Transport in insect respiratory systems

Biological flow networks, present in the vasculature of plants and animals, are a foundational feature of life. The connection between structure and function in these systems is key for understanding their development as well as their ability to adapt to adverse conditions. The problem of how vasculature delivers oxygen to tissues has been studied in many contexts, yet a comprehensive data set to test transport models is lacking due to the inherent complications of imaging a significant portion of living vasculature in full detail. The respiratory system of insects is an ideal model system: its structure can be imaged clearly and entirely because it is relatively simple compared to mammalian vasculature and because it can be tagged with fluorescent protein markers to increase image contrast. In Drosophila melanogaster larvae, the respiratory system is a dense tubular network of hollow channels permeating the body, reaching within microns of each living cell. Oxygen delivery is driven by diffusion: air enters through external openings and fills the channels. Gas exchange occurs primarily in branched tree-like structures known as terminal cells, which have permeable walls allowing oxygen to leak out and become absorbed by the surrounding tissue. We present a model of perfusion-based transport on a network, analyzing the oxygen concentration field predicted by this model when applied to our data set of hundreds of terminal cells. This physical modeling allows us to map the distribution of cellular structures to a distribution of oxygen fluxes that these cells deliver.