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Bulletin of Mathematical Biology

, Volume 39, Issue 5, pp 587–595 | Cite as

Kinetics of isobaric counterdiffusion

  • George Karreman
  • Christian J. Lambertsen
Article

Abstract

Isobaric inert gas counterdiffusion has been demonstrated to produce gas lesions in man (Lambertsen and Idicula, 1975) and lethal gas embolism in animals (Lambertsen, Cunnington and Cowley, 1975). Equations have been derived for the stable-state supersaturation pressures developing at interfaces during inert gas counterdiffusion (Graveset al., 1973). The present analysis is a mathematical treatment of the kinetics of the isobaric counterdiffusion of a pair of gases through a membrane consisting of two layers composed of substances with different diffusion coefficients and solubilities for each of the gases involved. The time to reach the stable supersaturation state due to isobaric counterdiffusion, even when circulatory transport and pulmonary washout times are included, is found to be at least an order of magnitude smaller than the time required for visible bubble formation and tissue distortion.

Keywords

Urticaria Diffusion Profile Diffusion Front Tissue Distortion Circulatory Transport 
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Literature

  1. Graves, D. J., J. Idicula, C. J. Lambertsen and J. A. Quinn. 1973. “Bubble Formation Resulting from Counterdiffusion Supersaturation: A Possible Explanation for Isobaric Inert Gas ‘Urticaria’ and Vertigo.”Phys. Med. Biol.,18, 256–264.CrossRefGoogle Scholar
  2. Lambertsen, C. J., J. P. W. Cunnington and J. R. M. Cowley. 1975. “The Dynamics and Composition of Spontaneous, Continuous Gas Embolism in the Pig during Isobaric Gas Counterdiffusion.”Fedn Proc.,34, 452.Google Scholar
  3. — and J. Idicula, 1975. “A New Gas Lesion Syndrome in Man, Induced by ‘Isobaric Gas Counterdiffusion.”J. Appl. Physiol.,39, 434–443.Google Scholar
  4. Landahl, H. D. 1953. “An Approximation Method for the Solution of Diffusion and Related Problems.”Bull. Math. Biophys.,15, 49–61.MathSciNetGoogle Scholar

Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • George Karreman
    • 1
  • Christian J. Lambertsen
    • 1
  1. 1.Institute for Environmental Medicine, Bockus Research Institute and Department of PhysiologyUniversity of Pennsylvania Medical CenterPhiladelphiaU.S.A.

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