E52 Tracheal System and Gas Transport

Topic

An insect's tracheal system constitutes the network of tubes that delivers oxygen directly to each of the insect's tissues—entering through spiracles—without requiring a dedicated oxygen-transporting circulatory system; this stands in contrast to hemolymph, which operates based on hydraulic pressure.

Fickian diffusion is the primary transport mechanism within the insect's finest tracheoles; however, within the considerably larger tracheae, convection assisted by the insect's abdominal ventilatory movements may occur.

The Péclet number distinguishes between these two regimes: a low Péclet number indicates that Fickian diffusion dominates over convection, whereas a high Péclet number indicates that convection dominates over diffusion.

Kleiber's scaling law describes how an insect's oxygen consumption scales with its body mass. Consequently, if the insect's body mass is greater, its oxygen consumption is also greater—according to Kleiber's law—though it increases at a lower rate than the mass itself. Consequently, this model—based on the network of tubes delivering oxygen directly to each tissue—uses the steady-state diffusion equation to predict a specific maximum body radius for the insect; beyond this limit, oxygen can no longer diffuse rapidly enough to reach the center of the tissue. This explains why giant Paleozoic insects could exist only when atmospheric oxygen concentrations were significantly higher than today's, and why modern insects remain limited in size. The fact that the available atmospheric oxygen concentration is lower means that the maximum body radius an insect can sustain—as determined by the steady-state diffusion equation concluding this model—is likewise smaller.

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