Asymmetries arising from the space-filling nature of vascular networks

TL;DR

This paper investigates the structural principles of vascular networks, comparing empirical data with models constrained by biological principles, revealing trade-offs in space-filling strategies that optimize resource delivery.

Contribution

It introduces a numerical method to analyze space-filling strategies in vascular networks and demonstrates how combining biological principles improves model accuracy.

Findings

Empirical data from human and mouse networks show specific structural features.

Models constrained by multiple principles better match real network structures.

Trade-offs between material use and efficiency are critical in network design.

Abstract

Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the capillary level. The structural features of the network that accomplish this density and ubiquity of capillaries are often called space-filling. There are multiple strategies to fill a space, but some strategies do not lead to biologically adaptive structures by requiring too much construction material or space, delivering resources too slowly, or using too much power to move blood through the system. We empirically measure the structure of real networks (18 humans and 1 mouse) and compare these observations with predictions of model networks that are space-filling and constrained by a few guiding biological principles. We devise a numerical method that enables the investigation of space-filling strategies and determination of which biological principles influence network structure. Optimization for only a single principle creates unrealistic networks that represent an extreme limit of the possible structures that could be observed in nature. We first study these extreme limits for two competing principles, minimal total material and minimal path lengths. We combine these two principles and enforce various thresholds for balance in the network hierarchy, which provides a novel approach that highlights the trade-offs faced by biological networks and yields predictions that better match our empirical data.