Autoregressive and bispectral analysis techniques: EEG applications

Brain-region specific autism prediction from electroencephalogram signals using graph convolution neural network

BACKGROUND

Brain variations are responsible for developmental impairments, including autism spectrum disorder (ASD). EEG signals efficiently detect neurological conditions by revealing crucial information about brain function abnormalities.

OBJECTIVE

This study aims to utilize EEG data collected from both autistic and typically developing children to investigate the potential of a Graph Convolutional Neural Network (GCNN) in predicting ASD based on neurological abnormalities revealed through EEG signals.

METHODS

In this study, EEG data were gathered from eight autistic children and eight typically developing children diagnosed using the Childhood Autism Rating Scale at the Central Institute of Psychiatry, Ranchi. EEG recording was done using a HydroCel GSN with 257 channels, and 71 channels with 10-10 international equivalents were utilized. Electrodes were divided into 12 brain regions. A GCNN was introduced for ASD prediction, preceded by autoregressive and spectral feature extraction.

RESULTS

The anterior-frontal brain region, crucial for cognitive functions like emotion, memory, and social interaction, proved most predictive of ASD, achieving 87.07% accuracy. This underscores the suitability of the GCNN method for EEG-based ASD detection.

CONCLUSION

The detailed dataset collected enhances understanding of the neurological basis of ASD, benefiting healthcare practitioners involved in ASD diagnosis.

Detection of quadratic phase coupling by cross-bicoherence and spectral Granger causality in bifrequencies interactions

Quadratic Phase Coupling (QPC) serves as an essential statistical instrument for evaluating nonlinear synchronization within multivariate time series data, especially in signal processing and neuroscience fields. This study explores the precision of QPC detection using numerical estimates derived from cross-bicoherence and bivariate Granger causality within a straightforward, yet noisy, instantaneous multiplier model. It further assesses the impact of accidental statistically significant bifrequency interactions, introducing new metrics such as the ratio of bispectral quadratic phase coupling and the ratio of bivariate Granger causality quadratic phase coupling. Ratios nearing 1 signify a high degree of accuracy in detecting QPC. The coupling strength between interacting channels is identified as a key element that introduces nonlinearities, influencing the signal-to-noise ratio in the output channel. The model is tested across 59 experimental conditions of simulated recordings, with each condition evaluated against six coupling strength values, covering a wide range of carrier frequencies to examine a broad spectrum of scenarios. The findings demonstrate that the bispectral method outperforms bivariate Granger causality, particularly in identifying specific QPC under conditions of very weak couplings and in the presence of noise. The detection of specific QPC is crucial for neuroscience applications aimed at better understanding the temporal and spatial coordination between different brain regions.

Extraction and assessment of diagnosis-relevant features for heart murmur classification

This paper presents a heart murmur detection and multi-class classification approach via machine learning. We extracted heart sound and murmur features that are of diagnostic importance and developed additional 16 features that are not perceivable by human ears but are valuable to improve murmur classification accuracy. We examined and compared the classification performance of supervised machine learning with k-nearest neighbor (KNN) and support vector machine (SVM) algorithms. We put together a test repertoire having more than 450 heart sound and murmur episodes to evaluate the performance of murmur classification using cross-validation of 80-20 and 90-10 splits. As clearly demonstrated in our evaluation, the specific set of features chosen in our study resulted in accurate classification consistently exceeding 90% for both classifiers.

Bispectral analysis of overnight airflow to improve the pediatric sleep apnea diagnosis

