Wavelet bispectral analysis for the study of interactions among oscillators whose basic frequencies are significantly time variable

Methamphetamine alters the circadian oscillator and its couplings on multiple scales in Per1/2/3 knockout mice

Disruptions to circadian rhythms in mammals are associated with alterations in their physiological and mental states. Circadian rhythms are currently analyzed in the time domain using approaches such as actograms, thus failing to appreciate their time-localized characteristics, time-varying nature and multiscale dynamics. In this study, we apply time-resolved analysis to investigate behavioral rhythms in Per1/2/3 knockout (KO) mice and their changes following methamphetamine administration, focusing on circadian (around 24 h), low-frequency ultradian (around 7 h), high-frequency ultradian (around 30 min), and circabidian (around 48 h) oscillations. In the absence of methamphetamine, Per1/2/3 KO mice in constant darkness exhibited a dominant, ∼7 h oscillation. We demonstrate that methamphetamine exposure restores the circadian rhythm, although the frequency of the methamphetamine sensitive circadian oscillator varied considerably compared to the highly regular wild-type circadian rhythm. Additionally, methamphetamine increased multiscale activity and induced a circabidian oscillation in the Per1/2/3 KO mice. The information transfer between oscillatory modes, with frequencies around circadian, low-frequency ultradian and high-frequency ultradian activity, due to their mutual couplings, was also investigated. For Per1/2/3 KO mice in constant darkness, the most prevalent coupling was between low and high-frequency ultradian activity. Following methamphetamine administration, the coupling between the circadian and high-frequency ultradian activity became dominant. In each case, the direction of information transfer was between the corresponding phases from the slower to faster oscillations. The time-varying nature of the circadian rhythm exhibited in the absence of Per1/2/3 genes and following methamphetamine administration may have profound implications for health and disease.

Directional coupling detection through cross-distance vectors

Inferring the coupling direction from measured time series of complex systems is challenging. We propose a state-space-based causality measure obtained from cross-distance vectors for quantifying interaction strength. It is a model-free noise-robust approach that requires only a few parameters. The approach is applicable to bivariate time series and is resilient to artefacts and missing values. The result is two coupling indices that quantify coupling strength in each direction more accurately than the already established state-space measures. We test the proposed method on different dynamical systems and analyze numerical stability. As a result, a procedure for optimal parameter selection is proposed, circumventing the challenge of determining the optimal embedding parameters. We show it is robust to noise and reliable in shorter time series. Moreover, we show that it can detect cardiorespiratory interaction in measured data. A numerically efficient implementation is available at https://repo.ijs.si/e2pub/cd-vec.

Efficient syncope prediction from resting state clinical data using wavelet bispectrum and multilayer perceptron neural network

Neurally mediated syncope (NMS) is the most common type of syncope, and head up tilt test (HUTT) is, so far, the most appropriate tool to identify NMS. In this work, an effort to predict the NMS before performing the HUTT is attempted. To achieve this, the heart rate variability (HRV) at rest and during the first minutes of tilting position during HUTT was analyzed using both time and frequency domains. Various features from HRV regularity and complexity, along with wavelet higher-order spectrum (WHOS) analysis in low-frequency (LF) and high-frequency (HF) bands were examined. The experimental results from 26 patients with history of NMS have shown that at rest, a time domain entropy measure and WHOS-based features in LF band exhibit significant differences between positive and negative HUTT as well as among 10 healthy subjects and NMS patients. The best performance of multilayer perceptron neural network (MPNN) was achieved by using an input vector consisted of WHOS-based HRV features in the LF zone and systolic blood pressure from the resting period, yielding an accuracy of 89.7%, assessed by 5-fold cross-validation. The promising results presented here pave the way for an early prediction of the HUTT outcome from resting state, contributing to the identification of patients at higher risk NMS. The HRV analysis along with systolic blood pressure at rest predict NMS using a multilayer perceptron neural network.

