Control-Relevant Modeling of the Antitumor Effects of 9-Nitrocamptothecin in SCID Mice Bearing HT29 Human Colon Xenografts

  • John M. Harrold
  • Julie L. Eiseman
  • Erin Joseph
  • Sandra Strychor
  • William C. Zamboni
  • Robert S. Parker


The mathematical model structure selected to describe system behavior is at least partially dependent on the proposed use of the model. In this paper, a pharmacokinetic(PK)/pharmacodynamic (PD) model for use in drug delivery algorithm synthesis is developed. The antitumor agent 9-nitrocamptothecin (9NC) was administered orally to severe combined immunodeficient (SCID) mice bearing subcutaneously implanted HT29 human colon xenografts, and the effect of 9NC on those xenografts was characterized. Different PK model structures were considered in characterizing the dynamics of the drug concentration in the plasma. Akaike’s Information Criterion (AIC) was used to select the model structure maximizing fit accuracy while simultaneously minimizing the number of model parameters. The resulting PK model was a set of coupled linear ordinary differential equations able to describe the nonlinear dynamic behavior (e.g. plateauing, etc.) of the drug concentrations observed in the plasma. Pharmacodynamics were modeled by characterizing tumor growth in both the untreated and drug-treated animals. The resulting PK/PD model related drug administration to effect, and this model has a structure that facilitates future control algorithm synthesis. Control algorithms in this context would directly utilize PK/PD model predictions. These predictions would be used to determine the amount and frequency of drug administration in order to reduce the tumor burden without violating clinically relevant constraints. This methodology could then be used to aid the clinician in selecting dose levels and schedules, and extension to patient tailored treatment may eventually be feasible with this approach.


