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[16:51 26/2/2009 5283-Millsap-Ch28.tex] Job No: 5283 Millsap: The SAGE Handbook of Quantitative Methods in Psychology Page: 675 675–696

PART IV

Specialized Methods


28Neuroimaging Analysis I:Electroencephalography

Josep Marco-Pal larés, Este la Camara,Thomas F. Münte and Antoni Rodr íguez-Fornel ls

COGNITIVE NEUROSCIENCE ANDNEUROIMAGING TECHNIQUES

Cognitive neuroscience has been termed thebiology of mind. As such it is, to a largeextent at least, a science about the humanmind, as many of the higher cognitive func-tions, including language processing, episodicmemory and executive functions, can best orexclusively be studied in human subjects. Tofulfil its promise, cognitive neuroscience is inneed of techniques that can serve as windowsto the brain as it carries out the processes thatmake up the mind. Since human participantsare under study, these techniques need to benon-invasive.

In light of this, the recent success ofcognitive neuroscience can be attributed totwo factors: the increasingly sophisticatedexperimental designs that are borrowedfrom cognitive science and psychology, and,importantly for the present Chapter, themethodological developments in neuroimag-ing techniques.

In the present Chapter and the follow-ing one we will concentrate on the two

major and most widely used neuroimagingtechniques, namely methods derived fromelectroencephalography (EEG) and (func-tional) magnetic resonance imaging (fMRI).While EEG has been around for about 80years, recent methodological advances insignal analysis have led to a renewed interestin EEG-based experiments. Functional MRI,while having a much shorter history of littlemore than 15 years, has already reacheda high level of sophistication, but moredevelopments regarding analysis techniquesare to be expected.

For space reasons, we will not discuss otherneuroimaging techniques here, but wouldlike to point out that each of these possessunique properties that make them valuabletools in cognitive neuroscience. Near infra-red spectroscopy (NIRS) uses near-infra-redlight to non-invasively measure changes inthe concentration of oxygenated (O2Hb) anddeoxygenated (HHb) hemoglobin. Light fromthe near-infra-red spectrum can penetrate theskull and reaches the underlying cortex, whereit is partly absorbed and partly reflected. Fromthe amount of reflected near infra-red light, it


678 SPECIALIZED METHODS

is possible to calculate changes in the concen-tration of O2Hb and HHb.The main advantageof NIRS is that it can be used in participantsthat are not able to perform tasks in an fMRIscanner (e.g., infants, severely compromisedpatients), and moreover with tasks that couldnot be performed in a scanner (such aspointing, object manipulation, and so forth).Multichannel systems can be used to providedata with reasonable spatial resolution. Werefer the reader to Obrig and Villringer (2003)for a technical description and Horovitz andGore (2004) for an application to a cognitiveneuroscience question.

Positron emission tomography (PET)yields tomographic pictures of the brainbased on the decay of injected radioactivetracers. Whereas PET studies of task-relatedchanges in blood flow (using 15O-labeledwater or butanol, for example) have mostlybeen replaced by fMRI, PET gains increasingimportance in cognitive neurosciencebecause of its ability to map neurotransmitterchanges during cognitive and other tasks (seeMonchi et al., 2006 for an application), andthe density of Alzheimer disease plaques(see Cohen, 2007, for a review of thetechnique).

Whereas transcranial magnetic stimulationmight not be considered a neuroimagingtechnique in the strict sense, the abilityto create virtual lesions in normal humanparticipants has great potential, in particularwhen combined with other neuroimagingtechniques such as event-related brain poten-tials (ERPs) (see Rollnik et al., 2004, for anexample) or fMRI (see, Ruff et al., 2007, for anexample). We will now turn to the discussionof the EEG signal.

SPATIAL AND TEMPORALPROPERTIES OFELECTROENCEPHALOGRAPHYAND (FUNCTIONAL) MAGNETICRESONANCE IMAGING SIGNALS

When groups of neurons are involved ininformation processing, they show a change

in their firing rate. The physiological phe-nomena associated with this change can bedetected and recorded by several neuroimag-ing methods, i.e., EEG, magnetoencephalog-raphy (MEG), fMRI and PET. Of these,EEG and fMRI are currently the most widelyused brain imaging techniques. As previouslystated, EEG is usually recorded using between16 to 128 electrodes that are placed onthe intact scalp, whereas fMRI providesinformation about the hemodynamic responseof several thousands of voxels into which thebrain is divided. The spatial information offMRI (in the order of few mm) is thereforemuch better than the one obtainable by EEG(cm). This disadvantage of EEG is balancedby its superb temporal resolution (millisec-onds), which compares to several secondsin fMRI.

Whereas the information provided by fMRIand EEG respectively may in some sensebe viewed as complementary, with fMRIanswering the ‘where’ and EEG the ‘when’question in neural processing, it must becautioned that there is no directly establishedrelationship between fMRI and EEG signals(Logothetis et al., 2001). While both signalsare very different in nature and in theirtemporal and spatial properties, they lendthemselves to treatment by similar math-ematical and statistical methods, because:(1) the spectral (1/f) behavior of thesesignals indicate the participation of neuralactivity on different scales; (2) they bothrequire extraction of the task-related signalfrom background activity and noise (i.e.,noise of the recording device, muscle-activity,heartbeat, head or eye movements); and(3) the experimental designs used in cognitiveneuroscience are similar in EEG and fMRI.The latter point is particularly true sincethe introduction of event-related designs infMRI studies. In the following sections,we will illustrate the different analyticalapproaches used in EEG signal (see alsoChapter 29 for MRI analysis and thosemethods of analysis which are common toboth techniques, e.g., independent componentanalysis).


