Positional Effects of a Fly’s Wing Vein in the Asymmetric Distribution of Hydraulic Resistances

Abstract

Insect wing vein networks facilitate blood transport with unknown haemodynamic effects on their structures. Fruit flies have the posterior cross vein (PCV) that disrupts the symmetry of the network topology and reduces the total pressure loss during blood transport; however, the impact of its various positions among species has not been examined. This study investigated the haemodynamic effects of this vein with various connecting positions. By analogising venous networks to hydraulic circuits, the flow rates and pressure losses within the veins were derived using Poiseuille’s and Kirchhoff’s laws. The results showed that the total pressure loss decreased for both PCV connections near the wing’s base. In an idealised circuit imitating the network topology, applied high hydraulic resistances as one-sided as those along the edge of the wing, the same pressure loss response as that in the actual network was demonstrated, but not within a symmetric resistance distribution. Therefore, the most proximal PCV minimises the pressure loss within the asymmetric resistance distribution, indicating an evolutionary adaptation to reducing the pressure loss in certain species with this vein near the base. Our findings highlight the possible optimisation of the flies’ wing morphology to maintain the functions of the liquid transport networks and flight devices simultaneously.

Keywords

• insect wing veins
• blood flow
• pipe network
• fluid mechanics
• hydraulic resistance
• network topology