The dimensionality of the human visual evoked scalp potential

Evaluation of PCA and ICA of simulated ERPs: Promax vs. Infomax rotations

Independent components analysis (ICA) and principal components analysis (PCA) are methods used to analyze event-related potential (ERP) and functional imaging (fMRI) data. In the present study, ICA and PCA were directly compared by applying them to simulated ERP datasets. Specifically, PCA was used to generate a subspace of the dataset followed by the application of PCA Promax or ICA Infomax rotations. The simulated datasets were composed of real background EEG activity plus two ERP simulated components. The results suggest that Promax is most effective for temporal analysis, whereas Infomax is most effective for spatial analysis. Failed analyses were examined and used to devise potential diagnostic strategies for both rotations. Finally, the results also showed that decomposition of subject averages yield better results than of grand averages across subjects.

The effects of nicotine on the 13 Hz steady-state visually evoked potential

OBJECTIVES

The high alpha/low beta range of the spontaneous EEG appears to be particularly sensitive to the effects of nicotine. The present study examined the acute effects of nicotine on the topography of the 13 Hz steady-state visually evoked potential (SSVEP).

METHODS

Thirteen moderate smokers participated in a repeated-measures design. The amplitude and latency of the SSVEP elicited by an unstructured sinusoidal 13 Hz flicker following a <0. 05 mg nicotine cigarette were compared to those following a 0.8 mg nicotine cigarette.

RESULTS

The nicotine condition was associated with an increase in the amplitude of the SSVEP, when compared to the placebo condition, and this increase was greatest in central and right parietal regions. The latency of the SSVEP was reduced in the nicotine condition in bilateral frontal and right parietal regions.

CONCLUSIONS

These results are similar to the effects of nicotine seen in studies examining spontaneous EEG, and are consistent with other studies indicating that the 13 Hz SSVEP indexes brain electrical activity in the high alpha/low beta range. The findings are discussed in terms of possible functional significance of nicotine-induced cortical activation in this frequency range.

The usefulness of the Laplacian in principal component analysis and dipole source localization

Evoked potentials are difficult to analyze because multiple sources are active simultaneously. Principal component analysis and dipole localization are two techniques that have been used to disentangle overlapping sources. Both of these techniques have problems. Principal component analysis suffers from a rotation ambiguity. Dipole localization suffers from biases when the model used to derive the sources from the scalp potentials is misspecified. Using computer simulations we demonstrate that by applying both of these techniques to the Laplacian of the voltages rather than to the raw voltages the problems associated with the two techniques are reduced. Computer programs for the analyses are presented in an Appendix.

A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres

Berg and Scherg's fast computation method is extended to multilayer anisotropic spheres. The Berg parameters can be dependent upon a dipole radial parameter or not, depending on the actual sphere conductivities and the layer the dipole is within. To find the Berg parameters, no specific electrode locations are required. Berg and Scherg's method is generally applicable whenever de Munck and Peters's addition-subtraction method can be used.

Steady-state visually evoked potential topography during the Wisconsin card sorting test

This paper describes, for the first time, changes in steady-state visually evoked potential (SSVEP) topography associated with the performance of a computerised version of the Wisconsin card sort test (WCS). The SSVEP was recorded from 64 scalp sites and was elicited by a 13 Hz spatially uniform visual flicker presented continuously while 16 subjects performed the WCS. in the WCS, the sort criterion was automatically changed after subjects had sorted 10 cards correctly. Feedback on the 11th card always constituted a cue for a change in the sort criterion. It was found that in the 1-2 sec interval after the occurrence of the cue to change sort criterion, the prefrontal, central and right parieto-temporal regions showed a pronounced attenuation in SSVEP amplitude and an increase in phase lag. These changes, interpreted as an increase in regional cortical activity, are not apparent in the equivalent portions of the WCS when the sort criterion does not need to be changed. These results indicate that the levels of prefrontal and right parieto-temporal activity varied during the performance of the WCS, peaking at the times a change in sort criterion was required.

Model misspecification detection by means of multiple generator errors, using the observed potential map

Due to model misspecification, currently-used Dipole Source Localization (DSL) methods may contain Multiple-Generator Errors (MulGenErrs) when fitting simultaneously-active dipoles. The size of the MulGenErr is a function of both the model used, and the dipole parameters, including the dipoles' waveforms (time-varying magnitudes). For a given fitting model, by examining the variation of the MulGenErrs (or the fit parameters) under different waveforms for the same generating-dipoles, the accuracy of the fitting model for this set of dipoles can be determined. This method of testing model misspecification can be applied to evoked potential maps even when the parameters of the generating-dipoles are unknown. The dipole parameters fitted in a model should only be accepted if the model can be shown to be sufficiently accurate.