NEUROIMAGING ANALYSIS: ELECTROENCEPHALOGRAPHY 679

ELECTROENCEPHALOGRAPHY ANDEVENT-RELATED BRAIN POTENTIALS

Basic designs

The basic experimental approach in usingEEG and ERPs in cognitive neuroscienceis, in principle, not different from thatin other areas of cognitive science. Rigidcontrol of participant behavior is usuallyrequired, and care must be taken to isolatethe cognitive process under study by theexperimental manipulation. There are a fewaspects, however, in which basic design ofEEG/ERP experiments differs from exper-iments elsewhere in cognitive science orexperimental psychology. First, owing to thelow signal-to-noise ratio of single trial ERPs,responses from multiple single trials need tobe averaged together. Depending on the sizeof the component under study, a minimumof 10 (e.g., in the case of the error-relatednegativity) to up to several hundred (e.g.,in the case of selective attention effects)single trials need to be averaged together.To generate enough trials to yield a reliableand robust ERP might not be problematic inmost cases, but it can be a limiting factor inother areas. For some experiments in psycho-linguistics there are simply not enough stimuliavailable (see Weyerts et al., 1997, for anexample).

A major advantage of the ERP approachis that it is possible to study responses tostimuli to which no overt behavioral answeris required. We will illustrate this by twoexamples taken from the areas of selectiveattention and language processing. Considera typical selective attention ERP experimentlike the following: the participant is requiredto look at the center of a video monitor.Left and right of the fixation point, randomseries of blue and red bars appear at a rateof about three stimuli per second, most ofa certain height with a few just slightlytaller. The participant’s task is to attend toa particular class of stimuli (e.g., the redbars on the left) and to respond to the rarelyoccurring slightly taller bars by button press.

In this situation, we are able to investigatethe attentional filter processes for the stimuli:indeed, ERPs to all stimuli on the attendedside of the display show signs of (spatial)attentional enhancement. Those stimuli thatshare both location and color, but not height,with the target stimulus are associated withan additional selection negativity signifyingselection of the color feature (see Hillyardand Münte, 1984, for a full description ofthe experiment). Importantly, this informationabout the hierarchical selection implementedin the human brain would not be available withpurely behavioral measures.

In the domain of language research, partic-ipants are often required to read materials inorder to perform a certain (mock) task. Sucha task might entail that participants need toanswer certain questions on the materials dur-ing the break between experimental blocks.Unbeknownst to the subjects, the materialsare manipulated in a certain way. Consider forexample the following materials (taken fromMatzke et al., 2002):

(1) Die begabte Sängerin entdeckte den talen-tierten Gitarristen.

The gifted singer (Fem.Nom.?Acc.?) discovered thetalented guitar player (Masc.Acc.).

(2) Die begabte Sängerin entdeckte der talentierteGitarrist.

‘The gifted singer (Fem.Nom.?Acc.?) discovered thetalented guitar player (Masc.Nom.).

′

Meaning: The talented guitar player discoveredthe gifted singer.

In both sentences, the first noun phrase(die begabte Sängerin) is identical but caseambiguous. It could be nominative (as in(1)) and thus serve as the subject of the sen-tence, or accusative case (as in (2)) and thusserve as the object. Importantly, in German,the dis-ambiguation of the sentence takesplace only at the second noun phrase (der/dentalentierte/n Gitarristen) but both versions ofthe sentence are perfectly grammatical. Bystudying the ERPs to these sentences in aword-by-word fashion, it is possible to gleaninformation about syntactic processing in thebrain without directing participants’ attention



Table 28.1 Types of stimuli in the attentionexperiment

Location Color Height

Left/red/tall + + +Left/red/small + + −Left/blue/tall + − +Left/blue/small + − −Right/red/tall − + +Right/red/small − + −Right/blue/tall − − +Right/blue/small − − −

to the different grammatical constructions.Note that functional imaging with fMRIshares some of these advantages. Indeed, anfMRI study using the same materials has beenperformed (Bahlmann et al., 2007).

The experimental examples discussed so farhave (implicitly) made use of the subtractionlogic first introduced to psychology by theDutch scientist Donders. Indeed, such logicunderlies many ERP and fMRI studies.Consider the attention experiment mentionedabove. Again, we examine the situation inwhich the tall red bars on the left are attended.The other types of stimuli can be classified asshown in Table 28.1.

By rotating attention conditions, severaldifferent ERPs can be recorded for eachparticular stimulus type. The effects ofattentional selection by location, color andsize can thus be obtained by subtraction of thedifferent ERPs. It has, however, been pointedout that such logic assumes that there is nointeraction between the different processesunder study, an assumption that is not true inevery case. Alternatively therefore, factorialdesigns may be employed (see Osman, 1998;Sternberg, 1998).

Standard statistical analysis ofelectroencephalographyevent-related brain potentials(time-domain approach)

Event-related potentials can be thought of asminute voltage fluctuations that are buriedwithin an ongoing EEG. Therefore, ERPsbenefit greatly from signal averaging toenhance their signal-to-noise ratio (SNR).

To this end, biosignals are digitized at a fixedrate (for cognitive ERPs 150 to 1000 pointsper second and channel are usually recorded).Together with the EEG trigger events (relatedto the onset of a stimulus, a response, or amovement), these are recorded. The eventsof interest are repeated and a time-lockedsignal average is then calculated across thetrial epochs for each time point of the epoch.Formally, this can be expressed as follows:if Xj(t) represents the voltage at a particularelectrode at time t and trial j, the signalaverage is defined as:

Xt = 1

J

J∑j=1

Xjt (1)

Usually, Xjt is considered the sum of signal ofinterest St plus random noise Njt (backgroundEEG and measurement error). Using thismethod, signal averaging improves the SNR.However, note that this view, as discussedbelow, might not be entirely true as it seemsthat at least some parts of the ERP are broughtabout by phase resetting of the ongoing EEG.The signal power σ̂ 2

s , noise power σ̂ 2N , and

SNR can be estimated using:

σ̂ 2s = 1

T

T∑t=1

X̄2t − 1

Jσ̂ 2

N

σ̂ 2N = 1

T (J − 1)

J∑j=1

(T∑

t=1

(Xjt − X̄2

t

)2)

≈ Variable X̄t

SNR = σ̂ 2S

/σ̂ 2

N (2)

One of the key assumptions of signalaveraging is that the signal is invariant acrosstrials. This is clearly not the case, as ithas been shown that some ERP components,such as the P300, vary in a trial by trialmanner. If, for example, latency jitter ispresent for a specific component this will leadto a smearing out of the component in thesignal average, and the peak amplitude ofthe average will thus not properly reflect thecomponent’s amplitude in single trials. Forcertain purposes, realigning the single trials by



moving a template (usually the conventionalaverage or part of a sine-wave) across thesingle trial epoch and searching for the time-point at which the template and the singletrial have the greatest cross-correlation hastherefore been tried. This time-point is thenused to realign the single trials (see, forexample, Wastell, 1977).

