Topological Analysis of Multi-Network Threading in the Pancreas

Abstract The pancreas is a complex inner organ that develops through the concurrent formation of multiple interacting biological networks, but the geometric principles governing their spatial organization remain poorly understood. Here, we study pancreatic development by analysing loop structures in ductal, neuronal, and vascular networks using tools from topological data analysis. In particular, we employ the application of chromatic persistence, which is designed to detect topological interactions between distinct subsets of a structure; this is used to quantify how loops from different networks become spatially entangled. Our analysis reveals distinct developmental timelines for loop formation, progressive entanglement between ducts and vasculature, and spatial concentration of threading toward the organ interior, providing a geometric characterisation of coordinated network development in the pancreas.