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 Nonlinear Behavior in Voltage Source Converter Control in Wind Farms Based on Higher-Order Spectral Analysis

In recent years, the sub-synchronous oscillation (SSO) accidents caused by wind power have received extensive attention. A method is needed to distinguish if nonlinear behavior exists in the recorded equal-amplitude accident waveforms, so that different methods can be adopted to analyze the mechanism of the oscillation. The theory of higher-order statistics (HOS) has become a powerful tool for detection of nonlinear behavior (DNB) in production quality control since 1960s. However, HOS analysis has been applied in mechanical condition monitoring and fault diagnosis, even after being introduced into the power system and wind farms. This paper focuses on the voltage source converter (VSC) control systems in wind farms and tries to detect the nonlinear behavior caused by the bilateral or unilateral saturation hard limits based on HOS analysis. First, the traditional describing function is extended to obtain more frequency domain information, and hereby the harmonic characteristics of bilateral and the unilateral saturation hard limit are studied. Then the bispectrum and trispectrum are introduced as HOS, which are extended into bicoherence and tricoherence spectrums to eliminate the effects from linear parts in the VSC control system. The effectiveness of DNB and classification based on HOS is strictly proved and its detailed calculation and estimation process is illustrated. Finally, the proposed method is demonstrated and further discussed through simulation results

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