Abstract
In this paper we consider the problems of modeling the tumor growth and optimize the chemotherapy treatment. A biologically based model is used with the goal of solving an optimization problem involving discrete delivery of antineoplastic drugs. Our model is formulated via compartmental analysis in order to take into account the cell cycle. The cost functional measures not only the final size of the tumor but also the total amount of drug delivered. We propose an algorithm based on the discrete maximum principle to solve the optimal drug schedule problem. Our numerical results show nice interpretations from the medical point of view.
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References
K.J. Almquist and H.T. Banks, “A theoretical and computational method for determining optimal treatment schedules in fractionated radiation therapy,”Mathematical Bioscience 29 (1976) 159–176.
K. Bahrami and M. Kim, “Optimal control of multiplicative control systems arising from cancer chemotherapy,”IEEE Transactions on Automatic Control (1975) 537–542.
J.H. Goldie and A.J. Coldman, “A mathematical model for relating the drug sensitivity of tumor to their spontaneous mutation rate,”Cancer Treatment Reports 63 (1979) 1727–1733.
J.H. Goldie, A.J. Coldman and G.A. Gudauskas, “Rational for the use of alternating noncross-resistant chemotherapy,”Cancer Treatment Report 66 (1982) 439–449.
M. Kim, K. Bahrami and K.B. Woo, “A discrete-time model for cell age, size and DNA distribution of proliferating cells, and its application to the movement of the labelled cohort,”IEEE Transactions on Biomedical Engineering 21 (1984) 387–398.
C.E. Pedreira, V.B. Vila and M. Schettini, “A system approach to cancer chemotherapy,”Proceedings of 7° Congresso Brasileiro de Automática, CBA—IFAC (1988) 1050–1055.
H.E. Skipper and S. Perry, “Kinetics of normal and leukemic leukocyte populations and relevance to chemotherapy,”Cancer Research 30 (1970) 1883–1897.
G.W. Swan, “Optimization of human cancer radiotherapy,”Lecture Notes in Biomathematics, Vol. 42 (Springer, New York, 1981).
G.W. Swan, “Cancer chemotherapy: Optimal control using the Verkulst—Pearl equation,”Bulletin of Mathematical Biology 48 (1986) 381–404.
G.W. Swan, “Optimal control analysis of a cancer chemotherapy problem,”IMA Journal of Mathematical Applications in Medicine and Biology 4 (1987) 171–184.
G.W. Swan and T.L. Vincent, “Optimal control analysis in the chemotherapy of IgG multiple myeloma,”Bulletin of Mathematical Biology 30 (1977) 317–337.
M. Takahashi, “Theoretical basis for cell cycle analysis: I, labeled mitosis wave method,”Journal of Theoretical Biology 13 (1968) 202–211.
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Dedicated to Mrs. Amalia Gordon.
This research is part of PUC—RJ/Hospital de Oncologia/INAMPS Cientific Agreement.
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Pedreira, C.E., Vila, V.B. Optimal schedule for cancer chemotherapy. Mathematical Programming 52, 11–17 (1991). https://doi.org/10.1007/BF01582876
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DOI: https://doi.org/10.1007/BF01582876