channels described in de- tails in our previous works (Ba~ar et al., 1975b ; Ba~ar, 1976). Table 4 further shows the mean values of EP components in the same frequency bands and the
corresponding mean enhancement factors. All these values were obtained from 11 experiments by using 11 different cats. In each experiment a round 40 sets of combined E E G - E P epochs (EEG-EPograms) were evaluated.
As one recognizes immediately, in some of the brain nuclei the spontaneous activity components have large rms-values in some frequency channels. For example, in the 0 frequency range the medial geni- culate nucleus and the h ippocampus depict spon- taneous activities with larger magnitudes in com- parison to those of other nuclei. The activity in the channel recorded in the medial geniculate nucleus is also relatively large. Even so, the EP components of the medial geniculate nucleus in c~ and fl frequency channels has largest values.
The study of the s tandard deviations shows, that the variability in El? components is markedly higher than the variability in E E G frequency components . The enhancement factor in the low frequency band of 1-8 Hz are small in compar ison to those in higher frequencies.
3.6. Predictability of Evoked Potentials from E E G
An impor tant feature of the observation of strong resonances in the brain is their qualitatively repeatable structure along with enormous fluctuations in the enhancement factor. The study of earlier results (Ba~ar et al., 1975b, c, 1976a, b) and the data presented in precedent sections showed that, during the study of
12
X (Enhancement factor) 5
X ACOUSTICAL 4 O TEX 3
2
1 __1 l I I I
20 40 60 80 100 IaV Filtered EEGrms X 5
X-" MEDIAL 4 . ~ OENICULATE X:UCL 2 : �9
1
- - L .... I I I I
40 60 8 0 100 120 pV Filtered EEGrm s
X ( Enhancement factor) 5
FILTER 8-20 Hz
X
4
3
2
I
0
5
4
3i
2
I
"~_ INFERIOR o %,~ COLLICULUS
" ' " �9
I I I I
20 40 60 80 wV Filtered EEGrm s
�9 ~ ~
~ " RETICULAR ~ ii ORMATION
I I I I 20 40 60 80 pV
FiLtered EEGrm s
Fig. 9. Plots of the enhancement factor in the waking stage versus the magnitude of spontaneous EEG in the e-/~ frequency range. Along the abscissa is the rms value of the EEG-component, recorded for a duration of 1 s prior to stimulus, and along the ordinate is the enhancement factor. Dots in the plots represent the individual results obtained by successive stimulation trials during the same experimental session
individual nuclei, and frequency components, the en- hancement factor has a strong dependence on the voltage of the spontaneous activity which precedes immediately the stimulation. The results indicated that, in a defined frequency range, the increase of EEG- amplitudes has reciprocal influence on the magnitude of enhancement factors, and this was the encouraging factor to make predictions on the magnitudes of EP- components, basing only on rms-values of the filtered EEG just preceding the stimulation. Figure 9 illus- trates plots of the enhancement factor in the c~- fl band versus the rms value of the filtered EEG in the same frequency range. Along the abscissa is the rms value of the filtered EEG voltages, recorded for a duration of 1 s just prior to stimulus, and along the ordinate is the corresponding enhancement factor. The plots of Fig. 9 show that it is possible to predict the EP-components basing on the rms values before stimulation: it exists an almost linear relationship between the rms-EEG prior to stimulus and the enhancement factor in the same frequency range. Basing on similar plots from 11 cats, a mean error of 28 % was attained in the pre- diction of actual EP-components, thus indicating pre- dictability of roughly 70 Too for the responses of studied brain centers, in the e - f l frequency range.
We give here only the example of the responses in the e frequency range. However, there exist similar predictability possibilities also for the other relevant frequency bands which are existent in the frequency characteristics. We will discuss the further possibilities implied by the predictability of EPs from the preceding EEG in the Discussion.
4. Discussion of the Results
4.1. Synchronization and Coupling of Resonances in the Responses of Various Brain Centers in ~ and ~ Frequency Ranges
The question, whether the resonance phenomena oc- cur synchronously in various structures of the brain, is answered by the results of Sect. 3.3. From Figs. 3 and 4 one can recognize that upon stimulation there exists, in the e and /~ frequency ranges, a congruency in fre- quency and phase for potentials recorded from various centers in almost all pairings of recording electrodes. As an immediate observation from Figs. 3-5 we can state that the studied brain nuclei act, by application of sensory stimulation, as coupled oscillators without phase lag in e and fl frequencies.
