Modeling full-scale leaf venation networks

by Lars Erik J. Skjegstad, Julius B. Kirkegaard

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.