Prior to quantifying waveform changes inthe average potential, it can be advisable toapply filters that enhance the signal-to-noiseratio for the effects of interest. For exam-ple, the error-related negativity (ERN)(seeGehring et al., 1995) has a frequencyaround 5–6 Hz. To remove contamination byoverlapping slow positive waves and by highfrequency activity, it might be useful to applya band-pass filter to remove activity below 2Hz and above 8 Hz to best bring out the ERNactivity.

After the average ERP is obtained for sev-eral experimental conditions, say for stimuli inthe right visual field while they are attendedand for the same types of stimuli when theyare outside of the focus of attention, the nextanalysis step is waveform quantification [foran introduction to standard ERPmeasures, seeLuck (2005) and Picton et al. (2000)]. Thewaveforms are characterized by peaks andtroughs that lend themselves to quantification(see Figure 28.1 for an illustration). The usualpractice is to determine amplitudes relative to

Figure 28.1 Typical parameters determinedfrom the event-related potential waveforms.I. Peak amplitude. II. Peak latency. III. Meanamplitude/area. IV. Peak-to-peak amplitude.

a baseline period (e.g., −100 to 0 ms relativeto the onset of the event). The voltage of thebaseline period is set to 0. Typical parametersthat are determined from the waveforms are:

(i) Peak amplitude: the most negative or mostpositive point relative to the baseline isdetermined within a defined time window.

(ii) Peak latency : the latency of the mostnegative of most positive point within a timewindow is determined relative to the onsetof the time-locking event.

(iii) Mean amplitude: the mean amplitude withina given time window is determined; thismeasure is equivalent to an area measure.

(iv) Peak-to-peak amplitude: in cases wereseveral peaks and troughs occur in quicksuccession it might be adequate to deter-mine the amplitude difference between twosuccessive peaks.

(v) Onset latency : the onset latency of a com-ponent is notoriously difficult to determine.

Several suggestions have been made to givean estimate of the onset latency. For example,it might be estimated by determining the time-point at which the amplitude of the risingflank of the component has reached 15% (orsome other fraction) of the peak amplitude.This is known as fractional amplitude latency.Alternatively, fractional area latency might bedetermined.

Sometimes, the determination of the onsetlatency is problematic because of residualnoise in the waveform. Miller et al. (1998)have therefore suggested a ‘jack-knifing’method based on measuring the differencein the onset latencies of two experimentalconditions. While this method has been sug-gested for the measurement of the lateralizedreadiness potential (LRP), it can readily beapplied to other components as well (seeBanfield et al., 2006, for an example).

Before measurements are taken of wave-forms, it is sometimes useful to performwaveform subtraction to reduce the effectsof component overlap and to bring out theeffect of a specific experimental manipulation.Consider, for example, a selective attentionparadigm in which stimuli in the right visualfield are attended in one condition and not



attended in another. If the waveforms obtainedin the unattended condition are subtractedfrom those in the attended condition, theresulting difference wave presumably reflectsthe attention effect proper, and quantificationof the difference wave should thereforeprovide a direct measure of the neuralcorrelates of selective attention. However, thecomputation of difference waves is not a goodidea in every case. Consider the situationin which a peak is shifted in latency fromone condition to the next, where subtractionwill introduce a ‘ghost-component’ into thedifference wave that will be misleading in theinterpretation.

One important advantage of the ERPtechnique is that the resulting data are mul-tidimensional, and that the spatial distributionof effects can be taken into account. Indeed,measurements are usually obtained fromseveral electrode sites, and the resulting data-sets lend themselves to statistical analysisby repeated measures analysis of variance(with electrode-sites being treated as one ormore factors). One of the potential strengthsof such an approach is that conditions cannot only be distinguished by effects atcertain scalp sites, but also by a differentialdistribution of an effect across multiple scalpsites. The latter would be reflected by acondition x electrode-site interaction in ananalysis of variance. In such a situation,one might be inclined to assume that neuralgenerators that are at least partly differentmight be at work in the two conditions.McCarthy and Wood (1985) have pointedout, however, that there is a fundamentalincompatibility between the additive modelupon which analysis of variance (ANOVA)are based and the multiplicative effect onERP voltages produced by differences insource strength. Using simulations, theyshowed that highly significant interactionsinvolving electrode location can be obtainedbetween scalp distributions with identicalshapes generated by the same source. Theysuggested a scaling method to eliminateoverall amplitude differences between exper-imental conditions before an ANOVA isperformed. In other words, McCarthy and

Wood (1985) suggested that condition xelectrode-site interactions that survive vectorscaling are indicative of true differences inneural generators between conditions. Morerecently, however, it has been pointed outby Urbach and Kutas, (2002) that evenfor ideal distributions of generators andsurface potentials, the extent to which vectorscaling refines conclusions about generatordistributions is limited: ‘prior to amplitudenormalization, differences in scalp distribu-tions show that neural generators differ insome combination of location, polarity, andrelative or overall strength. After amplitudenormalization, residual differences merelyattest to the fact that neural generators differin some combination of location, polarity,or relative strength, that is, that they differin spatial configuration. Of all the possiblecombinations of differences in generatorlocations, polarities, and strengths that couldaccount for the different scalp distributions,amplitude normalization at best only rules outone special case: namely, where the generatorsin the two conditions all have the samelocations and polarities and differ in strengthby the same multiplicative factor’(Urbach andKutas, 2006). In this sense, these researcherssuggest that non-normalized data should beused in assessing condition x electrode-siteinteractions (see further discussion in Luck,2005).

