A stochastic model for the origin and treatment of tumors containing drug-resistant cells
- 168 Downloads
A stochastic model for the chemotherapy of experimental tumors is presented. The focus of this model is on the presence of drug-resistant mutants and their influence on eventual treatment outcome. Equations are derived for the joint probability-generating function for the number of chemo-sensitive and chemo-resistant cells. The model is extended to two drugs and it is shown how the model may be used to make deductions regarding the optimum scheduling of therapy.
KeywordsStem Cell Resistant Cell Transitional Cell Stem Cell Compartment Stem Cell Division
Unable to display preview. Download preview PDF.
- Carmen, M. D., J. M. Schornagel, R. S. Rivest, S. Srimatkandada, R. S. Portlock, D. Duffy and J. R. Bertin. 1984. “Resistance to Methotrexate Due to Gene Amplification in a Patient with Acute Leukemia.”J. clin. Oncol. 2, 16–20.Google Scholar
- — and—. 1986. “Factors Affecting the Development of Permanent Drug Resistance and its Impact upon Neo-adjuvant Chemotherapy.” InPreoperative (Neo-adjuvant) Chemotherapy. Berlin: Springer (to appear).Google Scholar
- Day, R. 1984. “A Tumor Growth Model with Applications to Treatment Policy and Protocol Choice.” Thesis submitted to Harvard School of Public Health, Boston, MA.Google Scholar
- John, F. 1982.Partial Differential Equations, 4th Edn, pp. 9–14. New York: Springer.Google Scholar
- Ling, V. 1982. “Genetic Basis of Drug Resistance in Mammalian Cells.” InDrug and Hormone Resistance in Neoplasia, Vol. 1, pp. 1–20. Boca Raton, FL: CRC Press.Google Scholar
- MacKillop, J., A. Ciampi, J. E. Till and R. N. Buick. 1983. “Stem Cell Model of Human Tumor Growth: Implications for Tumor Cell Clonogenic Assays.”J. natn. Cancer Inst. 70, 9–16.Google Scholar
- Mode, C. J. 1971.Multitype Branching Processes—Theory and Applications. New York: American Elsevier.Google Scholar
- Skipper, H. E. 1978. “Cancer Chemotherapy I: Reasons for Success and Failure of Treatment of Murine Leukemias with the Drugs now Employed Treating Human Leukemias.” Ann Arbor. MI: University Microfilms Inc.Google Scholar
- Trent, J. M., R. N. Buick, S. Olson, R. C. Horns and R. T. Schimke. 1984. “Cytologic Evidence for Gene Amplification in Methotrexate Resistant Cells Obtained from a Patient with Ovarian Adenocarcinoma.”J. clin. Oncol. 2, 8–15.Google Scholar