The bulletin of mathematical biophysics

, Volume 6, Issue 3, pp 125–131 | Cite as

On the theory of blood-tissue exchanges: I. Fundamental equations

  • R. E. Smith
  • Ens M. F. Morales H-V (S)


A mathematical analysis of the absorption of an inert gas by a heterogeneous system ofn phases, e.g., a limb consisting ofn tissues, is presented. The total uptake of gas, ϕ(t), up to timet is given in terms of arterial concentration, cardiac delivery, blood volume, and the volume, permeability, and partition coefficient of each tissue. The theory predicts how the uptake curve should change in shape under a variety of physiological conditions, and how from the numerical values of the constants the values of certain tissue constants, e.g. permeabilities, may be obtained.


Partition Coefficient Total Uptake Penetration Rate Numerical Magnitude Uptake Curve 
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  1. Rashevsky, N. 1938.Mathematical Biophysics. University of Chicago Press, Chicago.zbMATHGoogle Scholar
  2. Smith, R. E., and Morales, M. F. 1944. (In press.) “On the Theory of Blood-Tissue Exchanges: II. Applications.”Bull. Math. Biophysics,6, 133.Google Scholar

Copyright information

© The University of Chicago Press 1944

Authors and Affiliations

  • R. E. Smith
    • 1
  • Ens M. F. Morales H-V (S)
    • 1
  1. 1.Naval Medical Research InstituteNational Naval Medical CenterBethesda

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