The measurement techniques discussed sofar reveal data about peaks and troughsof the waveform, but not necessarilyabout ERP components. In neurophysiologi-cal/psychological terms, a component can bethought of as being generated by a neuralor cognitive process, while in a statisticalsense a component explains experimentalvariance [see discussion for conceptual issuesregarding ERPs, Rugg and Coles (1996)].Peaks and troughs may thus come about bythe superimposition of several components.There have been a number of suggestionsfor decomposing ERP waveforms in orderto isolate their components, among themprincipal component analysis (PCA) or, morerecently, independent component analysis(discussed in Chapter 29). PCA uses the



time points on waveforms from differentsubjects, different electrodes, and differentexperimental conditions to define components(for details, see Picton et al., 2000). In sta-tistical terms, PCA identifies orthogonal axesof maximal variance in a multidimensionalspace defined by the variables. Generally,these axes are rotated according to the varimaxprocedure, which introduces a certain degreeof arbitrariness. PCAsolutions are not unique,as many rotations of the factors are possible.Also, the selection of experimental conditions,electrode sites, number of subjects and soon will determine the factor structure ofa given experiment. Thus, it is difficult tocompare factor structures across experimentsand to identify components across differentstudies.

Statistical analysis of multichannel EEGdata is problematic, since the many channelsand multiple conditions in one experimentoften call for multiple statistical tests, therebyincreasing the chance of type I errors(rejecting the null hypothesis when it is true).The best way to circumvent this problemis by replication of initial findings in asecond independent group of subjects, i.e.,by running a confirmatory study. The typicalcorrections used to compensate for increasedtype I error (e.g., Bonferroni type corrections)may over-correct, since data from adjacentelectrodes are correlated and not indepen-dent. Whereas rigid and theoretically well-grounded methods for statistical correctionshave been described in functional imaging andhave become standard procedures in that field(see below), such procedures have been lesswidely performed in ERP research and are farfrom being standardized.

Artifact rejection and correctionalgorithms

Prior to further processing and averaging,the EEG has to be checked for undesirableelectrical noise and artifacts resulting frommovements, eye movements and blinking,and muscular activity. Artifacts may eitherbe rejected (i.e., those stretches of the

signal contaminated are removed from furtherprocessing) or corrected.

For artifact rejection, the most widely usedcriterion is to establish a threshold value forartifact amplitude (usually between ±50 and±100 µV). Another common procedure isto reject those trials that present a specifiedabnormally steep slope or drift. Finally,trials presenting technical problems (such asamplifier saturation) are also removed fromfurther analysis. If participants are not givenspecific instructions about artifacts or visualfeedback about the effects of blinking andmoving in the EEG, between 15% and 30%of the trials require rejection. However, ifparticipants collaborate and brief pauses orblinking periods are introduced (if possibleincorporated into the design of the task), therejection rate is about 10%.

Such ‘rejection’ techniques will be prob-lematic in situations in which the number oftrials per condition is very low (e.g., below25), which is the case, for example, in somepsycho-linguistic studies, or in studies withpatients or special populations (newborns,children, etc.). Thus, it is necessary insuch cases to remove the noise from thecontaminated signal in order to be able to usemost of the trials in the averaging process.Most commonly used algorithms for cleaningblinks and ocular movement are based onregression analysis. In this type of analysis,the contamination of each electrode by a cer-tain type of artifact is assessed by computinga propagation factor, which is used to removethe estimated signal influence (Verleger et al.,1982). Another approach is to use dipolemodeling to isolate the ocular activity (Bergand Scherg, 1991).Although the latter methodseems to work reasonably well (see Lins et al.,1993), the most important problem of suchapproaches is that ocular electrodes might alsopick up EEG activity proper and that thesemethods might therefore also remove partof the signal of interest. Alternatively, it hasbeen proposed that the application of BlindSource Separation techniques to EEG/ERPdata can reliable remove ocular, muscular andelectrical noise artifacts from the raw signal(Jung et al., 2000).



Source analysis

While temporal information can be readilyinferred from a scalp-recorded EEG, the ques-tion as to where a particular signal is comingfrom has been of interest for EEG researchersfrom the very beginning, first to localize focal(epileptic) activity and nowadays to pinpointneural structures responsible for particularcognitive operations.

A first important issue in the localization ofthe sources of the EEG is the use an adequatenumber of electrodes. While the recording,storage and analysis of up to 256 electrodesis no longer technically a problem, increas-ing the number of electrodes will prolongthe recording session. Thus, a compromisebetween the number of electrodes and the timeneeded to run the experiment is necessary.Lantz et al. (2003) have shown that goingfrom 32 to 64 electrodes markedly changeslocalization results, but that a further increaseof electrode density yields little additionalprecision.

Electrogenesis of scalp potentialsThe electrical potential recorded in the scalpis a consequence of the electrical activityof large assemblies of neurons that areactivated synchronously. Although the exactelectrogenesis is not fully understood, it issupposed that the activity registered usingEEG is related to the influx of positive ionsacross the post-synaptic membrane when aneurotransmitter is released. In addition, thereis a re-distribution of charges in the outerpart of the membrane. If several (thousand)neurons depolarize synchronously, the totalnet current can be recorded at the scalp byusing macro-electrodes (see Figure 2A and Band Nunez and Srinivasan, 2005).

