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Saturable Fractal Pharmacokinetics and Its Applications

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Mathematical Methods and Models in Biomedicine

Abstract

In this chapter we discuss an application of fractal kinetics under steady state conditions to model the enzymatic elimination of a drug from the body. A one-compartment model following fractal Michaelis–Menten kinetics under a steady state is developed and applied to concentration-time data for the cardiac drug mibefradil in dogs. The model predicts a fractal reaction order and a power law asymptotic time-dependence of the drug concentration. A mathematical relationship between the fractal reaction order and the power law exponent is derived. The goodness-of-fit of the model is assessed and compared to that of four other models suggested in the literature. The proposed model provides the best fit to the data. In addition, it correctly predicts the power law shape of the tail of the concentration-time curve. The new fractal reaction order can be explained in terms of the complex geometry of the liver, the organ responsible for eliminating the drug. Furthermore, we investigate the potential for identifying global characteristics in the pharmacokinetics of the anticancer drug paclitaxel. An analysis of data in the literature yields both clearance curves and dose-dependency curves that are accurately described by power laws with similar exponents.

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Authors and Affiliations

  1. Department of Physics, University of Alberta, Edmonton, AB, Canada, T6G 2J1

    Rebeccah E. Marsh & Jack A. Tuszyński

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  1. Rebeccah E. Marsh
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  2. Jack A. Tuszyński
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Correspondence to Jack A. Tuszyński .

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Editors and Affiliations

  1. , Mathematics and Statistics, Southern Illinois University Edwardsvill, Edwardsville, 62026, Illinois, USA

    Urszula Ledzewicz

  2. , Electrical and Systems Engineering, Washington University, Brookings Drive 1, Saint Louis, 63130, Missouri, USA

    Heinz Schättler

  3. Mathematical Biosciences Institute, Ohio State University, W. 18th Avenue 231, Columbus, 43210-1292, Ohio, USA

    Avner Friedman

  4. Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Eugene Kashdan

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Marsh, R.E., Tuszyński, J.A. (2013). Saturable Fractal Pharmacokinetics and Its Applications. In: Ledzewicz, U., Schättler, H., Friedman, A., Kashdan, E. (eds) Mathematical Methods and Models in Biomedicine. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4178-6_12

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