Pediatric Obstructive Sleep Apnea (OSA) is a respiratory disease whose diagnosis is performed through overnight polysomnography (PSG). Since it is a complex, time-consuming, expensive, and labor-intensive test, simpler alternatives are being intensively sought. In this study, bispectral analysis of overnight airflow (AF) signal is proposed as a potential approach to replace PSG when indicated. Thus, our objective was to characterize AF through bispectrum, and assess its performance to diagnose pediatric OSA. This characterization was conducted using 13 bispectral features from 946 AF signals. The oxygen desaturation index ≥3% (ODI3), a common clinical measure of OSA severity, was also obtained to evaluate its complementarity to the AF bispectral analysis. The fast correlation-based filter (FCBF) and a multi-layer perceptron (MLP) were used for subsequent automatic feature selection and pattern recognition stages. FCBF selected 3 bispectral features and ODI3, which were used to train a MLP model with ability to estimate apnea-hypopnea index (AHI). The model reached 82.16%, 82.49%, and 90.15% accuracies for the common AHI cut-offs 1, 5, and 10 events/h, respectively. The different bispectral approaches used to characterize AF in children provided complementary information. Accordingly, bispectral analysis showed that the occurrence of apneic events decreases the non-gaussianity and non-linear interaction of the AF harmonic components, as well as the regularity of the respiratory patterns. Moreover, the bispectral information from AF also showed complementarity with ODI3. Our findings suggest that AF bispectral analysis may serve as a useful tool to simplify the diagnosis of pediatric OSA, particularly for children with moderate-to-severe OSA.

Fault Detection of Wind Turbine Induction Generators through Current Signals and Various Signal Processing Techniques

In the wind industry (WI), a robust and effective maintenance system is essential. To minimize the maintenance cost, a large number of methodologies and mathematical models for predictive maintenance have been developed. Fault detection and diagnosis are carried out by processing and analyzing various types of signals, with the vibration signal predominating. In addition, most of the published proposals for wind turbine (WT) fault detection and diagnosis have used simulations and test benches. Based on previous work, this research report focuses on fault diagnosis, in this case using the electrical signal from an operating WT electric generator and applying various signal analysis and processing techniques to compare the effectiveness of each. The WT used for this research is 20 years old and works with a squirrel-cage induction generator (SCIG) which, according to the wind farm control systems, was fault-free. As a result, it has been possible to verify the feasibility of using the current signal to detect and diagnose faults through spectral analysis (SA) using a fast Fourier transform (FFT), periodogram, spectrogram, and scalogram.

Higher-order spectral analysis of spontaneous speech signals in Alzheimer's disease

An early and accurate diagnosis of Alzheimer's disease (AD) has been progressively attracting more attention in recent years. One of the main problems of AD is the loss of language skills. This paper presents a computational framework for classifying AD patients compared to healthy control subjects using information from spontaneous speech signals. Spontaneous speech data are obtained from 30 AD patients and 30 healthy controls. Because of the nonlinear and dynamic nature of speech signals, higher order spectral features (specifically bispectrum) were used for analysis. Four classifiers (k-Nearest Neighbor, Support Vector Machine, Naïve Bayes and Decision tree) were used to classify subjects into three different levels of AD and healthy group based on their performance in terms of the HOS-based features. Ten-fold cross-validation method was used to test the reliability of the classifier results. The results showed that the proposed method had a good potential in AD diagnosis. The proposed method was also able to diagnose the earliest stage of AD with high accuracy. The method has the great advantage of being non-invasive, cost-effective, and associated with no side effects. Therefore, the proposed method can be a spontaneous speech directed test for pre-clinical evaluation of AD diagnosis.

Sleep apnea: a review of diagnostic sensors, algorithms, and therapies

While public awareness of sleep related disorders is growing, sleep apnea syndrome (SAS) remains a public health and economic challenge. Over the last two decades, extensive controlled epidemiologic research has clarified the incidence, risk factors including the obesity epidemic, and global prevalence of obstructive sleep apnea (OSA), as well as establishing a growing body of literature linking OSA with cardiovascular morbidity, mortality, metabolic dysregulation, and neurocognitive impairment. The US Institute of Medicine Committee on Sleep Medicine estimates that 50-70 million US adults have sleep or wakefulness disorders. Furthermore, the American Academy of Sleep Medicine (AASM) estimates that more than 29 million US adults suffer from moderate to severe OSA, with an estimated 80% of those individuals living unaware and undiagnosed, contributing to more than $149.6 billion in healthcare and other costs in 2015. Although various devices have been used to measure physiological signals, detect apneic events, and help treat sleep apnea, significant opportunities remain to improve the quality, efficiency, and affordability of sleep apnea care. As our understanding of respiratory and neurophysiological signals and sleep apnea physiological mechanisms continues to grow, and our ability to detect and process biomedical signals improves, novel diagnostic and treatment modalities emerge.

