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 electrophysiologic 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 microcomputer 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
the remaining values of the map located outside the electrode positions must be estimated from this saintly from a finite number of electrodes represents a sampling of the spatial activity over the scalp. Conse activity. One technique for deriving these values is linear interpolation In the case of a four-point interpolation the map is divided into boxes whose corners are defined by real data. The interpolated points within the boxes are calculated by the weighted sum of the four real data points, based on their distance from the interpolated point. Although linear interpolation is the most popular technique, polynomial regression and surface spline interpolation have been employed as alternative procedures. These methods reduce the discontinuities inherent linear interpolation and offer better estimates of extreme values. Polynomial regression has the addition advantage of permitting quantitative comparisons between maps by taking into account the topograpl information represented in the map. Maps can be presented in any of several projections to assist in interpretation[Zappulla, 1991]. The most common projection is the top view which presents the spatial distribution of variables from all leads simulta- leously. Lateral, posterior, and anterior projections highlight focal areas of interest. Although mapping presents a method by which spatial information can be efficiently communicated, it is important to be alert to the artifacts that ca from map construction and manipulation. Topographic spatial artifacts that can lead to misinterpretation include ring enhancement around a spike using source-derivation references, spatial aliasing arising from linear interpolation which causes maximal activity to be mapped at electrode sites, the enhancement of activity away from the midline, and the attenuation of midline activity on amplitude asymmetry maps centrifugal effect) The quality of the spatial information derivable from EEG recordings depends upon the number of recording electrodes, the choice of the reference electrode, and the conductive properties of intracranial and extracranial structures. The localization of cortical activity from scalp recordings assumes that the potentials recorded from the scalp reflect cortical activity generated in proximity to the recording electrode. Therefore, the greater the density of recording electrodes, the more accurate the estimate of the spatial distribution of scalp potentials and the localization of cortical generators. However, since the distance between the cortical source and recording electrode, as well as the low conductivity of the skull, results in a selective attenuation of small dipole fields, most available EEG information can be obtained with an average scalp-electrode spacing of 2 cm. Topographic maps are constructed from monopolar electrodes referenced to a common cephalic (linked ears or mandible, chin and nose)or noncephalic (linked clavicles or a balanced sternum-vertebra) electrode Although the reference electrode should be free of any EEG activity, in practice most cephalic electrodes contain some EEG activity, while noncephalic electrodes are a potential source of EKG or muscle activity. Differentia amplification of an EEG-contaminated reference electrode can decrease or cancel similar activity in neighboring electrodes, while at electrodes distant from the reference, the injected activity will be present as a potential of opposite polarity. Similarly, noncerebral potentials can be injected into scalp electrodes and misinterpreted as cerebral activity. Therefore, a nonneutral reference electrode can result in misleading map configurations Several techniques have been applied to circumvent this problem. The construction of multiple maps using several different references can sometimes assist in differentiating active and reference electrode activity. This can be accomplished by acquiring serial EEG records using different references. Alternatively, various references can be acquired simultaneously during acquisition, and various montages can be digitally reconstructed, post hoc A more computationally intensive method for localizing a source at an electrode involves calculating the cal source activity at any one electrode based on the average activity of its neighbors, weighted by their distance from the source. The technique has the advantage of suppressing potentials that originate outside the measure- ment area and weighing factors for implementing source deviation techniques for each of the electrodes in the 10-20 system are available Another reference technique, the average head reference, uses the average activity of all active electrodes the common reference. In this approach, the activity at any one electrode will vary depending upon the activity at the site of the reference electrode, which can be anywhere on the recording montage. Therefore, for Nnumber of recording electrodes, each being a potential reference, there are N-l possible voltage measurements at eacl instant of time for each electrode Maps constructed using the average head reference represent a unique solution to the problem of active reference electrodes in that the average reference produces an amplitude-weighted reference-free map of maximal and minimal field potentials. Power maps constructed from the average reference e 2000 by CRC Press LLC