13
Moreover, the significant increase of coherency upon stimulation suggest a hypothesis, that spon- taneously active oscillators in various brain structures act as a whole, in the frequency range between 8 and 25 Hz, upon stimulation�9
When two signals are' practically independent, the coherency function, computed from these two signals is nearly zero for all frequencies. But, if they are closely related over a limited range of frequencies, the coherency function would take values near unity for this specific frequency range, and it is almost zero for other frequencies. In the latter case, the two signals are said highly coherent within certain frequency limits and incoherent outside this limits. Coherency function, however, suppresses any phase in for- mation concerning the two signals (Glaser and Ruchkin, 1976). In other words, although the coherence function can provide the frequency bands where the two signals under study are coherent or incoherent, it cannot supply any information if there is a phase lag between these signals. This information together with the value of the preferred phase angle, if any, can be estimated by the phase spectrum. We do not present here, however, any analysis with phase spectra. Because, regardless of the phase relations between spon- taneous activities of all pairings of the studied brain structures, one clearly sees in Figs. 3 and 4 that, in the e-/~ frequency range, the phase difference between all the simultaneously recorded EPs be- comes nearly zero following the stimulus : the responses are almost congruent in the time scale. In this kind of time-domain pre- sentation of data there is also the additional information of the enhancement factor, which is not included in the presentation of phase spectra�9
According to the consideration above and to our results we assume that the oscillators in various brain structures act either simultaneously in being triggered by a common gating mechanism, or they affect each other immediately. This congruency in phase and time is certainly not due to volume conduction, since it does not exist any significant phase-locking nor high coher- encies before stimulation (see Figs. 3 and 4, and compare with the coherence functions of Fig. 7). The question, whether there is a neural conduction between centers can not be analyzed in the scope of this study. However, in the e and/3 frequencies, because of the fast neural conduction velocity this effect cannot be used to measure the initiating source.
If we follow the chain of findings by the study of simultaneously recorded and filtered EEG-EPograms we will confront the following evidence: the increase and decrease of the magnitudes in EP-components and enhancement factors in various brain nuclei occur with similar weights as the findings of Sect. 3.3 shows (see Fig. 6 and Table 1). In other words, if in the ~- /~ frequency range the magnitude of GEA-response (and also the corresponding enhancement factor) reaches it highest value, the magnitude of the RF-response, HI- response and IC-response also reach their maximal values, and vice versa. This important result indicates the existence of a central (and/or general) command mechanism which regulates the intensity of response components in the c~-/~ frequency channels (i.e., a
mechanism which grossly regulates the responsiveness state of the brain). However, as we have seen in Sect. 3.6, and as we will also discuss in the next Sect. 4.2, the response components in a given brain structure depends also strongly on its own spon- taneous activity. We also know that the coherencies of spontaneous activities between various brain nuclei are not usually high (Table 2 and Fig. 7). This infor- mation is important in showing that the local differ- ences in the spontaneous activities are significantly high before stimulation. Accordingly, additional to the postulated central command mechanism which re- gulates the overall responsiveness of the brain, there should exist secondary local mechanisms in different brain structures, these mechanisms being mostly de- pendent on the magnitude of local spontaneous ac- tivity. Certainly, the coherency function of the spon- taneous activity shows variability when one considers the values throughout all the possible pairings of electrode locations, and may also vary in various experimental conditions. This fact was already shown by the relevant study of Elazar and Adey (1967), who studied the coherence functions computed from the spontaneous activity pairings of some cortical, thala- mic, reticular, and limbic structures. Our rationale by evaluating the coherence function is the quantification of changes at the moment of stimulation. Therefore, we defined an "overall coherency" (see Table 2) which describes, in a given frequency band, the mean value of coherencies between all the combinations of studied brain structures. The overall coherency shows a signifi- cant increase upon stimulation. There are certainly relevant neurophysiological implications when one is interested in the study of specific relations of the studied nuclei. They are, however, not in the scope of the present study.
