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Mathematical approaches to optimization of cancer chemotherapy. (English) Zbl 0404.92004

92C50 Medical applications (general)
49K15 Optimality conditions for problems involving ordinary differential equations
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[1] Almquist, K. J. and H. T. Banks. 1976. ”A Theoretical and Computational Method for Determining Optimal Treatment Schedules in Fractionated Radiation Therapy”Math. Biosci.,29, 159–179. · Zbl 0334.92005
[2] Aroesty, J., T. Lincoln, N. Shapiro and G. Boccia. 1973. ”Tumor Growth and Chemotherapy: Mathematical Methods, Computer Simulation, and Experimental Foundations.”Math. Biosci.,17, 243–300. · Zbl 0257.92002
[3] Berenbaum, M. C. 1969. ”Dose-response Curves for Agents that Impair Cell Reproductive Integrity.”Br. J. Cancer,23, 434–445.
[4] Bremermann, H. 1970. ”A Global Method for Unconstrained Optimization.”Math Biosci.,9, 1–15. · Zbl 0212.51204
[5] Goodman, L. and A. Gilman. 1970.The Pharmacological Basis of Therapeutics, 4th edn. pp. 17–19. New York: Macmillan.
[6] Laird, A. K. 1969. ”Dynamics of Growth in Tumors and Normal Organisms.”Human Tumor Cell Kinetics, NCI Monograph V 30, pp. 15–28.
[7] Leitmann, G. 1974.Cooperative and Non-cooperative Many Player Differential Games, International Centre for Mechanical Sciences Course Lectures. No. 190. Springer Verlag Udine.
[8] Leitmann, G. 1966.An Introduction to Optimal Control. New York: McGraw-Hill. · Zbl 0196.46302
[9] Nicolini, C. 1976. ”The Principles and Methods of Cell Synchrony in Cancer Chemotherapy.”BBA 458 (1976), pp. 243–282.
[10] Nicolini, C., E. Milgram, F. Kendall and W. Giaretti. 1977. ”Mathematical Models for Drug Actionin vitro”Growth Kinetics and Biochemical Regulation of Normal and Malignant Cells. (Eds. B. Drewinko and R. M. Humphrey. Baltimore: Williams & Williams.
[11] Nicolini, N. and F. Kendall. 1975. ”Monte Carlo Simulation of Drug Action in Intact Animals.”Mathematical Modeling in Cell Kinetics (Ed. A. J. Valleron) pp. 81–83. Ghent: European Press Medikon.
[12] Swan, G. and T. Vincent. 1977. ”Optimal Control Analysis in the Chemotherapy of IgC Multiple Myeloma.”Bull. Math. Biol.,39, 317–337. · Zbl 0354.92041
[13] Yu, P. L. and G. Leitmann. 1974. ”Non-dominated decisions and Cone Convexity in Dynamic Multicriteria Decision Problems.”JOTA,14, (5) 573–584. · Zbl 0273.90003
[14] Zeleny, M. 1974. Linear Multiobjective Programming Lecture Notes in Economics and Mathematical Systems.” Vol. 95. New York: Springer-Verlag. · Zbl 0325.90033
[15] Zietz, S. 1977. ”Mathematical Modeling of Cellular Kinetics and Optimal Control Theory in the Service of Cancer Chemotherapy.” Ph.D. Thesis, Dept. of Math., University of California, Berkeley.
[16] Zietz, S., C. Desaire, M. Grattarola, and C. Nicolini. 1978. ”Deterministic Mathematical Models to Obtain Optimized Drug Metabolism and Cell Kinetic Parameters as a Function of Dosage from Both Autoradiographic and Flow Microfluorimetric Analysis.” In:Biomathematics and Cell Kinetics (Ed. A.-J. Valleron), pp. 431–438. Amsterdam: Elsevier.
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