Spectral Exponents of the Twelve-Lead ECG

Spectral Exponents of the Twelve-Lead ECG Reveal the Anatomy of Cardiac Conduction Disorders and a Bifurcation Between Aging and Disease

Theodor Spiro | ORCID 0009-0004-5382-9346 | tspiro@vaika.org

📄 Preprint: paper/main.pdf — bioRxiv submission ID BIORXIV/2026/717157 🧮 Main analysis script: generate_paper_figures.py 📊 Kaggle notebook (reproducible): The Heartbeat at the Edge of Chaos 📦 Archived release (Zenodo DOI): 10.5281/zenodo.19945065

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Brief Summary

We extract the spectral exponent β — the slope of the aperiodic (1/f^β) component of the ECG power spectrum — from 412,730 twelve-lead recordings across three continents. The analysis demonstrates that:

1. β is diagnostic. Each cardiac diagnostic category produces a characteristic β-profile; conduction disturbances show the strongest divergence from healthy controls (Cohen's d = 0.99).
2. β encodes conduction anatomy. A classifier distinguishes complete left from complete right bundle branch block with AUC = 0.982 on PTB-XL (Germany).
3. The result replicates exactly across populations. AUC = 0.982 on Chapman-Shaoxing (China), AUC = 0.979 on CODE-15% (Brazil) — despite factor-of-two variation in absolute β-values across recording equipment.
4. β captures information beyond standard morphology. For CLBBB vs CRBBB classification, QRS duration alone gives AUC = 0.688; β-vector gives AUC = 0.988 (ΔAUC = +0.300).
5. Aging and disease drive β in opposite directions. Healthy aging flattens the spectrum (ρ = −0.179), overt conduction disease steepens it — creating a bifurcation from the healthy operating point.
6. Honest null result. β does not independently predict mortality after full adjustment (HR = 1.02, p = 0.83). It is a diagnostic marker of conduction anatomy, not a prognostic biomarker.

The geometry of the twelve-lead β-vector is determined by conduction system anatomy and is reproducible across equipment, ethnicity, and geography — a cross-population invariant of cardiac electrophysiology.

Datasets

Dataset	Country	N	Sampling Rate
PTB-XL	Germany	21,799	500 Hz
Chapman-Shaoxing	China	45,152	500 Hz
CODE-15%	Brazil	345,779	400 Hz

Repository structure

├── paper/
│   ├── main.tex                        # Preprint manuscript (LaTeX source)
│   ├── main.pdf                        # Compiled preprint
│   ├── cover_letter_elife.tex/pdf      # Cover letter for journal submission
│   └── figures/                        # All publication figures (PDF + PNG)
├── generate_paper_figures.py           # Main analysis: generates Figures 1–5
├── generate_supplementary.py           # Supplementary tables and figures
├── kaggle_notebook.ipynb               # Reproducible analysis notebook
├── criticality_analysis.py             # Core IRASA pipeline (PTB-XL)
├── diagnostic_classification.py        # CD subtype classification
├── niche_analysis.py                   # Subclinical detection + spatial fingerprints
├── aging_analysis.py                   # Aging trajectories + breakpoint analysis
├── external_validation_chapman.py      # Chapman-Shaoxing replication
├── external_validation_code15.py       # CODE-15% replication + mortality
└── results/                            # Cached β-features and intermediate figures
    ├── beta_features.csv               # PTB-XL β-features (all 21,799 records)
    ├── chapman_beta_features.csv       # Chapman β-features
    └── code15_beta_features.csv        # CODE-15% β-features

Reproducing the analysis

# 1. Install dependencies
pip install numpy pandas scipy scikit-learn matplotlib wfdb lifelines

# 2. Download datasets:
#    - PTB-XL → ptb-xl/
#    - Chapman-Shaoxing → chapman-shaoxing/
#    - CODE-15% → code15/

# 3. Extract β-features for PTB-XL (~30 min)
python criticality_analysis.py

# 4. External validations (~1–2 h each)
python external_validation_chapman.py
python external_validation_code15.py

# 5. Generate all paper figures (uses cached features, ~2 min)
python generate_paper_figures.py
python generate_supplementary.py

All key results from the manuscript reproduce exactly — see commit history for verification log.

Citation

If you use this work, please cite the preprint:

Spiro, T. (2026). Spectral Exponents of the Twelve-Lead ECG Reveal the Anatomy of Cardiac Conduction Disorders and a Bifurcation Between Aging and Disease. bioRxiv [DOI to be added after acceptance].

And the archived code release:

Spiro, T. (2026). ecg-spectral-exponents (v1.0.0). Zenodo. https://doi.org/10.5281/zenodo.19945065

Contact

Theodor Spiro — tspiro@vaika.org

License

MIT (see LICENSE)