Advection, diffusion and delivery over a network

TL;DR

This paper introduces an algorithm to precisely compute resource concentration in networks considering advection, diffusion, and delivery, and explores its implications in biological systems like vascular and fungal networks.

Contribution

It presents an exact calculation method for resource transport in networks with loss or delivery, and analyzes biological network models to understand resource distribution mechanisms.

Findings

Increasing blood volume and transporters can decrease glucose delivery rate.

Fungal networks can effectively transport resources without active transport in growth.

Active transport in fungi may be unnecessary for long-range resource movement.

Abstract

Many biological, geophysical and technological systems involve the transport of resource over a network. In this paper we present an algorithm for calculating the exact concentration of resource at any point in space or time, given that the resource in the network is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. We consider the implications of advection, diffusion and delivery for simple models of glucose delivery through a vascular network, and conclude that in certain circumstances, increasing the volume of blood and the number of glucose transporters can actually decrease the total rate of glucose delivery. We also consider the case of empirically determined fungal networks, and analyze the distribution of resource that emerges as such networks grow over time. Fungal growth involves the expansion of fluid filled vessels, which necessarily involves the movement of fluid. In three empirically determined fungal networks we found that the minimum currents consistent with the observed growth would effectively transport resource throughout the network over the time-scale of growth. This suggests that in foraging fungi, the active transport mechanisms observed in the growing tips may not be required for long range transport.