Abstract
The pharmacokinetics of antineoplastic drugs based on compartmental models are combined with deterministic exponential growth models of tumors containing drug-resistant and sensitive cells. Model predictions for single-drug therapy are compared with in vivodata obtained by other investigators for L1210 t-cell leukemia in mice treated with BCNU and AraC and for in vitrotreatment of L1210 with Ara-C. The model and data compare favorably in terms of rate of tumor growth and duration of drug action for both constant infusion and bolus delivery of the drugs.
Similar content being viewed by others
References
J. H. Goldie and A. J. Coldman. The genetic origin of drug resistance in neoplasm: Implications for systemic therapy.Cancer Res. 44:3643–3653 (1984).
J. H. Goldie and A. J. Coldman. A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate.Cancer Treat. Rep. 63:1727–1733 (1979).
A. J. Coldman and J. H. Goldie. A model for the resistance of tumor cells to cancer chemotherapeutic agents.Math. Biosci. 65:291–307 (1963).
K. Bischoff, R. Dedrick, D. Zaharko, and J. Longstreth. Methotrexate pharmacokinetics.J. Pharm. Sci. 60:1128–1133 (1971).
R. Dedrick, D. Zaharko, R. Bender, W. Bleyer, and R. Lutz. Pharmacokinetic considerations on resistance to anticancer drugs.Cancer Chemother. Rep. 59:795–804 (1975).
K. Woo, L. Brenkus, and K. Wiig. Analysis of the effects of antitumor drugs on cell cycle kinetics.Cancer Chemother. Rep. 59:847–860 (1975).
C. Finn and W. Sadee. Determiniation of 5-fluoroucil (NSC-19893) plasma levels in rats and man by isotope dilution-mass fragmentography.Cancer Chemother. Rep. 59:279–286 (1975).
A. Coldman and J. Goldie. A mathematical model of drug resistance in neoplasm In N. Bruchovsky and J. Goldie (eds.),Drug and Hormone Resistance in Neoplasm, Vol. 1, CRC Press, Boca Raton, Florida, 1982.
H. Skipper, F. Schabel, and J. Mellet,et al. Implications of biochemical, cytokinetic, pharmacologic, and toxicologic relationships in the design of optimal therapeutic schedules.Cancer Chemother. Rep. 54:431–450 (1970).
G. Levy. Relationship between pharmacological effects and plasma or tissue concentration of drugs in man. In. D. Davies and B. Prichard (eds.),Biological Effects of Drugs in Relation to Their Plasma Concentrations, MacMillan, London, 1973.
K. Himmelstein and K. Bischoff. Models of ARA-C chemotherapy of L1210 leukemia in mice.J. Pharmacokin. Bipharm. 1:69–81 (1973).
K. Himmelstein and K. Bischoff. Mathematical representations of cancer chemotherapy effects.J. Pharmacokin. Biopharm. 1:51–68 (1973).
W. Jusko. A pharmacodynamic model for cell-cycle specific chemotherapeutic agents.J. Pharmacokin. Biopharm. 1:175–201 (1973).
L. Norton and R. Simon. Tumor size, sensitivity to therapy, and design of treatment schedule.Cancer Treat. Rep. 61:1307–1317 (1977).
H. Skipper. Pharmacological basis of cancer chemotherapy: Closing remarks. InPharmacological Basis of Cancer Chemotherapy, Symposium on Fundamental Cancer Research, University of Texas, 1974, pp. 713–726.
B. Hill. Cancer chemotheraphy. The relevance of certain concepts of cell cycle kinetics.Biochim. Biophys. Acta. 516:389–417 (1978).
R. Tallarida and L. Jacob.The Dose-Response Relation in Pharmacology, Springer-Verlag, New York, 1979.
J. Jacquez.Compartmental Analysis in Biology and Medicine, Elsevier, Amsterdam, 1972.
R. Brown. Compartmental system analysis: State of the art.IEEE Trans. Biomed. Eng. BNE-27 (1):1–11 (1980).
A. Rescigno and G. Segre.Drug and Tracer Kinetics, Blaisdell, Massachusetts, 1966.
G. Swan and T. Vincent. Optimal control analysis in the chemotherapy of Ig multiple myeloma.Bull. Math. Biol. 39:317–337 (1977).
G. Brunton and T. Wheldon. The Gompertz equation and the construction of tumor growth curves.Cell Tissue Kinet. 13:455–460 (1980).
M. Gibaldi and D. Perrier.Pharmacokinetics, Marcel Dekker, New York, 1975.
F. Schabel, M. Skipper, M. Trader, W. Laster, T. Corbett, and D. Griswold. Concepts for controlling drug resistant tumor cells. In M. Mourisden and T. Palshof (eds.),Breast Cancer—Experimental and Clinical Aspects, Pergamon Press, Oxford, 1980, pp. 199–221.
H. Skipper. Booklets 11, 12, 16, 17, Southern Research Institute, Birmingham, Alabama, 1980.
S. Shackney. A computer model for tumor growth and chemotherapy, and its application to L1210 leukemia treated with cytosine arabinoside (NSC-63878).Cancer Chemother. Rep. 54:399–429 (1970).
T. Vietti, F. Valeriote, R. Kalish, and D. Coulter. Kinetics of cytotoxicity of VM-26 and VP-16-213 on L1210 leukemia and hematopoietic stem cells.Cancer Treat. Rep. 62:1313–1320 (1978).
M. Berenbaum. Criteria for analysing interactions between biologically active agents.Adv. Cancer Res. 35:269–235 (1981).
K. Chadwick and H. Leenhouts.The Molecular Theory of Radiation Biology. Springer-Verlag, Berlin, 1981.
W. Bruce, B. Meeker, and F. Valeriote. Comparison of the sensitivity of normal hematopoietic and transplanted lymphoma colony-forming cells to chemotherapeutic agents administeredin vivo.J. Natl Cancer Inst. 37:233–245 (1966).
T. Borsa, G. Whitmore, and F. Valeriote. Studies on the persistence of methotrexate, cytosine arabinoside, and leucovorin in serum of mice.J. Natl. Cancer Inst. 42:235–242 (1969).
H. Skipper, F. Schabel, and W. Wilcox. Experimental evaluation of potential anticancer agents. XIII. On the criteria and kinetics associated with “curability” of experimental leukemia.Cancer Chemother. Rep. 35:1–111 (1964).
J. Lankelma and E. Van der Kleijn. The plasma concentration of methotrexate. In F. Merkus (ed.),The Serum Concentration of Drugs, Excerpta Medica. Amsterdam, 1980, pp. 244–249.
P. Leme, P. Creaven, L. Allen, and M. Berman. Kinetic model for the disposition and metabolism of moderate and high dose methotrexate (NSC-740) in man.Cancer Chemother. Rep. 59:811–817 (1975).
S. Chuang. Mathematic models for cancer chemotherapy: Pharmacokinetic and cell kinetic considerations.Cancer Treat. Rep. 59:827–842 (1975).
S. Chuang and H. Lloyd. Analysis and identification of stochastic compartment models in pharmacokinetics: Implication for cancer chemotherapy.Math. Biosci. 22:57–74 (1974).
Author information
Authors and Affiliations
Additional information
The work described in this paper was supported by the National Health and Medical Research Council of Australia.
Rights and permissions
About this article
Cite this article
Duc, H.N., Nickolls, P.M. Multicompartment models of cancer chemotherapy incorporating resistant cell populations. Journal of Pharmacokinetics and Biopharmaceutics 15, 145–177 (1987). https://doi.org/10.1007/BF01062341
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01062341