Numerical simulation of a stochastic model for cancerous cells submitted to chemotherapy
A stochastic model is proposed to study the problem of inherent resistance by cell populations when chemotherapeutic agents are used to control tumor growth. Stochastic differential equations are introduced and numerically integrated to simulate expected response to the chemotherapeutic strategies as a function of different parameters. Satisfactory demonstration runs of the model indicate that it could represent a useful tool in verifying the results of experimental and clinical chemotherapy courses and planning treatment strategies. Some types of behaviour are illustrated graphically.
Key wordsCell resistance Stochastic models Simulation
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- 1.Andersen, P. K., Borgan, ø.: Counting process models for life history data. Scand. J. Statist. 12, 97–158 (1985)Google Scholar
- 2.Crump, K. S., Hoel, D. G.: Mathematical model for estimating mutation rates in cell populations. Biometrika 61, 237–252 (1974)Google Scholar
- 3.Gihman, I. I., Skorohod, A. V.: Stochastic differential equations. Berlin Heidelberg New York: Springer 1972Google Scholar
- 4.Coldman, A. J., Goldie, J. H.: A model for the resistance of tumor cells to cancer chemotherapeutic agents. Math. Biosci. 65, 291–307 (1983)Google Scholar
- 5.Law, L. W.: Origin of the resistance in leukaemic cells to folic acid antagonist. Nature 169, 628–629 (1952)Google Scholar
- 6.Rossi, C., De Paolis, L., Benassi, M.: A stochastic model of chemotherapy for tumor disease. Invited contribution to the 46th session of the International Statistical Institute, Proceedings Tokio 1987Google Scholar
- 7.Rumelin, W.: Numerical treatment of stochastic differential equations. SIAM J. Numer. Anal. 19, 604–613 (1982)Google Scholar
- 8.Skipper, H. E., Schabel, F. M., Lloyd, H.: Dose-response and tumor cell repopulation rate in chemotherapeutic trials. In: Rozownky, A. (ed.) Advances in cancer chemotherapy, vol. 1, pp. 205–253. New York: Marcel-Dekker 1979Google Scholar