© 2000 by CRC Press LLC from a finite number of electrodes represents a sampling of the spatial activity over the scalp. Consequently, the remaining values of the map located outside the electrode positions must be estimated from this sampled activity. One technique for deriving these values is linear interpolation. In the case of a four-point interpolation, the map is divided into boxes whose corners are defined by real data. The interpolated points within the boxes are calculated by the weighted sum of the four real data points, based on their distance from the interpolated point. Although linear interpolation is the most popular technique, polynomial regression and surface spline interpolation have been employed as alternative procedures. These methods reduce the discontinuities inherent in linear interpolation and offer better estimates of extreme values. Polynomial regression has the additional advantage of permitting quantitative comparisons between maps by taking into account the topographic information represented in the map. Maps can be presented in any of several projections to assist in interpretation [Zappulla, 1991]. The most common projection is the top view which presents the spatial distribution of variables from all leads simultaneously. Lateral, posterior, and anterior projections highlight focal areas of interest. Although mapping presents a method by which spatial information can be efficiently communicated, it is important to be alert to the artifacts that can arise from map construction and manipulation. Topographic spatial artifacts that can lead to misinterpretation include ring enhancement around a spike using source-derivation references, spatial aliasing arising from linear interpolation which causes maximal activity to be mapped at electrode sites, the enhancement of activity away from the midline, and the attenuation of midline activity on amplitude asymmetry maps (centrifugal effect). The quality of the spatial information derivable from EEG recordings depends upon the number of recording electrodes, the choice of the reference electrode, and the conductive properties of intracranial and extracranial structures. The localization of cortical activity from scalp recordings assumes that the potentials recorded from the scalp reflect cortical activity generated in proximity to the recording electrode. Therefore, the greater the density of recording electrodes, the more accurate the estimate of the spatial distribution of scalp potentials and the localization of cortical generators. However, since the distance between the cortical source and recording electrode, as well as the low conductivity of the skull, results in a selective attenuation of small dipole fields, most available EEG information can be obtained with an average scalp-electrode spacing of 2 cm. Topographic maps are constructed from monopolar electrodes referenced to a common cephalic (linked ears or mandible, chin and nose) or noncephalic (linked clavicles or a balanced sternum-vertebra) electrode. Although the reference electrode should be free of any EEG activity, in practice most cephalic electrodes contain some EEG activity, while noncephalic electrodes are a potential source of EKG or muscle activity. Differential amplification of an EEG-contaminated reference electrode can decrease or cancel similar activity in neighboring electrodes, while at electrodes distant from the reference, the injected activity will be present as a potential of opposite polarity. Similarly, noncerebral potentials can be injected into scalp electrodes and misinterpreted as cerebral activity. Therefore, a nonneutral reference electrode can result in misleading map configurations. Several techniques have been applied to circumvent this problem. The construction of multiple maps using several different references can sometimes assist in differentiating active and reference electrode activity. This can be accomplished by acquiring serial EEG records using different references. Alternatively, various references can be acquired simultaneously during acquisition, and various montages can be digitally reconstructed, post hoc. A more computationally intensive method for localizing a source at an electrode involves calculating the local source activity at any one electrode based on the average activity of its neighbors, weighted by their distance from the source. The technique has the advantage of suppressing potentials that originate outside the measurement area and weighing factors for implementing source deviation techniques for each of the electrodes in the 10–20 system are available. Another reference technique, the average head reference, uses the average activity of all active electrodes as the common reference. In this approach, the activity at any one electrode will vary depending upon the activity at the site of the reference electrode, which can be anywhere on the recording montage. Therefore, for N number of recording electrodes, each being a potential reference, there are N – 1 possible voltage measurements at each instant of time for each electrode. Maps constructed using the average head reference represent a unique solution to the problem of active reference electrodes in that the average reference produces an amplitude-weighted reference-free map of maximal and minimal field potentials. Power maps constructed from the average reference
best depict the spatial orientation of the generating field, and the areas with extreme values are closest to the generating processes [Zappulla, 1991 Topographical maps represent an efficient format for displaying the extensive amount of data generated by quantitative analysis. However, for reasons discussed above, the researcher and clinician must be cautious in deriving spatial and functional conclusions from mapped data. Although the replicability of map configurations across subjects or experimental conditions may represent a useful basis for experimental and diagnostic clas sification, judgments concerning the localization of cortical generators or functional localization of cerebral activity are less certain and more controversial. Research continues on defining models and validating assump- ons that relate scalp potentials to cortical generators in an attempt to arrive at accurate mathematical solutions that can be applied to mapping functions Defining Terms Bispectra: Computation of the frequency distribution of the EEg exhibiting nonlinear behavior. Cross spectra: Computation of the energy in the frequency distribution of two different electrical signal