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A Dynamical Systems Analysis of the Indirect Response Model with Special Emphasis on Time to Peak Response

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Abstract

In this paper we present a mathematical analysis of the four classical indirect response models. We focus on characteristics such as the evolution of the response R(t) with time t, the time of maximal/minimal response Tmax and the area between the response and the baseline AUC R , and the way these quantities depend on the drug dose, the dynamic parameters such as Emax and EC50 and the ratio of the fractional turnover rate kout to the elimination rate constant k of drug in plasma. We find that depending on the model and on the drug mechanism function, Tmax may increase, decrease, decrease and then increase, or stay the same, as the drug dose is increased. This has important implications for using the shift in Tmax as a diagnostic tool in the selection of an appropriate model

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Authors and Affiliations

  1. Mathematical Institute, Leiden University, PB 9512, 2300, RA, Leiden, The Netherlands

    Lambertus A. Peletier

  2. Centrum voor Wiskunde en Informatica, PB 94079, 1090, GB, Amsterdam, The Netherlands

    Lambertus A. Peletier

  3. DMPK & Bioanalytical Chemistry, AstraZeneca R&D Mölndahl, AP305, S-43183, Mölndahl, Sweden

    Johan Gabrielsson

  4. Wilde Wingerdlaan 22, 2803, WC, Gouda, The Netherlands

    Jacintha den Haag

Authors
  1. Lambertus A. Peletier
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  2. Johan Gabrielsson
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  3. Jacintha den Haag
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Correspondence to Lambertus A. Peletier.

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Peletier, L.A., Gabrielsson, J. & Haag, J.d. A Dynamical Systems Analysis of the Indirect Response Model with Special Emphasis on Time to Peak Response. J Pharmacokinet Pharmacodyn 32, 607–654 (2005). https://doi.org/10.1007/s10928-005-0047-x

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  • DOI: https://doi.org/10.1007/s10928-005-0047-x

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