Mathematical Biosciences and Engineering, 2011, 8(2): 325-354. doi: 10.3934/mbe.2011.8.325

Primary: 92C45, 80A30; Secondary: 34-02.

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A model of competing saturable kinetic processes with application to the pharmacokinetics of the anticancer drug paclitaxel

1. Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2J1
2. Department of Experimental Oncology, Faculty of Medicine and Dentistry, University of Alberta, Edmonton, Alberta, T6G 2J1
3. Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4

A saturable multi-compartment pharmacokinetic model for the anti-cancer drug paclitaxel is proposed based on a meta-analysis of pharmacokinetic data published over the last two decades. We present and classify the results of time series for the drug concentration in the body to uncover the underlying power laws. Two dominant fractional power law exponents were found to characterize the tails of paclitaxel concentration-time curves. Short infusion times led to a power exponent of $-1.57 \pm 0.14$, while long infusion times resulted in tails with roughly twice the exponent. Curves following intermediate infusion times were characterized by two power laws. An initial segment with the larger slope was followed by a long-time tail characterized by the smaller exponent. The area under the curve and the maximum concentration exhibited a power law dependence on dose, both with compatible fractional power exponents. Computer simulations using the proposed model revealed that a two-compartment model with both saturable distribution and elimination can reproduce both the single and crossover power laws. Also, the nonlinear dose-dependence is correlated with the empirical power law tails. The longer the infusion time the better the drug delivery to the tumor compartment is a clinical recommendation we propose.
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