Electroencephalogram(EEG): Recordings of the electrical potentials produced by the brain. Fast Fourier transform(FFT): Algorithms that permit rapid computation of the Fourier transform of an electrical signal, thereby representing it in the frequency domain. Magnitude squared coherence(MSC): A measure of the degree of synchrony between two electrical signals at specific frequencies. Power spectral analysis: Computation of the energy in the frequency distribution of an electrical signal. Quadratic phase coupling: A measure of the degree to which specific frequencies interact to produce a third Related Topic 108.1 Introduction erences M. Brazier, Electrical Activity of the Nervous System, 3rd ed. Baltimore: Williams and Wilkins, 1968 J.D. Bronzino, M. Kelly, C Cordova,Utilization of amplitude histograms to quantify the EEG: Effects of systemic administration of morphine in the chronically implanted rat,"IEEE Trans. Biomed. Eng, 28(10), 673, 1981 J D. Bronzino, "Quantitative analysis of the EEG: General concepts and animal studies, IEEE Trans. Biomed. Eng,31(12),850, J.W. Cooley and J.S. Tukey, An algorithm for the machine calculatio of complex Fourier series, Math Comput 19,267,1965 A S. Givens and A. Remond, Eds,"Methods of analysis of brain electrical and magnetic signals, in EEG Handbook, vol 1, Amsterdam: Elsevier, 1987. S.M. Kay and S L Maple,Spectrum analysis-A modern perspective, " Proc. IEEE. 69, 1380, 1981 G.V. Kondraski, " Neurophysiological measurements, in Biomedical Engineering and Instrumentation, J D Bronzino, Ed, Boston: PWS Publishing, pp. 138-179, 1986. C L. Nikias and M.R. Raghuveer,Bispectrum estimation: A digital signal processing framework," Proc. IEEE, 75,869,198 T. Ning and J.D. Bronzino, "Bispectral analysis of the rat EEG during different vigilance states, "IEEE Trans Biomed.Eng,36(4),497,1989 T Ning and J.D. Bronzino,Bispectral analysis of the EEG in developing rats, in Proc. Workshop Higher-Order Spectral Anal, Vail, Colo: 1989b, pp. 235-238 T. Ning and J.D. Bronzino, Autoregressive and bispectral analysis techniques: EEG applications, "Special Issue on Biomedical Signal Processing, IEEE Eng. Med. Biol. Mag, 9, 47, 1990. J.R. Smith, Automated analysis of sleep EEg data, "in Clinical Applications of Computer Analysis of EEG and Other Neurophysiological Signals, EEG Handbook, revised series, vol 2, Amsterdam: Elsevier, 1986, Pp 93-130 c2000 by CRC Press LLC
© 2000 by CRC Press LLC best depict the spatial orientation of the generating field, and the areas with extreme values are closest to the generating processes [Zappulla, 1991]. Topographical maps represent an efficient format for displaying the extensive amount of data generated by quantitative analysis. However, for reasons discussed above, the researcher and clinician must be cautious in deriving spatial and functional conclusions from mapped data. Although the replicability of map configurations across subjects or experimental conditions may represent a useful basis for experimental and diagnostic classification, judgments concerning the localization of cortical generators or functional localization of cerebral activity are less certain and more controversial. Research continues on defining models and validating assumptions that relate scalp potentials to cortical generators in an attempt to arrive at accurate mathematical solutions that can be applied to mapping functions. Defining Terms Bispectra: Computation of the frequency distribution of the EEG exhibiting nonlinear behavior. Cross spectra: Computation of the energy in the frequency distribution of two different electrical signals. Electroencephalogram (EEG): Recordings of the electrical potentials produced by the brain. Fast Fourier transform (FFT): Algorithms that permit rapid computation of the Fourier transform of an electrical signal, thereby representing it in the frequency domain. Magnitude squared coherence (MSC): A measure of the degree of synchrony between two electrical signals at specific frequencies. Power spectral analysis: Computation of the energy in the frequency distribution of an electrical signal. Quadratic phase coupling: A measure of the degree to which specific frequencies interact to produce a third frequency. Related Topic 108.1 Introduction References M. Brazier, Electrical Activity of the Nervous System, 3rd ed., Baltimore: Williams and Wilkins, 1968. J.D. Bronzino, M. Kelly, C. Cordova, “Utilization of amplitude histograms to quantify the EEG: Effects of systemic administration of morphine in the chronically implanted rat,” IEEE Trans. Biomed. Eng., 28(10), 673, 1981. J.D. Bronzino, “Quantitative analysis of the EEG: General concepts and animal studies,” IEEE Trans. Biomed. Eng., 31(12), 850, 1984. J.W. Cooley and J.S. Tukey, “An algorithm for the machine calculatio of complex Fourier series,” Math Comput., 19, 267, 1965. A.S. Givens and A. Remond, Eds., “Methods of analysis of brain electrical and magnetic signals,” in EEG Handbook, vol. 1, Amsterdam: Elsevier, 1987. S.M. Kay and S.L. Maple, “Spectrum analysis—A modern perspective,” Proc. IEEE. 69, 1380, 1981. G.V. Kondraski, “Neurophysiological measurements,” in Biomedical Engineering and Instrumentation, J.D. Bronzino, Ed., Boston: PWS Publishing, pp. 138–179, 1986. C.L. Nikias and M.R. Raghuveer, “Bispectrum estimation: A digital signal processing framework,” Proc. IEEE, 75, 869, 1987. T. Ning and J.D. Bronzino, “Bispectral analysis of the rat EEG during different vigilance states,” IEEE Trans. Biomed. Eng., 36(4), 497, 1989a. T. Ning and J.D. Bronzino, “Bispectral analysis of the EEG in developing rats,” in Proc. Workshop Higher-Order Spectral Anal., Vail, Colo.: 1989b, pp. 235–238. T. Ning and J.D. Bronzino, “Autoregressive and bispectral analysis techniques: EEG applications,” Special Issue on Biomedical Signal Processing, IEEE Eng. Med. Biol. Mag., 9, 47, 1990. J.R. Smith, “Automated analysis of sleep EEG data,” in Clinical Applications of Computer Analysis of EEG and Other Neurophysiological Signals, EEG Handbook, revised series, vol. 2, Amsterdam: Elsevier, 1986, pp. 93–130