OBJECTIVE

This article reviews the current engineering approaches for the detection and treatment of sleep apnea.

APPROACH

It discusses signal acquisition and processing, highlights the current nonsurgical and nonpharmacological treatments, and discusses potential new therapeutic approaches.

MAIN RESULTS

This work has led to an array of validated signal and sensor modalities for acquiring, storing and viewing sleep data; a broad class of computational and signal processing approaches to detect and classify SAS disease patterns; and a set of distinctive therapeutic technologies whose use cases span the continuum of disease severity.

SIGNIFICANCE

This review provides a current perspective of the classes of tools at hand, along with a sense of their relative strengths and areas for further improvement.

Respiration estimation and apnea detection using fuzzy logic

This paper presents a fuzzy logic-based respiration monitoring algorithm that is capable of providing accurate respiration rate and detecting apnea episodes. The proposed algorithm employs several signal processing techniques to extract useful features that signify different respiratory behaviors. We implement a fuzzy logic-based system that examines the extracted respiratory signal features and categorizes the respiratory signals into respiration, body motion, and apnea. The performance of the underlying algorithm is validated using both the MIT physiology database and in-house respiration measurements.

Mixture of autoregressive modeling orders and its implication on single trial EEG classification

Autoregressive (AR) models are of commonly utilized feature types in Electroencephalogram (EEG) studies due to offering better resolution, smoother spectra and being applicable to short segments of data. Identifying correct AR's modeling order is an open challenge. Lower model orders poorly represent the signal while higher orders increase noise. Conventional methods for estimating modeling order includes Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Final Prediction Error (FPE). This article assesses the hypothesis that appropriate mixture of multiple AR orders is likely to better represent the true signal compared to any single order. Better spectral representation of underlying EEG patterns can increase utility of AR features in Brain Computer Interface (BCI) systems by increasing timely & correctly responsiveness of such systems to operator's thoughts. Two mechanisms of Evolutionary-based fusion and Ensemble-based mixture are utilized for identifying such appropriate mixture of modeling orders. The classification performance of the resultant AR-mixtures are assessed against several conventional methods utilized by the community including 1) A well-known set of commonly used orders suggested by the literature, 2) conventional order estimation approaches (e.g., AIC, BIC and FPE), 3) blind mixture of AR features originated from a range of well-known orders. Five datasets from BCI competition III that contain 2, 3 and 4 motor imagery tasks are considered for the assessment. The results indicate superiority of Ensemble-based modeling order mixture and evolutionary-based order fusion methods within all datasets.

A novel method for early diagnosis of Alzheimer's disease based on higher-order spectral estimation of spontaneous speech signals

One main challenge for medical investigators is the early diagnosis of Alzheimer's disease (AD) because it provides greater opportunities for patients to be eligible for more clinical trials. In this study, higher order spectra of human speech signals during AD were explored to analyze and compare the quadratic phase coupling of spontaneous speech signals for healthy and AD subjects using bispectrum and bicoherence. The results showed that the quadratic phase couplings of spontaneous speech signal of persons with Alzheimer's were reduced compared to healthy subject. However, the speech phase coupled harmonics shifted to the higher frequencies in Alzheimer's than healthy subjects. In addition, it was shown not only are there significant differences between Alzheimer's and control subjects in parameters estimated, but also the speech patterns appeared to have fluctuated in both types of spontaneous speech.

