Abstract
This paper presents a description of the procedure for building a structured model of a complex pharmacokinetic system on using its transfer function. The example employed is that of the pharmacokinetic system based on gentamicin plasma concentrations after intravenous and intratracheal administration to guinea pigs, describing the pathway of the drug into the systemic circulation after the extravascular injection mentioned. The structured model selected consisted of a submodel of a proportional linear subsystem, two submodels of simple linear dynamic subsystems with time constants of 0.135±0.065 hr (95% I.C.) and 0.052±0.288 hr, submodels of parallel subsystems with time delays of 0.254±0.046 hr and 1.135±0.288 hr, connected in serial. Two estimates of the mean residence time of the total amount of gentamicin in the system, i.e. 0.347 and 0.335 hr, were obtained, based on the system frequency and structured model, respectively. From the methodological point of view, our paper demonstrates the efficiency of combination of modelling in the frequency and in the time domain, designed to facilitate studies of pharmacokinetic systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akaike, H. 1976. Canonical correlation analysis of time series and the use of an information criterion. InSystem Identification; Advances and Case Studies, R. K. Mehera and D. G. Lainiotis (Eds), pp. 27–93. London: Academic Press.
Dedík, L. and M. Ďurišová. 1994. Frequency response method in pharmacokinetics.J. Pharmacokin. Biopharm. 22, 293–307.
Dedík, L. and M. Ďurišová. 1995. CXT—A programme for analysis of linear dynamic systems in the frequency domain.Int. J. Bio-Med. Comput., accepted.
Ďurišová, M. and L. Dedík. 1994. Comparative study of human pentacaine pharmacokinetics in time and frequency domain.Meth. Find. Exp. Clin. Pharmacol. 16, 219–232.
Levy, E. C. 1959. Complex curve fitting.IRE Trans. Automat. Contr. 4, 37–43.
Padè, H. 1892. Sur la representation approchée d'une function par des fraction rationelles.Ann. de l'Ecole Normale. 9, 1–93.
Schoukens, J. and R. Pintelon. 1991.Identification of Linear Systems. A Practical Guide for Accurate Modelling. London: Pergamon Press.
Singh, M. G. 1987.Systems and Control Encyclopedia, Theory, Technology, Application. Oxford: Pergamon Press.
Trnovec, T., M. Ďurišová, Z. Kállay, J. Navarová, O. Tomčíková, M. Kettner, F. Faltus and M. Erichleb. 1984. Pharmacokinetics of gentamicin administered intratracheally or as an inhalation aerosol to guinea pigs.Drug Metab. Disp. 12, 641–644.
Wagner, J. G. 1975. Do you need a pharmacokinetic model, and, if so which one?J. Pharmacokin. Biopharm. 3, 457–478.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ďurišová, M., Dedík, L. & Balan, M. Building a structured model of a complex pharmacokinetic system with time delays. Bltn Mathcal Biology 57, 787–808 (1995). https://doi.org/10.1007/BF02458295
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02458295