The surface activity is very dependent onthe position and geometry of the neuronsinvolved, as can be seen in Figure 2C.Hence, ‘closed field’ configurations, whereneurons are not aligned in parallel may notproduce detectable fields at the scalp. Inaddition, the electric potential presents a veryfast decay with distance (see Figure 2D),and is further attenuated by the tissues

between the source of the potential andthe scalp electrode (i.e., skull and scalp).Hence, EEG is dominated by activity fromthose areas presenting an ‘ordered’ geometryand relatively close to the scalp. Pyramidalneurons in the neocortex are thus the maingenerators of EEG signals. They comprisethree-quarters of all cortex neurons and canfire synchronously, because of the localdensity of excitatory interneurons. Whereaselectrical activity from subcortical structuresis less well detected given the non-orderednature of the cell assemblies and the longdistance to the scalp, activity of somestructures such as auditory nerve or somebrain stem structures can be detected atthe scalp. Because the activity of interestis very small in these cases (less than 1µV; see Harkins, McEvoy, and Scott, 1979),many hundreds or even thousands of stimulusrepetitions are necessary.

The application of the physical rules ofelectromagnetism (the Maxwell equations)to the brain electromagnetic currents allowsestablishing two main problems. The forwardproblem states that, given a source andthe electrical characteristics and positionof the different layers of the brain, wecan unequivocally determine the electricalpotential generated by this source. In contrast,the goal of an inverse problem is to finda solution that is compatible with certainvoltage distribution. Unfortunately, infinitesolutions exist compatible with a certainvoltage map given that this is an ill-posed problem. Although some physiologicalconstraints (see below for implementations)can be reasonably imposed (i.e., sources ofEEG can only be generated in the brain),the inverse problem continues to be achallenge.

Scalp current densityA first approach in increasing the spatialresolution of the EEG is the applicationof the scalp current source density scalpcurrent density (SCD) approach. It is basedon the application of a 2D Laplacian operator(∇2) in two dimensions to the scalp EEGpotential data. It can be demonstrated that this



Figure 28.2 Electrogenesis of brain potentials. (A) Current flow generated in a neuralassembly of pyramidal neurons. (B) The direction of the current flow in the brain depends onthe position of pyramidal neurons in the brain. (C) Voltage activity generated in the scalp bya radial (blue dipole, left scalp voltage) and tangential (red dipole, right scalp voltage)electrical dipole. (D) Voltage activity generated in the scalp by a deep (green dipole, left scalpvoltage) and superficial (yellow dipole, right scalp voltage) radial dipole.



measure is equivalent to finding the variationof the normal component of the electricalfield, and that it is related to changes in thenormal SCD, creating ‘sources’ and ‘sinks’of current density. Another interpretation ofthe Laplacian operator is that it acts as aspatial high-pass filter, enhancing the spatialresolution but also amplifying the noise of thesignal. Several techniques have been proposedfor computing the SCD, with the Hjorthmethod (Hjorth, 1975) and spherical splines(Perrin et al., 1989) being the most widelyused.

An example of the advantages of usingSCD instead of voltage data can be foundin Figure 28.3. Two sources located in theleft and right supratemporal cortex generatea midline frontocentral voltage distribution.The application of an SCD algorithm suggeststwo sources, corresponding to the two internalgenerators. In spite of the favorable resultin this example, the application of SCD

can be also very problematic because ofnoise amplification. Also, it can only provideinformation about possible surface sources,because voltage fields generated by deepsources dissipate and spread across thescalp.

The inverse problemThe inverse problem consists of findingthe current density sources that produce acertain voltage. It is inherently ill-posed asthere is no unique solution for solving theproblem.

Source estimation procedures can bedivided in two main groups: dipolar solutionsand distributed solutions. In dipolar solutions,the number of sources that are used in themodeling is set a priori based on a prioriconstraints (e.g., anatomical or physiologicalinformation). Then, this fixed number ofdipoles is placed in the brain and their positionand orientation is found by minimizing

Figure 28.3 Illustration of source current density (SCD) computation. Two dipoles are placedin the scalp at temporal areas. The isovoltage map shows a central positivity. The applicationof an SCD algorithm distinguishes two sources. As can be seen, the picture given by the SCDis closer to the real source configuration.



the difference between the scalp potentialproduced by the dipoles (computed usingthe forward solution) and the real scalppotentials. In the distributed models, the head(or only those regions that can reasonablybe assumed to generate brain potentials) isdivided into a large number of voxels anda solution is found by imposing certainconstraints.

Dipolar solutionsGiven a certain geometry (location of thedifferent tissues), the voltage produced bya dipole located in any part of the braincan be easily computed (forward model).The first solutions of inverse problems usedthe forward solution to solve the inverseone. The idea was simple: the number ofsources (dipoles) was defined a priori anddifferent plausible physiological locationswere selected for the dipoles. Also, theorientation of the dipoles could be defineda priori based on physiological parameters(i.e., the same orientation as the correspondingpyramidal neurons). The forward problemwas computed for all possible solutions, andthe voltage map that best explained the realvoltage distribution was selected. In addition,the explained variance of the solution gave anestimate of the goodness of fit of the dipolarsolution.

Although in use for more than 20 years(Scherg and von Cramon, 1985), dipolar solu-tions are still popular given their simplicityand the fact that they provide good solutionswhen few and spatially circumscribed sourcesare expected that contribute to the observeddistribution.They do, however, have a numberof limitations. First, the number of dipolesof a solution has to be defined a priori.Second, selecting a large number of dipolesincreases computation time significantly,making it unfeasible to work with manysources.

Distributed modelsDistributed models search for the solution ofthe inverse problem in a 3D mesh composedby a large number of voxels (generallyexceeding the number of electrodes used to

register the data). The problem is generallyill-posed, since there are more solutions thanequations. There are several different ways oftackling this problem, and the most commonlyused are dealt with below.

L2 norm solutions.These are based on minimization of themodulus of the density vector; in otherwords, choosing the minimum energy vector.Depending on the choice of the constraintsimposed to the problem, solutions can presentdifferent characteristics. The most frequentlyused is the weighted minimum norm solutionwith low-resolution tomography (LORETA),which is based on the weighted modulus min-imization by a Laplacian operator (Pascual-Marqui et al., 1994) resulting in a smoothedsolution. This is one of the most widely usedmethods for EEG source localization.

