ysiology 64 (2007) 18–23www.elsevier.com/locate/ijpsycho

International Journal of Psychoph

Theory of the normal waking EEG: From single neurones to waveformsin the alpha, beta and gamma frequency ranges

Robert Miller ⁎

Otago Centre for Theoretical Studies in Psychiatry and Neuroscience, Department of Anatomy and Structural Biology, School of Medical Science,University of Otago, P.O. Box 913, Dunedin, New Zealand

Received 20 May 2006; received in revised form 24 June 2006; accepted 13 July 2006Available online 25 September 2006

Abstract

The classic alpha rhythm, recorded intracortically, consists of alternating surface-negative troughs and briefer surface-positive peaks. Thetroughs are associated with neuronal hyperpolarization, the peaks with brief depolarization and burst firing. Each hyperpolarization is mainly apotassium potential, lasting ∼ 100 ms. Depolarization and burst firing arise when this inactivates. In the desynchronized state, membrane potentialis poised just below threshold. Firing in vivo is somewhat irregular and non-bursting. It is suggested that EEG bistability (classic alpha vsdesynchronization) corresponds to bistability of single pyramidal cells. In vitro, paired pulses lead to depression of synaptic transmission insynapses linking two pyramidal cells, but to facilitation in synapses linking pyramidal cells to inhibitory neurones. These effects should berecruited by burst firing in vivo. Thus, enhancement of inhibitory and excitatory transmission occur respectively during the classic alpha rhythm,and the desynchronized state. As a result both states tend to be self-sustaining. In the desynchronized state high frequency (gamma or beta) activitypredominates. In simulations, gamma activity has been modeled as the behaviour of cortical networks where populations of excitatory andinhibitory neurones interact. These simulations assume conduction times between neurones to be negligible. However, this is not true for long-distance interactions. Introduction into the models of plausible conduction delays should slow the oscillation frequency. The activated cortex canthen produce not only gamma activity but also beta, and sometimes alpha activity. Thus, alpha frequencies can arise both in the “idling” cortex(classic alpha), and in the activated cortex, although the respective mechanisms are quite different.© 2006 Elsevier B.V. All rights reserved.

Keywords: EEG; Gamma; Beta; Alpha; Paired pulse; Up-state; Down-state

1. Introduction

The electroencephalogram (EEG) is usually described interms of its frequency components, which range over two ordersof magnitude, from 1 to 100 Hz (oscillation periods from 10 to1000 ms). By convention this range is subdivided into “gamma”(35 Hz upwards), “beta” (13–35 Hz), “alpha” (8–13 Hz), “theta”(4–8 Hz) and “delta” (1–4 Hz) bands. In the normal wakingEEG, theta and delta activities are rare or non-existent. The focusof this article is therefore the oscillations in the alpha, beta andgamma ranges. The aim is to provide a theoretical frameworkwith which to explain massed electrical activity (seen in theEEG) in terms of activity in single cortical neurones.

⁎ Tel.: +64 3 479 7362; fax: +64 3 479 7254.E-mail address: robert.miller@stonebow.otago.ac.nz.

0167-8760/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.ijpsycho.2006.07.009

Two quite different neurodynamic principles are invoked.The first underlies the classic alpha rhythm (Berger rhythm), andthe transition from this to the so-called “desynchronized” state ofthe cortex. These two states of the EEG are often seen asreflecting, respectively, “idling” activity, and the active state ofthe cortex. The second principle applies just to the activatedcortex, and is derived from simulations which attempt to accountfor the gamma rhythm. By simple extension, these simulationscan be used to explain rhythms at lower frequencies (beta, alpha,and under some circumstances even lower frequencies). As aresult, EEG activity in the alpha band receives contributionsfrom both of the mechanisms proposed. This helps to unravel thecomplex status of the alpha rhythm: While traditionally it hasbeen held to be an “idling rhythm”, much recent evidence hasemphasized that activity in the 8–13 Hz band can have preciseand repeatable correlations with information processing in avariety of cognitive tasks (Başar, 1997, 2004).

Fig. 1. Electrocorticogram from motor cortex of monkey, showing classic alphaactivity (from Dusser de Barenne and McCulloch, 1936, used with permissionfrom the American Journal of Physiology).

