Abstract
Linear compartmental models are being widely used to model pharmacokinetic systems. Most of these models are deterministic and the statistical analysis of such models has been studied extensively. Many deterministic models are illustrated in other papers of this volume, and recent reviews are also given by Gibaldi and Perrier (1982), Godfrey (1983), and Jacquez (1985).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chiang, C. L., 1980. “An Introduction to Stochastic Processes and Their Applications,” Krieger, Huntington, NY.
Cobelli, C., and Toffolo, G., 1985. Compartmental and noncompartmental models as candidate classes for kinetic modeling. Theory and computational aspects, in “Mathematics and Computers in Biomedical Applications,” J. Eisenfeld and C. DeLisi, eds., North-Holland, Amsterdam.
DiStefano, J.J. III, and Landaw, E. M., 1984. Multiexponential, multicompartmental, and noncompartmental modeling. I. Methodological limitations and physiological interpretations, Am. J. Physiol. 246 (Regulatory Integrative Comp. Physiol. 15): R65l.
France, J., Thornley, J. H. M., Dhanoa, M. S., and Siddons, R. C., 1985. On the mathematics of digesta flow kinetics. J. theor. Biol. 113:743.
Gibaldi, M., and Perrier, D., 1982. “Pharmacokinetics,” ed. 2, Marcel Dekker, New York.
Godfrey, K., 1983. “Compartmental Models and Their Applications,” Academic Press, New York.
Gross, A. J., and Clark, V. A., 1975. “Survival Distributions: Reliability Applications in the Biomedical Sciences,” Wiley, New York.
Hughes, T. H. and Matis, J. H., 1984. An irreversible two-compartment model with age-dependent turnover rates, Biometrics. 40:501.
Jacques, J. A., 1985, “Compartmental Analysis in Biology and Medicine,” ed. 2, Univ. of Michigan Press, Ann Arbor, MI.
Johnson, N. L., and Kotz, S., 1970. “Continuous Univariate Distributions - 1.” Wiley, New York.
Kalbfleisch, J. D., Lawless, J. F., and Vollmer, V. M., 1983. Estimation in Markov models from aggregate data, Biometrics. 39:907.
Kodell, R. L., and Matis, J. H., 1976. Estimating the rate constant in a two-compartment stochastic model, Biometrics. 32:377.
Matis, J. H., 1970. Stochastic compartmental analysis: Model and least squares estimation from time series data. Ph.D. Dissertation. Texas A&M University, College Station, TX.
Matis, J. H., 1972. Gamma time-dependency in Blaxter’s compartmental model, Biometrics. 28:597.
Matis, J. H., 1987. The case for stochastic models of digesta flow. J. theor. Biol. 124:371.
Matis, J. H., and Gerald, K. B., 1986. On selecting optimal response variables for detecting treatment effects in a two-compartment model, in “Modelling of Biomedical Systems,” J. Eisenfeld and M. Whitten, eds., North-Holland, Amsterdam.
Matis, J. H., and Hartley, H. O., 1971. Stochastic compartmental analysis: Model and least squares estimation from time series data, Biometrics. 27:77.
Matis, J. H., and Wehrly, T. E., 1984. On the use of residence time moments in the statistical analysis of age-dependent stochastic compartmental systems, in “ Mathematics in Biology and Medicine,” S. L. Paveri-Fontana and V. Capasso, eds., Springer-Verlag, New York.
Matis, J. H., and Wehrly, T. E., 1985. Modeling pharmacokinetic variability on the molecular level with stochastic compartmental systems, in “Variability in Drug Therapy,” M. Rowland, L. B. Sheiner, and J. L. Steiner, eds.. Raven, New York.
Matis, J. H., and Wehrly, T. E., and Gerald, K. B., 1985. Use of residence time moments in compartmental analysis, Am. J. Physiol. 249 (Endocinol. Metab. 12): E409.
Matis, J. H., Wehrly, T. E., and Metzler, C. M., 1983. On some stochastic formulations and related statistical moments of pharmacokinetic models, J. Pharmacokinet. Biopharm. 11:77.
Mehata, K. M., and Selvam, D. D., 1986. A class of general stochastic compartmental systems, Bull. Math. Biol. 48:509.
Metzler, C. M., and Weiner, D. L., 1985. “PCNONLIN User’s Guide.” Statistical Consultants, Lexington, KY.
Purdue, P., 1975. Stochastic theory of one compartment and two compartment systems. Bull. Math. Biol. 36:577.
Rescigno, A., and Segre, G., 1966. “Drug and Tracer Kinetics,” Blaisdell, Waltham, MA.
Rescigno, A., and Matis, J. H., 1981. On the relevance of stochastic compartmental models to pharmacokinetic systems, Bull. Math. Biol. 43:245.
Wagner, J. G., 1971. “Biopharmaceutics and Relevant Pharmacokinetics,” Drug Int., Hamilton, IL.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer Science+Business Media New York
About this chapter
Cite this chapter
Matis, J.H. (1988). An Introduction to Stochastic Compartmental Models in Pharmacokinetics. In: Pecile, A., Rescigno, A. (eds) Pharmacokinetics. NATO ASI Series, vol 145. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5463-5_6
Download citation
DOI: https://doi.org/10.1007/978-1-4684-5463-5_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-5465-9
Online ISBN: 978-1-4684-5463-5
eBook Packages: Springer Book Archive