The combined CSD and fPCA method:• Improves topographic specificity over EEG field potentials• Yields reference-free spectral measures similar in form to those used in

conventional EEG analyses• Yields orthogonal Spectral FactorsSpectral Factors consistent with the analyzed data as

opposed to simple, predetermined rectangular frequency bands• Automatically removes EMG, EOG and electrical artifacts• Provides replicable Alpha FactorsAlpha Factors with characteristic peaks and

topographies• Allows anatomical interpretations of regional findings that are

impossible with conventional EEG measures

ConclusionsConclusions

• The volume conduction of field potentials from neuronal generators approximates Ohm’s Law for a conductive medium, varying linearly over distance

• Concurrent generators produce additive field potential effects

• Linear EEG properties are preserved in the frequency domain: Fourier transformation is linear and reversible, but complex-valued

Linear Properties of EEGLinear Properties of EEG

• Based on simplifications of Poisson's equation, relating current generators to the negative spatial derivative of the field potential in a conductive medium

• Removes volume-conducted activity• Provides a concise, reference-free simplification of a field

topography• Indicates neuronal depolarization as a current sink

(negativity), repolarization or hyperpolarization as a current source (positivity)

• Estimates are real (magnitude and sign)

Properties of CSD Properties of CSD

IIdentification and separation of reference-free spectral EEG components: Combining Current Source Density (CSD) and frequency Principal Components Analysis (fPCA)dentification and separation of reference-free spectral EEG components: Combining Current Source Density (CSD) and frequency Principal Components Analysis (fPCA) Craig E. Tenke and Jürgen KayserCraig E. Tenke and Jürgen Kayser

Department of Biopsychology, New York State Psychiatric Institute, New York

Impact of Reference on Frequency SpectraImpact of Reference on Frequency Spectra

ReversibleTransformation

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EEG Time Series: A single cosine wave topography that varies linearly across the midline sites (Fpz, Fz, Cz, Pz), shown for a Fpz and Cz reference. Fourier Transformation: Fourier spectra are linearly and reversibly related to the temporal data. Since the simulated data are simple cosines, the complex spectra consist of real numbers. Color maps show spherical spline interpolations for a 12-channel EEG montage with lateral activity identical to midline sites. Amplitude Spectrum: Amplitude of Fourier Spectra (i.e., amplitude of frequency spectrum via Pythagorean Theorem). The amplitude spectrum is identical to the Fourier spectrum when and only when components are real and positive (FPz reference), but differs markedly when they are not (Cz reference).

Fourier Maps(data w/o asymmetry)

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Field Potential Topographies CSD Topographies

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Linear midline gradientLateral = midline

Linear midline gradientAsymmetry added to mid-frontal sites: F3 = F3 - .5 µV F4 = F4 + .5 µV

Impact of Reference on Spectral Topographies of Field Potential and CSDImpact of Reference on Spectral Topographies of Field Potential and CSD

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Fourier Maps (data w/o asymmetry): While field potentials of Fourier maps shift in amplitude and sign depending on the chosen reference, both produce identical CSD maps (approximately zero due to the linear gradient). Fourier Maps (asymmetric data): When a hemispheric asymmetry is added to mid-frontal sites (left < right), it is evident in the field potential Fourier maps for both reference schemes. The “frontal generators” of the asymmetry are evident from the CSD maps.Amplitude Maps (asymmetric data): Nonlinear transformations commonly used in spectral analysis (power or absolute value) may distort a field topography and even reverse the direction of an asymmetry. In contrast, the equivalent transformation of CSD data preserves all information about the location of current generators without distortion. Only phase information related to concurrent source/sink properties is lost.

Amplitude spectra of CSD from resting EEG:

• Clarify and separate key features of the resting EEG, including:

(1) AlphaAlpha peak that is largest at posteriorposterior sites (eyes closed)(2) Low frequency EOG artifactsLow frequency EOG artifacts, largest near eyes (eyes closed)(3) EMG artifactsEMG artifacts largest near face (e.g., Fp1/2, eyes open)(4) Electrical artifacts at 6060 and 70 Hz70 Hz (at Fz)

Waveform Comparison:

• CSD Alpha peak at inferior sites (P8P8) has a lower peak frequency and includes more theta (4-8 Hz) than the midline (PzPz) alpha peak

• Alpha is also seen at Fz (eyes closed), and is partially separable from a lower frequency peak

Overview of Amplitude Spectra of CSD Overview of Amplitude Spectra of CSD

Amplitude Spectra of CSD from Resting EEG Amplitude Spectra of CSD from Resting EEG

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Waveform Comparison Waveform Comparison

• Fourier Spectra are complex, with both amplitude (Pythagorean Theorem) and phase (angle from real axis)

• Power Spectra simplify EEG variance, integrating squared amplitudes over frequency (i.e., Mean Squared)

• Power Spectra have empirical and theoretical value independent of the EEG applications (e.g., random process models, systems theory, etc.)