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2. The classic alpha rhythm

The first definite EEG phenomenon to be described was arhythm of frequency 8–13Hz, most prominent over the posteriorpart of the head when eyes are closed, which usually ceaseswhen the eyes are opened (Berger, 1929). This is the “classic”alpha rhythm. With scalp recording, there is inevitable signalaveraging over several cm2. Therefore, what is seen with scalprecording is limited to activity which is coherent over such alarge area. The actual mechanism of the classic alpha rhythm isbetter studied on a smaller scale, with subdural or intracorticalelectrodes. These few studies, some of them from before 1950(Dusser de Barenne andMcCulloch, 1936; Bremer, 1949) can besupplemented by data on a number of other electrographicphenomena, which, while not spontaneous alpha rhythms, prob-ably involve similar mechanisms, allowing them to be used asmodels of the classic alpha rhythm. Amongst these is the aug-menting rhythm, first described by Dempsey and Morison(1943): regular rhythmic electrical stimuli within the alphafrequency range, applied to the thalamus, evoke a distinctiveform of electrographic response from the cortex, at the samefrequency. These rhythmic responses are not present for the firststimulus of a train, but grow in amplitude over a series of stimuli.Similar resonant responses, selective to the alpha frequencyrange, occur when rhythmic photic stimuli are given (Adrian andMatthews, 1934). Moreover, single sensory stimuli, or electricalstimuli delivered to ascending sensory pathways (Adrian, 1936)evoke rhythmic responses at alpha frequencies.

On the basis of evidence obtained in these circumstances, thefollowing points can be made about the alpha rhythm, andrelated phenomena. (i) The classic alpha rhythm is not a sym-metrical sinusoid, but appears as a peak (positive when recordedfrom the cortical surface), arising out of a more prolongednegative trough (see Fig. 1). This is not apparent in scalp-re-corded EEG traces. (ii) In depth profiles, this peak/troughwaveform reverses in sign at a depth of 0.6–1.0 mm (Spencerand Brookhart, 1961a,b), roughly between deep lamina III andlamina V of the cortex. (iii) These waveforms spread tan-gentially, especially in the region of lamina IV/V, so that suchneural activity is coherent over a substantial area of the cortex(Castro-Alamancos and Connors, 1996). (iv) When recordingcombines single-unit activity and massed potentials, it is clearthat the surface-positive peak is accompanied by rapid burstfiring (at frequencies above 100 Hz) in the principal neurones(pyramidal cells) of laminae III–V. (v) In intracellular studies,the trough in the massed potential records is accompanied bydeep hyperpolarization, broken at intervals of ∼100 ms byepisodes of depolarization and burst firing (Calvet et al., 1964)(see Fig. 2).

The relation between prolonged hyperpolarization and burstfiring requires further consideration, and is best revealed byevidence on augmenting responses. In a series of stimuli to thethalamus, the first few stimuli fail to produce the prolongedtrough in surface potentials (Spencer and Brookhart, 1961).Only after a few stimuli does the peak/trough sequence becomeestablished. When augmenting responses are established, testingstimuli delivered to the thalamus at various delays after a burst of

impulses have effects which differ according to the delay(Grossman et al., 1967). In the first 50 ms, the testing pulse isessentially unable to produce any excitatory response in theimpaled neurone. At longer delays, increasing as time elapsestowards the expected time of the next burst, the thalamic teststimulus can produce excitatory responses with burst firing. Burstfiring thus appears to depend on the duration of prior hyper-polarization, and this in turn depends on the vigor of the precedingburst.

Biophysical analysis of the prolonged hyperpolarizationshows it to have two components (Nunez et al., 1993). For thefirst 50 ms, the hyperpolarized potential can be reversed byintracellular chloride injection, and has a reversal potential ofabout − 70 mV, compatible with its being a chloride-mediatedIPSP (see Fig. 3) — presumably a rebound inhibitory effectmediated by local cortical inhibitory interneurones. However,after 50 ms, when burst firing in response to a stimulus isincreasingly permitted, the reversal potential is far more neg-ative, and not reversed by chloride injection (Fig. 3). This latehyperpolarization thus appears to be a potassium potential.

