Journal of Pharmacokinetics and Biopharmaceutics

, Volume 26, Issue 6, pp 649–672 | Cite as

Diffusion-Limited, but Not Perfusion-Limited, Compartmental Models Describe Cerebral Nitrous Oxide Kinetics at High and Low Cerebral Blood Flows

  • David J. Doolette
  • Richard N. Upton
  • Cliff Grant


This study aimed to evaluate the relative importance of diffusion-limited vs. perfusion-limited mechanisms in compartmental models of blood–tissue inert gas exchange in the brain. Nitrous oxide concentrations in arterial and brain efferent blood were determined using gas chromatographic analysis during and after 15 min of nitrous oxide inhalation, at separate low and high steady states of cerebral blood flow (CBF) in five sheep under halothane anesthesia. Parameters and model selection criteria of various perfusion- or diffusion-limited structural models of the brain were estimated by simultaneous fitting of the models to the mean observed brain effluent nitrous oxide concentration for both blood flow states. Perfusion-limited models returned precise, credible estimates of apparent brain volume but fit the low CBF data poorly. Diffusion-limited models provided better overall fit of the data, which was best described by exchange of nitrous oxide between a perfusion-limited brain compartment and an unperfused compartment. In individual animals, during the low CBF state, nitrous oxide kinetics displayed either fast, perfusion-limited behavior or slow, diffusion-limited behavior. This variability was exemplified in the different parameter estimates of the diffusion limited models fitted to the individual animal data sets. Results suggest that a diffusion limitation contributes to cerebral nitrous oxide kinetics.

