Diffusion-Reaction in Space-Filling Networks: Oxygen Transport in the Lung

1. Introduction The space-filling fractal network in the human lung creates a remarkable distribution system for gas exchange. Landmark studies have demonstrated how the fractal network guarantees minimum energy dissipation [1], slows air down with minimum hardware [2], maximizes the gas-exchange surface area [3], and creates respiratory flexibility between rest and exercise [4]. Here we investigate how the fractal architecture affects oxygen exchange under varying physiological conditions, with respect to performance metrics in terms of diffusive transport, local oxygen currents, and total oxygen current. We present a renormalization calculation of the diffusion current of oxygen across the branched network of acinar airways, from minimal structural and physicochemical data, which describes how oxygen concentrations drop in the airways as oxygen crosses the alveolar membrane system (stationary diffusion-reaction process) [5]. The calculated oxygen currents agree well with measured values. The results exhibit wide-ranging adaptation to changing process parameters, including the ability to rapidly switch from a low oxygen uptake rate at rest to high rates at exercise, and the ability to maintain a constant oxygen uptake rate in the event of a change in permeability or surface area (" surface poisoning ").