Imaging Data-based Model Description Combining OptimalTransport and Phase-field Model

The geometrical properties of a cell are not merely passive consequences of cellular function but actively regulate key biological processes during development, morphogenesis, and disease. Although modern live-imaging techniques now allow detailed monitoring of cell morphology, incorporating such complex geometrical information into mathematical models has remained a major challenge. Conventional modeling approaches often rely on artificial cell shape assumptions or purely in silico constructions, and discrete imaging data remain fundamentally mismatched with continuous biochemical models based on differential equations. As a result, current models struggle to accurately reproduce biochemical dynamics within realistic, dynamically changing cell geometries. To overcome these limitations, we establish a novel mathematical framework, Imaging Data-based Model Description (IDMD), which integrates Optimal Transport (OT) theory with phase-field (PF) modeling to bridge imaging data and mathematical models. Using live-imaging data from in vitro cultured cells and the one-cell C. elegans embryo, we demonstrate the versatility of our framework. By directly incorporating real cell geometry into mathematical modeling, our framework provides a powerful new avenue for investigating how geometrical constraints regulate biochemical pattern formation and cell-fate decisions. More broadly, this study highlights a promising direction for integrating modern data science techniques with mathematical modeling, opening new conceptual and methodological possibilities for understanding geometry-driven biological processes in development and disease.