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.

Bispectral Analysis of Heart Rate Variability to Characterize and Help Diagnose Pediatric Sleep Apnea

Pediatric obstructive sleep apnea (OSA) is a breathing disorder that alters heart rate variability (HRV) dynamics during sleep. HRV in children is commonly assessed through conventional spectral analysis. However, bispectral analysis provides both linearity and stationarity information and has not been applied to the assessment of HRV in pediatric OSA. Here, this work aimed to assess HRV using bispectral analysis in children with OSA for signal characterization and diagnostic purposes in two large pediatric databases (0-13 years). The first database (training set) was composed of 981 overnight ECG recordings obtained during polysomnography. The second database (test set) was a subset of the Childhood Adenotonsillectomy Trial database (757 children). We characterized three bispectral regions based on the classic HRV frequency ranges (very low frequency: 0-0.04 Hz; low frequency: 0.04-0.15 Hz; and high frequency: 0.15-0.40 Hz), as well as three OSA-specific frequency ranges obtained in recent studies (BW1: 0.001-0.005 Hz; BW2: 0.028-0.074 Hz; BWRes: a subject-adaptive respiratory region). In each region, up to 14 bispectral features were computed. The fast correlation-based filter was applied to the features obtained from the classic and OSA-specific regions, showing complementary information regarding OSA alterations in HRV. This information was then used to train multi-layer perceptron (MLP) neural networks aimed at automatically detecting pediatric OSA using three clinically defined severity classifiers. Both classic and OSA-specific MLP models showed high and similar accuracy (Acc) and areas under the receiver operating characteristic curve (AUCs) for moderate (classic regions: Acc = 81.0%, AUC = 0.774; OSA-specific regions: Acc = 81.0%, AUC = 0.791) and severe (classic regions: Acc = 91.7%, AUC = 0.847; OSA-specific regions: Acc = 89.3%, AUC = 0.841) OSA levels. Thus, the current findings highlight the usefulness of bispectral analysis on HRV to characterize and diagnose pediatric OSA.

Deep learning classification for improved bicoherence feature based on cyclic modulation and cross-correlation

This paper aims to present an improved bicoherence spectrum (IBS) combined with cyclic modulation spectrum (CMS) and cross-correlation that is suitable for classification of hydrophone signals involving deep learning (DL). First, the proposed feature utilizes the all-phase fast Fourier transform to modify the spectrum leakage caused by CMS; this can be used to detect line spectra with low signal-to-noise ratios (SNRs). Second, the cross-correlation and bispectrum are both exploited to suppress non-periodic line spectra interference from CMS. Based on numerous numerical simulations and experimental verification, compared with CMS and conventional bispectrum, the prominent characteristics of IBS include: detecting higher-precision periodic harmonics without single-line interference, superior robustness under low SNR, and greatly reducing the data redundancy. In addition, to test the performance of IBS for DL application, three deep belief network (DBN)-based classifiers-DBN-softmax, DBN-support vector machine, and DBN-random forest-are introduced and employed for five experimental scenarios (including ships and underwater source). The results indicate that benefiting from DBN pre-training, the IBS classification accuracy of DBN-based models is generally higher than 80%.

Alterations in Maternal-Fetal Heart Rate Coupling Strength and Directions in Abnormal Fetuses

Because fetal gas exchange takes place via the maternal placenta, there has been growing interests in investigating the patterns and directions of maternal-fetal cardiac coupling to better understand the mechanisms of placental gas transfer. We recently reported the evidence of short-term maternal–fetal cardiac couplings in normal fetuses by using Normalized Short Time Partial Directed Coherence (NSTPDC) technique. Our results have shown weakening of coupling from fetal heart rate to maternal heart rate as the fetal development progresses while the influence from maternal to fetal heart rate coupling behaves oppositely as it shows increasing coupling strength that reaches its maximum at mid gestation. The aim of this study is to test if maternal-fetal coupling patterns change in various types of abnormal cases of pregnancies. We applied NSTPDC on simultaneously recorded fetal and maternal beat-by-beat heart rates collected from fetal and maternal ECG signals of 66 normal and 19 abnormal pregnancies. NSTPDC fetal-to-maternal coupling analyses revealed significant differences between the normal and abnormal cases (normal: normalized factor (NF) = −0.21 ± 0.85, fetus-to-mother coupling area (A_fBBI→ mBBI) = 0.44 ± 0.13, mother-to-fetus coupling area (A_mBBI→ fBBI) = 0.46 ± 0.12; abnormal: NF = −1.66 ± 0.77, A_fBBI→ mBBI = 0.08 ± 0.12, A_mBBI→ fBBI = 0.66 ± 0.24; p < 0.01). In conclusion, maternal-fetal cardiac coupling strength and direction and their associations with regulatory mechanisms (patterns) of developing autonomic nervous system function could be novel clinical markers of healthy prenatal development and its deviation. However, further research is required on larger samples of abnormal cases.

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.