L1 norm solutionsIn L1 norm solutions, the minimization isperformed using the L1 norm. One of themost popular applications of the L1 minimumnorm is the FOCUSS approach (Gorodnitskyet al., 1995). In general, L1 solutions providesources less sparse than L2 minimum normsolutions, but their application is difficultbecause they must be computed recursively.

Other solutionsOther solutions proposed to solve the inverseproblem are:

• Standardized solutions : based on standardizationof the estimation of the currents, given thecovariance matrix of estimated noise (Dale et al.,2000; Pascual-Marqui, 2002).

• Beamformer solutions : based on spatial filters(Van Veen et al., 1997).

• Biophysical restrictions based solutions : i.e.,ELECTRA (Grave de Peralta et al., 2000).

• Combination of two different solutions: i.e.,shrinking LORETA-FOCUSS (Liu et al., 2004).

The impact of these solutions in the literatureis limited at present and therefore they are notdiscussed in any more detail.



Analysis of the frequencycomponents ofelectroencephalography

Spectral properties ofelectroencephalographyA remarkable property of the EEG is its oscil-latory behavior. Traditionally, the frequencybands have been divided into delta (1–4 Hz),theta (4–8 Hz), alpha (8–12 Hz), beta (12–25Hz) and gamma (> 25 Hz) bands. Systematicchanges to these EEG bands can be found asa function of behavioral states (i.e., sleep orwakefulness), cognitive tasks, drug intake orneuropsychiatric disorders. The description ofsuch spectral components is therefore a keyaspect of EEG studies.

The most widely used spectral analysisapproach is based on the fast Fourier trans-form (FFT). As stated by the Fourier theorem,a signal s(t) can be decomposed as a sum ofsinusoidal signals. In the Fourier approach,this can be written as:

s(t) =∫ ∞

−∞S(ω)e2π iωtdω (3)

being:

S(ω) =∫ ∞

−∞s(t)e−2π iωxdx (4)

S(ω) are complex coefficients, whose squaregives a measure of the power at the frequencyω. This is the value that has traditionally beenused to determine the power of each EEGfrequency band.

To illustrate this, in Figure 28.4 wehave generated a signal composed from twosinusoidal signals: one with a frequency of5 Hz, and the other with a frequency of 17Hz and half the amplitude of the first. Inaddition, we have added some white noise tothe signal (Figure 28.4A and B). The Fouriertheorem can then be applied to the resultingsignal. The left part of Figure 28.4C showsthe result of the complex S(ω). Two maximacorresponding to the sinusoidal signals arefound. To better see these values, we cancompute the power spectra of the signal

by squaring S(ω). In this representation, wecan clearly see two peaks at the frequenciescorresponding to the component signals.

The need for time-frequency approachesOne of the main problems of the FFT andrelated methods is the fact that temporalinformation is lost in the computation of thespectral content, which is not always adequatein the study of cognitive functions. Althoughsome states change the global spectral contentof the EEG (i.e., the presence of slow wavesin the deep sleep is greater than in awakestates), spectral properties of the EEG maychange rapidly in other conditions, i.e., after astimulus presentation, during the performanceof a task, etc. In such situations, short-livedchanges in certain frequency bands may occurthat need to be detected by adequate methods.

In Figure 28.5 we have illustrated anexample of two different trials that presentsimilar responses. At 200 ms there is analpha band (10 Hz) response and at about700 ms there is an increase in the beta range(20 Hz) that lasts 100 ms. The FFT analysis(Figure 28.5B) shows a global increase inthe 5–20 Hz range but there is neither aclear delineation of the frequencies involvednor any information on the timing. However,when performing a time-frequency analysis, aclear enhancement of the alpha band from 100to 200 ms and of the beta band from 700 to 800ms is seen. Hence, the information providedby the time-frequency approach is richer andmore appropriate for cognitive neuroscienceapplications.

Figure 8.5 also shows another importantaspect of the time-frequency approach. Thetwo examples are not only different in theirspectral content (10 and 20 Hz respectively),but also in their phase. As can be observed,the activity in the first example is phaselocked; that is, its peaks and valleys coincidein time with regard to the stimulus. Thisresults in a clearly visible ERP (mean of thesingle trials), a type of response known as anevoked response. While the increase in poweroccurs at similar time points, the responsesare not phase locked in the second example(the vertical red line coincides with a peak



Figure 28.4 Fourier transform computation. (A) A signal is created combining three originalsignals: a 5-Hz signal, a 17-Hz signal and random noise. (B) By adding the two sine wavesignals and the noise, a combined signal is obtained. (C) The left panel shows the complexsignal of the fast Fourier transform (FFT) applied to the data. Each complex point in the graphis associated with a specific frequency. Two main frequencies are retrieved with peaks at 5and 17 Hz. The right panel shows the square of the magnitude of FFT at each frequency. Again,two main peaks reflect the frequencies of the initial signals. Note that square of themagnitude of the 5-Hz signal is greater than the 17-Hz signal, as in the original signals.

in the first trial and a valley in the secondtrial). Hence, in a time-domain average, theresponses are partially or totally cancelledand therefore do not contribute to the ERP(or produce only a very small signal, asin Figure 28.5). Note that this problem isusually greater for fast oscillations than forlow frequency oscillations, as well as foroscillations with a longer latency with regardto the stimulus onset.