Although in the present paper it is not possible to study in details the synchrony of higher frequency components in the studied brain nuclei, we will give an illustrative example in order to show that a good synchrony (or coupling effect) does also exist for frequency components higher than 25 Hz. In Fig. 10 the magnitudes of all the frequency components in the studied nuclei are given for a sequence of 7 sets of EPs (event 1 to event 7). The vertical bars present the voltage magnitudes belonging to each frequency chan- nel in relative units. (The first bar covers the frequency channel of t -SHz , the second l ~ 1 5 H z , the third 15-25 Hz, etc., as given in the legend to this figure). As
�9 we know from Fig. 1, these approximate frequency bands may not exactly coinside with the corresponding frequency channels in all the simultaneously obtained frequency characteristics of the studied nuclei. However, we use this graphical representation of Fig. 10 in order to show, roughly, that the increases or
Fig. 10. A graphical representation of the harmonious increase and decrease in the magnitudes of response components recorded from a given brain structure (as revealed by horizontal comparison), and of the synchrony in the magnitudes of respective frequency components simultaneously recorded from different structures (as revealed by vertical comparison). Events numbered from 1-7 represent the seven successive stimulus presentations in a single experiment with one cat. Each bar represents, in relative units, the magnitude of the corresponding frequency component in the response recorded from a given brain structure in a certain event. For the illustrated example, the six vertical bars in each group correspond, from left to right, respectively to the six frequency components with the following band limits for each of the studied nuclei: GEA (1-6, 6-10, 10-20, 20M7, 47-100, 110-180 Hz); MG (1-6, 6-10, 10-28, 36-72, 72-130, 160-240Hz); IC (2--8, 8-13, 13-28, 39-80, 80-150, 150-240Hz); RF (1-8, 8-17, 17-26, 35-80, 80-130, 150-240Hz); HI (2--7, 8-14, 14-29, 30-60, 68-105, 110-180Hz)
decreases in the magnitude of higher frequency- response components of various nuclei are also in a striking harmony, as is the case for the responses in lower frequencies.
4.2. The Predictability of Grossly Recorded Evoked Potentials from EEG
In Sect. 3.6 the predictability of the magnitude of EP- components has been handled for the c~-/? frequency range. Although in the present study other frequency components (l-8Hz components and components higher than 25 Hz) were not especially handled, in the rule, the magnitude of EP-components are also linearly predictable by using the rms-values of EEG prior to stimulation. What does this mean ? Why do we try to predict the EP-components from EEG? Firstly, these results can enable us to compute hypothetical single evoked potentials of the nuclei in defined waking or sleep stages with all the frequency components. The divergence between hypothetical results and measured EPs can be used as an important tool in behaviour experiments or experiments with pathological subjects in order to search for the eventual source of variabil- ities. Secondly, this predictability supports further our findings concerning the important relation between EEG and EPs : the fact that the EP-components can be predicted, with a reasonably high accuracy, from the spontaneous activity is a further step for the under- standing of the synchronization effect after stimulation. If we hypothetize that maximal EEG amplitude is a result of maximal synchrony of individual neural generators, than we can conclude that in cases of higher synchrony of EEG (thus higher EEG ampli-
tudes) the enhancement factor will not be large: the stimulation can not increase any more the amount of synchronized generators. This consideration is also included in the network-experiments of Sect. 4.3.
