Integration of the A7-HBM-ΩΦ Model with the Pellis Golden Biomedical Function (PGFF): Experimental Validation Using Seven Independent Datasets Including Simultaneous EEG-ECG Recordings from Healthy, Epileptic, and Cardiac Patients

Background The golden ratio (Φ ≈ 1.618) represents a universal mathematical principle appearing in the organization of various biological systems. The A7-HBM-ΩΦ model (Al-Olofi, 2025) provides an integrated framework of seven brain frequency bands arranged according to Φ, with a control parameter β regulating the direction of information flow. In parallel, the Pellis Golden Biomedical Function (PGFF) (Pellis, 2025) offers a unified diagnostic language for measuring fractal harmony deviations across physiological systems. While both models provide promising theoretical frameworks, neither has been experimentally validated on simultaneous brain-heart recordings from healthy and pathological populations. This study bridges this gap by analyzing seven independent datasets encompassing healthy subjects, epilepsy patients, and cardiac patients. Objective This work aims to build a bridge between the two models by developing a computational engine that applies A7-HBM-ΩΦ principles to physiological data (HRV and EEG) and extracts a unified fractal coherence index (PA-FCI), suitable as a shared diagnostic tool, and to validate it across seven independent datasets. Methods A system of seven coupled Stuart-Landau oscillators with a β-dependent coupling matrix was developed and numerically simulated. Twenty-eight attractors (4 per band) were added according to the original model. The system was applied to seven datasets: (1) 147 RR interval recordings (HRV) from the PhysioNet database of healthy subjects (aged 1 month to 55 years); (2) 278 young healthy adults from the HYPOL database (19–30 years) for external validation; (3) 14 epilepsy patients from the Siena Scalp EEG Database with simultaneous EEG (29 channels) and EKG recordings; (4) 22 healthy subjects from the PhysioUnicaDB database with simultaneous EEG (61 channels) and ECG recordings; (5) 23 patients from the Sudden Cardiac Death Holter Database (ECG only); (6) 87 cardiac patients from the MIMIC-III Waveform Database with simultaneous EEG and ECG; (7) a pooled healthy cohort combining datasets 1, 2, and 4 (n = 447). Unified HRV measures, Φ-coherence (the proximity of dominant frequency ratios to Φ), phase-amplitude coupling (PAC) for six key frequency pairs (δ→γ, θ→γ, α→Ω, σ→Ω, β→γ, γ→Ω), and the PA-FCI index were calculated. Extensive validation including internal consistency, sensitivity analysis, cross-validation, robustness testing, and external validation across independent datasets was performed. Results · PhysioNet (n=147): Mean Φ-coherence = 0.612 ± 0.183 (95% CI: 0.581–0.641; p=0.64 vs. 0.618). Mean PA-FCI = 0.593 ± 0.147. · HYPOL (n=278): Mean Φ-coherence = 0.618 ± 0.165 (95% CI: 0.598–0.638; p=0.41 vs. 0.618). Mean PA-FCI = 0.601 ± 0.142. No significant difference from PhysioNet (p=0.72). No sex differences (p=0.34). · Siena (n=14, interictal): Mean Φ-coherence = 0.615 ± 0.170; mean PAC deviated <3.5% from reference; mean total PA-FCI = 0.591 ± 0.024. Pre-ictally (30 min before seizures), total PA-FCI dropped to 0.523 ± 0.035 (p<0.001) and to 0.481 ± 0.042 during seizures. Negative correlation with seizure frequency (r = -0.41, p<0.01). · PhysioUnicaDB (n=22): Mean Φ-coherence = 0.616 ± 0.168 (95% CI: 0.542–0.690); mean PAC = 0.610 ± 0.025 (deviation <0.3% from theory); mean total PA-FCI = 0.605 ± 0.022; strong PAC-Φ coherence correlation (r = 0.73, p<0.001). · Sudden Cardiac Death (n=23, ECG only): Mean Φ-coherence = 0.523 ± 0.145 (95% CI: 0.461–0.585), significantly lower than healthy (p<0.001). Mean overall PA-FCI = 0.541 ± 0.142, and 1 hour before death = 0.515 ± 0.038. · MIMIC-III Cardiac (n=87, EEG+ECG): Mean Φ-coherence = 0.535 ± 0.140; mean PAC = 0.583 ± 0.045 (7–9% below reference); mean total PA-FCI = 0.530 ± 0.035; PAC-Φ coherence correlation (r = 0.68, p<0.001). PA-FCI decreased with disease severity (NYHA I→IV: 0.561→0.498, p<0.001). Conclusion : These results provide the first comprehensive experimental validation of the Φ-harmony principle across seven independent datasets, including HRV-only and simultaneous EEG-ECG recordings from healthy, epileptic, and cardiac subjects. The PA-FCI index emerges as a universal, robust, and clinically relevant metric for quantifying fractal health. Its ability to detect pre-ictal states in epilepsy and pre-terminal decline in cardiac patients, with a well-defined healthy baseline (0.605 ± 0.022) and warning threshold (0.55), opens new avenues for early diagnosis and personalized medicine. This work establishes bidirectional brain-heart integration: brain disease affects the heart (Siena), and heart disease affects the brain (MIMIC-III), both captured by the same unified metric. It fulfills the vision of a unified diagnostic language bridging mathematics, physiology, and clinical practice.