inert gas perfusion diffusion sheep numerical solution of differential equations 


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  1. 1.
    S. S. Kety. The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev. 3:1–40 (1951).PubMedGoogle Scholar
  2. 2.
    Y. Ohta and L. E. Farhi. Cerebral gas exchange: perfusion and diffusion limitations. J. Appl. Physiol. 46:1164–1168 (1979).PubMedGoogle Scholar
  3. 3.
    S. S. Kety, M. H. Harmell, H. T. Broomell, and C. B. Rhode. The solubility of nitrous oxide in blood and brain. J. Biol. Chem. 173:487–496 (1948).PubMedGoogle Scholar
  4. 4.
    N. A. Lassen and A. Klee. Cerebral blood flow determination by saturation and desaturation with krypton. Circ. Res. 16:26–32 (1965).PubMedCrossRefGoogle Scholar
  5. 5.
    R. N. Upton, C. Grant, and G. L. Ludbrook. An ultrasonic doppler venous outflow method for the continuous measurement of cerebral blood flow in conscious sheep. J. Cerebral Blood Flow Metab. 14:680–688 (1994).CrossRefGoogle Scholar
  6. 6.
    W. B. Runciman, A. H. Ilsley, L. E. Mather, R. J. Carapetis, and M. M. Rao. A sheep preparation for studying interactions between blood flow and drug disposition. I: Physiological profile. Br. J. Anaesth. 56:1015–1028 (1984).PubMedCrossRefGoogle Scholar
  7. 7.
    M. J. Molloy, I. P. Latto, and M. Rosen. Analysis of nitrous oxide concentrations in whole blood. Br. J. Anaesth. 45:556–562 (1973).PubMedCrossRefGoogle Scholar
  8. 8.
    G. D. Byrne, A. C. Hindmarsh, K. R. Jackson, and H. G. Brown. A comparison of two ODE codes: GEAR and EPISODE. Comput. Chem. Eng. 1:133–147 (1977).CrossRefGoogle Scholar
  9. 9.
    B. S. Garbow, G. Giunta, J. N. Lyness, and A. Murli. Software for an implementation of Weeks' method for the inverse Laplace transform problem. Assoc. Comput. Mach. Trans. Math. Software 14:163–170 (1988).CrossRefGoogle Scholar
  10. 10.
    J. G. Wagner. Pharmacokinetics for the Pharmaceutical Scientist, Technomic Publishing, Lancaster, 1993, pp. 293–298.Google Scholar
  11. 11.
    P. Ebinger. Quantitative investigation of visual brain structures in wild and domestic sheep. Anat. Embryol. (Berlin) 146:313–323 (1975).CrossRefGoogle Scholar
  12. 12.
    H. M. Duvernoy, S. Delon, and J. L. Vannson. Cortical blood vessels of the human brain. Brain Res. Bull. 7:529–579 (1981).CrossRefGoogle Scholar
  13. 13.
    P. Brodersen, P. Sejrsen, and N. A. Lassen. Diffusion bypass of xenon in brain circulation. Circ. Res. 32:363–369 (1973).PubMedCrossRefGoogle Scholar
  14. 14.
    H. R. Weiss. Measurement of cerebral capillary perfusion with a fluorescent label. Microvasc. Res. 36:172–180 (1988).PubMedCrossRefGoogle Scholar
  15. 15.
    M. Anwar, J. Weiss, and H. R. Weiss. Quantitative determination of morphometric indices of the total and perfused capillary network of the newborn pig brain. Pediatr. Res. 32:542–546 (1992).PubMedCrossRefGoogle Scholar
  16. 16.
    M. F. Morales and R. E. Smith. On the theory of blood-tissue exchange of inert gases: VI. Validity of approximate uptake expressions. Bull. Math. Biophysics 10:191–200 (1948).CrossRefGoogle Scholar
  17. 17.
    P. Scheid, M. Meyer, and J. Piiper. Elements for modeling inert gas washout from heterogeneous tissues. Adv. Exp. Med. Biol. 180:65–72 (1984).PubMedCrossRefGoogle Scholar
  18. 18.
    J. Piiper and P. Scheid. Model for capillary-alveolar equilibration with special reference to O2 uptake in hypoxia. Resp. Physiol. 46:193–208 (1984).CrossRefGoogle Scholar
  19. 19.
    J. L. Atkinson, R. E. Anderson, and T. M. J. Sundt. The effect of carbon dioxide on the diameter of brain capillaries. Brain Res. 517:333–340 (1990).PubMedCrossRefGoogle Scholar
  20. 20.
    P. L. Altman and D. S. Dittmer. Respiration and Circulation, Federation of American Societies for Experimental Biology, Bethesda, MD, 1971.Google Scholar
  21. 21.
    J. B. Bassingthwaighte and C. A. Goresky. In R. M. Berne and N. Sperelakis (eds.), Section 2: The Cardiovascular System, Handbook of Physiology, 4, Part 1, American Physiological Society, Bethesda, MD, 1984, pp. 549–626.Google Scholar
  22. 22.
    E. D. F. Motti, H.-G. Imhof, and M. G. Yasargil. The terminal vascular bed in the superficial cortex of the rat. J. Neurosurg. 65:834–846 (1986).PubMedCrossRefGoogle Scholar
  23. 23.
    R. Abounader, J. Vogel, and W. Kuschinsky. Patterns of capillary plasma perfusion in brains in conscious rats during normocapnia and hypercapnia. Circ. Res. 76:120–126 (1995).PubMedCrossRefGoogle Scholar
  24. 24.
    A. Villringer, A. Them, U. Lindauer, K. Einhaupl, and U. Dirnagl. Capillary perfusion of the rat brain cortex. An in vivo confocal microscopy study. Circ. Res. 75:55–62 (1994).PubMedCrossRefGoogle Scholar
  25. 25.
    T. Lango, T. Morland, and A. O. Brubakk. Diffusion coefficients and solubility coefficients for gases in biological fluids: a review. Undersea Hyperb. Med. 23:247–272 (1996).PubMedGoogle Scholar
  26. 26.
    L. D. Homer and P. K. Weathersby. How well mixed is inert gas in tissues? J. Appl. Physiol. 60:2079–2088 (1986).PubMedGoogle Scholar
  27. 27.
    S. Bjorkman, D. R. Stanski, H. Harashima, R. Dowrie, S. R. Harapat, D. R. Wada, and W. F. Ebling. Tissue distribution of fentanyl and alfentanil in the rat cannot be described by a flow limited model. J. Pharmacokin. Biopharm. 21:255–279 (1993).CrossRefGoogle Scholar
  28. 28.
    T. Kawashiro, A. C. Carles, S. F. Perry, and J. Piiper. Diffusivity of various inert gases in rat skeletal muscle. Pflügers Arch. 359:219–230 (1975).PubMedCrossRefGoogle Scholar
  29. 29.
    M. Weiss. Moments of physiological transit time distributions and the time course of drug disposition in the body. J. Math. Biol. 15:305–318 (1982).PubMedCrossRefGoogle Scholar
  30. 30.
    M. S. Roberts and M. Rowland. A dispersion model of hepatic elimination: 1. Formulation of the model and bolus considerations. J. Pharmacokin. Biopharm. 14:227–260 (1986).CrossRefGoogle Scholar
  31. 31.
    M. Weiss and M. S. Roberts. Tissue distribution kinetics as determinant of transit time dispersion of drugs in organs: Application of a stochastic model to the rat hindlimb. J. Pharmacokin. Biopharm. 24:173–196 (1996).CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • David J. Doolette
    • 1
  • Richard N. Upton
    • 1
  • Cliff Grant
    • 1
  1. 1.Department of Anaesthesia and Intensive CareThe University of AdelaideAdelaideAustralia

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