HeartUnloadNet: A cycle-consistent graph network with reduced supervision for predicting unloaded cardiac geometry...

The unloaded cardiac geometry, representing the zero-stress and zero-strain reference state of the heart, is fundamental for personalized biomechanical modeling of cardiac function. However, this state cannot be directly observed in vivo, as clinical imaging only captures pressure-loaded geometries such as those at end-diastole. Traditional inverse finite element solvers are commonly used to reconstruct the unloaded geometry, but they require iterative optimization, are computationally expensive, and may suffer from convergence issues. The objective of this study was to develop an efficient and accurate deep learning framework to predict the unloaded left ventricular geometry directly from clinical end-diastolic states.

We propose HeartUnloadNet, a graph attention-based neural network that incorporates both mesh topology and physiological parameters, including pressure, myocardial stiffness, and fiber orientation. The framework employs a cycle-consistent bidirectional training strategy, allowing reduced supervision by enforcing that the predicted unloaded state can reconstruct the original end-diastolic geometry. The model was trained and validated on 10,350 finite element simulations generated across diverse anatomical shapes and physiological conditions. Performance was evaluated using geometric metrics such as Dice similarity coefficient, Hausdorff distance, mean distance, and standard deviation of nodal errors.

HeartUnloadNet achieved sub-millimeter accuracy, with a Dice similarity coefficient of 0.986 ± 0.023 and a Hausdorff distance of 0.083 ± 0.028 cm. Compared to conventional inverse finite element solvers, the framework was over 100,000 times faster, with an average inference time of 0.02 seconds per case. Ablation studies demonstrated that cycle consistency enabled the model to maintain high accuracy even when only 3% of the training data were labeled. The method consistently outperformed baseline architectures across all evaluation metrics.

HeartUnloadNet provides a scalable and accurate alternative to traditional inverse finite element approaches for estimating the unloaded cardiac geometry. By combining mesh-aware learning with physiological conditioning and reduced supervision, the framework achieves real-time performance while maintaining biomechanical fidelity. This work establishes a foundation for future integration of learning-based surrogates into clinical workflows, supporting patient-specific cardiac modeling and real-time functional assessment.