Integrating Simulated Clinical Outcomes and Nonlinear HRV Metrics in Fibromyalgia Rehabilitation: A Dual-Layer Metric- and Signal-Level Simulation Framework

Nonlinear heart rate variability (HRV) metrics may complement scales, but metric-level simulation alone cannot test algorithm implementation or stability under signal imperfections. We evaluated a dual-layer simulation framework for fibromyalgia rehabilitation research. Layer A used a synthetic dataset (n = 48; seed 20,260,724) and 1000 Monte Carlo replicates in five scenarios. Layer B verified Higuchi fractal dimension (HFD), detrended fluctuation analysis (DFA α), and a finite-time divergence index on canonical signals and 120 synthetic 10 min RR interval tachograms analyzed at 2, 5, and 10 min, with 1% and 5% artifact burdens and varied settings. Under the null scenario, family-wise rejection rates were 3.6% for longitudinal tests and 5.5% for correlations; a latent common cause scenario produced correlation rejections in 95.9% of replicates. Canonical checks yielded HFD values of 1.029 for a sinusoid and 1.999 for white noise, while logistic-map divergence was 0.694, close to ln(2) = 0.693. In tachograms, HFD varied mainly with kmax, DFA with artifacts and scale range, and divergence with duration and embedding; no divergence fit met the R2 ≥ 0.90 criterion. The framework separates statistical performance from signal processing validity but provides no evidence of treatment efficacy, autonomic recovery, or biomarker validity.