Properties of EEG Power SpectraProperties of EEG Power Spectra

• Factors derived from dataset• PCA uses a linear statistical model to produce orthogonal

components• Factors are useful for identifying and defining temporal

measures

Properties of PCAProperties of PCA

• Power Spectra impede inferences about underlying EEG generators, because information is lost when the data are squared (i.e., linear volume conduction properties not preserved)

• CSD calculation (Laplacian, Hjorth, etc.) is impossible after nonlinear transformation (i.e., the measure is physiologically unintelligible)

• Power estimates are not proportional to the underlying (linear) EEG field potentials

• Logarithmic transformations correct skew of Power Spectrum, but exaggerate systematic, low amplitude noise

Problems with EEG Power SpectraProblems with EEG Power Spectra

Subjects:Subjects: N =143 right-handed adults (n = 63 healthy adults and n = 82 clinically depressed outpatients, pooled across two separate studies)

RecordingsRecordings: Resting 30-channel EEG from four 2-min time periods (order of eyes open/closed counterbalanced as OCCO or COOC across subjects), referenced to nose tip (Grass, 10K gain; 0.1 - 30 Hz band pass; recorded using NeuroScan at 200 samples/s); vertical and horizontal EOG recorded differentially

Signal processing:Signal processing: Data were segmented into 1.28 s epochs (50% overlap), yielding a frequency resolution of 0.78 Hz; artifactual data eliminated from epoched data under visual guidance (semi-automated procedure)

CSD:CSD: CSD waveforms were computed for each accepted epoch using the spherical spline method of Perrin et al. (1989) [lambda = 10-5; 50 iterations; m = 4)

Spectral Analysis:Spectral Analysis: Hanning window (50%) applied to each CSD epoch; mean Power Spectra (PS) computed across epochs for each condition (i.e., eyes open/ closed), and subsequently converted to a RMS Amplitude Spectra (square root of Power Spectra, proportional to the amplitude of an underlying sinusoid)

fPCA:fPCA: Amplitude Spectrum data from 0-77.2 Hz (100 points = 100 variables) submitted to unrestricted covariance-based Principal Components Analysis, using electrodes (31) x Conditions (2) x participants (145) as 8990 cases, followed by unscaled Varimax rotation (Kayser & Tenke, in press)

MethodsMethods

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Unscaled Varimax Rotated Factor Loadings for fPCA Computed from RMS Amplitude Spectra of temporal CSD

ResultsResults

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Topographies of first nine fPCA Factor Scores(96.14% variance of Amplitude Spectra)

Low AlphaLow Alpha High AlphaHigh Alpha AlphaAlphaEOG ArtifactEOG ArtifactEMG ArtifactEMG Artifact

High Variance(88.59% total)

Factors 6-9(additional 7.55%)

60 Hz60 Hz Low BetaLow Beta Alpha ResidualAlpha Residual High BetaHigh Beta

• First five factors accounted for almost 90% of the variance of the CSD Amplitude Spectra; AlphaAlpha activity was represented by Factors 1, 3 and 5Factors 1, 3 and 5

• Factors 2 and 4 extracted known physiological physiological artifactsartifacts (EMG, EOG)• Factors 6-9 each accounted for less than 2% of the variance (60.16 Hz: 1.98%; low

beta: 17.97 Hz, 1.94%; 8.59 Hz, 1.92%; high beta: 23.44 Hz)

Overview of fPCA solutionOverview of fPCA solution

• Factor 1Factor 1 is a prominent (26.53% variance) low alpha factor that overlaps theta. It has a posterior/inferior topography, as well as a secondary topography on the frontal midline.

• Factor 3Factor 3 is a prominent (18.11%) high alpha factor with a medial parietal topography.

• Factor 5Factor 5 also has a medial parietal topography, is intermediate in frequency, and less prominent than the others (7.43%).

• These three alpha factors showed a condition dependencecondition dependence and consistent consistent topographies across four groupstopographies across four groups of participants [i.e., two independent samples of healthy adults (DC,CE) and depressed patients (DD,DE)].

