Blasting neuroblastoma using optimal control of chemotherapy

Mathematical Biosciences and Engineering

Volumn 6, Issue 3, 2009, Pages 451-467

  Collins, Craig ^a   Fister, K Renee ^a   Key, Bethany ^a   Williams, Mary ^a  

^a MURRAY STATE UNIVERSITY   (United States)

Author keywords

Chemotherapy; Optimal control; Topotecan

Indexed keywords

ANTINEOPLASTIC AGENT; GRANULOCYTE COLONY STIMULATING FACTOR; TOPOTECAN;

ARTICLE; BIOLOGICAL MODEL; CHILD; COMPUTER SIMULATION; DRUG ADMINISTRATION; DRUG EFFECT; HUMAN; IMMUNOLOGY; NEUROBLASTOMA; NEUTROPHIL;

ANTINEOPLASTIC AGENTS; CHILD; COMPUTER SIMULATION; DRUG ADMINISTRATION SCHEDULE; GRANULOCYTE COLONY-STIMULATING FACTOR; HUMANS; MODELS, IMMUNOLOGICAL; NEUROBLASTOMA; NEUTROPHILS; TOPOTECAN;

EID: 70349647034     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2009.6.451     Document Type: Article

References (36)

1. http://www.rxlist.com/cgi/genoric/topotec-cp.htm 7/26/2007.
2. http://www.cancerbackup.org.uk/Cancertype/Childrenscancers/ Type8ofchildrenscancers/Neuroblastoma 2/19/2007.
3. http://www.cancer.org/docroot/cri/content/cri-2-4-lx-what-is- neuroblastoma31.asp 2/19/2007.
4. http://www.news-medical.net/?id=11131 2/6/2007.
5. http://www.stjude.org/media/0,2561,453-2086-19957,00.html 2/12/2007.
6. http://www.cancer.gov/cancertopics/pdq/treatment/neuroblastoma/patlent/ 2/19/2007.
7. http://www.springer-link.com/content/?k=Camptothecin 2/19/2007.
8. http://apps.need.ede.gov/uscs/Table.aspx?Group=TableChild\&Year=2003\ &Display=n 7/17/2007.
9. J. L. Boldrini and M. I. S. Costa, The influence of fixed and free final time of treatment on optimal chemotherapeutic protocols, Mathematical and Computer Modelling, 27 (1998), 59-72.
10. M. I. S. Costa, J. L. Boldrini and R. C. Bassanezi, Chemotherapeutic treatments involving drug resistance and level of normal cells as a criterion of toxicity, Mathematical Biosciences, 125 (1994), 211-228.
11. L. G dePillis, W. Gu, K. R. Fister, T. Head, K. Maples, T. Neal, A. Murugan and K. Yoshida, Chemotherapy for tumors: An analysis of the dynamics and the study of quadratic and linear optimal controls, Mathematical Biosciences (2006) accepted.
12. K. R. Fister, S. Lenhart and J. S. McNally, Optimizing chemotherapy in an HIV model, Elect. J. Diff. Eqns., 32 (1998), 1-12.
13. K. R. Fister and J. C. Panetta, Optimal control applied to cell-cycle-specific cancer chemotherapy, SIAM J. Appl. Math., 60 (2000), 1059-1072.
14. K. R. Fister and J. Panetta, Optimal control applied to competing chemotherapeutic cell-kill strategies, SIAM J. Appl. Math, 63 (2003).
15. Wendell H. Fleming and Raymond W. Rishel, "Deterministic and Stochastic Optimal Control," Springer-Verlag, New York, 1975.
16. R. A. Gatenby and P. K. Maini, Modelling a new angle on understanding cancer, Nature, 410 (2002), 462.
17. W. Hackbush, A numerical method for solving parabolic equations with opposite orientations, Computing, 20 (1978), 229-240.
18. R. F. Hartl, S. P. Sethi and R. G. Vickson, A survey of the maximum principles for optimal control problems with state constraints, SIAM Review, 37 (1995), 181-218.
19. M. I. Kamien and N. L. Schwartz, "Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, Volume31 of Advanced Textbooks in Economics," 2nd Edition, North-Holland, 1991.
20. D. E Kirk, "Optimal Control Theory: An Introduction," Dover Publications, Inc., 1970.
21. M. Kim, S. Perry and K. B. Woo, Quantitative approach to the design of antitumor drug dosage schedule via cell cycle kinetics and systems theory, Ann. Biomed. Engng, 5 (1977), 12-33.
22. D. Kirschner, S. Lenhart and S. Serbin, Optimal control of the chemotherapy of HIV, J. Math. Biol., 35 (1997), 775-792.
23. A. Langler, A. Christaras, K. Abshagen, K. Krauth, B. Hero and F. Berthold,.http: //www. ncbi .nlm. nih.. gov/sites/entrez2/19/2007.
24. U. Ledzewicz, T. Brown and H. Schattler, Comparison of optimal controls for a model in cancer chemotherapy with l1 and l2 type objectives, Optimization Methods and Software, 19(2004), 339-350.
25. U. Ledzewicz and H. Schattler, Drug resistance in cancer chemotherapy as an optimal control problem, Discrete and Continuous Dynamical Systems - Series B, 6 (2006), 129-150.
26. S. Lenhart and J. T Workman, "Optimal Control Applied to Biological Models," CRC Press, 2007.
27. D. L. Lukes, "Differential Equations: Classical to Controlled," Volume 162, Academic Press, 1982.
28. J. M. Murray, Optimal control for a cancer chemotherapy problem with general growth and loss functions, Math. Biosci., 98 (1990), 273-287.
29. J. M. Murray, Some optimality control problems in cancer chemotherapy with a toxicity limit, Math. Biosci., 100 (1990), 49-67.
30. J. C. Panetta, M. Kirsten, A. J. Gajjar, G. Nair, M. Fouladi and C. Stewart, A mechanistic mathematical model of temozolomide myelosuppression in children with high-grade gliomas, Mathematical Biosciences 186 (2003), 29-41.
31. J. C. Panetta, P. Schaiquevich, V. M. Santana, M. A. O'Shaughnessy and C. F Stewart, Using pharmacokinetic and pharmacodynamic modeling and simulation to evaluate importance of schedule in topotecan therapy for pediatric neuroblastoma, Clinical Cancer Research, 14 (2008), 318-325.
32. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes," Gordon and Breach, 1962.
33. G. W. Swan and T. L Vincent, Optimal control analysis in the chemotherapy of IgG multiple myeloma, Bulletin of Mathematical Biology, 39 (1977), 317-337.
34. G. W. Swan, Optimal control in some cancer chemotherapy problems, Internat. J. Systems Sci., 11 (1980), 223-237.
35. G. W. Swan, An optimal control model of diabetes mellitus, Bull. Math. Bio., 44 (1982), 793-808.
36. Y. Tsuchida and T. Shitara, Topotecan and irinotecan in the treatment of pediatric solid tumors, Current Pediatric Reviews, I (2005), 55-66.