However, the mean of single trial time-frequency decompositions does show aresponse that it is not affected by thecancellation effect. Such non-phase-lockedresponses are known as induced responses.The detection of induced responses requiressingle-trial time-frequency analysis. The dif-ferent nature of evoked and induced responsesalso underscores the importance of studyingthe phase of the signal. Indeed, some studies



Figure 28.5 Trial by trial time-frequency decomposition. (A) Two trials are depicted with twosignals in each: a 10-Hz signal time-locked with respect to the stimulus onset (evoked activity)and a 20-Hz non-phase-locked signal (induced activity). The average of the signals is observedin the corresponding ERP waveform. In this average waveform, the 20-Hz signal has almostbeen abolished in the time-domain average. The time-frequency decomposition of theaverage ERP waveform (right) shows only the increase at the 10-Hz but not at 20-Hz signal.In contrast, the time-frequency decomposition of each single trial shows both signals, and thisinformation remains when both decompositions are subsequently averaged together (rightpanel). Hence, induced activities cannot be studied by applying time-frequency analysis to theaveraged ERP responses. (B) The FFT similarly fails to detect both signals.

have demonstrated that the phase of the EEGcan be altered during cerebral processing(Fuentemilla et al., 2006; Makeig et al.,2002)1. Given that the phase of the signalcan only be studied effectively in single-trial data, a complete time-frequency studyshould involve time-frequency trial by trialcomputation of any increase/decrease ofpower and phase alignment of the signal. Toquantify the degree of phase alignment, ameasure referred to as inter-trial coherence

(ITC) (Makeig et al., 2002) or phase-lockingfactor (Tallon-Baudry et al., 1996) is used:

ITC = 1

n

∣∣∣∣∣n∑

i=1

Si(ω)

|Si(ω)|

∣∣∣∣∣ (4)

where Si(ω) is the coefficient at frequency ωof the i-th trial. ITC gives a measure of thedegree of similarity of phase over differenttrials. It ranges from 0 to 1, with 0 indicatinga randomly distributed phase over different



trials, and 1 a perfect match of phase indifferent trials.

Application of frequency analysis toelectroencephalography dataIn the following section, we will describe threeof the most widely used methods: (1) theclassical method for computing event-relatedsynchronization/desynchronization (ERS andERD) based on filtering the data at differentfrequency bands; (2) the short FFT method,in which the data is divided into windowsof identical length to which FFT is applied;and (3) the wavelet analysis, where the samemother wavelet is contracted or dilated tovariable length windows.

The first proposal to analyze changes in thepower of brain electrical signals was made byPfurtscheller and Aranibar (1977) to assessincreases (ERS) and decreases (ERD) ofpower in certain frequency bands as comparedto baseline (see Figure 28.6C): (1) the EEGsingle trial data is first filtered at the selectedfrequency band; (2) the amplitude is thensquared and the mean of all trials is computed;finally (3) the percent of increase/decrease ofpower with respect to baseline is computed.

In the short fast Fourier Transform (SFFT),an FFT is applied to successive short timeintervals (see Figure 28.6D). The originalsignal is convoluted by using sinusoidalsignals in a fixed temporal window, obtainingestimations of the power and phase at differentfrequencies and time ranges. The problemcomes from the use of a fixed time window tocompute the FFT: if good temporal resolutionis needed, a short window is required, whereasa good frequency resolution requires longwindows. In other words, there is a trade-off between the temporal and frequencyresolution, as short time windows compriseless cycles for the sine signals and hencelead to bad spectral resolution. Increasingthe length of the windows, on the otherhand, decreases temporal resolution. Thisproblem has limited the use of SFFT inEEG analysis.

Finally the most widely used method iswavelet analysis (illustrated in Figure 28.6E),in which the signal is not convoluted by a sine

or a cosine, but by a certain signal, namelythe mother wavelet. The shape of this signalis the same for all frequencies, but the motherwavelet is expanded or contracted dependingon the frequency studied (based on a certainparameter, called the scale a).The convolutionis performed at all the time points by movingthe wavelet across time using a certain latencyshift b, which led to the name continuouswavelet transform (CWT). Mathematically,the convolution between the signal s(t)and themother wavelet ψ (

b,at)can be written as:

Wψb,a s(t) =∞∫

−∞s(t)ψ∗

b,a(t)dt (5)

being ψ(t) the mother wavelet and ψb,a(t):

ψ(b,at) = 1√

aψ

(t − b

a

)(6)

Several mother wavelets can be used in thecomputation of the EEG. The most widelyused are the morlet and complex morletwavelets that comprise a sinusoidal functionenveloped by a Gaussian.

As can be seen in Figure 28.6D and E,there are some differences between SFFT andwavelet analysis: in short FFT the length ofthe windows used is constant, whereas inwavelet analysis they change with frequency.While in short FFT the number of cycles ofthe sinusoidal signal changes with frequency,the shape of the wavelet is always thesame in wavelet analysis. However, in thelatter method, there is an inverse relationshipbetween the length of the window in the timeand frequency domains: when the frequencyincreases, the length of the window is shorterin the time domain, but larger in the frequencydomain.

One common aspect of all three methods isthat after the application of the particular algo-rithm, data are squared to avoid cancellationwhen averaging different trials and to convertcomplex numbers (i.e., in complex morletwavelets) to real power. For most applications,power changes need to be related to a certainbaseline. Thus, the interest is


Figure 28.6 Illustration of methods for analyzing the spectral content of a brain electricalsignal. (A) A real electroencephalogram (EEG) waveform is used for the analyses. (B) The staticapproach using a fast Fourier transform (FFT) provides no temporal information. The signalpresents a typical 1/f decay, with a decrease at 50 Hz due to a notch filter applied to the data.(C) Classical method for time-frequency decomposition. The data is band-pass filtered,squared and referenced to a baseline. (D) Short-time FFT. An FFT is applied in fixed temporalwindows. Then the data is squared and referenced to baseline. (E) Wavelet approach. Awavelet analysis is applied. In this analysis, the temporal and frequency windows vary theirlength as a function of the frequency. Finally the data is squared and referenced to baseline.



not in the absolute value of the power at acertain frequency, but its task- or state-relatedrelative increase or decrease. Referencing thebaseline also avoids problems due to the 1/fbehavior of EEG data, which generally leadsto greater power at lower frequencies (see,FFT in Figure 28.6B).

Statistical analysis ofelectroencephalography oscillatory activityWhile the power computed by spectraltechniques follows a χ2 distribution (Kiebel,et al., 2005) have demonstrated that certaintransformations of the spectral data allow theuse of the general linear model (GLM) foranalysis. One way of performing tests is tocompute the average in a spectral and tempo-ral window. The central limit theorem ensuresthat these averages will follow the Gaussianassumptions. Averaging over several trialsis similar. For single trial analysis, log orpower transformations generate distributionsclose to Gaussian. The conclusion of Kiebelet al. (2005) therefore was that EEG powermeasures can be analyzed using parametricstatistics.

