Principal components analysis of Laplacian waveforms as a generic method for identifying ERP generator patterns: II. Adequacy of low-density estimates
Introduction
Current source density (CSD) transformation of scalp surface potentials is commonly used as a reference-free method to sharpen ERP topographies in a physiologically-meaningful fashion (e.g. Kayser and Tenke, 2006, Nunez and Westdorp, 1994). CSD or surface Laplacian and other deblurring techniques frequently combine high-resolution EEG (64 or more channels) with realistic head models obtained by structural magnetic resonance imaging (e.g. Babiloni et al., 1996, Babiloni et al., 2000, Babiloni et al., 2001, Gevins, 1996, Gevins, 1998, Gevins et al., 1999). In an influential report based on synthetic (i.e. noise-free) and real, single-subject 64-channel ERP data, Junghöfer et al. (1997) have argued that more than 100 recording sites are needed to guarantee reasonable accuracy of surface Laplacian estimates, and concluded ‘that nothing meaningful can be inferred about unknown sources’ when using a low-density 10–20 system EEG montage. Srinivasan et al. (1998), also using simulated data and 19, 32, 64, or 129 sites of an individual ERP recording to estimate spatial aliasing, similarly concluded that a sufficient density of sensors (i.e. a minimum of 128) is required for adequate spatial sampling of the electrical field at scalp. This conclusion is frequently reiterated, and with it the notion that high-density recordings are a prerequisite for using CSD methodology.1
Low-resolution CSDs are sometimes preferable to overresolved CSDs, particularly when the differentiation of sink and source activity is entirely adequate (e.g. Tenke et al., 1993). This assertion rests on the fact that the measured voltage (potential difference) is a volume integral, and is thereby effectively reinforced and stabilized over distance. An overresolved estimate (i.e. when the generator spans a number of electrodes) may be subject to greater measurement and computational noise relative to estimates of the local field potential gradient, from which the CSD is computed. Recent simulation studies have also verified that the advantage of dense electrode recordings for CSD methodology is compromised with increased noise levels (Babiloni et al., 2004, Ryynänen et al., 2004). Moreover, high-density CSD is disproportionately affected by the imprecision in electrode placement, as well as by inter-electrode variability at the electrode-scalp interface (Greischar et al., 2004, Tenke and Kayser, 2001). Sufficient electrode connectivity and accurate (i.e. reliable) scalp placements are affected by a number of variables, including individual differences (e.g. hair texture or scalp dryness) and acquisition hardware (e.g. sensor properties), all of which impact on the signal-to-noise ratio.
In contrast to field potentials, which may be directly measured, CSD waveforms and topographies must always be estimated, regardless of the simplicity or complexity of model that is used to compute them. The issue, then, is not whether low-density CSDs are perfectly accurate representations of the true Laplacian, but rather whether low-resolution CSDs are helpful for summarizing and interpreting surface potential topographies. In this regard, Babiloni and colleagues have shown the usefulness of low-resolution CSD methodology for clinical settings, in which dense electrode array EEGs may be difficult to record. For example, a 9-channel surface Laplacian used for a brain computer interface (BCI) device provided a reasonable approximation of a full-resolution surface Laplacian (Babiloni et al., 2001). Furthermore, reasonable estimates of both surface Laplacian and low-resolution brain electromagnetic tomography (LORETA; Pascual-Marqui et al., 1994) were obtained from a standard 10–20 system montage consisting of only 19 channels for group data of Alzheimer Disease patients and healthy adults (Cincotti et al., 2004). Likewise, using a subset of 19 electrodes combined with independent component analysis (ICA; Makeig et al., 2000) for estimating event-related synchronization of motor-related beta activity on an individual basis was equally effective as a realistic high-resolution (128-channel) surface Laplacian combined with individual MRI data (Foffani et al., 2004).
While individual CSD topographies may be highly specific and unique, such specificity is largely lost with the analysis of group data. However, a loss of individual specificity is an intentional characteristic for areas of basic research in which the focus is on the discovery of general principles and rules. As pointed out by Junghöfer et al. (1997), averaging over subjects results in spatial low-pass filtering, yielding a loss of spatial resolution when compared to individual averages, but also reducing the error of spatial undersampling. This principle is directly comparable to the temporal low-pass filter resulting from group averages, which can effectively compensate for temporally under-sampled data or an insufficient analog/digital data acquisition and conversion, given the considerable variation in peak latency and amplitude of sequential ERP components across individuals. Despite the uniqueness of individual ERP averages, grand mean ERP waveforms are widely accepted as summaries as long as topographic or latency jitter is acceptable for all comparisons of interests (i.e. groups and/or conditions). Notably, the (temporal) information provided by typical group ERPs recorded at 100 samples/s is not improved by increasing data acquisition to 1000 samples/s, because the highest frequency contribution to the group signal (i.e. less than 10 Hz for P1–N1 amplitude as the steepest deflection) was sufficiently sampled at the lower rate. By analogy, one would expect that the same principles apply to the spatial domain when analyzing and interpreting group data.
To the best of our knowledge, the effects of using more than 100 channels vs. using only a limited 10–20-system montage on the spatial pattern of cognitive ERP activity for the analysis of group data have not been reported. Using an existing dense electrode array EEG data set previously recorded from 17 healthy adults during tonal and phonetic oddball tasks (Kayser et al., 2000), and applying unrestricted, temporal principal components analysis (PCA) with Varimax rotation of the covariance loadings (Kayser and Tenke, 2003) as an exhaustive and elaborate approach to summarize high- or low-resolution CSD activity derived from these data, the present study sought to fill this gap by systematically comparing and contrasting high- and low-resolution CSD estimates and their PCA solutions.
Section snippets
Participants
Out of the original sample of 66 right-handed, healthy adults (see Kayser and Tenke, 2006, for screening details), 24 participants were also tested in a second ERP recording session using a 129-channel geodesic sensor net system (Electrical Geodesics, Inc.). The study had been approved by the institutional review board, and these volunteers, who had given written consent, were again paid $15/h for their participation in this second session, which took place 2–7 days after the first ERP
Behavioral data
Mean response latency for correct button press responses was faster for tones (M=435.6 ms, SD=92.2) compared with syllables (M=476.0 ms, SD=107.9; task main effect, F[1,16]=7.27, P=.02). The mean hit rate exceeded 99% in all press conditions (tonal=99.5%, SD=1.6; phonetic=99.1%, SD=1.6), with no significant ANOVA effects. A comparable mean hit rate was observed for silent count, revealing marginally significant differences between tonal (M=98.3%, SD=3.3) and phonetic stimuli (M=96.0%, SD=4.6;
Discussion
Surface Laplacian estimates derived from a standard 31-channel, 10–20 system EEG montage with an established spherical spline interpolation (Perrin et al., 1989, Perrin et al., 1990) were found to be surprisingly accurate approximations of CSD estimates derived from a 129-channel, dense electrode array using the same spherical spline interpolation. For a group of 17 healthy adults, grand mean CSD waveforms and all identified CSD components, using unrestricted temporal PCA as an efficient means
Acknowledgements
This research was supported by grants MH36295, MH50715, MH58346, MH59342 and SI0RR11460 from the National Institute of Mental Health (NIMH).
We greatly appreciate the assistance of Nil Bhattacharya, Barbara Stuart, Paul Leite and Jeffrey Hudson with data collection, storage, preprocessing and artifact screening.
Waveform plotting software was written by Charles L. Brown, III.
Preliminary findings of these data have been presented at the 40th Annual Meeting of the Society for Psychophysiological
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