Enhanced precision of tensor electrocardiography through increased cumulative distribution function resolution: Validation in healthy individuals

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Abstract Deep-learning ECG analysis is advancing rapidly but lacks stable, physiologically interpretable indicators to anchor explainable artificial intelligence (AI). Tensor cardiography (TCG) models electrocardiographic (ECG) waveforms as differences between pairs of cumulative distribution functions (CDFs), representing collective myocardial action potential transitions. However, the original 4-CDF model has limitations in fitting P waves and complex QRST patterns. This study aimed to evaluate whether increasing the number of CDFs from 4 to 10 improves TCG fitting accuracy and to characterize normative distributions of 10-CDF parameters in healthy individuals. Participants were recruited through occupational health screening at Tobu Railway Co., Ltd. (n = 415) and from the Nippon Medical School Hospital ECG database (n = 29). Standard 12-lead ECGs from 444 healthy participants, including 345 men and 99 women with a mean age of 46.9 years, were analyzed using TCG software. Reconstruction accuracy was assessed using RMSE, paired t-tests, and Cohen’s d. The 10-CDF model achieved significantly lower RMSE values across all leads than the 4-CDF model, with all p values < 0.0001 and very large effect sizes. In representative leads, RMSEs for the 4-CDF versus 10-CDF models were 0.0256 versus 0.0061 in lead II, 0.0230 versus 0.0063 in lead V1, and 0.0265 versus 0.0062 in lead V5. The coefficient of determination improved from a median of 0.952 with the 4-CDF model to 0.997 with the 10-CDF model in lead II. Parameter dispersion was reduced, suggesting improved estimation stability. Two new parameters, T_mean_diff and RT_mean_duration, were derivable from the expanded model; RT_mean_duration showed significant correlations with age and body surface area. In conclusion, increasing the CDF resolution from 4 to 10 significantly enhanced ECG waveform reconstruction accuracy and parameter stability. These findings provide normative distributions of 10-CDF TCG parameters and may support future explainable AI-based ECG analysis. Author summary Deep-learning approaches have rapidly advanced electrocardiogram (ECG) analysis, but many models function as black boxes with indicators that are difficult for clinicians to interpret. There is a growing need for stable, physiologically meaningful ECG measurements to make artificial intelligence (AI) more explainable. Tensor cardiography (TCG) addresses this need by representing ECG waveforms using cumulative distribution functions (CDFs) based on myocardial electrical activity models, providing interpretable parameters. In this study, we increased the number of CDFs from four to ten to extract more precise quantitative information from ECGs of 444 healthy individuals. The 10-CDF model reconstructed ECG waveforms with substantially greater accuracy than the original 4-CDF model, reducing fitting errors by approximately 75%. We also characterized normative reference distributions for the expanded model and identified two new parameters that capture details of cardiac electrical activity not available in the original 4-CDF model. These findings suggest that the expanded TCG model provides a stable, interpretable framework for future AI-assisted and wearable ECG analysis. By linking waveforms to physiological parameters, TCG may help support earlier and more transparent detection of heart disease.

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