0010.020030,0 0.010.020.030.0 Averaged power spectrum REM REM sleep EEG from CAl sleep EEG from dentate gyrus FI IGURE 115.4 A and B represent the averaged power spectra of 80 4-s epochs of REM sleep(sampling rate =128 Hz) obtained from hippocampal CAl and the dentate gyrus, respectively. Note that both spectra exhibit clear power peaks at Hz(theta)and 14-Hz( beta)frequencies. C and D represent the bispectrum of these same epochs from CAl and the dentate gyrus, respectively. Computation of the bicoherence index at 7 Hz shows significant quadratic phase coupling at this frequency, indicating that the 14-Hz peak is not spontaneously generated, but results from quadratic phase coupling In theory, both methods will lead to the same cross-bispectrum when data length is infinite. However, with finite data records, direct and indirect methods generally lead to cross-bispectrum estimates with different shapes(Fig. 115.4). Therefore, like power spectrum estimation, users have to choose an appropriate method to extract the information desired Topographic Mapping Computerized tomography(CT)and magnetic resonance imaging(MRI) have demonstrated the impact of spatial displays on data interpretation and analysis. Similarly, mapping techniques have been applied to elec trophysiologic data to depict the spatial information available from multielectrode recordings. This effort has been assisted by the development and implementation of low-cost, high-resolution graphic displays on micro computer systems. The data are frequently presented as two-dimensional topographic color maps [ Zappulla, 1]. In the time domain, color values depict the changes in potential across the scalp at each time point. This is exemplified by mapping peaks of an evoked potential or the spatial distribution of an epileptic spike. Temporal changes in the spatial distribution of voltage can be presented graphically as a series of maps constructed at adjacent time points or by cartooning the topographic maps over the time interval of interest. In the frequency domain, color coding can be used to spatially map power, covariance, and phase values. These maps may be constructed for the broadband activity or for selective frequency components Unlike CT and mRI displays where each picture element or pixel value represents real data, most of the pixels comprising an EEG and ER topographic map consist of interpolated values. This is because the activity c2000 by CRC Press LLC© 2000 by CRC Press LLC In theory, both methods will lead to the same cross-bispectrum when data length is infinite. However, with finite data records, direct and indirect methods generally lead to cross-bispectrum estimates with different shapes (Fig. 115.4). Therefore, like power spectrum estimation, users have to choose an appropriate method to extract the information desired. Topographic Mapping Computerized tomography (CT) and magnetic resonance imaging (MRI) have demonstrated the impact of spatial displays on data interpretation and analysis. Similarly, mapping techniques have been applied to elec￾trophysiologic data to depict the spatial information available from multielectrode recordings. This effort has been assisted by the development and implementation of low-cost, high-resolution graphic displays on micro￾computer systems. The data are frequently presented as two-dimensional topographic color maps [Zappulla, 1991]. In the time domain, color values depict the changes in potential across the scalp at each time point. This is exemplified by mapping peaks of an evoked potential or the spatial distribution of an epileptic spike. Temporal changes in the spatial distribution of voltage can be presented graphically as a series of maps constructed at adjacent time points or by cartooning the topographic maps over the time interval of interest. In the frequency domain, color coding can be used to spatially map power, covariance, and phase values. These maps may be constructed for the broadband activity or for selective frequency components. Unlike CT and MRI displays where each picture element or pixel value represents real data, most of the pixels comprising an EEG and ER topographic map consist of interpolated values. This is because the activity FIGURE 115.4 A and B represent the averaged power spectra of 80 4-s epochs of REM sleep (sampling rate = 128 Hz) obtained from hippocampal CA1 and the dentate gyrus, respectively. Note that both spectra exhibit clear power peaks at 7- Hz (theta) and 14-Hz (beta) frequencies. C and D represent the bispectrum of these same epochs from CA1 and the dentate gyrus, respectively. Computation of the bicoherence index at 7 Hz shows significant quadratic phase coupling at this frequency, indicating that the 14-Hz peak is not spontaneously generated, but results from quadratic phase coupling