4.3. Review of the Coupling in Neural Pools in Various Brain Structures
Forcing of a Population of Self-Oscillatory Networks
The analysis of forcing of the self-oscillatory biological system (brain) led us to the following consideration. If the firing of neurons (and/or neural pools) are in a state of regular firing resulting from a complete firing synch- tony, it is to be expected that the excited structure will be less responsive. On the contrary, in a noisy state of irregular firing (or partial discharge synchrony) the responsiveness will be greater, since the number of firing-units which can be driven by the stimulus will certainly be larger. In the case of strong resonances we hypothetized an immediate transition of neural groups from partial synchrony to almost complete discharge synchrony (Ba~ar et al., 1976b). In order to explain this view we constructed the electronic network seen in Fig. 11A, which consisted of 100 individual generators (self-oscillatory units, firing units, or relaxation oscil- lators). In our previous studies, we used also an electronic relaxation oscillator for a model-description of the interactions between the spontaneous activity of the brain and the stimulation signals, as well as for the understanding of various patterns in the brain output resulting from these interactions (Ba~ar, 1976). This model which consisted of a single relaxation oscillator was not satisfactory however, to demonstrate the probabilistic character of the amplitude enhancement
15
| SYNCHRONIZATION I @ on- lo,ng activity response SWITCHES ^ q, ^ �9
w, / ~ "~ synchr, bus / ~ /, ~ f ,. ~ State of the
stim. 1"~ q Network stirn, bus ooeoo A A A A a . A A A . . . . , input ooooo
OOOOO J
I ZZ) OOOOe
OOOOO OOINDO 5 ~ m I I l l l l l ~,$oo ,
50n -~ f i r ings- -~ I F = = -
�9 synchr. (100"7,) I
o free (0"/,) n STOP SWITCHES ] FOR ON-GOING �9 silent ( 0 % ) average (N=64) i UNIT FIRING
I
' f integrated output 2()0 msec ~ stirn.
on-going activity I response @
�9 ', A State of the ~.,_..~.~,1 A A / ' N h l I ~ . A . / ~ , State of the
88888 o o o o o O O O O O ~ 1 7 6 1 7 6 1 7 6 1 7 6 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 oO80 oo oo~)~8 ooooo ooooo
�9 synchr.( 07~ ~ �9 synchr. o free (1007o) o free �9 sitent ( 07~ average ( N = 6 4 ) ~ / ~ , ~ , / % �9 silent
I V -
' ' I 200msec stim.
on-going activity , response ,.A I A,
(07~ 1 (80%) (20%) average (N=6/,) I
I
i ,i 200 msec
stim.
Fig. 11. A The model network consisting of 100 relaxation oscillator units with different frequencies, covering a band of 8-14 Hz. The network can be brought to various synchrony states by means of the synchronization switches. By means of the stop-switches, the free oscillations of any unit can be inhibited, forming a silent unit which provides no firing pulse unless it is externally stimulated. The unit firings of 2 ms in duration are summed over a sink resistor of 50 s and are integrated with a suitable time constant. B-D Examples of the integrated output patterns consisting of two consequtive parts recorded before and after the onset of stimulation pulses, which are externally applied during different states of the network. The states of the network is illustrated graphically at the left side of each case. For comparison of their response magnitudes, the average patterns of 64 successively recorded outputs are also given for each state
observed in the brain responses upon identical stimuli (Ba~ar et al., 1976b). The electronic model network described below shows, in a way, the behavior of a probabilistic harmonic oscillator, which was employed as a theoretical model in the study of the important relation between the spontaneous EEG and brain responses (Ba~ar et al., 1976a).
In this network, each of the 100 oscillators has the ability of spontaneous firing i n a defined frequency range (in the example of our network : the generators fire between 8 and 14 Hz). The activity of individual
generators are integrated in the output of the network. The network is built in such a way that the generators can be brought to a state of full synchrony, partial synchrony or complete loss of synchrony (asynchrony); Depending on the number of the synchronization switches in on or off positions, full synchrony, partial synchrony or complete asynchrony for the firing units U 1 to U10 o can be reached (Fig. llA). The circuit allows also the following experiment. A number of oscillators, U, can be brought to a silent behavior in the absence of excitation ; in this case those U units~fire
16
only upon stimulation. This mode of working is in- spired from recent neurophysiological findings where a new class of single neurons showing no spontaneous activity in waking, REM sleep, and slow wave sleep was found in the brain stem of unrestrained cat. Siegel and McGinty (1976) recently showed that these cells discharge only in response to specific stimuli and remain silent in the absence of stimulation. These so called "silent cells" were widely distributed in the pons and midbrain and constituted a major percentage of neurons. In the following we will give only a short description of the network, since such a network could have been also built by using several other techniques (for example, digital computed simulation). We also want to emphasize that this network was not built in order to show how the brain's spontaneous activity is generated. Therefore, the firing units are not nec- essarily representative (analogues) of neurons in their kind of spontaneous discharge. The firing unit, U, represents only a self-oscillating unit which can be coupled with several other units, and which can be electrically excited (stimulated), provided that a certain threshold is reached and the excitation does not take place during a refractory period. There are inexcitable states followed by excitable states. Only concerning these black-box features, the U-units resemble neurons.