Further biophysical analysis, in slice preparations, has beenconducted byDeisz (1996). Pyramidal cells were hyperpolarizedby a current step. On release from hyperpolarization, a depolar-izing shift occurred (taking the membrane potential to morepositive levels than the prior resting potential), and this could beaccompanied by burst firing. Importantly, the vigor of thisrebound depolarization increased with increasing duration of theprior hyperpolarization, approaching maximum amplitude forhyperpolarizations of duration 75–12 ms (mean∼ 90ms). Deiszinferred that hyperpolarization activates a potassium current,which then inactivates over a period of about 90 ms. Deiszsuggests that, in vivo, this time course sets the frequency rangefor the classic alpha rhythm (Fig. 4).

3. The dynamics of the desynchronized state

In intracellular studies of single pyramidal cells,, in vivo,membrane potential is bistable, there being a “down-state” withhyperpolarization, and an “up-state”, where membrane poten-tial is held, poised just a few mV negative of threshold forfiring (Inubushi et al., 1978; Timofeev et al., 2001). These twostates correlate with EEG states, respectively where slow-wavesleep (or classic alpha activity) can occur, and the desynchro-nized waking state. Because the EEG and single unit bistabilitymatch each other, the single unit bistability can be assumed tobe coherent over a substantial area of the cortex. The ionicmechanism of the up-state has been examined in a number ofstudies in slice preparation. Pyramidal cell dendrites can

Fig. 2. Alpha-rhythm in cat (local anesthesia and flaxedil). Upper trace:Intracellular record from neurone at a depth of about 800 μm. Middle trace:electrocorticogram from transcortical derivation (0–1000 μm). Reprintedfrom Electroencephalography and Clinical Neurophysiology, volume 17,Calvet et al. (1964) Étude stratigraphique corticale de l'activité EEG spontaneé.pp. 105–125. Copyright 1964, with permission from the InternationalFederation of Clinical Neurophysiology.

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generate calcium or sodium spikes (Kim and Connors, 1993;Amitai et al., 1993), which propel membrane potential towardsthe threshold, in response to synaptic activation. However, asmembrane potential approaches the threshold, a type of potas-sium current (the “A”-current) is opened, to restrain thedepolarizing shift (Schwindt et al., 1988; Spain et al., 1991;Locke and Nerbonne, 1997). Such currents are presumed tohold membrane potential within ∼5 mV of threshold in the“up-state”.

Fig. 3. A: Effect of intracellular chloride diffusion on IPSPs in cortical cell. 10 min chReversal potential for cortical IPSP. The early part of the IPSP has a reversal poten− 93 mV. (From Nunez et al, 1993; used with permission from the Journal of Neur

The temporal patterning of impulses in single pyramidal cellsalso shows two modes. In slice preparations, firing may consisteither of bursts, or of a regular non-bursting pattern. Somepyramidal cells switch from one to the other pattern accordingto the prevailing membrane potential (McCormick et al., 1985;Foehring and Wyler, 1990) — bursting when hyperpolarized(presumably using mechanisms such as those described for theclassic alpha rhythm), and regular spiking when depolarized tonear threshold. In vivo there is a similar bimodality, except thatin the “up-state”, firing, while definitely non-bursting, is some-what irregular, rather than regular (Inubushi et al., 1978; Sternet al., 1997). Since up-states and down-states are coherent overa large area of the cortex, this bimodality is characteristic notjust of single pyramidal cells, but of large cortical networks.This raises the question of how bimodality in single cells alsobecomes a network property.

The following argument provides a tentative answer to thisquestion. It is based on what is known about the behaviour ofsynaptic transmission in response to two afferent impulsesspaced close together in time (see Fig. 5). In vitro, when twoneighbouring neurones are impaled, with a connecting synapticlink (probably a unitary synapse), it is possible to study suchbehaviour. Moreover, one can compare the properties of syn-apses connecting one pyramidal cell with another (Py→Py

loride diffusion (left) reverses the early part of the IPSP but not the later part. B:tial between − 63 and − 77 mV. The later part has a reversal potential near toophysiology).

Fig. 4. A: Superimposed records of membrane potential changes during and afterhyperpolarizing current pulses of increasing duration, in a bursting neurone inpresence of TTX and Cd++. D: Plot of depolarizing shift on cessation ofhyperpolarization vs duration of hyperpolarization. Reprinted with permissionfrom Neuroscience, Volume 70 Deisz, R. A tetrodotoxin-insensitive sodiumcurrent initiates burst firing of neocortical neurons. pp. 341–351. Copyright1996.

