The Modeling and Quantification of Rhythmic to Non-rhythmic Phenomenon in Electrocardiography during Anesthesia

Variations of instantaneous heart rate appears regularly oscillatory in deeper levels of anesthesia and less regular in lighter levels of anesthesia. It is impossible to observe this "rhythmic-to-non-rhythmic" phenomenon from raw electrocardiography waveform in current standard anesthesia monitors. To explore the possible clinical value, I proposed the adaptive harmonic model, which fits the descriptive property in physiology, and provides adequate mathematical conditions for the quantification. Based on the adaptive harmonic model, multitaper Synchrosqueezing transform was used to provide time-varying power spectrum, which facilitates to compute the quantitative index: "Non-rhythmic-to-Rhythmic Ratio" index (NRR index). I then used a clinical database to analyze the behavior of NRR index and compare it with other standard indices of anesthetic depth. The positive statistical results suggest that NRR index provides addition clinical information regarding motor reaction, which aligns with current standard tools. Furthermore, the ability to indicates the noxious stimulation is an additional finding. Lastly, I have proposed an real-time interpolation scheme to contribute my study further as a clinical application.Comment: Doctoral Dissertatio

Current state of nonlinear-type time-frequency analysis and applications to high-frequency biomedical signals

Motivated by analyzing complicated time series, nonlinear-type time-frequency analysis became an active research topic in the past decades. Those developed tools have been applied to various problems. In this article, we review those developed tools and summarize their applications to high-frequency biomedical signals

When interpolation-induced reflection artifact meets time-frequency analysis

While extracting the temporal dynamical features based on the time-frequency analyses, like the reassignment and synchrosqueezing transform, attracts more and more interest in bio-medical data analysis, we should be careful about artifacts generated by interpolation schemes, in particular when the sampling rate is not significantly higher than the frequency of the oscillatory component we are interested in. In this study, we formulate the problem called the reflection effect and provide a theoretical justification of the statement. We also show examples in the anesthetic depth analysis with clear but undesirable artifacts. The results show that the artifact associated with the reflection effect exists not only theoretically but practically. Its influence is pronounced when we apply the time-frequency analyses to extract the time-varying dynamics hidden inside the signal. In conclusion, we have to carefully deal with the artifact associated with the reflection effect by choosing a proper interpolation scheme

Wave-shape function analysis -- when cepstrum meets time-frequency analysis

We propose to combine cepstrum and nonlinear time-frequency (TF) analysis to study mutiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and we propose a new algorithm, named de-shape synchrosqueezing transform (de-shape SST). The mathematical model, adaptive non-harmonic model, is introduced and the de-shape SST algorithm is theoretically analyzed. In addition to simulated signals, several different physiological, musical and biological signals are analyzed to illustrate the proposed algorithm

Nonparametric and adaptive modeling of dynamic seasonality and trend with heteroscedastic and dependent errors

Seasonality (or periodicity) and trend are features describing an observed sequence, and extracting these features is an important issue in many scientific fields. However, it is not an easy task for existing methods to analyze simultaneously the trend and {\it dynamics} of the seasonality such as time-varying frequency and amplitude, and the {\it adaptivity} of the analysis to such dynamics and robustness to heteroscedastic, dependent errors is not guaranteed. These tasks become even more challenging when there exist multiple seasonal components. We propose a nonparametric model to describe the dynamics of multi-component seasonality, and investigate the recently developed Synchrosqueezing transform (SST) in extracting these features in the presence of a trend and heteroscedastic, dependent errors. The identifiability problem of the nonparametric seasonality model is studied, and the adaptivity and robustness properties of the SST are theoretically justified in both discrete- and continuous-time settings. Consequently we have a new technique for de-coupling the trend, seasonality and heteroscedastic, dependent error process in a general nonparametric setup. Results of a series of simulations are provided, and the incidence time series of varicella and herpes zoster in Taiwan and respiratory signals observed from a sleep study are analyzed