A Short Description of the Network
The model network consists of 100 relaxation oscil- lators with different relaxation periods, ranging from 70-125ms and, thus, covering a frequency range of 8-14 Hz. Each unit basicly consists of two monostable multivibrators with forward and backward connec- tions in order to create relaxation oscillations, and of a third one which provides 2 ms-pulses when the unit is triggered either internally or by an external stimulus. These unit firings with a duration of 2 ms are summed by means of a multi-input potentiometric circuit; the pulses enter the circuit through the corresponding 10 K~-resistors and they are summed over a 50 f~-sink resistor. The summed pulses of all the units are then integrated by means of an operational amplifier with a suitable integration time. The output of the network is the voltage measured after the integration. External stimuli are distributed to all the units through the stimulation bus. The firing pulses from the fastest unit, whose frequency is around 14 Hz, are also provided for all the units through the synchronization bus. But, whether a specific unit is brought to synchrony or not depends on the position of the synchronization switch of this unit. If the switch is on, the unit receives the synchronization pulses ; if not, due to a connection to ground, the unit is free from the pulses from the fastest
unit, and it continues to have its spontaneous activity. The spontaneous activity of a unit can only be in- terrupted by setting the corresponding stop-switch to its ground position. If this is done, this particular unit cannot give any spontaneous firing; however, it can still give a single pulse when it is excited by an external stimulus.
The timings of the units are so adjusted that all the units have 65ms-refractory periods, not coinciding necessarily in time. Therefore, each unit has an inexcit- able state with a duration of 65 ms, and an excitable state with a duration of T-65 ms, Tbeing the relaxation period of the unit. Since each free unit has a different period within the limits of 70 and 125 ms, the probabil- ity that a certain unit is in its excitable state is between 5/70 and 60/125. The fastest unit has the lowest probability to be excited by randomly presented exter- nal stimuli, and vice versa. Hence, if some of the units are brought to synchrony with the fastest unit, the minimum excitation probability is imposed on the units synchronized, regardless the original probability values assigned to them before synchronization. And, due to a partial synchrony, this reduction in overall responsiveness of the network is accompanied by a relative amplitude increase in the spontaneous in- tegrated activity of the network. This behavior of the model network is, in fact, in accord with the results of actual measurements carried out on various nuclei of the cat brain.
Experiments with the Network
According to Elul (1968), if we record the gross response of a population of neurons, it will be always an oscillation when a small number of generators are in synchrony. In general, if the output from a single generator is V, then given a population of N generators which are synchronized the summed output will be NV. When the generators lose synchrony among them-
selves, the output will decrease to I /N V. It is obvious that the maximal output from a group of generators is attained when they are all in synchrony; even if the output from each generator is not decreased, the summed output will diminish when the generators lose synchrony (Elul, 1968). The scope of Elul is important for the understanding of the experiments with our network, presented as follows:
a) Stage of Full Synchrony with no Silent Units. Figure l lB shows the results of an experiment where all the U-units of the network are brought to full synchrony by setting all the switches up. (The ampli- tude of the spontaneous oscillations vary directly as the number of synchronized generators.) When the network is stimulated with an external electrical stimu-
17
lating signal (step function or impulse function) there is no signal change in the output. The output signal is not amplified against the spontaneous activity. The ratio response/spontaneous activity = 1. As it is expected, the spontaneous signal has an almost sinusoidal behavior. The average curve of 64 events also shows that there is no response in this case.
b) Stage of Complete Asynchrony with no Silent Units. Figure l lC shows the results of an experiment where all the U-units of the network are free or asynch- ronous. As one observes immediately, the spontaneous signal has no more the shape of the pure sinusoid and the spontaneous activity (spontaneous integrated ac- tivity) has much lower voltages against the activity in the fully synchronized stage (compare with Fig. llB). (Signals arising from nonsynchronized generators in- crease only as the square root of the number of generators.) Upon application of the stimulation signal we observe always a response in the form of an amplitude increase with a time-locking within the first 100ms. The enhancement factor (i.e., the ratio of the maximal response amplitude to the rms value of the spontaneous activity), may reach values up to 3. At the bottom, the average curve of 64 events is also given.
