`a`
Mathematical Biosciences and Engineering (MBE)
 

On optimal and suboptimal treatment strategies for a mathematical model of leukemia
Pages: 151 - 165, Issue 1, February 2013

doi:10.3934/mbe.2013.10.151      Abstract        References        Full text (353.7K)           Related Articles

Elena Fimmel - Mannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 Mannheim, Germany (email)
Yury S. Semenov - Moscow State University of Railway Engineering, Obraztsova 15, Moscow, 127994, Russian Federation (email)
Alexander S. Bratus - Moscow State University of Railway Engineering, Obraztsova 15, Moscow, 127994, Russian Federation (email)

1 E. K. Afenya and D. E. Bentil, Models of acute myeloblastic leukemia and its chemotherapy, in "Computational Medicine, Public Health, and Biotechnology Part I. World Scientific" New Jersey, (1995), pp. 397.
2 E. K. Afenya, Cancer treatment strategies and mathematical modeling, in "Mathematical Models in Medical and Health Sciences" (eds. M. A. Horn, G. Simonett and G. F. Webb), Vanderbilt University. Nashville, (1998), 1-8.
3 E. K. Afenya and C. P. Calderón, Modeling disseminated cancers: A review of mathematical models, Comm. Theor. Biol., 8 (2003), 225-253.
4 E. K. Afenya and C. P. Calderón, A brief look at a normal cell decline and inhibition in acute leukemia, J. Can. Det. Prev.,, 20 (1996), 171-179.
5 E. K. Afenya, Acute leukemia and chemotherapy: a modeling viewpoint, Math. Biosci., 138 (1996), 79-100.
6 A. V. Antipov and A. S. Bratus', Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a heterogeneous tumor, Zh. Vychisl. Mat. Mat. Fiz., 49 (2009), 1907-1919       
7 A. S. Bratus, E. Fimmel, Y. Todorov, Y. S. Semenov and F. Nürnberg, On strategies on a mathematical model for leukemia therapy, Nonlinear Analysis: Real World Applications, 13 (2012), 1044-1059.       
8 B. D. Clarkson, Acute myelocytic leukemia in adults, Cancer, 30 (1972), 1572-1582.
9 B. Djulbegovic and S. Svetina, Mathematical model of acute myeloblastic leukemia: an investigation of a relevant kinetic parameters, Cell Tissue Kinet., 18 (1985), 307-319.
10 M. Engelhart, D. Lebiedz and S. Sager, Optimal control for selected cancer chemotherapy ODE models: A view on the potential of optimal schedules and choice of objective function, Mathematical Biosciences, 229 (2011), 123-134.       
11 A. F. Filippov, "Differential Equations with Discontinuous Righthand Sides," Springer, 1988.       
12 K. R. Fister and J. C. Panetta, Optimal control applied to competing chemotherapeutic cell-kill strategies, SIAM Journal on Applied Mathematics, 63 (2003), 1954-1971.       
13 K. R. Fister and J. C. Panetta, Optimal control applied to cell-cycle-specific cancer chemotherapy, SIAM Journal on Applied Mathematics, 60 (2000), 1059-1072.       
14 C. L. Frenzen and J. D. Murray: A cell kinetics justification for Gompertz equation, SIAM J. Appl. Math., 46 (1986), 614-624.       
15 C. Guiot, P. G. Degiorgis, P. P. Delsanto, P. Gabriele and T. S. Deisboeck, Does tumour growth follow a universal law?, J. Theor. Biol., 225 (2003), 147-151.       
16 "Handbook of Cancer Models with Applications," (W.-Y. Tan, L. Hanin Eds.) Ser. Math. Biology and Medicine; World Scientific. Vol. 9, 2008.
17 N. H. G. Holford and L. B. Sheiner, Understanding the dose-effect relationship-clinical application of pharmacokinetic-pharmacodynamic models, Clin. Pharmacokin, 6 (1981), 429-453.
18 D. E. Kirk, "Optimal Contol Theory: An Introduction," Prentice-Hall, 1970
19 U. Ledzewicz, A. d'Onofrio, H. Maurer and H. Schaettler, On optimal delivery of combination therapy for tumors, Mathematical Biosciences, 222 (2009), 13-26.       
20 U. Ledzewicz and H. Schaettler, Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy, Mathematical Biosciences, 206 (2007), 320-342.       
21 A. S. Matveev and A. V. Savkin, Optimal control regimens: influence of tumours on normal cells and several toxicity constraints, IMA J. Math. Appl. Med. Biol., 18 (2001), 25-40.
22 L. Norton and R. Simon, The Norton-Simon Hypothesis: designing more effective and less toxic chemotherapeutic regimens, Nature Clinical Practice, 3 Nr. 8, (2006).
23 L. Norton and R. Simon, Tumor size, sensitivity to therapy, and design of treatment schedules, Cancer Treat Rep., 61(1977) Oct, 1307-1317. PubMed PMID: 589597.
24 J. C. Panetta, A mathematical model of breast and ovarian cancer treated with paclitaxel, Mathematical Biosciences, 146 (1997), 89-113.       
25 S. I. Rubinow and J. L. Lebowitz, A mathematical model of the acute myeloblastic leukemic state in man, Biophys. J., 16 (1976), 897-910.
26 F. Schabel, Jr., H. Skipper and W. Wilcox, Experimental evaluation of potential anti-cancer agents. XIII. On the criteria and kinetics associated with curability of experimental leukemia, Cancer Chemo. Rep., 25 (1964), 1-111.
27 L. B. Sheiner and N. H. G. Holford, Determination of maximum effect, Clin. Pharmacology & Therapeutics, 71 (2002), pp.304.
28 G. W. Swan and T. L. Vincent, Optimal control analysis in the chemotherapy of IgG multiple myeloma, Bull. Math. Biol., 39 (1977), 317-337.
29 Y. Todorov, E. Fimmel, A. S. Bratus, Y. S. Semenov and F. Nürnberg, An optimal strategy for leukemia therapy: A multi-objective approach, Russian Journal of Numerical Analysis and Mathematical Modelling, 26 (2011), 589-604.       

Go to top