HeartUnloadNet: A Weakly-Supervised Cycle-Consistent Graph Network for Predicting Unloaded Cardiac Geometry from Diastolic States

The unloaded cardiac geometry (i.e., the state of the heart devoid of luminal pressure) serves as a valuable zero-stress and zero-strain reference and is critical for personalized biomechanical modeling of cardiac function, to understand both healthy and diseased physiology and to predict the effects of cardiac interventions. However, estimating the unloaded geometry from clinical images remains a challenging task. Traditional approaches rely on inverse finite element (FE) solvers that require iterative optimization and are computationally expensive. In this work, we introduce HeartUnloadNet, a deep learning framework that predicts the unloaded left ventricular (LV) shape directly from the end diastolic (ED) mesh while explicitly incorporating biophysical priors. The network accepts a mesh of arbitrary size along with physiological parameters such as ED pressure, myocardial stiffness scale, and fiber helix orientation, and outputs the corresponding unloaded mesh. It adopts a graph attention architecture and employs a cycle-consistency strategy to enable bidirectional (loading and unloading) prediction, allowing for partial self-supervision that improves accuracy and reduces the need for large training datasets. Trained and tested on 20,700 FE simulations across diverse LV geometries and physiological conditions, HeartUnloadNet achieves sub-millimeter accuracy, with an average DSC of 0.986 and HD of 0.083 cm, while reducing inference time to just 0.02 seconds per case, over 10^5 times faster and significantly more accurate than traditional inverse FE solvers. Ablation studies confirm the effectiveness of the architecture. Notably, the cycle-consistent design enables the model to maintain a DSC of 97% even with as few as 200 training samples. This work thus presents a scalable and accurate surrogate for inverse FE solvers, supporting real-time clinical applications in the future.