c) All the Generators are Either Asynchronous or are Silent Units; No Synchronized Generators. In this case 20 of the 100 U-units are silent generators, and 80 of them are completely free or asynchronous. None of the generators are brought to synchrony. As Fig. l i D illustrates, the enhancement factors are high, and can reach values up to 4. The time-locking is perfect. Averaged curve of 64 events is also given at the bottom. (It is obvious that with a larger percentage of the silent generators in the network, much higher values of the enhancement factors can be reached.)
This network was not built to be used as a model for the simulation of the neurophysiology of brain responsiveness or of the mechanism of sustained firing ability. It rather provides an illus- trative demonstration for the gross responsiveness of a system consisting of firing units which can undergo various synchrony and asynchrony stages, regardless the nature of the firing mechanism. (The firing mechanism is treated as a black box.) Hence, from results of the experiments with the network, we recognize immediately that the enhancement factors do increase when the number of asynch- ronous (or free) firing units increases. On the contrary, when the number of synchronized U generators increases there is less re- sponsiveness, the enhancement factors are lower. Moreover, the time-locking in the response pattern is weakened. Upon addition of the silent generators to the network the system can be brought much easily to a responsive stage where a perfect time-locking is observed following the stimulation. Further increase in the enhancement factors can be reached only by increasing the ratio of the silent generators to the spontaneously firing generators in the network.
In a given brain structure, the synchrony among individual generators and the existence of silent gene-
rators can describe, in part, the variability of enhance- ment factors in evoked potentials. According to the results of Sect. 3.6, the response amplitude of brain evoked potentials can be roughly predicted when the voltage of the spontaneous activity is known. The on- going activity of the network of Fig. 11 also allows predictions of the enhancement factors. However, the accuracy is somewhat higher than the accuracy in evoked potential experiments. Because, there exists, certainly, several other factors influencing the magni- tude of real evoked potentials.
Beurle (1956) treated a network of a population of cells which were randomly distributed throughout a certain volume, by using anatomical observations of the cat's visual cortex. Beurle's treatment was essen- tially statistical in that he considered the behavior of groups of cells rather than the responses of individual units within the system. He pointed out that properties of the net would depend critically upon the proportion of "excitable cells" and the fraction of "used cells", or those that were refractory of recent activity. Although the aim of considering Beurle's network was different from our consideration, it is important to note that similar concepts emerge from theoretical conside- rations and from our experimental findings on the responsiveness of population of neurons in specific brain structures.
5. Suggestions and Comments for Investigators Working Toward Theories of Signal Transmission in the Brain
The general features of the dynamics of grossly re- corded brain potentials which are deduced immediate- ly from our investigations, can be described as follows :
1) Synchronization of Resonance Phenomena. The re- sonance phenomena occur synchronously in various structures of the brain. The responsiveness in the studied brain nuclei shows that, upon stimulation, they act as coupled oscillators without phase lag in c~ and frequencies.
2) It is demonstrated, that there is no phase shift between well developed single EP responses of all the measured nuclei in a frequency range up to 25 Hz. (This information could not have been obtained with the information based only on AEP-measurements.)
3) The present study combines EEG and EP record- ings, such that, one is able to make comparisons between EEG and EPs in absolute magnitudes (and not in relative terms based on the comparisons of power spectra and amplitude frequency characteris-
18
tics). The tables, which give us mean value-amplitudes of the spontaneous activity and evoked potential re- cordings are not data obtained during specific be- havioral or pathological studies. Therefore, further studies should be undertaken, in order to show how the combined EEG-EP recordings change upon in pathological or specific behavioral (or psychological) condictions.
4) The combined study of the dynamics of single EEG- EP recordings serves to the understanding of the coherency before and after the stimulation: the impor- tant coherency increase in evoked potentials can be interpreted, at the first glance, as a stimulus induced- regulation of energy increase in the form of accumu- lation in certain discrete frequency channels, accom- panied by the phase stabilization effect of the stimulation.
