Dimensionality reduction in soft, adaptive flow networks

Biological flow networks—such as the arterial and venous circulation, the lymphatic system, and the gastrovascular canals of jellyfish—are inherently soft structures whose function emerges from strong fluid–structure interactions. Due to the large scale and geometric complexity of these networks, modeling them in full using computational fluid dynamics (CFD) quickly becomes impractical. In this work, we present recent efforts to dimensionally reduce the problem of flow in networks of soft, deformable vessels to a tractable set of equations that retain the essential physics. We show how the dynamics of soft tubes actuated by either a centralized pump (as in the heart) or distributed peristaltic motion (as in the lymphatic system and jellyfish) can be captured through simplified continuum or lumped-parameter models. These reduced descriptions reproduce key experimental behaviors and yield analytically solvable limits that lead to testable, and often counterintuitive, predictions. Our frameworks offer bridges between complex, fully resolved simulations and minimal models that reveal the fundamental physical principles governing transport in soft biological networks.