Insidious errors in dipole parameters due to shell model misspecification using multiple time-points

Insidious errors in dipole modeling due to shell model misspecification in a spherical model were examined analyzing multiple time-points using the constraints of a commonly-used DSL (Dipole Source Localization) method. The computer simulation examined the differences in the fit dipole parameters for the same generator under two circumstances: 1) when computed as a single dipole active alone, and 2) when computed as a member of a simultaneously-active dipole pair. The computations were done using a simplification by which the dipole parameters computed from multiple time-points can be correctly assessed by computing dipole parameters at only two virtual time-points. Using multiple time-points in the DSL generally resulted in less error than if only a single time-point was used. However, how much improvement cna be achieved by using multiple time-points, as compared with a single time-point, is a function of many factors, such as the location and orientation of the dipoles, and the relative magnitudes and overlap of the waveforms (i.e., time-varying magnitudes) of the dipoles, as well as the model used in the fitting. Further, it was shown that it is incorrect to assume that a multiple-time-point DSL will compute a zero magnitude for generators during quiescent intervals. Additionally, it was shown that a "correction" to reduce error for one pair of waveforms will not be applicable to other waveforms. Also, even if location errors are eliminated, magnitude and orientation errors can still be shown to be present. Finally, iterative reduction of the least-square error between the observed and predicted surface maps leads to increasing errors in dipole parameters. We conclude that a DSL with model misspecification can contain insidious (undetectable) errors.

Standardized varimax descriptors of event related potentials: basic considerations

This paper describes a set of proposed standardized quantitative descriptors of event-related potentials, based upon principal component varimax analysis (PCVA). No claim is made that these mathematical descriptors correspond to discrete neurophysiological processes which generate the ERP. However, adoption and prospective evaluation of such a set of precise, standardized descriptors of the quantitative ERP may eventually result in advances like those which resulted from adoption of equally arbitrary standardized descriptors for QEEG. PCVA was performed on data from normal subjects and from groups of patients with a wide variety of psychiatric disorders ("Abnormals"). This yielded two sets of factor waveshapes, Normal and Abnormal, which were closely similar. Reconstruction of the normal and abnormal ERP data with either set of factors yielded almost identical allocation of variance. These results gave acceptable reassurance that factors derived from normal population could reasonably be used to describe ERP waveshapes from patients. The ERPs at each electrode of the 10/20 System in a "training group" of normal subjects were then reconstructed. The resulting distributions of factor scores were transformed to achieve Gaussianity. Mean values and standard deviations were obtained for the normative distribution of each factor score, the root mean square deviation, the residual and the absolute ERP power at each electrode. Individual ERPs could then be reconstructed with the normal factors, and the resulting factor scores rescaled to "probability of abnormal morphology" by Z-transformation. Statistical probability maps could be generated by using a color scale in standard deviation units. These methods were used to evaluate visual and auditory ERPs from an independent normal "test group" and the patients in the Abnormal sample. High specificity and sensitivity were obtained for many factor Z- scores. Multiple discriminant functions were constructed which separated normal from abnormal patients with high, replicable accuracy. Further development and testing of these descriptors may make them clinically useful.

Analysis of striate activity underlying the pattern onset EP of children

The checkerboard onset Evoked Potential (EP) does not obtain its adult form before puberty. To determine the site of origin of these processes we studied the origin of the checkerboard onset EP in a group of 10 children between the ages of 6 and 16 years. Since the development of the waveform of the pattern onset EP varies with check size we also studied the dependence of these EPs on check size. The child checkerboard onset EPs described in this paper are dominated by a single source. Following an equivalent dipole source localization approach, the position, orientation and variation in strength of the equivalent dipole is estimated. The position and orientation of this dipole indicates an origin in the primary visual cortex (area 17). The variation in strength of the dipole changes from a single positive deflection, specific for children of 8 years and younger, into a negative-positive complex for the children studied between the age of 9 and 16 years. These changes in waveform must be due to changes in the activity pattern of the striate cortex.

Equivalent dipole estimation of spontaneous EEG alpha activity: two-moving dipole approach

A method of estimating equivalent moving and fixed dipoles from the scalp-recorded EEG alpha waves, with the realistic geometry of the head taken into account, is presented. Twenty-one silver electrodes were used to collect spontaneous EEG alpha waves on the scale. Four models, the single-moving dipole model, the single-fixed dipole model, the two-moving dipole model and the two-fixed dipole model were applied to approximate the EEG alpha field on the scalp. The algorithm, based on a least-squares fit for estimating the moving and the fixed dipoles by using a realistically shaped head model, is described. The numerical accuracy of the algorithm is also evaluated by a computer simulation. It is found that the spontaneous EEG alpha activity observed on the scalp can be represented by two equivalent moving dipoles, simultaneously located separately in the occipital regions of the right and the left hemisphere, at a depth of 4-6 cm beneath the scalp, with a goodness-of-fit of up to 97 per cent for all subjects examined. The excellent fit of the two-moving dipole model to the EEG human alpha activity is also compared with the single-dipole fit.

