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.

💡 Research Summary

The dissertation by Y‑Ting Lin addresses a previously under‑explored physiological phenomenon observed during general anesthesia: the transition of instantaneous heart rate (IHR) from a regular, rhythmic pattern in deep anesthesia to an irregular, non‑rhythmic pattern as anesthesia lightens. Although clinicians have qualitatively noted this “rhythmic‑to‑non‑rhythmic” behavior, no quantitative metric existed, nor was the underlying mechanism clarified.

To fill this gap, the author proposes an adaptive harmonic model that represents IHR as a sum of time‑varying sinusoidal components (fundamental frequency and its harmonics) with slowly varying amplitudes and phases. The model is mathematically justified under smoothness and frequency‑separation conditions, ensuring that the signal can be decomposed into a deterministic harmonic part (the “rhythmic” component) and a stochastic residual (the “non‑rhythmic” component).

For practical extraction of these components, the work employs a multitaper synchrosqueezing transform (MT‑SST). This advanced time‑frequency analysis technique first reduces spectral leakage by averaging across multiple orthogonal tapers, then re‑assigns energy to instantaneous frequency curves, yielding a high‑resolution time‑varying power spectrum (tvPS). From the tvPS the author computes two quantities: Rhythmic Power (the summed power of identified harmonic ridges) and Non‑rhythmic Power (the remaining background power). The Non‑rhythmic‑to‑Rhythmic Ratio (NRR) is defined as log10(Non‑rhythmic Power / Rhythmic Power). A larger NRR indicates dominance of irregular fluctuations, which the author hypothesizes corresponds to lighter anesthesia or nociceptive stimulation.

A substantial clinical dataset (over 150 patients undergoing various surgical procedures) was assembled, containing raw ECG, BIS, end‑tidal anesthetic concentrations, and annotated events such as loss of consciousness, skin incision, muscle movement, and return of consciousness. The NRR index was computed offline for each patient and compared against standard depth‑of‑anesthesia monitors (BIS, HRV‑based indices, PSI). Statistical evaluation used serial Prediction Probability (sPK) analysis, correlation with estimated effect‑site sevoflurane concentration, and paired comparisons across event boundaries.

Key findings include:

1. Higher predictive power – NRR achieved sPK values >0.85 for detecting loss of consciousness, skin incision, and first motor reaction, outperforming BIS and HRV measures.
2. Earlier detection of nociception – During skin incision, NRR rose significantly 5–10 seconds before any observable change in BIS or heart‑rate variability, suggesting heightened sensitivity to sympathetic activation.
3. Strong inverse correlation with anesthetic depth – NRR decreased as sevoflurane concentration increased (Pearson r ≈ –0.68, p < 0.001), confirming its relationship with depth of hypnosis.
4. Multi‑component dynamics – In several recordings, two or more harmonic ridges were present simultaneously, reflecting complex autonomic modulation; nevertheless, the NRR remained a robust single‑value summary.

Beyond validation, the dissertation tackles real‑time implementation, a critical step for clinical adoption. Since MT‑SST traditionally requires batch processing, the author designs a blending operator based on B‑splines to interpolate uneven R‑R intervals into a continuous signal suitable for online analysis. The operator combines local polynomial interpolation with a global smoothing kernel, enabling a causal, low‑latency (≈200 ms) computation of the tvPS and thus the NRR index. Preliminary tests on a 1 kHz sampled ECG stream demonstrated feasible real‑time performance on a standard workstation.

The work acknowledges several limitations: reliance on accurate R‑peak detection (errors propagate to NRR), focus on inhalational anesthetic (sevoflurane) and surgical incision as the primary stimulus, and the computational load of MT‑SST which may require hardware acceleration for embedded monitor integration. Future directions proposed include extending validation to intravenous agents, pediatric and geriatric populations, and optimizing the algorithm for FPGA or GPU platforms.

In conclusion, Lin’s dissertation introduces a theoretically sound, physiologically motivated, and empirically validated metric—NRR—that captures a subtle autonomic signature of anesthetic depth and nociceptive events. By coupling an adaptive harmonic representation with multitaper synchrosqueezing, the study bridges signal‑processing advances and clinical anesthesia monitoring, offering a pathway toward richer, real‑time patient state assessment in the operating room.