Generative Flow-Matching Modeling of the Neurodevelopmental Connectome via Dynamic Hypergraphs

Abstract

Human brain structure datasets are regularly small and lack a representative sample of target phenotypes. Augmenting these is often challenging due to highly complex patterns of connectivity, and this issue is particularly emphasized when there are significant target class imbalances. We introduce a model that enables the generation of novel data instances and data exploration. Specifically, we consider the case of preterm birth, where datasets include very few preterm individuals. We present a diffusion-style flow-matching framework, whereby conditioning on continuous gestational age (GA), the model learns the underlying geometry of the brain and can reproduce differences in connectivities for infants born at varying numbers of weeks. This approach is inspired by the brain's fundamental capacity for self-organization. Moreover, to understand the real implications of varying GA on the organization of the developing brain, we integrate a dynamic hypergraph layer. This allows the model to dynamically learn the higher-order dependencies that evolve in the brain, facilitating the generation of biologically plausible structural topologies. To ensure appropriateness and sufficiency in the generated networks, we utilize biologically informed losses. Additionally, we compare the generation with key graph metrics commonly employed in neurobiological studies of brain structure. Our model results demonstrate biologically realistic connectivity patterns discovered through the dynamic hypergraph approach. The code is publicly available at: https://github.com/Katherine-Birch/Generative-Flow-Matching-Modeling-of-the-Neurodevelopmental-Connectome-via-Dynamic-Hypergraphs