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We investigate oxygen transport to and across alveolar membranes in the human lung, the last step in the chain of events that takes oxygen through the bronchial airways to the peripheral, acinar airways. This step occurs by diffusion. We carry out analytic and numerical computations of the oxygen current for fractal, space-filling models of the acinus, based on morphological data of the acinus and appropriate values for the transport constants, without adjustable parameters. The computations address the question whether incoming oxygen reaches the entire available membrane surface (reaction-limited, unscreened oxygen current), a large part of the surface (mixed reaction/diffusion-limited, partly screened current), or only the surface near the entrance of the acinus (diffusion-limited, completely screened current). The analytic treatment identifies the three cases as sharply delineated screening regimes and finds that the lung operates in the partial-screening regime, close to the transition to no screening, for respiration at rest; and in the no-screening regime for respiration at exercise. The resulting currents agree well with experimental values. We test the analytic treatment by comparing it with numerical results for two-dimensional acinus models and find very good agreement. The results provide quantitative support for the conclusion, obtained in other work, that the space-filling fractal architecture of the lung is optimal with respect to active membrane surface area and minimum power dissipation. At the level of the bronchial tree, we show that the space-filling architecture provides optimal slowing down of the airflow from convection in the bronchial airways to diffusion in the acinar airways.

Gas Diffusion through the Fractal Landscape of the Lung: How Deep Does Oxygen Enter the Alveolar System?