Physiological-model-based neural network for modeling the metabolic–heart rate relationship during physical activities

Background and Objective: Heart failure (HF) poses a significant global health challenge, with early detection offering opportunities for improved outcomes. Abnormalities in heart rate (HR), particularly during daily activities, may serve as early indicators of HF risk. However, existing HR monitoring tools for HF detection are limited by their reliability on population-based averages. The estimation of individualized HR serves as a dynamic digital twin, enabling precise tracking of cardiac health biomarkers. Methods: This study introduces a novel physiological-model-based neural network (PMB-NN) framework to model the oxygen uptake ( V ̇ O 2 )-HR relationship during physical activities, establishing a physiology-grounded intermediate module for future daily life HR estimation from body movement signals. PMB-NN embeds physiological constraints, derived from our proposed simplified metabolic-HR physiological model (PM), into the neural network training process. The framework was trained and tested on individual datasets from 25 participants engaged in activities including resting, cycling, and running. HR estimation performance was evaluated for PMB-NN, comparing with benchmark fully connected neural network (FCNN) and PM, across three dimensions: numerical accuracy, physiological plausibility, and physiological interpretability. Furthermore, sensitivity analysis was conducted to verify the model’s robustness against input uncertainty. Results: The PMB-NN model adheres to human physiological principles while achieving high estimation accuracy, with median R 2 score of 0.88, RMSE of 9.96 bpm and MAE of 8.87 bpm, even in the presence of intermittent data. Comparative statistical analysis demonstrates that the PMB-NN achieves performance on par with FCNN while significantly outperforming PM ( p < 0 . 001 ). Meanwhile, PMB-NN reaches higher plausibility for HR- V ̇ O 2 coupling ( ρ = 1) than both FCNN (p = 0.028) and PM ( p < 0 . 001 ). Furthermore, PMB-NN is adept at identifying personalized parameters of the PM, enabling reasonable HR reconstruction. Sensitivity analysis reveals that PMB-NN yields an RMSE within 15 bpm despite input uncertainties of up to 20% Gaussian noise, 4% outliers, and an 18 s time lag. Conclusion: This study confirms the validity of the PMB-NN framework using precise metabolic inputs. This foundational validation enables future integration with wearable-based V ̇ O 2 estimation systems, ultimately paving the way for personalized, real-time cardiac monitoring during daily life physical activities to enhance HF risk detection.