Frequency response method in pharmacokinetics
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The paper presents the demonstration of applicability of the frequency response method in a bioavailability study. The frequency response method, common in system engineering, is based on an approximation of the frequency response of a linear dynamic system, calculated from input-output measurements, by a frequency model of the system transfer function in the frequency domain. In general, the influence of the system structure on the form of the system frequency response is much more distinct than on the form of the system output. This is of great advantage in modeling the system frequency response instead of the system output, commonly used in pharmacokinetics. After a brief theoretical section, the method is demonstrated on the estimation of the rate and extent of gentamicin bioavailability after intratracheal administration to guinea pigs. The optimal frequency model of the system describing the gentamicin pathway into the systemic circulation and point estimates of its parameters were selected by the approximation of the system frequency response in the frequency domain, using a noniterative algorithm. Two similar estimates of the system weighting function were independently obtained: the weighting function of the selected frequency model and the weighting function estimated by the numerical deconvolution procedure. Neither of the estimates of the weighting function does decrease monotonously after the maximum of about 2.2–2.5 unit of dose·hr−1 recorded approximately 0.1 hr after drug administration. Both estimates show a marked additional peak approximately at 0.3 hr after administration and possible peaks in the further time period. We hypothesized that the loop found in the frequency response calculated and in the selected optimal frequency model, the high-order of this model, and several peaks identified in the estimates of the system weighting function indicated the complexity of the system and the presence of time delays. Three estimates of the extent of gentamicin intratracheal bioavailability obtained by the three different ways: directly from the calculated frequency response, calculated using the selected frequency model, and by the deconvolution method were 0.950, 0.934, and 0.907 respectively. Thus the conclusion can be made that gentamicin injected intratracheally to guinea pigs is almost completely available.
Key Wordslinear dynamic system frequency response frequency response method weighting function bioavailability gentamicin
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- 1.J. Schoukens and P. Pintelon.Identification of Linear Systems. A Practical Guide to Accurate Modeling, 1st ed., Pergamon Press, London, 1991.Google Scholar
- 7.L. Finkelstein and E. R. Carson.Mathematical Modeling of Dynamic and Biological Systems, Research Studies Press, London, 1985.Google Scholar
- 8.J. M. van Rossum, G. Steyger, T. van Uem, G. J. Binkhorst, and R. A. A. Maes. Pharmacokinetics by using mathematical systems dynamics. In J. Eisenfeld and M. Witten (eds.),Modelling of Biomedical Systems, Elsevier, Amsterdam, 1986, pp. 121–126.Google Scholar
- 10.T. Trnovec, M. Ďurišová, Z. Kállay J. Navarová, O. Tomčíková, M. Kettner, F. Faltus, and M. Erichleb. Pharmacokinetics of gentamicin administered intratracheally or as an inhalation aerosol to guinea pigs.Drug Metab. Disp. 12:641–644 (1984).Google Scholar
- 11.H. Padé. Sur la representation approchée d'une function par des fraction rationelles.Ann. Ecole Normale 9:1–93 (1892).Google Scholar
- 13.L. Dedík and M. Ďurišová. Modeling of continuous systems in frequency domain.Kybernet. Informat. (Bratislava) 5:15–20 (1992).Google Scholar
- 14.L. Sachs. Angewandte Statistick. Vergleich einer empirischen Verteilung mit der Normalverteilung.Statistische Methoden und ihre Anwendungen, 5th ed., Springer-Verlag, Berlin, 1978, pp. 252–255.Google Scholar
- 17.T. Söderström and P. Stoica.System Identification, Prentice-Hall, Englewood Cliffs, 1989.Google Scholar