CardioODE-Track: Learning Bidirectional Cardiac Motion With Neural ODEs.

Accurate and temporally consistent cardiac motion tracking from dynamic imaging sequences is essential for quantitative functional assessment and disease analysis. However, existing learning-based approaches often struggle to preserve temporal coherence over long sequences and rarely exploit the intrinsic temporal structure of cardiac motion. In this article, we propose CardioODE-Track, a unified unsupervised framework for cardiac motion tracking. The framework first employs a frame-aware U-Net to estimate initial interframe (INF) motion fields, which are subsequently refined via continuous-time deformation modeling using neural ordinary differential equations (ODEs). This formulation enables smooth and incremental motion evolution across adjacent frames. To further enforce long-range temporal coherence, we introduce a bidirectional Lagrangian motion formulation that jointly estimates forward and backward motion flows under a bidirectional consistency constraint, explicitly capturing the temporal symmetry of cardiac deformation. Extensive experiments on the ACDC, M&Ms, and CAMUS datasets demonstrate that CardioODE-Track achieves more accurate, stable, and physiologically consistent cardiac motion tracking than state-of-the-art methods across imaging modalities. Code is available at https://github.com/ZhuCY1001/CardioODE-Track.