Practical Issues in Bispectral Analysis of Electroencephalographic Signals

Bispectral analysis is an advanced signal processing technique that quantifies quadratic nonlinearities (phase-coupling) among the components of a signal. There are only a few reports concerning the bispectrum of electroencephalogram (EEG). Barnett et al. (1) first reported the Bispectral analysis of EEG in 1971. Sigl and Chamoun (2) introduced the detailed principle and concept of bispectral analysis in 1994. Ning and Bronzino (3) reported the changes of bispectrum of the rat EEG during various vigilance states, and Muthuswamy et al. (4) reported the bispectral analysis of burst patterns in EEG. This analytic technique is also known as a core technology of the Bispectral Index System (BIS) monitor (Aspect Medical Systems, Natick, MA). Although bispectral analysis involves complicated mathematics, today’s computers are powerful enough for real-time Bispectral analysis of EEG data. Nevertheless, at the time of this writing, there were no reports accurately showing the relationship between the “depth of anesthesia” and bispectrum and bicoherence, normalized variable of bispectrum, of EEG. To investigate such relationship, we developed a software application that runs under Microsoft Windows 95/98® (Microsoft Corp. , Redmond, WA). While developing the software, we discovered several theoretical and practical problems with the bispectral analysis of EEG. The aim of this report was to confirm the methodology of bispectral analysis of EEG. Materials and Methods We custom built an application software named BSA (Bispectrum Analyzer), which analyzes EEG waveform and calculates its bispectrum. Developed with C++Builder Version 5® (Borland Japan Co. , Tokyo, Japan), BSA runs under Microsoft Windows 95/98. Details of the application are described in the following section. After securing institutional approval and informed consent from participants, we applied the software to analyze the EEG data of patients (n = 20) who underwent elective abdominal surgery under general anesthesia combined with epidural anesthesia. EEG (FP1-A1 lead) was monitored by using the 514X-2 EEG telemetry system (GE Marquette, Tokyo, Japan). FPz is used for body ground. The EEG high-cut filter was set at 60 Hz and the time-constant was set to 0. 3 s. The low-cut filter was not equipped with our EEG monitor. How Many Epochs Are Required? In computing the bispectrum, the EEG signal is first divided into a series of epochs. Because it is impossible to tell from a single epoch whether a signal is phase coupled, we have to examine multiple epochs to analyze phase coupling. Sigl and Chamoun (2) used 60-s EEG segments for bispectrum calculation. According to the A-10x0 Serial Port Technical Specification, provided by Aspect Inc. and the review by Rampil (5), the BIS monitor (A-1050) calculates bispectral data from 61. 5-s EEG segments (120 epochs). No evidence, however, has been reported to confirm whether 120 epochs are sufficient to produce reliable bispectral estimation. Consequently, we compared bicoherence values calculated from different numbers of epochs. Length of Epochs and Extent of Overlapping Sigl and Chamoun (2) used 4-s epochs, whereas the BIS monitor (A-1050) used 2-s epochs (5). Both methods use subsequent epochs that overlap the previous one by 75%. The power spectrum can be calculated from any length of epoch, but a longer epoch would be more likely to be affected by artifacts. According to Nikias and Raghuveer (6), an overlapping method is effective in increasing the total number of epochs in the restricted sampling records. Therefore, we adopted length and overlapping of epochs identical to those of BIS. The BSA Application Currently, for real-time processing, BSA supports the REX5054B analog-to-digital converter (PCMCIA card, 12 bit 4 channel; Ratoc Co. , Osaka, Japan) and collects EEG wave data via this converter. Normally, because bispectrum comprises two wave components, bispectrum values are usually plotted three-dimensionally. However, three-dimensional plotting is too complex and time-consuming for real-time processing with available computing resources. Therefore, we opted for two-dimensional plotting, which displays calculated values in color-spectral scale (topographical plotting in Figure 1. ) Figure 1: Typical patterns of bispectrum, bicoherence, and power spectrum during isoflurane anesthesia (isoflurane = 0. 9%) calculated from 360 epochs. Bispectrum values (in log scale) and bicoherence values are plotted topographically. The power spectrum is a plot of log values. BSA requires an EEG monitor, which gathers 0. 5–47. 5 Hz of EEG and is equipped with an analog output. BSA also has an offline mode to allow more detailed analysis of acquired data. Further development, BSA for BIS, allows the use of a BIS monitor (A-1050) as the EEG source. Algorithm for Data Processing EEG wave data were sampled at 512 Hz and digitized data were used for analysis. After artifact detection, wave data were down sampled at 128 Hz by averaging every four samples. This over-sampling technique can improve the accuracy of data sampling. After applying a Blackman window function, the Fourier transform of each epoch is computed. The power spectrum of each epoch is calculated by Cooley and Tukey’s fast Fourier transformation algorithm (7), and the 0. 5–47. 5 Hz (0. 5 Hz step) power spectrum components are used for bispectral analysis. Bispectrum values and bicoherence values are calculated according to the equations shown in the Appendix. Data Sampling and Statistics We compared the values of bicoherence calculated from 120, 240, 360, 480, 600, and 720 epochs. (End-tidal concentration of isoflurane was reached at 0. 7% 30 min before data sampling and was maintained for >1 h. ) We calculated bicoherence at two pairs of frequencies, BIC₈ (8. 0 Hz, 8. 0 Hz) and BIC₂0 (20. 0 Hz, 20. 0 Hz). Seven bicoherence values were calculated and averaged in each of the six groups. Each bicoherence value is calculated from randomly selected artifact-free periods. Initially, we checked the difference of variance values by F-test. Mean values were compared by using the Scheffé multiple comparison test;P values 1000 bispectrum values and is a logarized value, which makes the variance much smaller. Furthermore, the BIS monitor used other variables such as the relative β ratio from power spectral analysis and the burst suppression ratio from time domain analysis. During induction of, or recovery from, anesthesia, BIS readings rapidly change, but the relative β ratio, which is derived from power spectrum, is most heavily weighed on BIS values at the anesthetic level, as reported by Sleigh et al. (8). We used bicoherence instead of bispectrum in this report. Bispectrum values are influenced by the amplitude of signals as well as the degree of phase coupling, whereas bicoherence values directly indicate the degree of phase coupling. Thus, bicoherence is most important in bispectral analysis. It is still necessary to observe and evaluate how bicoherence changes with levels of anesthesia. Our rather small number of clinical trials has indicated it may be possible to assess the precise depth of anesthesia by monitoring bicoherence. However, additional studies are needed to evaluate its clinical relevance and applicability. We conclude that bicoherence calculated from 360 2-second epochs is appropriate for clinical monitoring as well as for research purposes. To encourage scientific investigation and analysis of EEG during anesthesia, we are distributing BSA and BSA for BIS software for scientific research. Upon request, we will provide any information concerning the application algorithms. Downloads are available via the Internet from: http: //www. med. osaka-u. ac. jp/pub/ anes/www/software/software. E. html.