Meeting Abstract
The architecture of fluid transport systems has been well studied in many organisms. Diverse groups across taxa have evolved network geometries that tend toward the minimization of energy loss in fluid transport. Three basic principles apply to these networks: (1) transfer processes must occur over short spatial distances; (2) large and small vessels must be used for bulk flow and exchange sites, respectively; and (3) flow velocities must be limited across transfer sites. Optimal branching design is sometimes reflected in Murray’s law, which states that for laminar flow at any branch point, the radius of the parent vessel cubed equals the sum of the cubes of the radii (x=3) of the daughter vessels. This relationship balances forcing flow against the fluid’s viscosity with the costs of building and maintaining the system. Murray’s law has been found in networks such as mammalian circulatory vessels and the canal system in some species of sponges; however, Murray’s law has not yet been studied in the tracheal network of insects. Here, we utilized synchrotron microtomography of the beetle, Platynus decentis, a species that uses convective airflow to augment gas exchange. Tomographic data were obtained at the Advanced Photon Source at Argonne National Laboratory at beamline 2-BM. 3D segmentation and measurement of tracheal tubes with 16-20 µm diameters were performed using Avizo software. We identified tube branch points and measured the effective radii of both the parent and daughter vessels. Preliminary analysis suggests that Murray’s law does not apply in the tracheal system of this beetle species. Further analysis indicated that a diffusion-based design provided a better a fit, with an average exponent of approximately x=1.8. Supported by NSF 0938047.