Since the coherency values presented reflect the common and synchronized power measured from pair- ings of analyzed brain structures, one can conclude that, upon stimulation, a significant fraction of the common energy of all the studied brain centers is accumulated in a sharp frequency region between 10 and 13 Hz during the waking stage. Within the e- /~ frequency range, the energy stabilization following the stimulation is shifted to slightly higher frequencies during SWS (see the companion report, Ba~ar et al., 1979).
5) During SWS, there is an important power increase of the response components (and of the spontaneous activity) in the 1-40 Hz frequency range against similar frequency components during waking stage. The magnitudes of the response components higher than 40 Hz do not increase during SWS. The entire course of EP during SWS depict much more total energy than the entire course of EP during the waking stage.
6) In the study of frequency characteristics obtained from AEPs, we have been able to indicate prominent peaks of the amplitude in the ~ frequency range (for all the nuclei), in 40 Hz range (GEA, HI), in the 50-60 Hz range (MG and RF) and in the 70 Hz range (IC) (Ba~ar et al., 1975b). The mutual dependence of these com- ponents could be shown, however, only with the studies of single EEG-EP recordings which were re- corded simultaneously from these nuclei. A component analysis describing the mutual influences of various frequency components from the studied brain centers will be pertinent for pathological or behavioral studies, since it is shown that, in given nuclei, most of the frequency components are independent frequency components (Ba~ar et al., 1979, companion report).
7) Principle of Synchronized Selectivities : as revealed by the e and/3 components of simultaneously recorded EPs, as well as by the coherence functions computed for all possible pairings of the recording electrodes, the selectivities in the frequency range of 8-25 Hz (e - f l range), which are displayed by the frequency character- istics in the form of prominent and common amplitude maxima, are synchronized selectivities of the studied nuclei. A synchronization between these nuclei is observed in the time domain, regarding both the simultaneously recorded in-phase EP-components (Figs. 3 and 6) and the coupling and harmony in the proportional increase or decrease of their magnitudes in successive single EP recordings (Fig. 10). Between 8 and 25 Hz there exist, in fact, two distinct selectivities in ~ and/~ channels as revealed by the instantaneous frequency characteristics presented in Fig. 5. The pro- minent 8-25 Hz band in the amplitude characteristics of Fig. 1 is due to the fusion of c~ and/~ peaks resulting from the process of averaging, c~ and /~ channels are separated, however, also in most of the coherence function plots, despite the averaging procedure in their computation (Fig. 7).
8) lnternal Evoked Potentials. Our findings showed that the evoked responses in all the nuclei and in all the frequencies are strongly dependent on the spontaneous activities just prior to stimulus. There are cases in which the filtered EEG-EPograms depict already in the EEG portion ample potentials similar to the filtered EP signals immediately after stimulation (Figs. 3 and 4). The resemblance in the shapes of EPs and such EEG-bursts leads us to use the expression of "Internal Evoked Potentials" for the description of ample and synchronized EEG-recordings, which, in the rule, occur only upon stimulation. When before the stimulation relevant internal evoked potentials are recorded, usually the EPs induced by stimulation do not have large amplitudes. Accordingly, we assume that the evoked potential research with single EPs will be useful also in contributing to the understandings of EEG-population dynamics.
9) The Background Activity. From the present study and from our earlier studies (Ba~ar et al., 1975b, c, 1976a-c) it emerges that, in the understanding of brain evoked potentials, the spontaneous activity should not be considered as a background activity to be elim- inated by averaging procedure (Ungan and Ba~ar, 1976). The spontaneous activity prior to stimulus is a part of the evoked potentia ! . It is not possible to understand the real components in the EPs without the knowledge of the EEG prior to stimulus.
19
Appendix
The Definition of the EEG-EPogram
The EEG-EPogram is a b ra in po ten t ia l record which consists of a b o u t 1 s spon taneous act ivi ty (EEG or SEEG) jus t p r io r to st imulus, and the EP signal fol lowing the stimulus. F o r the analysis of responses in the lowest f requency range, for example 2 Hz range, a t ime pe r iod of abou t 5 s before s t imula t ion would be required, i.e. a b o u t 10 waves.
