Dynamic method preserves tissue structure for spatial data reconstruction
Dynamic Generalized Gromov-Wasserstein Optimal Transport
Machine LearningArtificial Intelligence
Summary
Matching patterns in complex biological data like tissues requires keeping track of both the layout of the tissue and how gene expressions change over time. Traditional methods handle this matching statically, missing continuous changes. The authors created a new way called TP-DATE that dynamically matches data while respecting tissue structure without needing simulations. Their approach improves the accuracy of reconstructing how tissues change and grow in 3D over time.
What this means in practice
- •For bioinformatics teams: Reconstruct continuous biological tissue dynamics from spatial gene expression data while preserving spatial structure.
- •For medical imaging developers: Improve alignment methods for dynamic 3D imaging data to maintain structural consistency during transformations.
Authors
Junda Ying, Zhiwei Zeng, Peijie Zhou, Lei Zhang
Abstract
Gromov--Wasserstein optimal transport (GW-OT) extends classical optimal transport by introducing structure-aware transport cost. This is particularly relevant for spatial transcriptomics, where dynamical reconstruction should preserve tissue structure in addition to matching expression patterns. While static formulations have been widely used for such structure-aware alignment, a general dynamic formulation for reconstructing continuous trajectories is still missing. We introduce Travelling Pair Dynamical Alignment and Trajectory Estimation (TP-DATE), a theoretical and computational framework to generalize GW-OT dynamically in a simulation-free manner. We formulate a broad class of static and dynamic Quadratic-form OT (QOT) through path actions and prove the static dynamic equivalence. We further develop travelling-pair flow matching, which allows interacting conditional paths and marginalizes their interactions into a single vector field. On synthetic and real spatial transcriptomics data, TP-DATE better preserves spatial structure and improves continuous 3D dynamics reconstruction.