Biological flow networks: Antagonism between hydrodynamic and metabolic stimuli as driver of topological transitions

Abstract

A plethora of computational models have been developed in recent decades to account for the morphogenesis of complex biological fluid networks, such as capillary beds. Contemporary adaptation models are based on optimization schemes where networks react and adapt vessel conductance toward given flow patterns. Recent numeric studies on network morphogenesis, incorporating uptake of metabolites by the embedding tissue, have indicated this conventional approach to be insufficient. Here, we systematically study a hybrid model intended to generate space-filling perfusion as well as optimal filtration of metabolites. As a result, we find hydrodynamic stimuli (wall-shear stress) and filtration based stimuli (uptake of metabolites) to be antagonistic as hydrodynamically optimized systems have suboptimal uptake qualities and vice versa. We show that a switch between optimization regimes is typically accompanied with a transition between topologically redundant meshes and spanning trees. Depending on the metabolite demand and uptake capabilities of the adapting networks, we further demonstrate the existence of nullity reentrance as a function of dissipation and the development of compromised phenotypes such as dangling nonperfused vessels and bottlenecks.