Interelectrode coherences from nearest-neighbor and spherical harmonic expansion computation of Laplacian of scalp potential

Section of Electroencephalography, Mayo Clinic, Rochester, MN 55905, USA.
Electroencephalography and Clinical Neurophysiology 10/1995; 95(3):178-88. DOI: 10.1016/0013-4694(95)00025-T
Source: PubMed


Interchannel coherence is a measure of spatial extent of and timing relationships among cerebral electroencephalogram (EEG) generators. Interchannel coherence of referentially recorded potentials includes components due to volume conduction and reference site activity. The laplacian of the potential is reference independent and decreases the contribution of volume conduction. Interchannel coherences of the laplacian should, therefore, be less than those of referentially recorded potentials. However, methods used to compute the laplacian involve forming linear combinations of multiple recorded potentials, which may inflate interchannel coherences. WE compared 3 methods of computing the laplacian: (1) modified Hjorth (4 equidistant neighbors to each electrode), (2) Taylor's series (4 nonequidistant neighbors), and (3) spherical harmonic expansion (SHE). Average interchannel coherence introduced by computing the laplacian was less for nearest-neighbor methods (0.0207 +/- 0.0766) but still acceptable for the SHE method (0.0337 +/- 0.0865). Average interchannel coherence for simulated EEG (random data plus a common 10 Hz signal) was less for laplacian than for referential data because of removal of the common referential signal. Interchannel coherences of background EEG and partial seizure activity were less with the laplacian (any method) than with referential recordings. Laplacians calculated from the SHE do not demonstrate excessively large interchannel coherences, as have been reported for laplacians from spherical splines.

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    • "When averaged across pairs of electrodes, the index R ij represents a measure of global synchronization strength R À Á . For this analysis, before computing the wavelet-coefficients, the raw EEG trials were first transformed with a modified version of the nearest-neighbor Hjorth Laplacian algorithm computed by Taylor's series expansion (Lagerlund et al., 1995 "
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    Full-text · Article · Dec 2010 · NeuroImage
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    • "The average of this index across pairs of electrodes represents a measure of global synchronization strength (R). For the bivariate synchronization analysis, a modified version of the nearestneighbour Hjorth Laplacian algorithm computed by Taylor's series expansion (Lagerlund et al., 1995 "
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    ABSTRACT: The ability to anticipate forthcoming events has clear evolutionary advantages, and predictive successes or failures often entail significant psychological and physiological consequences. In music perception, the confirmation and violation of expectations are critical to the communication of emotion and aesthetic effects of a composition. Neuroscientific research on musical expectations has focused on harmony. Although harmony is important in Western tonal styles, other musical traditions, emphasizing pitch and melody, have been rather neglected. In this study, we investigated melodic pitch expectations elicited by ecologically valid musical stimuli by drawing together computational, behavioural, and electrophysiological evidence. Unlike rule-based models, our computational model acquires knowledge through unsupervised statistical learning of sequential structure in music and uses this knowledge to estimate the conditional probability (and information content) of musical notes. Unlike previous behavioural paradigms that interrupt a stimulus, we devised a new paradigm for studying auditory expectation without compromising ecological validity. A strong negative correlation was found between the probability of notes predicted by our model and the subjectively perceived degree of expectedness. Our electrophysiological results showed that low-probability notes, as compared to high-probability notes, elicited a larger (i) negative ERP component at a late time period (400-450 ms), (ii) beta band (14-30 Hz) oscillation over the parietal lobe, and (iii) long-range phase synchronization between multiple brain regions. Altogether, the study demonstrated that statistical learning produces information-theoretic descriptions of musical notes that are proportional to their perceived expectedness and are associated with characteristic patterns of neural activity.
    Full-text · Article · Dec 2009 · NeuroImage
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    • "For each single subject the averaged MMN waveform was cross-correlated to the MMN grand-averaged envelope — defined as the minimum value among all electrodes for each time frame, of the control group, and the maximum delay value resulting from the cross-correlation was then used to align the individual MMN waveform. Prior to SCD estimation by mean of a Laplacian operator (Perrin et al., 1989), individual data were interpolated in a spherical scalp model using 1000 pixels by means of a Spherical Harmonics Expansion (Lagerlund et al., 1995), according to the method described by Ruffini et al. (2002). A scalp area was considered activated on the grand-average SCD map if 4 adjacent pixels showed p b 0.05 relative to prestimulus interval during 6 consecutive time frames using the Holmes non-parametric method, that is corrected from multiple comparisons (Holmes et al., 1996). "
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