Visual Analytics for Development and Evaluation of Order Selection Criteria for Autoregressive Processes

Order selection of autoregressive processes is an active research topic in time series analysis, and the development and evaluation of automatic order selection criteria remains a challenging task for domain experts. We propose a visual analytics approach, to guide the analysis and development of such criteria. A flexible synthetic model generator-combined with specialized responsive visualizations-allows comprehensive interactive evaluation. Our fast framework allows feedback-driven development and fine-tuning of new order selection criteria in real-time. We demonstrate the applicability of our approach in three use-cases for two general as well as a real-world example.

Comparison of higher order spectra in heart rate signals during two techniques of meditation: Chi and Kundalini meditation

The human heartbeat is one of the important examples of complex physiologic fluctuations. For the first time in this study higher order spectra of heart rate signals during meditation have explored. Specifically, the aim of this study was to analysis and compares the contribution of quadratic phase coupling of human heart rate variability during two forms of meditation: (1) Chinese Chi (or Qigong) meditation and (2) Kundalini Yoga meditation. For this purpose, Bispectrum was estimated by using biased, parametric and the direct (FFT) method. The results show that the mean Bispectrum magnitude of heart rate signals increased during Kundalini Yoga meditation, but it decreased significantly during Chi meditation. However, in both meditation techniques phase-coupled harmonics are shifted to the higher frequencies during meditation. In addition, it has shown that not only there are significant differences between rest and meditation states, but also heart rate patterns appear to be influenced by different types of meditation.

Local properties of vigilance states: EMD analysis of EEG signals during sleep-waking states of freely moving rats

Understanding the inherent dynamics of the EEG associated to sleep-waking can provide insights into its basic neural regulation. By characterizing the local properties of the EEG using power spectrum, empirical mode decomposition (EMD) and Hilbert-spectral analysis, we can examine the dynamics over a range of time-scales. We analyzed rat EEG during wake, NREMS and REMS using these methods. The average instantaneous phase, power spectral density (PSD) of intrinsic mode functions (IMFs) and the energy content in various frequency bands show characteristic changes in each of the vigilance states. The 2nd and 7th IMFs show changes in PSD for wake and REMS, suggesting that those modes may carry wake- and REMS-associated cognitive, conscious and behavior-specific information of an individual even though the EEG may appear similar. The energy content in θ₂ (6Hz-9Hz) band of the 1st IMF for REMS is larger than that of wake. The decrease in the phase function of IMFs from wake to REMS to NREMS indicates decrease of the mean frequency in these states, respectively. The rate of information processing in waking state is more in the time scale described by the first three IMFs than in REMS state. However, for IMF5-IMF7, the rate is more for REMS than that for wake. We obtained Hilbert-Huang spectral entropy, which is a suitable measure of information processing in each of these state-specific EEG. It is possible to evaluate the complex dynamics of the EEG in each of the vigilance states by applying measures based on EMD and Hilbert-transform. Our results suggest that the EMD based nonlinear measures of the EEG can provide useful estimates of the information possessed by various oscillations associated with the vigilance states. Further, the EMD-based spectral measures may have implications in understanding anatamo-physiological correlates of sleep-waking behavior and clinical diagnosis of sleep-pathology.

Automatic heart sounds detection and systolic murmur characterization using wavelet transform and AR modeling

This paper describes a signal processing procedure that identifies the first and the second heart sounds (S1 and S2), extracts the systole from the diastole, detects and characterizes the systolic murmur found within. The identification of heart sounds was facilitated by discrete wavelet transform (DWT) approximation using the Coiflet wavelet and followed by using indicators that quantify signal activity and strength. The systole was isolated and divided into smaller short segments where the signal activity measure and absolute amplitude were computed. S1 and S2, and the onset and duration of a systolic murmur were marked. Using the indices derived from AR modeling, a systolic murmur can be characterized by its timing, duration, pitch, and shape either as crescendo, decrescendo, crescendo-decrescendo, or plateau. The performance of the proposed procedure was evaluated and proved with clinically recorded systolic murmur episodes.

