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

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, Canada, Canada

2. 

Department of Experimental Oncology, Faculty of Medicine and Dentistry, University of Alberta, Edmonton, Alberta, T6G 2J1, Canada

3. 

Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada

Received  March 2010 Revised  August 2010 Published  April 2011

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.
Citation: Rebeccah E. Marsh, Jack A. Tuszyński, Michael Sawyer, Kenneth J. E. Vos. A model of competing saturable kinetic processes with application to the pharmacokinetics of the anticancer drug paclitaxel. Mathematical Biosciences & Engineering, 2011, 8 (2) : 325-354. doi: 10.3934/mbe.2011.8.325
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show all references

References:
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D. A. Beard and J. B. Bassingthwaighte, Power-law kinetics of tracer washout from physiological systems,, Ann. Biomed. Eng., 26 (1998), 775. doi: 10.1114/1.105.

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[7]

P. Chelminiak, R. E. Marsh, J. A. Tuszyński, J. M. Dixon and K. J. E. Vos, Asymptotic time dependence in the fractal pharmacokinetics of a two-compartment model,, Phys. Rev. E, 72 (2005), 1.

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[9]

A. Dokoumetzidis and P. Macheras, Fractional pharmacokinetics and pharmacodynamics,, J. of Pharmacokinetics and Pharmacodynamics, 36 (2009), 165. doi: 10.1007/s10928-009-9116-x.

[10]

A. Dokoumetzidis, R. Magin and P. Macheras, A commentary on fractionalization of multi-compartmental models,, J. of Pharmacokinetics and Pharmacodynamics, 37 (2010), 203. doi: 10.1007/s10928-010-9153-5.

[11]

F. Doz, J. C. Gentet, F. Pein, D. Frappaz, P. Chastagner, S. Moretti, G. Vassal, J. Arditti, O. Van Tellingen, A. Iliadis and J. Catalin, Phase I trial and pharmacological study of a 3-hour paclitaxel infusion in children with refractory solid tumors: A SFOP study,, British Journal of Cancer, 84 (2001), 604. doi: 10.1054/bjoc.2000.1637.

[12]

J. Fuite, R. Marsh and J. Tuszyński, Fractal pharmacokinetics of the drug mibefradil in the liver,, Phys. Rev. E, 66 (2002), 1.

[13]

H. Gelderblom, J. Verweij, D. M. van Zomeren, D. Buijs, L. Ouwens, K. Nooter, G. Stoter and A. Sparreboom, Influence of Cremophor EL on the bioavailability of intraperitoneal Paclitaxel,, Clin. Cancer Res., 8 (2002), 1237.

[14]

H. Gelderblom, S. D. Baker, A. Zhao, J. Verwij and A. Sparrreboom, Distribution of paclitaxel in plasma and cerebrospinal fluid,, Anti-cancer drugs, 14 (2003), 365. doi: 10.1097/00001813-200306000-00007.

[15]

K. Gelmon, E. Eisenhauer, C. Bryce, A. Tolcher, L. Mayer, E. Tomlinson, B. Zee, M. Blackstein, E. Tomiak, J. Yau, G. Batist, B. Fisher and J. Iglesias, Randomized phase II study of high-dose paclitaxel with or without amifostine in patients with metastatic breast cancer,, J. Clin. Oncol., 17 (1999), 3038.

[16]

L. Gianni, C. M. Kearns, A. Giani, G. Capri, L. Vigano, A. Lacatelli, G. Bonadonna and M. J. Egorin, Nonlinear pharmacokinetics and metabolism of paclitaxel and its pharmacokinetic/pharmacodynamic relationships in humans,, J. Clin. Oncol., 13 (1995), 180.

[17]

M. Gibaldi and D. Perrier, "Pharmacokinetics,", 2$^{nd}$ edition, (1982).

[18]

K. Gough, M. Hutchinson, O. Keene, B. Byrom, S. Ellis, L. Lacey and J. McKellar, Assessment of dose proportionality: report from the statisticians in the pharmaceutical industry/pharmacokinetics UK joint working party,, Drug Inf. J., 29 (1995), 1039.

[19]

A. Henningsson, M. O. Karlsson, L. Vigano, L. Gianni, J. Verweij and A. Sparreboom, Mechanism-based pharmacokinetic model for paclitaxel,, J. Clin. Oncol., 19 (2001), 4065.

[20]

M. T. Huizing, V. H. Misser, R. C. Pieters, W. W. ten Bokkel Huinink, C. H. Veenhof, J. B. Vermorken, H. M. Pinedo and J. H. Beijnen, Taxanes: A new class of antitumor agents,, Cancer Invest., 13 (1995), 381. doi: 10.3109/07357909509031919.

[21]

J. A. Jacquez, "Compartmental Analysis in Biology and Medicine,", BioMedware, (1996).

[22]

M. A. Jordan, R. J. Toso, D. Thrower and D. L. Wilson, Mechanism of mitotic block and inhibition of cell proliferation by taxol at low concentrations,, Proc. Natl. Acad. Sci. USA, 102 (1993), 9552. doi: 10.1073/pnas.90.20.9552.

[23]

M. A. Jordon and L. Wilson, Taxane Anticancer Agents: Basic Science and Current Status,, in, (1995), 138.

[24]

M. A. Jordan, Mechanism of action of antitumor drugs that interact with microtubules and tubulin,, Curr. Med. Chem. Anti-Canc. Agents, 2 (2002), 1.

[25]

M. O. Karlsson, V. Molnar, A. Freijs, P. Nygren, J. Bergh and R. Larsson, Pharmacokinetic models for the saturable distribution of paclitaxel,, Drug Metab. Dispos., 27 (1999), 1220.

[26]

C. M. Kearns, L. Gianni and M. J. Egorin, Paclitaxel pharmacokinetics and pharmaco-dynamics,, Semin. Oncol., 22 (1995), 16.

[27]

T. Y. Kim, D. W. Kim, J. Y. Chung, S. G. Shin, S. C. Kim, D. S. Heo, N. K. Kim and Y. J. Bang, Phase I and pharmacokinetic study of Genexol-PM, a cremophor-free, polymeric micelle-formulated paclitaxel, in patients with advanced malignancies,, Clin. Cancer Res., 10 (2004), 3708. doi: 10.1158/1078-0432.CCR-03-0655.

[28]

K. Kosmidis, V. Karalis, P. Argyrakis and P. Macheras, Michaelis-Menten kinetics under spatially constrained conditions: Application to mibefradil pharmacokinetics,, Biophys. J., 87 (2004), 1498. doi: 10.1529/biophysj.104.042143.

[29]

M. Lopez-Quintela and J. Casado, Revision of the methodology in enzyme kinetics: A fractal approach,, J. Theor. Biol., 139 (1989), 129. doi: 10.1016/S0022-5193(89)80062-1.

[30]

T. M. Ludden, S. L. Beal and L. B. Sheiner, Comparison of the akaike information criterion, the Schwartz criterion and the F-test as guides to model selection,, J. Pharmacokinet. Biopharm., 22 (1994), 431. doi: 10.1007/BF02353864.

[31]

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