Nonlinear interactions in the thalamocortical loop in essential tremor: A model-based frequency domain analysis

There is increasing evidence to suggest that essential tremor has a central origin. Different structures appear to be part of the central tremorogenic network, including the motor cortex, the thalamus and the cerebellum. Some studies using electroencephalogram (EEG) and magnetoencephalography (MEG) show linear association in the tremor frequency between the motor cortex and the contralateral tremor electromyography (EMG). Additionally, high thalamomuscular coherence is found with the use of thalamic local field potential (LFP) recordings and tremulous EMG in patients undergoing surgery for deep brain stimulation (DBS). Despite a well-established reciprocal anatomical connection between the thalamus and cortex, the functional association between the two structures during "tremor-on" periods remains elusive. Thalamic (Vim) LFPs, ipsilateral scalp EEG from the sensorimotor cortex and contralateral tremor arm EMG recordings were obtained from two patients with essential tremor who had undergone successful surgery for DBS. Coherence analysis shows a strong linear association between thalamic LFPs and contralateral tremor EMG, but the relationship between the EEG and the thalamus is much less clear. These measurements were then analyzed by constructing a novel parametric nonlinear autoregressive with exogenous input (NARX) model. This new approach uncovered two distinct and not overlapping frequency "channels" of communication between Vim thalamus and the ipsilateral motor cortex, defining robustly "tremor-on" versus "tremor-off" states. The associated estimated nonlinear time lags also showed non-overlapping values between the two states, with longer corticothalamic lags (exceeding 50ms) in the tremor active state, suggesting involvement of an indirect multisynaptic loop. The results reveal the importance of the nonlinear interactions between cortical and subcortical areas in the central motor network of essential tremor. This work is important because it demonstrates for the first time that in essential tremor the functional interrelationships between the cortex and thalamus should not be sought exclusively within individual frequencies but more importantly between cross-frequency nonlinear interactions. Should our results be successfully reproduced on a bigger cohort of patients with essential tremor, our approach could be used to create an on-demand closed-loop DBS device, able to automatically activate when the tremor is on.

Detection of low-frequency oscillations in renal blood flow

Detection of the low-frequency (LF; ∼0.01 Hz) component of renal blood flow, which is theorized to reflect the action of a third renal autoregulatory mechanism, has been difficult due to its slow dynamics. In this work, we used three different experimental approaches to detect the presence of the LF component of renal autoregulation using normotensive and spontaneously hypertensive rats (SHR), both anesthetized and unanesthetized. The first experimental approach utilized a blood pressure forcing in the form of a chirp, an oscillating perturbation with linearly increasing frequency, to elicit responses from the LF autoregulatory component in anesthetized normotensive rats. The second experimental approach involved collection and analysis of spontaneous blood flow fluctuation data from anesthetized normotensive rats and SHR to search for evidence of the LF component in the form of either amplitude or frequency modulation of the myogenic and tubuloglomerular feedback mechanisms. The third experiment used telemetric recordings of arterial pressure and renal blood flow from normotensive rats and SHR for the same purpose. Our transfer function analysis of chirp signal data yielded a resonant peak centered at 0.01 Hz that is greater than 0 dB, with the transfer function gain attenuated to lower than 0 dB at lower frequencies, which is a hallmark of autoregulation. Analysis of the data from the second experiments detected the presence of ∼0.01-Hz oscillations only with isoflurane, albeit at a weaker strength compared with telemetric recordings. With the third experimental approach, the strength of the LF component was significantly weaker in the SHR than in the normotensive rats. In summary, our detection via the amplitude modulation approach of interactions between the LF component and both tubuloglomerular feedback and the myogenic mechanism, with the LF component having an identical frequency to that of the resonant gain peak, provides evidence that 0.01-Hz oscillations may represent the third autoregulatory mechanism.

On the efficacy of the combined use of the cross-bicoherence with surrogate data technique to statistically quantify the presence of nonlinear interactions

The cross-bispectrum is an approach to detect the presence of quadratic phase coupling (QPC) between different components in bivariate signals. Quantification of QPC is by means of the cross-bicoherence index (CBI). The major limitations of the CBI are that it favors only the strongly coupled signals and its accuracy becomes compromised with noise and low coupling strength. To overcome this limitation, a statistical approach which combines CBI with a surrogate data method to determine the statistical significance of the QPC derived from bivariate signals is introduced. We demonstrate the accuracy of the proposed approach using simulation examples which are designed to test its robustness against noise contamination as well as varying levels of phase coupling and data lengths. Comparisons were made to the traditional CBI and the method based on the use of cross-bispectrum followed by a surrogate data technique. Our results show that the cross-bicoherence with surrogate data technique outperforms the two other methods compared in both sensitivity and specificity, and provides an unbiased and statistical approach to determining the presence of QPC in bivariate signals. These results are in contrast to our recent study where the auto-bispectrum combined with surrogate data approach had the best performance. Application of this approach to renal hemodynamic data was applied to renal stop flow pressure data obtained in the nephrons of the normotensive (N = 18) and hypertensive (N = 15) rats. We found significant nonlinear interactions between nephrons only when they are derived from the same cortical renal artery. The accuracy was 100% and verified by comparing the results to the known vascular connectivity between nephrons.

Nonlinear coupling is absent in acute myocardial patients but not healthy subjects

We investigated whether autonomic nervous system imbalance imposed by pharmacological blockades and associated with acute myocardial infarction (AMI) is manifested as modifications of the nonlinear interactions in heart rate variability signal using a statistically based bispectrum method. The statistically based bispectrum method is an ideal approach for identifying nonlinear couplings in a system and overcomes the previous limitation of determining in an ad hoc way the presence of such interactions. Using the improved bispectrum method, we found significant nonlinear interactions in healthy young subjects, which were abolished by the administration of atropine but were still present after propranolol administration. The complete decoupling of nonlinear interactions was obtained with double pharmacological blockades. Nonlinear couplings were found to be the strongest for healthy young subjects followed by degradation with old age and a complete absence of such couplings for the old age-matched AMI subjects. Our results suggest that the presence of nonlinear couplings is largely driven by the parasympathetic nervous system regulation and that the often-reported autonomic nervous system imbalance seen in AMI subjects is manifested as the absence of nonlinear interactions between the sympathetic and parasympathetic nervous regulations.