A novel method for EOG features extraction from the forehead

We have shown that the slow eye movements extracted from electrooculogram (EOG) signals can be used to estimate human vigilance in our previous work. However, the traditional method for recording EOG signals is to place the electrodes near the eyes of subjects. This placement is inconvenient for users in real-world applications. This paper aims to find a more practical placement for acquiring EOG signals for vigilance estimation. Instead of placing the electrodes near the eyes, we place them on the forehead. We extract EOG features from the forehead EOG signals using both independent component analysis and support vector machines. The performance of our proposed method is evaluated using the correlation coefficients between the forehead EOG signals and the traditional EOG signals. The results show that a correlation of 0.84 can be obtained when the users make 14 different face movements and for merely eye movements it reaches 0.93.

Vigilance detection based on sparse representation of EEG

Electroencephalogram (EEG) based vigilance detection of those people who engage in long time attention demanding tasks such as monotonous monitoring or driving is a key field in the research of brain-computer interface (BCI). However, robust detection of human vigilance from EEG is very difficult due to the low SNR nature of EEG signals. Recently, compressive sensing and sparse representation become successful tools in the fields of signal reconstruction and machine learning. In this paper, we propose to use the sparse representation of EEG to the vigilance detection problem. We first use continuous wavelet transform to extract the rhythm features of EEG data, and then employ the sparse representation method to the wavelet transform coefficients. We collect five subjects' EEG recordings in a simulation driving environment and apply the proposed method to detect the vigilance of the subjects. The experimental results show that the algorithm framework proposed in this paper can successfully estimate driver's vigilance with the average accuracy about 94.22 %. We also compare our algorithm framework with other vigilance estimation methods using different feature extraction and classifier selection approaches, the result shows that the proposed method has obvious advantages in the classification accuracy.

Automatic artifact removal from EEG - a mixed approach based on double blind source separation and support vector machine

Electroencephalography (EEG) recordings are often obscured by physiological artifacts that can render huge amounts of data useless and thus constitute a key challenge in current brain-computer interface research. This paper presents a new algorithm that automatically and reliably removes artifacts from EEG based on blind source separation and support vector machine. Performance on a motor imagery task is compared for artifact-contaminated and preprocessed signals to verify the accuracy of the proposed approach. The results showed improved results over all datasets. Furthermore, the online applicability of the algorithm is investigated.

A comparison of linear and chaotic measures for rat hippocampal EEG during different vigilance states

The correlation dimension was used in this paper as a quantifier to describe the chaotic behavior of sleep EEG recorded from the hippocampus of adult rats during vigilance states of quiet-waking, slow-wave sleep, and REM sleep. A modified Grassberger-Procaccia method was implemented to compute the correlation integral using a Euclidean distance normalized by the embedding dimension. The performance of the correlation dimension as a measure to characterize the sleep EEG was compared to the quantitative measures derived from linear autoregressive models. Even though linear and chaotic measures are based on completely different theories and concepts, our experimental results have indicated them both effective in capturing the characteristic differences of sleep EEG during various states. The preliminary results have also shown the correlation dimension being particularly effective in emphasizing the differences in regard to the chaotic behavior between the EEG activity in SWS and QW and REM sleep.

Quantitative analysis of heart sounds and systolic heart murmurs using wavelet transform and AR modeling

A quantitative approach integrating AR modeling and wavelet transform is presented in this paper to analyze the digitized phonocardiogram. The recognition of the first and the second heart sounds (S(1) and S(2)) were facilitated with wavelet transform without referring to the QRS waveform. We found that the Daubechies wavelet is most effective in identifying S(1) and S(2). In addition, the boundaries of S(1), S(2), and the onset and duration of the systolic murmur thus identified within the systole could be marked using the wavelet-filtered signal's strength. Furthermore, quantitative measures derived from a 2(nd) order AR model were used to delineate the configuration and pitch of the systolic murmur found within through piecewise segmentation. The proposed approach was tested and proved effective in delineating a set of clinically diagnosed systolic murmurs. The suggested AR and wavelet transform combined approach can be generalized with minor adjustments to delineate diastolic murmurs as well.

