Is the lung an optimal gas exchanger? (original) (raw)

We investigate gas transport and exchange in a model of the mammalian lung, from the perspective of thermodynamic optimization (second law energy efficiency). This approach to modeling the structure-function relation of the lung exploits the analogy between the respiratory organs and a chemical membrane reactor, and reveals that the design of the lung may be optimal for its function. We use methods from irreversible thermodynamics to give approximate expressions for the entropy production rate in the lung, and a variational approach to minimize the rate under meaningful functional constraints. The large-scale bronchial tree and small-scale alveolar sponge are modeled separately, to account for the different nature of mass-transport at the two scales (pressure-driven flow and diffusion, respectively). We prove that maximum energy efficiency requires equipartition of thermodynamic forces: pressure drop must be uniformly distributed across all the branches of the bronchial tree, and oxygen concentration drop must be uniformly distributed over the lung membrane. We show that the fractal-like architecture of the lung, the particular size of the gas-exchange units, and the subtle interplay between the airway tree and its vascular network are highly compatible with these requirements of equipartition.