Abstract
The purpose of this paper is first to show that for efficient diffusive transfer of oxygen to blood, the unit transfer system, namely the lung acinus, should be a space-filling surface with a fractal dimension equal to 3. Second, this unit transfer cell should not be too large. More precisely, the perimeter of a planar cut of the acinus should not be too large as compared with the ratio of the diffusivity of oxygen in air to alveolar membrane permeability. Maximal efficiency then imposes that the lung has to be divided into a large number of small diffusion cells. In exercise conditions the screening effects are decreased as the diffusion source enters more deeply into the structure. This is justified by the study of an “acinus Peclet number” which properly describes the transition zone from ventilation to diffusion inside the acinus. In that situation the oxygen flux is governed by the total acinar surface and the membrane thickness together with physiological limitations. It is shown here that the geometrical membrane diffusion capacityaloneobeys a scaling allometric power law with an exponent 0.9 similar to the exponent found for oxygen consumption at peak aerobic demand. This study shows that the design of the acini of animals of different sizes is such that, under physiological conditions prevailing in exercise, screening is negligible.
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Sapoval, B., Weibel, E.R., Filoche, M. (2002). Diffusion Screening, Acinus Size and Optimal Design of Mammalian Lungs. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8119-7_3
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DOI: https://doi.org/10.1007/978-3-0348-8119-7_3
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