A different approach has to be taken withthe analysis of phase. Typically, phase isnot analyzed individually but by using ITC(Equation 17), that is a measure of thedegree of the coherence between differenttrials. Statistical analysis of such data can beperformed by using bootstrap analysis (seeMakeig et al., 2002), or non-parametric tests(i.e., U-Mann Wilcoxon or Kruskal–Wallistest). Although ITC follow a Raleigh ratherthan a normal distribution, some studies havenevertheless used parametric tests (ANOVA).

Finally, it has to be noted that time-frequency analysis suffers from a severemultiple comparisons problem. Imagine astudy with 64 electrodes, with epochs of600 ms length at 500 Hz sampling rate(300 points) and frequencies studied from1 to 45 Hz. If comparisons are performedpoint by point, this yields 864,000 possibletests (64 electrodes x 300 time points x45 frequencies). This is very similar tothe number of comparisons performed infMRI studies. However, in contrast to fMRI,

the multiple comparison problem in time-frequency analysis has received only limitedattention.

To avoid the multiple comparisons prob-lem, many time frequency studies focus theirstatistical comparisons on certain spectral-temporal windows and electrodes where thedesired effects seem to be present. Thisa priori approach reduces the number ofcomparisons and possible false positives, andhence, the problem associated with them.A more straightforward solution is basedon non-parametric permutation tests (Marisand Oostenveld, 2007). In this approach, thetwo conditions are compared by means ofa standard statistical test (i.e., t-test), andpoints presenting statistical values greaterthan a certain value are selected. Clustersare created by joining adjacent points on atemporal, spectral and spatial (i.e., electrodescloser than 4 cm) basis. Then, a cluster-based statistic is computed on the sum ofthe values of the statistical test used in acluster, and the maximum of these valuesamong the different clusters is selected. Thenext step is the creation of a large numberof random partitions by randomly assigningsingle trials to the ‘conditions’. The statisticaltest is computed for each random partition,and in the points of the cluster presentingthe maximum cluster-based statistics. Thiscreates a histogram of the random partitions.Finally the proportion of random partitionsthat result in larger test statistics than thecluster-based statistics previously found iscomputed (p-value). Clusters presenting ap-value smaller than the critical alpha level(usually 0.05) are then accepted as presentingsignificant differences between conditions.

CONCLUSIONS

In the last 30 years the utilization of EEG sig-nals for studying brain functions has sufferedan important impulse. EEG measurementshave evolved from pure clinical settings (i.e.,diagnostic of epilepsy, polysomnography,exogenous evoked potentials, etc.) to becomeone of the most non-invasive techniques used



to the study brain functions and cognitiveprocesses. In addition, it is the only tech-nique (with MEG) that allows non-invasivelystudying brain functioning at the sub-secondtemporal domain. One important reason forthis reborn has been the incorporation ofEEG to the study of cognitive functions,such as language and executive functions.These domains were traditionally studiedusing behavioral data, but the incorporationof new experimental paradigms has allowedinvestigating the electrical signatures andoscillatory changes related to these functions.In this regards, several discoveries werecritical in the development of the researchin these fields, as for example, the N400component (related to semantic analysis),P600 (associated to syntactic processing) orthe error-related negativity (associated to thedetection of erroneous responses). At thesame time, and more recently, the advent ofnew techniques of analysis has allowed aricher interpretation of the results and hasopened a door to new ways of studyingelectrical responses associated to cognitivefunctions. Therefore the analysis of brainoscillations and their properties (changesin power and phase) by means of time-frequency analysis is today very importantin order to have an accurate description ofbrain functioning and brain dynamics. Inaddition, the possibility of localizing theneural sources of brain electrical activityallows better interpretation of results and theconfirmation of existing brain-wired theoriesor neural-constrained cognitive models. How-ever, the information provided with localizingtechniques has to be always interpretedcautiously and it has to be confirmed usingcomplementary techniques that have a betterspatial resolution, as for example fMRI (seeChapter 29).

In this regard, a promising future for EEGis to combine its information with otherfunctional techniques (such as fMRI, PET orTMS) and the application of new algorithmsand techniques in order to extract moreinformation from the raw data. However,the crucial point will be the creation ofnew research paradigms that allow studying

psychological functions in today still emerg-ing fields of cognitive neuroscience. Hencethere is a need of new paradigms that allowthe application of electroencephalographictechniques to social and developmental psy-chology, as well as to single-trial experiments.Only the combination of smarter paradigmsand powerful techniques of analysis will allowus to face the new challenges of psychologyand cognitive neuroscience.

NOTE

The figures in this chapter can be found at:http://cid-ea002f4aa27227e8.skydrive.live.com/self.aspx/Book%20Marco. Black andwhite versions (select only the six figures) areavailable at: http://cid-ea002f4aa27227e8.skydrive.live.com/self.aspx/Book|_black|_white>

NOTES

1 The study of phase has become increasinglyrelevant due to the controversy over the originof evoked potentials. The classical (evoked) theorysupports that the ERP arises from a fixed latencyfixed polarity response that appears in the EEG(acting as noise) de novo. As an alternative, it hasbeen proposed that the ERPs appear due to areorganization in the phase of the EEG backgroundsignal, that is consequently not regarded as noise butas containing relevant information that might affectthe EEG response (oscillatory model). Some studiesusing real data have suggested that both processesmight contribute to the ERP (Fuentemilla et al., 2006),making the study of phase important in EEG analysis.However, Yeung et al. (2004) proposed that currentmethods cannot dis-ambiguate the question aboutthe origin of the ERPs. These authors argued thatfinding an increase of the inter-trial phase coherencein parallel to the appearance of an ERP (powerincrease) does not fully support the oscillatory model,because this effect could also be explained by thepresence of a fixed latency and polarity response asproposed by the classical model.

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