Modeling Full-Scale Leaf Venation Networks

TL;DR

This paper extends hydrodynamic models of leaf venation to enable detailed comparison with real leaf images, providing insights into network formation, sink fluctuations, and scaling laws in reticulate venation.

Contribution

It introduces a method to directly compare hydrodynamic models with full leaf venation images and applies this to estimate sink fluctuations and derive Murray's law exponents.

Findings

Model can be directly compared to leaf images at the vein level.

Estimated sink fluctuation parameter is consistent across species.

Derived exponents for Murray's law in reticulate venation networks.

Abstract

The vascular network of leaves, comprising xylem and phloem, is a highly optimized system for the delivery of water, nutrients, and sugars. The design rules for these naturally occurring networks have been studied since the time of Leonardo da Vinci, who constructed a local rule for comparing the widths of in- and outgoing veins at branch points. Recently, physical models have been developed that seek to explain the full morphogenesis of leaf venial networks in which veins grow in response to local hydrodynamic feedback. Although these models go beyond simple local rules, they are challenging to compare to experimental data. Here, we extend these hydrodynamic models to a state where the direct comparison with images of full leaves becomes possible on the level of individual veins. We present a dataset of the venial networks of leaves that maintain full network topology and use this to discuss the benefits and drawbacks of such a direct comparison. We apply our approach to the direct estimation of a sink fluctuation parameter, demonstrating consistency within distinct leaf species. Finally, we utilize the ability of the model to run on full leaves to define and calculate exponents for a Murray's law that applies to reticulate venation networks.