Continuous wavelet transform and higher-order spectrum: combinatory potentialities in breath sound analysis and electroencephalogram-based pain characterization

The combination of the continuous wavelet transform (CWT) with a higher-order spectrum (HOS) merges two worlds into one that conveys information regarding the non-stationarity, non-Gaussianity and nonlinearity of the systems and/or signals under examination. In the current work, the third-order spectrum (TOS), which is used to detect the nonlinearity and deviation from Gaussianity of two types of biomedical signals, that is, wheezes and electroencephalogram (EEG), is combined with the CWT to offer a time-scale representation of the examined signals. As a result, a CWT/TOS field is formed and a time axis is introduced, creating a time-bifrequency domain, which provides a new means for wheeze nonlinear analysis and dynamic EEG-based pain characterization. A detailed description and examples are provided and discussed to showcase the combinatory potential of CWT/TOS in the field of advanced signal processing.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Assessment of Quadratic Nonlinear Cardiorespiratory Couplings During Tilt-Table Test by Means of Real Wavelet Biphase

OBJECTIVE

In this paper, a method for assessment of quadratic phase coupling (QPC) between respiration and heart rate variability (HRV) is presented.

METHODS

First, a method for QPC detection is proposed named real wavelet biphase (RWB). Then, a method for QPC quantification is proposed based on the normalized wavelet biamplitude (NWB). A simulation study has been conducted to test the reliability of RWB to identify QPC, even in the presence of constant delays between interacting oscillations, and to discriminate it from quadratic phase uncoupling. Significant QPC was assessed based on surrogate data analysis. Then, quadratic cardiorespiratory couplings were studied during a tilt-table test protocol of 17 young healthy subjects.

RESULTS

Simulation study showed that RWB is able to detect even weak QPC with delays in the range of [Formula: see text] s, which are usual in the autonomic nervous system (ANS) control of heart rate. Results from the database revealed a significant reduction ([Formula: see text]) of NWB between respiration and both low and high frequencies of HRV in head-up tilt position compared to early supine.

CONCLUSION

The proposed technique detects and quantifies robustly QPC and is able to track the coupling between respiration and various HRV components during ANS changes.

SIGNIFICANCE

The proposed method can help to assess alternations of nonlinear cardiorespiratory interactions related to ANS dysfunction and physiological regulation of HRV in cardiovascular diseases.

Detecting Interactions between the Renal Autoregulation Mechanisms in Time and Space

OBJECTIVE

Our objective is to identify localized interactions between the renal autoregulation mechanisms over time.

METHODS

A time-varying phase-randomized wavelet bicoherence detector for quadratic phase coupling between tubuloglomerular feedback and the myogenic response is presented. Through simulations we show its ability to interrogate quadratic phase coupling. The method is applied to kidney blood flow and laser speckle imaging sequences of cortical perfusion from anesthetized rats before and after nonselective inhibition of nitric-oxide synthase.

RESULTS

Quadratic phase coupling in kidney blood flow data was present in four out of nine animals during the control period for 13.0 ± 5.6% (mean ± SD) of time and in five out of nine animals during inhibition of nitric-oxide synthase for 15.8 ± 8.2% of time. Approximately 60% of time-series extracted from laser speckle imaging pixels of the renal cortex showed significant quadratic phase coupling. Pixels with significant coupling had a median coupling length of 10.8 ± 2.2% and 12.1 ± 3.1% of time with the 95th percentile of pixels being coupled for 25.5 ± 4.4% and 30.9 ± 6.4% of time during control and inhibition of nitric-oxide synthase, respectively.

CONCLUSION

These results indicate quadratic phase coupling exists in short time intervals between tubuloglomerular feedback and the myogenic response and is detected more often in local renal perfusion signals than whole kidney blood flow in anesthetized rats.

SIGNIFICANCE

Combining the detector and laser speckle imaging provides identification of coordination between renal autoregulation mechanisms that is localized in time and space.

EEG-Based Tonic Cold Pain Characterization Using Wavelet Higher Order Spectral Features

A novel approach in tonic cold pain characterization, based on electroencephalograph (EEG) data analysis using wavelet higher order spectral (WHOS) features, is presented here. The proposed WHOS-based feature space extends the relative power spectrum-based (phase blind) approaches reported so far a step forward; this is realized via dynamic monitoring of the nonlinerities of the EEG brain response to tonic cold pain stimuli by capturing the change in the underlying quadratic phase coupling at the bifrequency wavelet bispectrum/bicoherence domain due to the change of the pain level. Three pain characterization scenarios were formed and experimentally tested involving WHOS-based analysis of EEG data, acquired from 17 healthy volunteers that were subjected to trials of tonic cold pain stimuli. The experimental and classification analysis results, based on four well-known classifiers, have shown that the WHOS-based features successfully discriminate relax from pain status, provide efficient identification of the transition from relax to mild and/or severe pain status, and translate the subjective perception of pain to an objective measure of pain endurance. These findings seem quite promising and pave the way for adopting WHOS-based approaches to pain characterization under other types of pain, e.g., chronic pain and various clinical scenarios.

