Neil E. Busacker

Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition

Principal component analysis (PCA) by singular value decomposition (SVD) may be used to analyze an epoch of a multichannel electroencephalogram (EEG) into multiple linearly independent (temporally and spatially noncorrelated) components, or features; the original epoch of the EEG may be reconstructed as a linear combination of the components. The result of SVD includes the components, expressible as time series waveforms, and the factors that determine how much each component waveform contributes to each EEG channel. By omission of some component waveforms from the linear combination, a new EEG can be reconstructed, differing from the original in useful ways. For example, artifacts can be removed and features such as ictal or interictal discharges can be enhanced by suppressing the remainder of the EEG. We developed a variation of this technique in which the factors that reconstruct the modified EEG from the original are stored as a matrix. This matrix is applied to multichannel EEG at successive times to create a new EEG continuously in real time, without redoing the time-consuming SVD. This matrix acts as a spatial filter with useful properties. We successfully applied this method to remove artifacts, including ocular movement and electrocardiographic artifacts. Removal of myogenic artifacts was much less complete, but there was significant improvement in the ability to visualize underlying activity in the presence of myogenic artifacts. The major limitations of the method are its inability to completely separate some artifacts from cerebral activity, especially when both have similar amplitudes, and the possibility that a spatial filter may distort the distribution of activities that overlap with the artifacts being removed.

Determination of 10–20 system electrode locations using magnetic resonance image scanning with markers

We determined locations of 33 scalp electrodes used for electroencephalographic (EEG) recording by placing markers in the positions determined by the 10-20 system and performing magnetic resonance image (MRI) scanning on volunteer subjects. Small Vaseline-filled capsules glued on the scalp with collodion produced easily delineated regions of increased signal on standard MRI head images. Measurements of each capsules coordinates in 3 dimensions were made from MRI scans. A spherical surface was fitted through the marker positions, giving an average radius and an origin (center of sphere). The coordinate axes were rotated to ensure that electrode Cz was on the z-axis and that the y-axis was oriented in the posterior-anterior direction. Two spherical (angular) coordinates were determined for each electrode. Spherical electrode coordinates for different subjects differed by less than 20 degrees in all cases. An average and standard deviation of the spherical coordinates were calculated for each electrode. Standard deviations of several degrees were obtained. The average spherical coordinates obtained were close to those expected on the basis of applying the 10-20 system of placement to an ideal sphere. These measurements provide data necessary for various analyses of EEG performed to help localize epileptic foci.

Characterization and Comparison of Local Onset and Remote Propagated Electrographic Seizures Recorded with Intracranial Electrodes

Summary: Purpose: To compared the ictal discharge patterns between local onset and remote propagated electrographic seizures recorded with chronic intracranial electrodes.

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

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) Taylors 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.

SUBCLINICAL RHYTHMIC ELECTROGRAPHIC DISCHARGES OF ADULTS (SREDA) REVISITED: A STUDY USING DIGITAL EEG ANALYSIS

Previous descriptions of the subclinical rhythmic electrographic discharges of adults (SREDA) have been based entirely on visual analysis of analog electroencephalographic (EEG) recordings. The introduction of digital electroencephalograms (EEGs) and advances in digital signal processing provide an opportunity to restudy in more depth the nature of SREDA. We identified nine patients who had SREDA diagnosed on a routine EEG recording since the introduction of digital EEG to our laboratory in August 1995. Following careful rereview using standard montages, six of these patients were determined to fulfill the traditional requirements for the diagnosis of SREDA, whereas three were believed to have other benign discharges. Review with Laplacian montages demonstrated that the site of the SREDA activity was maximal in the parietal region or parietocentrotemporal regions, whereas it was maximal in the temporal or frontotemporal regions in the non-SREDA discharges. Frequency analysis, using both the conventional fast Fourier transform (FFT) and time-frequency mapping with the Wigner FFT variant, demonstrated that the SREDA consisted of a complex mixture of multiple rapidly shifting frequencies which showed little spatial and temporal correlation. In contrast, the non-SREDA all consisted of a single dominant well-organized rhythmic frequency spectrum that remained stable throughout space and time.

