Mathematical model of a 12-lead electrocardiograms accounting for spatial dependencies

This article presents an innovative mathematical model for generating 12-lead electrocardiograms (ECG), based on a fundamentally novel approach to accounting for spatial dependencies between leads. The primary scientific contribution of this research lies in the development of a method utilizing linear transformation of a set of physiologically grounded basis signals representing projections of the heart's electric field, supplemented with correlated noise that accurately simulates real clinical interference. Unlike traditional generative models (VAE, GAN, Diffecg), which operate as "black boxes", the proposed model enables explicit control over the morphology of key waveforms (P, QRS, T) and strict adherence to physiological constraints, including Kirchhoff's laws for limb leads. This ensures anatomical consistency of signals across all 12 leads, an achievement not previously attained in similar studies. The model demonstrated high performance on the PhysioNet PTB-XL dataset: MSE = 0.015, cosine similarity = 0.94, F1-score = 0.88 for normal rhythms and 0.82 for arrhythmias. A significant advantage of the model is its computational efficiency (generation time 50 ms) and relatively low memory requirements (2.5 GB). Comparative analysis with contemporary generative models (VAE, GAN, CardioDiff) revealed the superiority of the proposed approach in interpretability, parameter control, and physiological authenticity of synthesized signals. The developed model opens new possibilities for creating high-quality synthetic ECG data essential for training AI-based medical diagnostic systems, as well as for applications in telemedicine and medical education. The integration of physical modeling with machine learning presents particular value for researchers and clinicians requiring interpretable and clinically reliable ECG generation tools.

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