Abstract
It is shown that the equation of inert gas uptake by a distinct parallel tissue-blood arrangement coincides, under certain conditions, with two formulations which neglect the possible existence of a blood-tissue barrier. The first of these approximations is the classic von Schrötter equation in continuous form, whereas the second is the empirical one frequently used by contemporary authors. The condition for coincidence is that the product of permeability and blood-tissue exchange surface greatly exceed the rate of blood flow to the tissue. It is difficult to examine this condition at present because of a dearth of gas permeability measurement and because apparently there exist no measurements of surface and flow on the same tissue. A compilation is made of such values as are available, and it is found that on the assumption that gas permeabilities are of the order of 1×10−3 cm sec−1, the conditions for neglecting the blood-tissue barrier may be met in many cases and certainly not met in many others. It is concluded that under these circumstances the more exact equations, taking into account the barrier, should be employed, at least until precise independent measurements justifying the approximations become available.
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Literature
Best, C. H., and Taylor, N. B. 1945.The Physiological Basis of Medical Practice. Baltimore: Williams and Wilkins.
Boycott, A. E., Damant, G. C. C., and Haldane, J. S. 1908. “The Prevention of Compressed Air Illness”,Jour. Hyg.,8, 343.
Gersh, I. and Still, M. A. 1945. “Blood Vessels in Fat Tissue. Relation to Problems of Gas Exchange”,Jour. Exp. Med.,81, 219–232.
Henderson, Y., and Haggard, H. W. 1943.Noxious Gases and the Principles of Respiration Influencing their Action. New York: Reinhold.
Holm-Jensen, J., Krogh, A., and Wartiovaara, V. 1944. “Some Experiments on the Exchange of Potassium and Sodium between Single Cells of Characeae and the Bathing Fluid.”Acta Bot. Fenn.,34, 3–22.
Krogh, A., 1936.The Anatomy and Physiology of Capillaries. New Haven: Yale University Press.
Morales, M. F., and Smith, R. E. 1944. “On the Theory of Blood-Tissue Exchanges: III. Circulation and Inert Gas Exchange at the Lung, with Special Reference to Saturation.”Bull. Math. Biophysics,6, 141–152.
Morales, M. F., and Smith, R. E., 1945a. “A Note on the Physiological Arrangement of Tissues.”Bull. Math. Biophysics,7, 47–51.
Morales, M. F. and Smith, R. E., 1945b. “The Physiological Factors which Govern Inert Gas Exchange.”Bull. Math. Biophysics,7, 99–106.
Sjöstrand, T. 1935. “On the Principles for Distribution of Blood in the Peripheral Vascular System.”Skand. Arch. Physiol.,71, 85–122.
Smith, R. E., and Morales, M. F. 1944a. “On the Theory of Blood-Tissue Exchanges: I. Fundamental Equations.”Bull. Math. Biophysics,6, 125–131.
Smith, R. E., and Morales, M. F., 1944b. “On the Theory of Blood-Tissue Exchanges: II. Applications.”Bull. Math. Biophysics,6, 133–139.
von Schrötter, H. 1906. “Der Sauerstoff in der Prophylaxe und Therapie der Luftdruckerkrankungen.” in Michaelis, M.,Handbuch der Sauerstofftherapie. Berlin: V. A. Hirschwald.
Teorell, T. 1937. “Kinetics of Distribution of Substances Administered to the Body. I. The Extravascular Modes of Aministration.”Arch. Internat. de Pharmacod,57, 205–224.
Teorell, T. 1937. “Kinetics of Distribution of Substances Administered to the Body. II. The Intravascular Modes of Administration.”Arch. Internat. de Pharmacod,57, 226–240.
Wartiovaara, V. 1944. “The Permeability oftolypellopsis Cells for Heavy Water and Methyl Alcohol.”Acta Bot. Fenn.,34, 3–22.
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Morales, M.F., Smith, R.E. On the theory of blood-tissue exchange of inert gases: VI. Validity of approximate uptake expressions. Bulletin of Mathematical Biophysics 10, 191–200 (1948). https://doi.org/10.1007/BF02477493
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DOI: https://doi.org/10.1007/BF02477493