Alpha Factor TopographiesAlpha Factor Topographies

Grouped by Factor 1 at Fz: Low Alpha (Factor 1) had a secondary Fz maximum. The secondary frontal topography was seen for individuals in both two replications using two groups. A consistent topography was also observed for subjects with high, medium or low Factor 1 scores at Fz.

Single Epoch for Representative High Fz Subject: Posterior and frontal midline Alpha topographies of Factor reflect linked, inverted current generators. The sharpness of the frontal midline topography suggests local field closure, as would be produced by an opposed pair of simultaneous regional dipoles.

Inferior and Frontal Generators? CETInferior and Frontal Generators? CET

Amplitude Spectrum of CSD Epoch [Hz]

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Single Epoch for Representative High Fz Subject

Lowpass filtered (15 Hz) CSD waveforms at FzFz (black line) and P8P8 (red) from a representative epoch in a subject with high factor scores for Factor 1. Waveform peaks at FzFz and P8P8 show current sources (warm colors) alternating with sinks (cold colors) between the two sites. The topography of the Amplitude Spectrum of this epoch reflects both midline frontal and posterior/inferior foci described by Factor 1. A single generator (or pair) is unlikely, since CSDs of dipolar ERP generators are less focal at a distance (e.g., N1).

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anxiety, and melancholic features. Biol Psychiatry, 2002, 52, 73-85. Perrin, F., Pernier, J., Bertrand, O. and Echallier, J.F. Spherical splines for scalp potential and current source density mapping. Electroencephalog. clin. Neurophysiol., 1989, 72, 184-187. Pivik R.T., Broughton R.J., Coppola R., Davidson R.J., Fox, N., and Nuwer, M.R.. Guidelines for the recording and quantitative analysis of electroencephalographic activity in research contexts. Psychophysiology, 1993, 30,547-58.Nunez, P.L. Electric Fields of the Brain: The neurophysics of EEG, New York: Oxford, 1981. Tenke,C.E. Statistical characterization of the EEG: the use of the power spectrum as a measure of ergodicity. Electroencephalog. Clin. Neurophysiol., 1986, 63, 488-493. Tenke,C.E., Schroeder, C.E., Arezzo, J.C. and Vaughan, H.G., Jr. Interpretation of high- resolution current source density profiles: a simulation of sublaminar contributions to the visual evoked potential. Exp. Brain Res., 1993, 94,183-192.

ReferencesReferences Bendat, J.S., and Piersol, A.G. Random Data: Analysis and measurement procedures. Wiley-Interscience, New York, 1971. Goncharova, I.I., McFarland, D.J., Vaughan, T.M., and Wolpaw, J.R. EMG contamination of EEG: spectral and topographic characteristics. Clin. Neurophysiol., 2003, 114, 1580-1593. Kayser, J., Tenke, C.E. Optimizing PCA methodology for ERP component identification and measurement: Theoretical rationale and empirical evaluation. Clin. Neurophysiol., in press. Kayser, J., Tenke, C.E., Debener, S. Principal components analysis (PCA) as a tool for identifying EEG frequency bands: I. Methodological considerations and preliminary findings. Psychophysiology, 2000, 37, S54. Pizzagalli, D.A., Nitschke, J.B., Oakes, T.R., Hendrick, A.M., Horras, K.A., Larson, C.L., Abercrombie, H.C., Schaefer, S.M., Koger, J.V., Benca, R.M., Pascual-Marqui, R.D., and Davidson, R.J. Brain electrical tomography in depression: the importance of symptom severity,

Electrophysiologic measures may provide useful information about the anatomical origin and physiological significance of an experi-mental finding. However, certain methodological choices severely limit the capacity for such inferences. Notable issues concern the impact of the (1) recording referencerecording reference and the (2) quantification quantification methodmethod itself (i.e., defining and measuring a component or frequency band).(1) The reference problem has been addressed by the parallel

application of different reference schemes. As an alternative, CSD methods (Laplacian, Hjorth, etc.) can be used as a true reference-free measure with a known correspondence to neuronal current generators.(2) The quantification problem has been addressed by defining

multiple, more loosely defined frequency bands tailored to the data.These problems are exacerbated in quantitative EEG studies that

apply nonlinear transformations to the data (e.g., logarithmic transformations, power or amplitude spectra, and asymmetry measures derived from them). We now describe a general, reference-free, data-driven method for simplifying and quantifying EEG CSD spectra using frequency PCA.

IntroductionIntroduction

http://psychophysiology.cpmc.columbia.edu

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