Abstract
Based on a stochastic pharmacokinetical model (which mirrors topological properties of the circulatory system) it is shown by reinterpreting results of Wise (1974) that if the transit times of circulating drug molecules have a generalized inverse Gaussian distribution the corresponding residence times are gamma distributed. The condition that the probability of elimination of a drug molecule in a single circulatory passage is sufficiently small appears to be valid for most drugs. Thus theoretical evidence is given for fitting blood concentration-time curves following bolus injection of a single dose by power functions of time.
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References
Barndorff-Nielsen, O., Blæsild, P., Halgreen, C.: First hitting time models for the generalized inverse Gaussian distribution. Stoch. Proc. Applic. 7, 49–54 (1978)
Cox, D. R.: Renewal Theory. New York: Wiley 1963
Eisenfeld, J.: Relationship between stochastic and differential models of compartmental systems. Math. Biosci. 43, 289–305 (1979)
Gibaldi, M., Perrier, D.: Pharmacokinetics. New York-Basel: Dekker 1982
Jørgensen, B.: Statistical properties of the generalized inverse Gaussian distribution. Lecture notes in statistics, Vol. 9, New York-Heidelberg-Berlin: Springer 1982
Homer, L. D., Small, A.: A unified theory for estimation of cardiac output, volumes of distribution and renal clearances from indicator dilution curves. J. Theoret. Biol. 64, 535–550 (1977)
Keilson, J., Kester, A., Waterhouse, C.: A circulatory model for human metabolism. J. Theoret. Biol. 74, 535–547 (1978)
Marcus, A. H., Becker, A.: Power laws in compartmental analysis-II. Numerical evaluation of semi-Markov models. Math. Biosci. 35, 27–45 (1977)
Matis, J. H., Wehrly, T. E., Metzler, C. M.: On some stochastic formulations and related statistical moments of pharmacokinetic models. J. Pharmacokin. Biopharm. 11, 77–92 (1983)
Norwich, K. H., Siu, S.: Power functions in physiology and pharmacology. J. Theoret. Biol. 95, 387–398 (1982)
Sheppard, C. W.: Basic principles of the tracer method. New York: Wiley 1962
Tucker, G. T., Jackson, P. R., Storey, G. C. A., Holt, D. W.: Amiodarone disposition: Polyexponential, power and gamma functions. Eur. J. Clin. Pharmacol., in press.
Vaughan, D. P., Hope, I.: Applications of a recirculatory stochastic pharmacokinetic model: Limitations of compartmental models. J. Pharmacokin. Biopharm. 7, 207–225 (1979)
Waterhouse, C., Keilson, J.: Transfer times across the human body. Bull. Math. Biophys. 34, 33–44 (1972)
Weiss, M.: Moments of Physiological transit time distributions and the time course of drug disposition in the body. J. Math. Biol. 15, 305–318 (1982)
Weiss, M.: Importance of tissue distribution in determining drug disposition curves. J. Theoret. Biol. 103, 649–652 (1983a)
Weiss, M.: Modelling of initial distribution of drugs following intravenous bolus injection. Eur. J. Clin. Pharmacol. 23, 121–126 (1983b)
Weiss, M.: Use of gamma distributed residence times in pharmacokinetics. Eur. J. Clin. Pharmacol. 25, 695–702 (1983c)
Weiss, M., Förster, W.: Pharmacokinetic model based on circulatory transport. Eur. J. Clin. Pharmacol. 16, 287–293 (1979)
Wise, M. E.: The evidence against compartments. Biometrics 27, 262 (1971a)
Wise, M. E.: Skew probability curves with negative powers of time and related to random walks in series. Stat. Neerland. 25, 159–180 (1971b)
Wise, M. E.: Interpreting both short and long term power laws in physiological clearance curves. Math. Biosci. 20, 327–337 (1974)
Wise, M. E.: Skew distributions in biomedicine including some with negative powers of time. In: Patil, G. P., Kotz, S., Ord, J. K. (eds.). Statistical distributions in scientific work. Dordrecht: Reidel Publ. Comp. 1975
Wise, M. E.: The need for rethinking on both compartments and modelling. In: Matis, J. H., Patten, B. C., White, G. C. (eds.). Compartmental analysis of ecosystem models. Fairland, Maryland: Int. Co-op. Publ. House 1979.
Wise, M. E., Osborn, S. B., Anderson, J., Tomlinson, R. W. S.: A stochastic model for turnover of radiocalcium based on the observed power laws. Math. Biosci. 2, 199–224 (1968)
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Weiss, M. A note on the rôle of generalized inverse Gaussian distributions of circulatory transit times in pharmacokinetics. J. Math. Biology 20, 95–102 (1984). https://doi.org/10.1007/BF00275864
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DOI: https://doi.org/10.1007/BF00275864