Technical report

Theoretical construct and synthetic reference

The reference used in this simulation was not intended to represent a physiologically normal patient tracing. In each Monte Carlo replicate, 30 independently generated reference-like fetal heart-rate signals were subjected to the complete preprocessing pipeline, converted to normalized power spectra, and combined by taking the binwise median. This median normalized spectrum defined the synthetic reference template, Q. Each independent test signal produced a normalized spectrum, P, and the FETAL spectral-divergence score was defined as the Jensen-Shannon divergence between P and Q [9]. Jensen-Shannon divergence was selected because it is symmetric, finite after numerical stabilization, and directly compares two normalized distributions defined on the same frequency grid. In contrast, Kullback-Leibler divergence is asymmetric and may become unstable when spectral bins approach zero. The present study did not seek to establish Jensen-Shannon divergence as superior to all alternative measures of spectral similarity; comparisons with metrics such as Wasserstein distance and cosine similarity remain appropriate for future patient-level development. The reference library was rebuilt independently in every replicate so that uncertainty in the synthetic template contributed to observed performance. No test signal contributed to the reference spectrum against which it was evaluated. The method could therefore fail if preprocessing attenuated the imposed spectral displacement, variation in the reference library obscured it, or artifacts generated greater within-group than between-group variation. The simulation was consequently designed as a falsifiable robustness assessment rather than a demonstration guaranteed by construction. This distinction is important because performance against a synthetic reference cannot establish physiological or clinical validity.

Simulation design and rationale for the spectral perturbations

Twelve Monte Carlo replicates were performed for each of five prespecified scenarios: null, weak shift, moderate shift, strong shift, and moderate shift under artifact stress [10]. Each replicate included 30 independently generated signals for construction of the synthetic reference library and two independent test groups consisting of 30 reference-like and 30 altered signals. Signals represented 10-minute fetal heart-rate recordings sampled at 4 Hz and incorporated baseline drift, two oscillatory components, autoregressive noise, decelerations, short intervals of missingness, and occasional maternal heart-rate contamination. The simulated spectral shifts were not derived from a specific effect size reported in a human study and were not intended to reproduce a validated physiological signature of fetal acidemia. Published observations suggesting that fetal compromise may be accompanied by redistribution of fetal heart-rate variability across frequencies provided the conceptual motivation for examining changes in spectral shape [6-8]. The broad low- and high-frequency framing was therefore informed conceptually by prior fetal heart-rate variability research, whereas the exact peak locations and the magnitudes of the weak, moderate, and strong displacements were selected as controlled mathematical perturbations rather than as quantitatively calibrated estimates of human physiology. In the altered signals, spectral peaks were progressively displaced within the prespecified low- and high-frequency regions while approximate total oscillatory power and broad low-/high-frequency allocation were preserved. This design allowed spectral shape to change without necessarily producing a corresponding change in overall signal amplitude or in the aggregate low-/high-frequency power ratio. The purpose was therefore to determine whether a full-spectrum comparison could detect within-band redistribution that might be missed by scalar summaries such as standard deviation or the low-/high-frequency ratio. The null scenario generated both test groups from the same underlying distribution. The weak-, moderate-, and strong-shift scenarios introduced progressively larger within-band peak displacements. The artifact-stress scenario combined the moderate shift with increased noise, missingness, decelerations, and maternal heart-rate contamination. This structure allowed the spectral-divergence score to remain uninformative under the null condition, fail to detect very small perturbations, improve as spectral separation increased, and lose performance when signal quality deteriorated. These simulated perturbations should not be interpreted as established biological changes caused by fetal acidemia. Their biological validity, direction, magnitude, and consistency must be determined in patient-level intrapartum recordings linked to clinical outcomes. The complete parameter settings used to generate the reference-like and altered signals are provided in the supplementary simulation code.

Signal processing

Values outside the physiologically plausible range of 50-210 beats/min were treated as missing. Signals with more than 20% missing data were rejected, while shorter gaps in retained signals were linearly interpolated. A smooth 60-second baseline was estimated and subtracted to reduce low-frequency baseline drift. Power spectral density was estimated using Welch’s method with 256-sample Hann windows and 50% overlap [11]. Spectral power between 0.02 and 0.80 Hz was retained and normalized to unit mass, allowing each spectrum to be interpreted as a distribution of relative power across the analyzed frequency grid. The FETAL spectral-divergence score was then calculated as the Jensen-Shannon divergence between each test spectrum and the independently generated median synthetic reference spectrum. Two scalar comparator features were evaluated. The first was the absolute deviation in time-domain standard deviation from the corresponding reference value. The second was the absolute deviation in the logarithm of the low-/high-frequency power ratio. These comparators were selected to test whether the simulated within-band redistributions could be detected using overall variability or broad frequency-band allocation rather than the full normalized spectrum.

Statistical evaluation

Discrimination between altered and reference-like test signals was summarized using the area under the receiver operating characteristic curve (AUROC) [12]. An AUROC was calculated separately for each replicate, scenario, and candidate feature. Scenario-specific performance was summarized using the median replicate-level AUROC. The reported 95% empirical Monte Carlo intervals were defined as the 2.5th and 97.5th percentiles of the replicate-specific AUROC values. These intervals were obtained directly from the Monte Carlo replicates and were not estimated using bootstrap resampling. They summarize variability across repeated realizations of the stated synthetic experiment and should not be interpreted as confidence intervals for diagnostic performance in a human population.

Reproducibility and ethical considerations

The simulations and analyses were implemented in Python 3.12 (Python Software Foundation, Wilmington, DE) using NumPy, SciPy, pandas, and scikit-learn [13]. The complete simulation code, preprocessing procedures, parameter settings, random-seed information, and replicate-level outputs are available as online supplementary material. The random-number generation procedure was fixed and documented in the supplementary code to permit reproducible generation of the Monte Carlo replicates. No human participants, identifiable information, clinical recordings, or animal data were used. Institutional research-ethics board review was therefore not required.

Results

Across 5,400 generated signals, including 3,600 independent test signals, the median AUROC for spectral divergence was 0.504 (95% empirical Monte Carlo interval, 0.415-0.653) under the null scenario and 0.466 (0.370-0.515) under the weak-shift scenario. Performance increased to 0.778 (0.605-0.896) for moderate shifts and 0.917 (0.858-0.970) for strong shifts. Moderate shifts combined with artifact stress yielded an AUROC of 0.714 (0.575-0.804). Median AUROCs ranged from 0.467 to 0.569 for standard-deviation deviation and from 0.478 to 0.543 for low-/high-frequency-ratio deviation. Figure 1 presents the analytic workflow, representative synthetic spectra, and scenario-specific performance.

Figure 1: FETAL theoretical framework and falsifiable in-silico evaluation(A) The reference is a median normalized spectrum derived from an independent synthetic reference library. (B) Representative synthetic spectra show the reference template, a reference-like test signal, and a strong-shift test signal. (C) Scenario-specific AUROCs demonstrate chance performance under the null and weak scenarios, improved discrimination with moderate and strong shifts, and degradation under artifact stress.FETAL: Fourier Evaluation of Tracings and Acidosis in Labor; AUROC, area under the receiver operating characteristic curve; LF/HF, low-frequency/high-frequency power ratio; SD, standard deviation.