Weighted averaging of evoked potentials

Weighted averages of brain evoked potentials (EP's) are obtained by weighting each single EP sweep prior to averaging. These weights are shown to maximize the signal-to-noise ratio (SNR) of the resulting average if they satisfy a generalized eigenvalue problem involving the correlation matrices of the underlying signal and noise components. The signal and noise correlation matrices are difficult to estimate and the solution of the generalized eigenvalue problem is often computationally impractical for real-time processing. Correspondingly, a number of simplifying assumptions about the signal and noise correlation matrices are made which allow an efficient method of approximating the maximum SNR weights. Experimental results are given using actual auditory EP data which demonstrate that the resulting weighted average has estimated SNR's that are up to 21% greater than the conventional ensemble average SNR.

Topography of the evoked potential to spatial localization cues

Visual tasks that are perceptually diverse might be expected to elicit unique evoked-potential waveforms that exhibit differing topographic maps. To investigate this possibility, multichannel visual-evoked potentials (VEPs) were recorded in response to several dot spatial localization stimuli that are physically similar yet produce different percepts (vernier offsets, steroscopic disparity, bisection, orientation, and relative displacement) to determine if the unique percepts arising from these stimuli reflect the activation of different cortical neural populations. The resulting evoked potentials were all similar in waveform, although the stereoscopic VEPs were relatively delayed. Topographic maps of the evoked-potential activity to each stimulus revealed a late major component with two independent foci: one 7 or more centimeters above the inion lateral to the midline, and the other at least 6 cm lateral to OZ. The scalp localization of both peaks was independent of both the position of the stimulus in the visual field and the particular stimulus cue presented. An asymmetric response to pattern appearance vs. disappearance indicated strong pattern specificity for each stimulus type except unreferenced motion. The timing of the VEP responses and relative insensitivity to retinal locus of stimulation suggest the involvement of higher cortical areas. The two map foci might be interpreted as activation of inferotemporal and parietal cortices whose roles are thought to be visual object interpretation and spatial attention and localization, respectively.

Measurement processes and spatial principal components analysis

Spatial principal components analysis (SPCA) applied to the ongoing EEG yields factor loadings which, when mapped, consistently reveal symmetrical patterns resembling the spherical harmonics. In this paper, we consider the mechanisms responsible for these characteristic patterns. In doing so, we demonstrate that volume conduction is one of a family of processes capable of generating such patterns with SPCA. It is shown that any series of measurements on a sphere in which the covariance is only a function of measurement site angular separation (shift invariant processes) will yield the spherical harmonics as the eigenvectors or factor loadings of the covariance matrix. Simulations further indicate that this effect is robust and not determined by the geometry of the measurement sites. In situations where shift invariant signals coexist with those generated at specific sites (anatomically specific processes), such as evoked potentials and some artifacts, it is shown that the anatomically specific signals do not influence the eigenvectors of the covariance matrix in a uniform or random fashion. The factors most influenced are those whose symmetry is similar to that of the site specific signal.

Unrestricted principal components analysis of brain electrical activity: issues of data dimensionality, artifact, and utility

Principal components analysis (PCA) was performed on the 1536 spectral and 2944 evoked potential (EP) variables generated by neurophysiologic paradigms including flash VER, click AER, and eyes open and closed spectral EEG from 202 healthy subjects aged 30 to 80. In each case data dimensionality of 1500 to 3000 was substantially reduced using PCA by magnitudes of 20 to over 200. Just 20 PCA factors accounted for 70% to 85% of the variance. Visual inspection of the topographic distribution of factor loading scores revealed complex loadings across multiple data dimensions (time-space and frequency-space). Forty-two non-artifactual factors were successful in classifying age, gender, and a separate group of 60 demented patients by linear discriminant analysis. Discrimination of age and gender primarily involved EP derived factors, whereas dementia primarily involved EEG derived factors. Thirty-eight artifactual factors were identified which, alone, could not discriminate age but were relatively successful in discriminating gender and dementia. The need to parsimoniously develop real neurophysiologic measures and to objectively exclude artifact are discussed. Unrestricted PCA is suggested as a step in this direction.