Detecting the harmonics of oscillations with time-variable frequencies

A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.

Significance testing for wavelet bicoherence and its application in analyzing nonlinearity in turbulent shear flows

Wavelet-based bispectral analysis has been applied in various physical and engineering fields in recent years, but discussion of its significance testing, which distinguishes statistically meaningful results from those due to random noise, has been scarce and incomplete in the literature. Previously derived significance levels for wavelet bicoherence were either preliminary or based on numerical simulations of a limited sample size. The present study reviewed relevant previous works analytically identified the sampling distribution of the estimated wavelet bicoherence and derived expressions for its significance levels for any given probability value. Its application in analyzing a turbulent shear flow around a bluff body was demonstrated in detail. The significance testing developed here helped to identify significant quadratic couplings among a triad of scales in a separated turbulent shear layer over very short time intervals. The results obtained here can be applied to a wide variety of research topics for detecting nonlinearity in physical systems.

Detecting couplings between interacting oscillators with time-varying basic frequencies: instantaneous wavelet bispectrum and information theoretic approach

In the natural world, the properties of interacting oscillatory systems are not constant, but evolve or fluctuating continuously in time. Thus, the basic frequencies of the interacting oscillators are time varying, which makes the system analysis complex. For studying their interactions we propose a complementary approach combining wavelet bispectral analysis and information theory. We show how these methods uncover the interacting properties and reveal the nature, strength, and direction of coupling. Wavelet bispectral analysis is generalized as a technique for detecting instantaneous phase-time dependence for the case of two or more coupled nonlinear oscillators whereas the information theory approach can uncover the directionality of coupling and extract driver-response relationships in complex systems. We generate bivariate time-series numerically to mimic typical situations that occur in real measured data, apply both methods to the same time-series and discuss the results. The approach is applicable quite generally to any system of coupled nonlinear oscillators.

Analysis of wheezes using wavelet higher order spectral features

Wheezes are musical breath sounds, which usually imply an existing pulmonary obstruction, such as asthma and chronic obstructive pulmonary disease (COPD). Although many studies have addressed the problem of wheeze detection, a limited number of scientific works has focused in the analysis of wheeze characteristics, and in particular, their time-varying nonlinear characteristics. In this study, an effort is made to reveal and statistically analyze the nonlinear characteristics of wheezes and their evolution over time, as they are reflected in the quadratic phase coupling of their harmonics. To this end, the continuous wavelet transform (CWT) is used in combination with third-order spectra to define the analysis domain, where the nonlinear interactions of the harmonics of wheezes and their time variations are revealed by incorporating instantaneous wavelet bispectrum and bicoherence, which provide with the instantaneous biamplitude and biphase curves. Based on this nonlinear information pool, a set of 23 features is proposed for the nonlinear analysis of wheezes. Two complementary perspectives, i.e., general and detailed, related to average performance and to localities, respectively, were used in the construction of the feature set, in order to embed trends and local behaviors, respectively, seen in the nonlinear interaction of the harmonic elements of wheezes over time. The proposed feature set was evaluated on a dataset of wheezes, acquired from adult patients with diagnosed asthma and COPD from a lung sound database. The statistical evaluation of the feature set revealed discrimination ability between the two pathologies for all data subgroupings. In particular, when the total breathing cycle was examined, all 23 features, but one, showed statistically significant difference between the COPD and asthma pathologies, whereas for the subgroupings of inspiratory and expiratory phases, 18 out of 23 and 22 out of 23 features exhibited discrimination power, respectively. This paves the way for the use of the wavelet higher order spectral features as an input vector to an efficient classifier. Apparently, this would integrate the intrinsic characteristics of wheezes within computerized diagnostic tools toward their more efficient evaluation.