A deep cardiac motion field analysis approach via global 2nd-order kinematic graph modeling

Cardiac motion analysis plays a vital role in the diagnosis and treatment of cardiovascular diseases. Existing methods can estimate displacement fields and model spatio-temporal patterns. However, they face two major limitations. First, they primarily focus on trajectory tracking, which fails to fully exploit higher-order kinematic dynamics that correlate with functional and material mechanics. Second, most approaches require solving complex differential equations during training, making them computationally expensive and difficult to converge stably. To overcome these limitations, we propose a mechanics-constrained cardiac motion analysis framework with two key innovations. First, we apply multi-order temporal differentiation on a graph-based cardiac representation. Nodal features capture displacement, velocity and acceleration, providing functional mechanics characterization. Edge features capture deformation, deformation rate and acceleration, providing material mechanics characterization. Second, we compute mechanical features directly on the graph. We employ graph convolutional networks to learn spatio-temporal patterns and use Kolmogorov-Arnold Networks for classification. This approach achieves systematical mechanical modeling with high efficiency and stable convergence. Experiments on private and public cine magnetic resonance imaging (cine-MRI) datasets demonstrate consistent improvements over existing methods in accuracy, interpretability and efficiency, showing the potential of mechanical modeling for cardiac motion analysis.