The extrastriate generators of the EP to checkerboard onset. A source localization approach

The cortical origin of the pattern onset EP has been investigated over a time window which covers the entire positive-negative-positive complex of the pattern onset EP. On the basis of a dipole source localization approach, the position, orientation and strength of the underlying sources of the pattern onset EP were estimated. For large check stimuli, chosen to have a weak edge specific component in the response, still two components are needed to account for the variance of the responses. Each component corresponds to a single dipole source, and both originate in the extrastriate cortex. These components dominate, respectively, the initial and the late positive peaks of the pattern onset EP. The equivalent dipole sources of the two components show different behaviors with respect to the position of the stimulus in the visual field. The topography and behavior of the equivalent dipole source underlying the early positive component suggest an origin in area 18. The invariance with stimulus location of the dipole source underlying the late positive component suggests an origin beyond area 18. The different topographies of the components also account for the differences in surface distribution of the pattern onset EP to large check stimulation of the upper and lower sectors of the visual field.

Quantified neurophysiology with mapping: statistical inference, exploratory and confirmatory data analysis

Topographic mapping of brain electrical activity has become a commonly used method in the clinical as well as research laboratory. To enhance analytic power and accuracy, mapping applications often involve statistical paradigms for the detection of abnormality or difference. Because mapping studies involve many measurements and variables, the appearance of a large data dimensionality may be created. If abnormality is sought by statistical mapping procedures and if the many variables are uncorrelated, certain positive findings could be attributable to chance. To protect against this undesirable possibility we advocate the replication of initial findings on independent data sets. Statistical difference attributable to chance will not replicate, whereas real difference will reproduce. Clinical studies must, therefore, provide for repeat measurements and research studies must involve analysis of second populations. Furthermore, Principal Components Analysis can be employed to demonstrate that variables derived from mapping studies are highly intercorrelated and data dimensionality substantially less than the total number of variables initially created. This reduces the likelihood of capitalization on chance. The need to constrain alpha levels is not necessary when dimensionality is low and/or a second data set is available. When only one data set is available in research applications, techniques such as the Bonferroni correction, the "leave-one-out" method, and Descriptive Data Analysis (DDA) are available. These techniques are discussed, clinical and research examples are given, and differences between Exploratory (EDA) and Confirmatory Data Analysis (EDA) are reviewed.

Investigation of multiple simultaneously active brain sources in the electroencephalogram

We present a method of investigating multiple simultaneously active brain sources that overlap both in space and time in the scalp electroencephalogram (EEG). In order to identify the contributions of the individual brain sources to measured potentials, we applied principal component analysis and various methods of rotating the principal components including a newly developed rotation procedure using frequency criteria. We related the results of these multivariate statistical techniques to a new physical model using multiple current dipoles with fixed anatomical locations and time-varying activities. We thus are able to study 3-dimensional location, time activity and interaction of multiple simultaneously active brain sources in the scalp EEG.

Principal components analysis for source localization of VEPs in man

This study defines and compares the topologies of the visual evoked potentials to various stimuli such as pattern onset/offset, pattern reversal, pattern motion and high frequency luminance flicker. The responses recorded from 24 occipital derivations were examined using a three sphere conductance model to represent the head, with the assumption that activity from an underlying cortical source is equivalent to a single dipole. Principal components analysis was used to find the dimensionality of the data space. From this analysis could be concluded that all stimuli evoked responses in the primary visual cortex. Only pattern onset, and to a lesser degree pattern offset and pattern reversal, yielded activity in higher visual areas. In particular it has been shown that the CI, CII interval of the pattern onset response has its origins in two different cortical regions. A fast positive (CI)-negative (part of the CII) component arises from area 18 (or 19), a slower negative (initial part of CII) component comes from area 17.

Spatio-temporal visually evoked scalp potentials in response to partial-field patterned stimulation

Visually evoked scalp potentials (VESP) have been recorded at 40 electrode sites from each of 3 subjects. Pattern appearance/disappearance was used for whole field and partial field stimulation. The data are displayed as equipotential maps. The topographical features of the equipotential maps show periods of stable organization followed by periods of relatively rapid change. The structure of the maps changes in a consistent pattern with the region of the retina stimulated; the first peak fits well within the framework of the cruciform model of striate cortex. The first and second peaks of the VESP appear to be caused by independent neural generators. The work reported in this paper shows major agreement with other authors and reconciles some points of disagreement between them.

Trigeminal evoked potentials in humans

Techniques were described for recording trigeminal evoked potentials in humans in response to maxillary gum stimulation. Variations in the responses as a function of stimulating and recording electrode position and stimulus intensity were presented. A standard methodology was proposed in order to obtain the characteristic response repeatedly. The characteristic triphasic wave form consisted, primarily, of an N20, P34, N51 sequence of deflections. Average latencies of components were derived from recordings following stimulation of the asymptomatic side of the face in a patient population. Indirect tests supported the view that muscle potentials did not significantly contribute to the characteristic response. It was concluded that the techniques were suitable for electrophysiological testing of fifth nerve function in routine clinical applications.