Use of principal component analysis in the frequency domain for mapping electroencephalographic activities: comparison with phase-encoded Fourier spectral analysis.

SummaryPrincipal component analysis (PCA) can separate multichannel electroencephalographic (EEG) epochs into linearly independent (temporally and spatially noncorrelated) components. Results of PCA include component time‐series waveforms and factors representing the contribution of each component to each electrode; these factors may be displayed as contour maps representing the topographic distribution of each component. However, PCA often does not achieve the most useful separation of components. PCA may be performed in the frequency domain to potentially improve results. After inspecting principal components of the frequency spectra, spectral values in a selected frequency range are multiplied by a chosen factor to emphasize (or de‐emphasize) these frequencies and PCA is redone, promoting the separation of different frequencies into different components. Phase‐encoded Fourier spectral analysis (PEFSA) uses multichannel complex Fourier spectra (amplitude and phase) to obtain positive or negative (phase‐encoded) potentials at each electrode for any selected frequency. These may be displayed as a contour map representing the topographic distribution of the selected frequency. Applying both techniques, we found that EEG activities of differing frequency were readily separated by PEFSA, while standard PCA often mixed activities with different frequencies into a single component. However, frequency‐domain PCA gave a component whose spatial distribution well matched PEFSA results. PCA is superior to PEFSA for separating activities with overlapping frequencies but differing spatial distributions. Preservation of phase information is an advantage of PEFSA and PCA over topographic maps that represent only amplitude (or power) at a given frequency. PCA or PEFSA maps can serve as a starting point for source localization.

Spectral analysis of slow modulation of EEG amplitude and cardiovascular variables in subjects with postural tachycardia syndrome

OBJECTIVE Previous studies have reported slow (<0.5 Hz) modulation of electroencephalographic (EEG) background amplitude and suggested that this reflects periodic neuronal activity in the brainstem, such as may be recorded from cardiovascular and respiratory centers in animals. We searched for a relationship between EEG amplitude modulation and modulation of simultaneously recorded cardiovascular variables and attempted to determine whether this relationship was altered in subjects with postural tachycardia syndrome (POTS). METHODS We recorded EEG, blood flow velocity in the middle cerebral artery (MCA), heart rate, respirations, and blood pressure from subjects with POTS and controls during head-up tilt. Time-frequency analysis of 0.512-s epochs of EEG was performed to determine peak alpha amplitude. Spectra were divided into 3 bands: ultraslow, middle, and respiratory. RESULTS EEG alpha amplitude modulation in all frequency bands was reduced in POTS subjects while supine. EEG modulation decreased in controls with head-up tilt but not in POTS subjects. Heart rate modulation in the respiratory frequency band decreased with head-up tilt and was significantly less (P<0.02) in ultraslow and respiratory frequency bands in POTS subjects after head-up tilt. Blood pressure and MCA flow velocity modulation in middle and respiratory bands increased with head-up tilt to a greater degree in POTS subjects. Blood pressure and MCA flow velocity modulation frequencies were moderately correlated, but correlations between EEG and cardiovascular variable modulation frequencies were generally low, being highest in the respiratory band but not statistically significant. CONCLUSION There are subtle differences in EEG amplitude modulation in subjects with POTS. Altered EEG amplitude modulation in POTS may reflect altered brainstem physiology in this disorder.

A general method for remontaging based on a singular value decomposition algorithm

Summary: The authors developed a general mathematic algorithm to convert any montage (referential, bipolar, or Laplacian) to any other by linear transformation. Input and output montages are described by matrices, and singular value decomposition is used to find the linear transformation. An error signal can be calculated from the input data to monitor remontaging validity. This algorithm also identifies output channels that cannot be obtained from the specified input. The authors tested this algorithm using an instrument that retrieves digitally encoded EEG data from videotape and produces signals in referential or bipolar form. They obtained good agreement when they compared referential and Laplacian data derived from bipolar output with the same montages calculated from referential output for the same EEG segment.