Abstract
Designing a dosage regimen for a pharmacokinetic system involves: 1) defining a patient-dependent a priori pharmacokinetic model, which includes structural, parameter, and observation uncertainties, and 2) defining an appropriate performance index to evaluate achievement of a clinically chosen therapeutic goal. The control problem then is to choose the dosage that optimizes the expected value of the performance index relative to the uncertainties present. The problem fits within the framework of “stochastic” control theory, i.e., control in the presence of uncertainty. However, little attention has been paid to this approach in clinical contexts. Most pharmacokinetic investigators have simply attacked the problem first by estimating values of the unknown parameters and then by controlling the system as if those parameter estimates were in fact the true values.
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
Schumitzky A: Adaptive control in drug therapy. In Ducrot H, et al. (eds): Computer aid to drug therapy and to drug monitoring. North-Holland, Amsterdam, 1978.
D’Argenio DZ, Schumitzky A: A program package for simulation and parameter estimation in pharmacokinetic systems. Computer Programs Biomed 9: 115–134, 1979.
Sheiner LB: Analysis of pharmacokinetic data using parameteric models. 1. Regression models. J Pharmacokin Biopharm 12: 93–117, 1984
Brown RF: Compartment system analysis: state of the art. IEEE Trans Biomed Eng BME-27, 1–11, 1980.
Godfrey K: Compartmental models and their application. Academic Press, London, 1983.
D’Argenio DZ: Optimal sampling times for pharmacokinetic experiments. J Pharmacokin Biopharm 9: 739–756, 1981.
Sheiner LB, Halkin H, Peck CP, Rosenberg B, Melmon KL: Improved computer-assisted digoxin therapy. Ann Int Med 82: 619–627, 1975.
Sawchuk RJ, Zaske DE, Cipolle RJ, Wargin WA, Strate RG: Kinetic model for gentamicin dosing with the use of individual patient parameters. Clin Pharmacol Ther 21: 362–369, 1977.
Jelliffe RW: Open-loop-feedback control of serum drug concentrations: pharmacokinetic approaches to drug therapy. Med Instrumen 4: 267–273, 1983.
Gaillot J, Steimer J-LJ, Mallet AJ, Thebault JJ, Bieder A: A priori lithium dosage regimen using population characteristics of pharmacokinetic parameters. J Pharmacokin Biopharm 7: 579–628, 1979.
Richter O, Reinhardt D: Methods for evaluating optimal dosage regimens and their application to theophylline. Int J Clin Pharm Ther Tox 20: 564–575, 1982.
Bard Y: Nonlinear parameter estimation. Academic Press, New York, 1974.
Peck CC, Sheiner LB, Nichols AC: The problem of choosing weights in nonlinear regression analysis of pharmacokinetic data. Drug Metab Rev 15: 133–148, 1984.
Katz D, Azen SP, Schumitzky A: Bayesian approach to the analysis of nonlinear models: implementation and evaluation. Biometrics 37: 137–142, 1981.
Bellman R: Adaptive control processes: a guided tour. Princeton University Press, Princeton, 1961.
Bertsekas DP: Dynamic programming and stochastic control. Academic Press, New York, 1976.
Bar-Shalom Y, Tse E: Concepts and methods in stochastic control. In Leondes CI (ed): Control and dynamic systems, vol. 12. Academic Press, New York, 1976.
Sorenson HW: An overview of filtering and stochastic control in dynamic systems. In Leondes CI (ed): Control and dynamic systems, vol. 12. Academic Press, New York, 1976.
Athans M (ed): Special issue on Linear Quadratic Gaussian problem. IEEE Trans Automatic Control AC-16, 1971.
Powers WF, Abbrecht PH, Covel DG: Systems and microcomputer approach to anticoagulant therapy. IEEE Trans Biomed Eng BME-27: 520–523, 1980.
Athans M, Castanon D, Dunn K, Greene CS, Lee WH, Sandeil NR, Willsky AS: The stochastic control of the F-8C aircraft using a multiple model adaptive control method. IEEE Trans Automatic Control AC-22: 768–780, 1977.
Jazwinski A: Stochastic processes and filtering theory. Academic Press, New York, 1970.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Schumitzky, A. (1986). Stochastic Control of Pharmacokinetic Systems. In: Maronde, R.F. (eds) Topics in Clinical Pharmacology and Therapeutics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4864-4_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4864-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9336-1
Online ISBN: 978-1-4612-4864-4
eBook Packages: Springer Book Archive