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synapses) with those connecting a pyramidal cell to an in-hibitory interneurones (Py→ I) synapses. For Py→Py synap-ses, paired pulse depression is usually seen. That is, when twoimpulses are initiated in the transmitting cell within 5–20 ms ofeach other, the response of the recipient cell to the secondimpulse is depressed (by as much as 50%) compared to theresponse to single isolated impulses (Thomson, 1997). In con-trast, for Py→ I synapses, paired pulse facilitation is seen: The

Fig. 5. Upper traces: EEG; middle traces: intracellular record from the corticalneurone; lower traces: electrooculogram. From left to right: slow-wave sleep;REM sleep; waking. Reproduced from Proceedings of the National Academy ofSciences, U.S.A. 98, 1924–1929, (Timofeev et al., 2001: Disfacilitation andactive inhibition in the neocortex during the natural sleep–wake cycle.).Copyright (2001) National Academy of Sciences, U.S.A.

response to the second of two close-spaced impulses is in-creased (by as much as five-fold) compared to those producedby isolated impulses (Thomson et al., 1993) (Fig. 6).

What could these findings mean for network behaviour invivo? Assuming that paired pulse effects occur in vivo as in vitro,they would be recruited during burst firing, since interspikeinterval in a burst is generally less than 10 ms. Since Py→Pytransmission shows paired pulse depression, such transmissionwill be optimally effective when burst firing does not occur, thatis, in the up-state (desynchronized state of the EEG). However,for Py→ I synapses, which show paired pulse facilitation, trans-mission would be optimally effective when bursting is likely,that is in the down-state (when the classic alpha rhythm may beseen). Hence, the excitation needed to produce the up-state isitself favored by the up-state, as a network property. It wouldthen require major synchronized inhibition acting on very manyneurones, to shift this to the deep hyperpolarization needed toreinstate the down-state. Likewise, the inhibition needed toproduce the down-state is itself favored by the burst firing whichoccurs preferentially in that state. Overall, cortical networks (notjust single neurones) are constrained to behave in a bimodalfashion, with two modes of relative stability. Major synchro-nized inhibition or excitation is required to shift from one modeto the other.

Fig. 6. Paired pulse effects, in dual impalement studies in cortical slices,depicted with superimposed traces: upper: paired pulse depression intransmission from one cortical pyramidal cell to another; lower: paired pulsefacilitation in transmission from a pyramidal cell to an interneuron. Reprintedwith permission from Journal of Physiology, Volume 502, Thomson, A.M.Activity-dependent properties of synaptic transmission at two classes ofconnections made by rat neocortical pyramidal axons in vitro. pp. 131–147.

Fig. 7. Results of simulation of local interaction between populations ofexcitatory and inhibitory neurones (128 pairs), showing emergence of ∼ 40 Hzrhythm (see text for details). Reproduced with permission, from Wennekers andPalm (2000), in Time and the brain. (Harwood Academic Publishers).

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What is the relation between such bistability and informationprocessing by the cortex? It is widely believed that informationis represented in the cortex by neural assemblies, that isdispersed collections of cells more strongly connected withinthemselves than to the surrounding majority of neurones. A keyquestion for understanding how neural assemblies operate is:“How many co-active synapses on a neurone are needed tobring it to threshold for firing?” In the down-state, because ofdeep hyperpolarization, it is likely to be as many as 30–40 (asassumed by Abeles, 1981). In the up-state, with membranepotential poised just below threshold for firing, and with unitaryEPSPs at maximum size, unaffected by paired pulse depression,it is likely to be quite small, perhaps 5 or less. In the down-state,because the alpha rhythm is coherent over a wide area, there isconsiderable redundancy. The information capacity availablefor representing percepts and concepts is low. In the up-state,with a low convergence ratio needed to fire pyramidal cells,active networks, intricately-patterned in space and time canemerge, each made up of only a tiny minority of all pyramidalcells and their connections. Many different networks of this sort(cell assemblies) may be able to emerge in different circum-stances. In this state, the cortex as a whole has a high capacity torepresent sensory, motor or cognitive information. The exacttiming of impulses in each pyramidal cell, when firing is non-bursting but irregular, would then depend on the contingenciesof temporal convergence of the rather few coactive synapsesneeded to fire such neurones in the up-state.

