Balancing efficiency and homogeneity of biomaterial transport in networks

¹ Department of Mathematics, Mechanics Division, University of Oslo - N-0851, Oslo, Norway
² Department of Physics, Harvard University - Cambridge, MA 02138, USA
³ Department of Organismic and Evolutionary Biology, Harvard University - Cambridge, MA 02138, USA

^(b) acarlson@math.uio.no (corresponding author)

Received: 8 March 2021
Accepted: 16 August 2021

Abstract

Transport of biomaterial in tubular networks is ubiquitous in nature, where examples include the endoplasmic reticulum, leaf venation or vessel networks in vertebrates. Flow feedback by adjustment of the local tube radius in response to a fluid flow is a pivotal mechanism to optimize the transport properties of a network. To describe liquid transport in tubular networks we develop a minimal mathematical model, which includes the interplay of the viscous flow feedback and the tubes elastic bending energy while conserving the network material. Flow feedback in pitted, branched and loopy networks is shown to lower their resistance, as compared to a feedback-free system, by local adaptations without the need for additional network material. Flow feedback in particular reduces the resistance in pitted and branched networks, directly linked with a reduction in the effective number of neighboring tubes. In loopy networks we find a direction-dependent flow resistance, with a prevailing transport direction set by the network geometry.