pharmacokinetics pharmacodynamics camptothecins 9-nitrocamptothecin dynamic modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. H. Lee. Modeling and identification for nonlinear predictive control: Requirements, current status and future research needs. In F. Allgöwer and A. Zheng (eds). Nonlinear Model Predictive Control: Assessment and Future Directions. Birkhäuser, 1999.Google Scholar
  2. 2.
    Morari, M., Zafiriou, E. 1989Robust Process ControlPrentice-HallEnglewood Cliffs, NJGoogle Scholar
  3. 3.
    F. Allgöwer, T. A. Badgwell, S. J. Qin, J. B. Rawlings, and S. J. Wright. Advances in control – highlights of ECC ’99, chapter Nonlinear Predictive Control and Moving Horizon Estimation – An Introductory Overview, Springer, London, 1999, pp. 391–449.Google Scholar
  4. 4.
    C. Cobelli and E. Carson. Modelling methodology for physiology and medicine, chapter 1, An Introduction to Modelling Methodology, Academic Press, San Diego, CA, 2001, pp. 1–44.Google Scholar
  5. 5.
    C. H. Takimoto and S. G. Arbuck. Cancer chemotherapy & biology, chapter 20, Topoisomerase I Targetting Agents: The Camptothecins (3rd edn). Lippincott Williams & Wilkins, 2001, pp. 579–646.Google Scholar
  6. 6.
    Liehr, J. G., Harris, N. J., Mendoza, J., Ahmed, A. E. 2000Pharmacology of camptothecin estersAnn. NY. Acad. Sci.922216223PubMedGoogle Scholar
  7. 7.
    Jung, L. L., Zamboni, W. C. 2001Cellular pharmacokinetic, and pharmacodynamic aspects of response to camptothecins: Can we improve it?Drug Resist. Update4273288CrossRefGoogle Scholar
  8. 8.
    Pantazis, P., Harris, N., Mendoza, J., Giovanella, B. 1994Conversion of 9-nitro-camptothecin to 9-amino-camptothecin by human blood cells in vitroEur. J. Heamatol.53246248Google Scholar
  9. 9.
    Pommier, Y., Pourquier, P., Urasaki, Y., Wu, J., Laco, G. S. 1999Topoisomerase I inhibitors: Selectivity and cellular resistanceDrug Resist. Update.2307318CrossRefGoogle Scholar
  10. 10.
    Jung, L. L., Ramanathan, R. K., Egorin, M. J., Jin, R., Belani, C. P., Potter, D. M., Strychor, S., Trump, D. L., Walko, C., Faikh, M., Zamboni, W. C. 2004Pharmacokinetic studies of 9-nitrocamptothecin on intermittent and continuous schedules of administration in patients with solid tumorsCancer Chemoth. Pharmacol54487496CrossRefGoogle Scholar
  11. 11.
    National Research Council (ed.). Guide for the Care and Use of Laboratory Animals. Institute of Laboratory Animal Resources Commission on Life Sciences. National Academy Press, Washington, DC, 1996.Google Scholar
  12. 12.
    R. Horvorka and P. Vicini. Modelling methodology for physiology and medicine, chapter 5, Parameter Estimation, Academic Press, San Diego, CA, pp. 107–152.Google Scholar
  13. 13.
    Chong, E. K. P., Żak, S. H. 1996An Introduction To OptimizationWiley InterscienceNew York, NYGoogle Scholar
  14. 14.
    R. S. Parker. Efficient nonlinear model predictive control: Exploiting the Volterra– Laguerre model structure. In Proceedings of CPC VI. CACHE Corporation, AIChE Symposia Series, 2002.Google Scholar
  15. 15.
    Liehr, J. G., Ahmed, A. E., Giovanella, B. C. 1996Pharmacokinetics of camptothecins administered orallyAnn. NY Acad. Sci.803157163PubMedGoogle Scholar
  16. 16.
    Akaike, H. 1979A Basian extension of the minimal AIC procedures of autoregressive model fittingBiometrika66237242Google Scholar
  17. 17.
    Norton, L. 1988A Gompertzian model of human breast cancer growthCancer Res.4870677071PubMedGoogle Scholar
  18. 18.
    Asachenkov, A., Marchuk, G., Mohler, R., Zuev, S. 1994Disease DynamicsBirkhäuserBoston, MAGoogle Scholar
  19. 19.
    Martin, R., Teo, K. L. 1994Optimal Control of Drug Administration in Cancer ChemotherapyWorld ScientificRiver Edge, NJGoogle Scholar
  20. 20.
    Martin, R. B., Fisher, M. E., Minchin, R. F., Teo, K. L. 1992Optimal control of tumour size used to maximize survival time when cells are resistant to chemotherapyMath. Biosci.110221252CrossRefPubMedGoogle Scholar
  21. 21.
    Herbst, R. S., Maddox, A-.M., Rothenberg, M. L., Small, E. J., Rubin, E. H., Baelga, J., Rojo, F., Hong, W. K., Swaisland, H., Averbuch, S. D., Ochs, J., LoRusso, P. M. 2002Selective oral epidermal growth factor receptor tyrosine kinase inhibitor ZD1839 is generally well-tolerated and has activity in non-small-cell lung cancer and other solid tumors: Results of a phase I trialJ. Clin. Oncol.2038153825CrossRefPubMedGoogle Scholar
  22. 22.
    Schellens, J. H. M., Heinrich, B., Lehnert, M., Gore, M. E., Kaye, S. B., Dombernowsky, P., Paridaens, R., Oosterom, A. T. , Verweij, J., Loos, W. J., Calvert, H., Pavlidis, N., Cortes-Funes, H., Wanders, J., Roelvink, M., Sessa, C., Seliner, K., Wissel, P. S., Gamucci, T., Hanauske, A. R. 2002Population pharmacokinetic and dynamic analysis of the topoisomerase I inhibitor lurtotecan in phase II studiesInvest. New Drug.208393CrossRefGoogle Scholar
  23. 23.
    Rajendra, R., Saleem, M. K., Schellens, J. H., Ross, D. D., Bates, S. E., Sinko, P., Rubin, E. H. 2003Differential effects of the breast cancer resistance protein on the cellular accumulation and cytotoxicity of 9-aminocamptothecin and 9-nitrocamptothecinCancer Res.6332283233PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • John M. Harrold
    • 1
  • Julie L. Eiseman
    • 2
    • 3
  • Erin Joseph
    • 2
  • Sandra Strychor
    • 2
  • William C. Zamboni
    • 2
    • 4
  • Robert S. Parker
    • 1
    • 2
  1. 1.Department of Chemical and Petroleum EngineeringUniversity of Pittsburgh School of EngineeringPittsburghUSA
  2. 2.Molecular Therapeutics and Drug Discovery ProgramUniversity of Pittsburgh Cancer InstitutePittsburghUSA
  3. 3.Department of PharmacologyUniversity of Pittsburgh School of MedicinePittsburghUSA
  4. 4.Department of Pharmaceutical ScienceUniversity of Pittsburgh School of PharmacyPittsburghUSA

Personalised recommendations