4. Gamma and beta activity

The activated state of the cortex, though referred to as“desynchronized” is not desynchronized in a strict sense. Thereis significant activity of rather low amplitude, and usually ofhigher frequency (beta and gamma ranges) compared to theclassic alpha rhythm. This activity is presumed to reflect theintricately-patterned impulse traffic in neural assemblies. Thehigher frequency (gamma band) activity cannot usually bedetected with scalp electrodes, because it is too localized toregister at scalp electrodes. With intracortical recording, theserhythms approximate much more closely to ideal sinusoidalwaveforms than does the classic alpha rhythm (Steriade et al.,1996). The coherence between gamma activity recorded at twoadjacent sites falls off steeply with distance, become negligibleat distances of 5 mm (Eckhorn, 2000). Electrographic activityin the beta range is obviously coherent over a larger distancethan this, because it can be recorded with scalp electrodes inhumans. In addition, there is increasing evidence that activity inthe alpha range occurs in the activated cortex, with manycorrelations with concurrent information processing beingdescribed (Klimesch, 2000; Başar, 2004). Obviously this is aform of electrographic activity very different from the classicalpha rhythm. Recent evidence suggests that in the activatedcortex, there is a regular inverse relationship between thefrequency of electrographic activity and the distance overwhich it is coherent (Von Stein and Sarnthein, 2000). Inaddition, the sort of information processing varies with thefrequency of electrographic activity, and the distance over

which it is coherent. For purely perceptual processing,presumably involving just the primary sensory cortex,gamma activity predominates; information processing at acognitive level evokes beta activity; and high-level processinginvolving working memory or top-down influence on percep-tual processes elicits alpha-frequency activity (von Stein andSarnthein, 2000).

A useful paper to help understand such relationships is asimulation of Wennekers and Palm (2000), explicitly of gamma-frequency activity, but capable of throwing light also on slowerrhythms of the active cortex. Their model consists of a one-dimensional row of excitatory and inhibitory neurones, theexcitatory ones influencing the corresponding inhibitory neu-rones, as well as their neighbouring excitatory neurones, whilethe inhibitory neurones feed back inhibition to neighbouringexcitatory neurones. The spread of activity to neighbouringexcitatory neurones occurs over a wider span for excitatory thanfor inhibitory connections (as is the case in the real cortex). Thetime course assumed for EPSPs (rise time of 1 ms, decay time of2 ms) is somewhat shorter than for IPSPs (rise time of 2 ms anddecay time of 4 ms). All transmission delays between oneneurone and another are assumed to be 1 ms, short comparedwith the neuronal integration time. No pacemaker oscillator isassumed. Nevertheless, when the network is set in motion, as anemergent property of its interactions, quasi-sinusoidal rhythmicactivity appears, with frequency of ∼ 40 Hz (cycle time of25 ms)(see Fig. 7). This is a population rhythm, not usuallydiscernible in spike trains from individual neurones in themodel (whose firing rate is mainly well below the populationoscillation frequency). One can assume that the frequency of thepopulation oscillation bears a fairly direct relation to theassumed delays in initiation of EPSPs and IPSPs, and thetransmission delays between neurones.

Suppose now that axonal conduction delays are introducedinto the model. This will not have much effect on populationoscillation frequency if conduction times between neuronesremain small compared to their own integration times. This islikely to be the case for local interactions (up to a few milli-meters). However, if interactions over wider distances are

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considered, axonal conduction times become more significant.In this case it is predicted that there be an inverse relationbetween distance over which coherence is seen and the fre-quency of the corresponding rhythms (as actually observed).Conduction delays in long corticocortical axons can be severaltens of milliseconds, even for conduction distances of ∼10 mm.Therefore it is likely that introduction of axonal conductiondelay into the Wennekers/Palm model could easily convertgamma frequency oscillations to beta frequency ones (withcycles times ranging from 30 to 70 ms). It is also quite possiblethat the same process for more widely-dispersed interactionscould produce activity in the active cortex in the alpha range(cycle time 77–125 ms) or even into the theta range. In all suchcases, one would predict that the waveform, as recorded withintracortical electrodes, should approximate to a sinusoidal os-cillation, which, in the case of alpha-band activity woulddistinguish it sharply from the classic alpha rhythm.

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