E E G means a g raph or record of the spon taneous electr ical act ivi ty f rom the encephalon, or brain. The EEG-EPogram would then mean a combined graph, consis t ing of the g raph of electr ical act ivi ty of the encepha lon and f rom the graph of evoked response of the encephalon. Therefore, there is some r edunda nc y when the te rm graph is used. However , nowadays , the terms E E G and EPs are used as measu red quant i t ies (or measured variables), ra ther than graphs. Accordingly , the express ion EEG-EPogram will be used to indicate the fol lowing bra in r eco rd :
EEG-EPogram = Spon taneous Act ivi ty of the Brain + Evoked Potent ia l .
References
Ba~ar, E. : A study of the time and frequency characteristics of the potentials evoked in the acoustical cortex. Kybernetik 10, 61-64 (1972)
Ba~ar, E.: Biophysical and physiological systems analysis. Massachusetts: Addison-Wesley, Advanced Book Program 1976
Ba~ar, E., Durusan, R., G6nder, A., Ungan, P. : Combined dynamics of EEG and evoked potentials. II. Studies of simultaneously recorded EEG-EPograms in the auditory pathway, reticular formation, and hippocampus of the cat brain during sleep. Biol. Cybernetics 34, 21-30 (1979)
Ba~ar, E., G6nder, A., Ozesmi, ~., Ungan, P. : Dynamics of brain rhythmic and evoked potentials. I. Some computational me- thods for the analysis of electrical signals from the brain. Biol. Cybernetics 20, 137-143 (1975a)
Ba}ar, E., GiSnder, A., Ozesmi, ~., Ungan, P. : Dynamics of brain rhythmic and evoked potentials. II. Studies in the auditory pathway, reticular formation, and hippocampus during the waking stage. Biol. Cybernetics 20, 145-160 (1975b)
Ba~ar, E., G6nder, A., Ozesmi, ~., Ungan, P. : Dynamics of brain rhythmic and evoked potentials. III. Studies in the auditory pathway, reticular formation, and hippocampus during sleep. Biol. Cybernetics 20, 161 169 (1975c)
Ba~ar, E., G/Snder, A., Rona, M., Ungan, P. : Resonance phenomena in the electrical activity of the brain. Abstract of the Third European Meeting on Cybernetics and Systems Research, Vienna, April 20-23, 1976a (proceedings in press)
Ba~ar, E., G~Snder, A., Ungan, P. : Important relation between EEG and brain evoked potentials. I. Resonance phenomena in sub- dural structures of the cat brain. Biol. Cybernetics 25, 27-40 (1976b)
Ba~ar, E., G/Snder, A., Ungan, P. : Important relation between EEG and brain evoked potentials. II. A systems analysis of electrical signals from the human brain. Biol. Cybernetics 25, 41-48 (1976c)
Ba~ar, E., Ungan, P. : A component analysis and principles derived for the understanding of evoked potentials of the brain : studies in the hippocampus. Kybernetik 12, 133-140 (1973)
Beurle, R.L.: Properties of a mass of cells capable of regenerating pulses. Proc. R. Soc. London, Set. B 240, 55-94 (1956)
Dumermuth, G., Fliihler, H. : Some modern aspects in numerical spectrum analysis of multichannel electroencephalographic data. Med. Biol. Eng. 5, 319-331 (1967)
Elazar, Z.,. Adey, W.R. : Electroencephalographic correlates of learn- ing in subcorticaI and cortical structures. Electroencephalogr. Clin. Neurophysiol. 23, 306-319 (1967)
Elul, R. : Randomness and synchrony in the generation of the electroencephalogram. In: Synchronization of EEG activity in epilepsies. Petsche, H., Brazier, M.A.B. (eds.), p. 59. Berlin, Heidelberg, New York: Springer 1968
Glaser, E.M., Ruchkin, D.S. : Principles of neurobiological signal analysis. New York: Academic Press 1976
Ungan, P., Ba~ar, E. : Comparison of Wiener filtering and selective averaging of evoked potentials. Electroencephalogr. Clin. Neurophysiol. 40, 516-520 (1976)
Received: February 27, 1979
Prof. Dr. E. Ba~ar Physiologisches Institut der Universit~it OlshausenstraBe 40/60 D-2300 Kiel Federal Republic of Germany