Quadriceps muscles vastus medialis obliques, rectus femoris and vastus lateralis compared via electromyogram bicoherence analysis

Bicoherence analysis is applied to electromyogram (EMG) data for vastus medialis obliques (VM), rectus femoris (RF) and vastus lateralis (VL) quadriceps muscles of 18 adult male subjects for isometric knee extension exercise. Mean average bicoherence for VM, RF and VL is 30.9 +/- 5.8, 26.0 +/- 1.2 and 25.4 +/- 1.4% respectively and repeated measures ANOVA differentiates the muscles on the basis of average bicoherence (F = 16.2 (1, 17), p = 0.0009, VM cf. VL and F = 15.4 (1, 17), p = 0.0011, VM cf. RF). Prominent regions representative of strong second-order phase coupling between constituent EMG frequencies are identified within VM and RF bicoherence spectra. No such prominent regions are identified for VL which is thought to be less activated than VM during the specified task. Hence, the degree of second-order phase coupling may increase as the level of muscle activation increases. The subject group consists of young (24.0 +/- 0.9 years) and elderly (68.9 +/- 0.9 years) subgroups that cannot be differentiated by standard indices (median and spectral edge frequency) to within p < 0.05 using the Mann-Whitney test. Average bicoherence differentiates the subgroups for RF (T = 9 (8,10), p < 0.005) but not for VM or VL. The application of a bicoherence threshold that takes harmonic amplitude into account graphically differentiates the subgroups for all muscle types. The findings suggest that nonlinear processes play a role within the EMG generation process and support a mechanomyogram bicoherence analysis study that shows nonlinear processes occur within active muscle fibre twitch summation patterns. A potential exists for bicoherence analysis to complement standard EMG frequency analysis techniques.

Bicoherence analysis of quadriceps electromyogram during isometric knee extension

Bicoherence analysis is applied to electromyogram (EMG) data for the vastus lateralis quadriceps muscle of 18 adult male subjects for isometric knee extension exercise. Bicoherence spectra display ridge-like features that are indicative of deterministic chaotic behaviour and similar to those reported for normal electrocardiogram and electroencephalogram bicoherence spectra. No other obvious features are visually identified within bicoherence spectra in response to the stimulus of isometric tension. Histograms that show the occurrence of constituent EMG frequencies associated with the strongest bicoherence display subtle fluctuations. Validation tests that include the analysis of white noise data show these fluctuations to most likely be a consequence of the normal time evolution of a deterministic chaotic process. The finding suggests that second-order phase coupling is not pronounced between any particular bands of constituent EMG frequencies for the vastus lateralis EMG generation process during the specified isometric task. Previous studies into bicoherence analysis of EMG data are not apparent in the literature for comparison. Since nonlinear processes are known, through mechanomyogram bicoherence analysis, to be significant within active muscle fibre twitch summation patterns, the finding does not exclude the potential for bicoherence analysis to complement standard EMG frequency analysis techniques in the area of sports rehabilitation and medicine. Further investigation is required to establish whether this potential exists. An introduction to bicoherence analysis theory is also presented.

Chaos in the brain: a short review alluding to epilepsy, depression, exercise and lateralization

Electroencephalograms (EEGs) reflect the electrical activity of the brain. Even when they are analyzed from healthy individuals, they manifest chaos in the nervous system. EEGs are likely to be produced by a nonlinear system, since a nonlinear system with at least 3 degrees of freedom (or state variables) may exhibit chaotic behavior. Furthermore, such systems can have multiple stable states governed by "chaotic" ("strange") attractors. A key feature of chaotic systems is the presence of an infinite number of unstable periodic fixed points, which are found in spontaneously active neuronal networks (e.g., epilepsy). The brain has chemicals called neurotransmitters that convey the information through the 10(16) synapses residing there. However, each of these neurotransmitters acts through various receptors and their numerous subtypes, thereby exhibiting complex interactions. Albeit in epilepsy the role of chaos and EEG findings are well proven, in another condition, i.e., depression, the role of chaos is slowly gaining ground. The multifarious roles of exercise, neurotransmitters and (cerebral) hemispheric lateralization, in the case of depression, are also being established. The common point of reference could be nonlinear dynamics. The purpose of this review is to study those nonlinear/chaotic interactions and point towards new theoretical models incorporating the oscillation caused by the same neurotransmitter acting on its different receptor subtypes. This may lead to a better understanding of brain neurodynamics in health and disease.

