Adaptive Node Positioning in Biological Transport Networks

TL;DR

This paper introduces a generalized hydrodynamic graph model that optimizes both node positions and edge widths, leading to more efficient and realistic biological transport networks, with insights into their formation and phase transitions.

Contribution

It extends existing models by allowing node position optimization using differentiable physics, improving the realism and efficiency of simulated biological networks.

Findings

Organic networks adapt to boundary irregularities and node misalignments.

A phase transition occurs where networks collapse below a critical conductivity threshold.

The model provides insights into early biological system formation.

Abstract

Biological transport networks are highly optimized structures that ensure power-efficient distribution of fluids across various domains, including animal vasculature and plant venation. Theoretically, these networks can be described as space-embedded graphs, and rich structures that align well with observations emerge from optimizing their hydrodynamic energy dissipation. Studies on these models typically use regular grids and focus solely on edge width optimization. Here, we present a generalization of the hydrodynamic graph model which permits additional optimization of node positioning. We achieve this by defining sink regions, accounting for the energy dissipation of delivery within these areas, and optimizing by means of differentiable physics. In the context of leaf venation patterns, our method results in organic networks that adapt to irregularities of boundaries and node misalignment, as well as overall improved efficiency. We study the dependency of the emergent network structures on the capillary delivery conductivity and identify a phase transition in which the network collapses below a critical threshold. Our findings provide insights into the early formation of biological systems and the efficient construction of transport networks.