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Further considerations in a theoretical description of gas transport in lung airways

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Abstract

A discrete one-dimensional model of convection-diffusion in branching alveolar ducts is described and it is shown that, for a suitable choice of effective axial dispersion, the solution closely approximates that for an axially symmetric representation, at least for Peclet numbers Pe<1. Following earlier work a composite model of a uniform lung is formed by matching such a respiratory pathway (now having the more convenient one-dimensional form) onto a trumpet representation of the conducting airways. Enhanced mixing due to heart action, and isotropic volume changes of trumpet (in addition to the pathway) during breathing are additional factors included.

Calculations are made of O2 concentrations during steady-state breathing and of the concentration of inert gas during single breath wash-out of a gas mixture containing it. Predicted alveolar levels in each case agree extremely well with published data, although no alveolar slope is obtained for the inert gas.

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Author notes

  1. Malcolm M. Davidson

    Present address: Applied Mathematics and Computing Division, AAEC Research Establishment, Lucas Heights, 2234, Sydney, Australia

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  1. Physiological Flow Studies Unit, Imperial College, London, UK

    Malcolm M. Davidson

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  1. Malcolm M. Davidson
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Davidson, M.M. Further considerations in a theoretical description of gas transport in lung airways. Bltn Mathcal Biology 43, 517–548 (1981). https://doi.org/10.1007/BF02462311

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  • DOI: https://doi.org/10.1007/BF02462311

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