Skip to main content
Log in

Moments of physiological transit time distributions and the time course of drug disposition in the body

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

Characterizing the tissue distribution kinetics of drugs by physiological and physico-chemical parameters and using a circulatory model the time course of blood concentration after intravenous injection is predicted for linear pharmacokinetic systems. The interrelationships between the first three (zero to second) moments of the distribution functions of organ transfer times, circulation times and residence times of drug molecules in the body are described. Utilizing literature data the model is applied to the analysis of lidocain kinetics in humans.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Benet, L. Z., Galeazzi, R. L.: Noncompartmental determination of the steady-state volume of distribution. J. Pharm. Sci. 68, 1071–1074 (1979)

    Google Scholar 

  • Benowitz, N., Forsyth, R. P., Melmon, K. L., Rowland, M.: Lidocaine disposition kinetics in monkey and man. I. Prediction by a perfusion model. Clin. Pharmacol. Ther. 16, 87–98 (1974)

    Google Scholar 

  • Boyes, R. N., Scott, D. B., Jebson, P. J., Godman, M. J., Julian, D. G.: Pharmacokinetics of lidocain in man. Clin. Pharmacol. Ther. 12, 105–116 (1971)

    Google Scholar 

  • Cooney, D. O.: Biomedical engineering principles. New York-Basel: M. Dekker 1976

    Google Scholar 

  • Cutler, D. J.: A linear recirculation model for drug disposition. J. Pharmacokin. Biopharm. 7, 101–116 (1979)

    Google Scholar 

  • Dedrick, R. L.: Animal scale-up. In: Teorell, T., Dedrick, R. L., Condliffe, P. G. (eds.). Pharmacology and pharmacokinetics. New York: Plenum Press 1974

    Google Scholar 

  • Goresky, C. A., Ziegler, W. H., Bach, G. G.: Capillary exchange modeling. Circ. Res. 27, 739–764 (1970)

    Google Scholar 

  • 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)

    Google Scholar 

  • Homer, L. D., Weathersby, P. K.: The variance of the distribution of traversal times in a capillary bed. J. Theoret. Biol. 87, 349–377 (1980)

    Google Scholar 

  • Keilson, J., Kester, A., Waterhouse, C.: A circulatory model for human metabolism. J. Theoret. Biol. 74, 535–547 (1978)

    Google Scholar 

  • Luecke, R. H., Thomason, L. E., Wosilat, W. D.: Physiological flow model for drug elimination in the rat. Comput. Progr. Biomed. 11, 88–98 (1980)

    Google Scholar 

  • Mintun, M., Himmelstein, K. J., Schroder, R. L., Gibaldi, M., Shen, D. D.: Tissue distribution kinetics of tetraethyl-ammonium ion in the rat. J. Pharmacokin. Biopharm. 8, 373–409 (1980)

    Google Scholar 

  • Pang, K. S., Rowland, M.: Hepatic clearance of drugs. I. Theoretical considerations of a “well-stirred” model and a “parallel tube” model. Influence of hepatic blood flow, plasma and blood cell binding, and the hepatocellular enzymatic activity on hepatic drug clearance. J. Pharmacokin. Biopharm. 5, 625–653 (1977)

    Google Scholar 

  • Perl, W.: Stimulus-response method for flows and volumes in slightly perturbed constant parameter system. Bull. Math. Biophys. 33, 225–233 (1971)

    Google Scholar 

  • Rescigno, A.: On transfer times in tracer experiments. J. Theoret. Biol. 39, 9–27 (1973)

    Google Scholar 

  • Rescigno, A., Michels, L. D.: On dispersion in tracer experiments. J. Theoret. Biol. 41, 451–460 (1973)

    Google Scholar 

  • Ricciardi, L. M.: Diffusion processes and related topics in biology. Lecture notes in biomathematics, Vol. 14. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  • Roberts, G. W., Larson, K. B., Spaeth, E. E.: The interpretation of mean transit time measurement for multiphase tissue systems. J. Theoret. Biol. 39, 447–475 (1973)

    Google Scholar 

  • Rowland, M., Benet, L. Z., Graham, G. G.: Clearance concept in pharmacokinetics. J. Pharmacokin. Biopharm. 1, 123–136 (1973)

    Google Scholar 

  • Sheppard, C. W.: Stochastic models for tracer experiments in the circulation. III. The lumped catenary system. J. Theoret. Biol. 33, 491–515 (1971)

    Google Scholar 

  • Tucker, G. T., Boas, R. A.: Pharmacokinetic aspects of intravenous regional anaesthesia. Anaesthesiology 34, 538–549 (1971)

    Google Scholar 

  • Tucker, G. T., Wiklund, L., Berlin-Wahlen, A., Mather, L. E.: Hepatic clearance of local anesthetics in man. J. Pharmacokin. Biopharm. 5, 111–122 (1977)

    Google Scholar 

  • Van Rossum, J. M., Van Ginneken, C. A. M.: Pharmacokinetic systems dynamics. In: Gladtke, E., Heimann, H. (eds.). Pharmacokinetics. Stuttgart-New York: Fischer 1980

    Google Scholar 

  • Vaughan, D. P., Hope, I.: Applications of a recirculatory stochastic pharmacokinetic model: Limitations of compartmental models. J. Pharmacokin. Biopharm. 7, 207–225 (1979)

    Google Scholar 

  • Waterhouse, C., Keilson, J.: Transfer times across the human body. Bull. Math. Biophys. 34, 33–44 (1972)

    Google Scholar 

  • Weiss, M.: Residence time and accumulation of drugs in the body. Int. J. Clin. Pharmacol. 19, 82–85 (1981)

    Google Scholar 

  • Weiss, M., Förster, W.: Pharmacokinetic model based on circulatory transport. Eur. J. Clin. Pharmacol. 16, 287–293 (1979)

    Google Scholar 

  • 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

    Google Scholar 

  • Yamaoka, K., Nakagawa, T., Uno, T.: Statistical moments in pharmacokinetics. J. Pharmacokin. Biopharm. 6, 547–558 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weiss, M. Moments of physiological transit time distributions and the time course of drug disposition in the body. J. Math. Biology 15, 305–318 (1982). https://doi.org/10.1007/BF00275690

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00275690

Key words

Navigation