A study of electroencephalographic descriptors and end-tidal concentration in estimating depth of anesthesia

OBJECTIVE

To study the usefulness of three electro-encephalographic descriptors, the average median frequency, the average 90% spectral edge frequency, and a bispectral variable were used with the anesthetic concentrations in estimating the depth of anesthesia.

METHODS

Four channels of raw EEG data were collected from seven mongrel dogs in nine separate experiments under different levels of halothane anesthesia and nitrous oxide in oxygen. A tail clamp was used as the stimulus and the dog was labeled as a non-responder or responder based on its response. A bispectral variable of the EEG (just before a tail clamp) and the estimated MAC level of halothane and nitrous oxide combined were the two features used to characterize a single data point. A neural network analysis was done on 48 such data points. A second neural network analysis was done on 47 data points using average 90% spectral edge frequency and the estimated MAC level. The average median frequency of EEG was also evaluated, although a neural network analysis was not done.

RESULTS

The first neural network needed nine weights in order to train and correctly classify all of the 12 points in the training set under a training tolerance of 0.2. It could correctly classify all of the remaining 36 data points as either belonging to responders or non-responders. A cross-validation procedure, which estimated the overall performance of the network against future data points, showed that the network misclassified two out of the 48 data points. The second neural network needed 25 weights in order to train and classify correctly all of the 26 points in the training set under a tolerance of 0.2. It was later able to classify all of the 21 points of the test group correctly.

CONCLUSIONS

The bispectral variable seems to reduce the non-linearity in the boundary separating the class of non-responders from the class of responders. Consequently, the neural network based on the bispectral variable is less complex than the neural network that uses a power spectral variable as one of its inputs.

An introduction to bispectral analysis for the electroencephalogram

The goal of much effort in recent years has been to provide a simplified interpretation of the electroencephalogram (EEG) for a variety of applications, including the diagnosis of neurological disorders and the intraoperative monitoring of anesthetic efficacy and cerebral ischemia. Although processed EEG variables have enjoyed limited success for specific applications, few acceptable standards have emerged. In part, this may be attributed to the fact that commonly used signal processing tools do not quantify all of the information available in the EEG. Power spectral analysis, for example, quantifies only power distribution as a function of frequency, ignoring phase information. It also makes the assumption that the signal arises from a linear process, thereby ignoring potential interaction between components of the signal that are manifested as phase coupling, a common phenomenon in signals generated from nonlinear sources such as the central nervous system (CNS). This tutorial describes bispectral analysis, a method of signal processing that quantifies the degree of phase coupling between the components of a signal such as the EEG. The basic theory underlying bispectral analysis is explained in detail, and information obtained from bispectral analysis is compared with that available from the power spectrum. The concept of a bispectral index is introduced. Finally, several model signals, as well as a representative clinical case, are analyzed using bispectral analysis, and the results are interpreted.

Nonlinear analysis of the hippocampal subfields of CA1 and the dentate gyrus

The paper discusses the use of nonlinear bispectral analysis in examining the hippocampal EEG collected at subfields of CA1 and the dentate gyrus during the vigilance state of REM sleep. The cross-bispectrum and its unique capabilities of detecting and quantifying quadratic nonlinear interactions occurring between these two hippocampal subfields are explained and demonstrated with simulation examples and EEG data. It was found in this study that quadratic nonlinear interactions exist between CA1 and the dentate gyrus in the 6-8 frequency band which dominates the theta (theta) rhythm observed in the hippocampal EEG during REM sleep. As a result, energy components around the frequency band of the second-order harmonics of theta rhythm are not totally spontaneous, but generated largely due to quadratic nonlinear interactions.