We present a geometric deep-learning method for reconstructing a temporally continuous mitral valve surface mesh from 3D transesophageal echocardiography sequences. Our approach features a supervised end-to-end deep learning architecture that combines a convolutional neural network-based voxel encoder and decoder with a graph neural network-based multi-resolution mesh decoder, all trained on sparse landmark annotations. Key elements of our methodology include a tube-shaped prototype mesh with labeled vertices, a specialized loss function to preserve the known inlet and outlet, and a rigid alignment system for anatomical landmarks. A custom term in the loss function prevents self-intersecting geometries within the valve mesh, promoting point correspondence and facilitating a continuous representation of valve anatomy over time. An ablation study evaluates the impact of different loss term configurations on model performance, highlighting the effectiveness of each individual loss term. Our Mitral Valve Graph Neural Network (MV-GNN) outperforms existing deep-learning methods on most distance metrics for the annulus and leaflets. The continuous valve motion representations generated by our approach (3D+t) exhibit distance measures comparable to our 3D solution, demonstrating its potential for analyzing mitral valve dynamics and enhancing personalized simulations for hemodynamic assessment and therapy planning.
