Optimal control of drug delivery to brain tumors for a distributed parameters model

Proceedings of the American Control Conference

Volumn 2, Issue , 2005, Pages 973-978

  Chakrabarty, Siddhartha P ^a   Hanson, Floyd B ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BRAIN; CELLS; CONTROLLED DRUG DELIVERY; DIFFUSION; DISTRIBUTED PARAMETER CONTROL SYSTEMS; EXTRAPOLATION; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; TISSUE; TUMORS;

BRAIN TUMORS; DISTRIBUTED PARAMETERS MODEL; DRUG CONCENTRATION; TUMOR CELLS;

OPTIMAL CONTROL SYSTEMS;

EID: 23944490712     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (20)

1. D. Acquafredda, "Brain Tumor Treatments: BCNU (Carmustine)," Musella Foundation, http://virtualtrials.com/bcnu2.cfm
2. Anonymous, "Brain Tumor Treatments: Gliadel® Wafer," Musella Foundation, 2004, http://www.virtualtrials.com/gliadel
3. R. P. Araujo and D. L. S. McElwain "A history of the study of solid tumour growth: The contribution of mathematical modelling," Bull. Math. Biol., vol. 66, pp. 1039-1091,2004.
4. H.H. Engelhard, "Brain tumors and the blood-brain barrier," Neuro-Oncology, The Essentials, pp. 49-53, Thieme Medical Publishers, Inc., New York 2000.
5. R.A. Gatenby and E.T. Gawlinski, "A reaction-diffusion model of cancer invasion," Cancer Research, vol. 56, pp. 5745-5753, December 15, 1996.
6. M.D. Gunzburger, Perspectives in Flow Control and Optimization, SIAM, Philadelphia, 2003.
7. R. Haberman, Elementary Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Prentice-Hall, Englewood Cliffs, NJ, 1983.
8. W. Hackbusch, "A numerical method for solving parabolic equations with opposite orientations," Computing, vol. 20, pp. 229-240, 1978.
9. F.B.Hanson and K.Naimipour, "Convergence of numerical method for multistate stochastic dynamic progamming," Proc. Int. Fed. of Auto. Control 12th World Congress, vol. 9, pp.501-504, 1993.
10. F.B.Hanson, "Techniques in Computational Stochastic Dynamic Programming," Control and Dynamic Systems: Advances in Theory and Applications, vol. 76, pp. 103-162, Academic Press, New York, April 1996.
11. H. B. Keller, Numerical Methods for Two-Point Boundary Value Problems, Gin Blaisdell, Waltham, MA, 1968.
12. D. E. Kirk, Optimal Control Theory: An Introduction, Prentice-Hall, Englewood Cliffs, NJ, 1970.
13. J. Mansuri, The Modelling of Tumor Growth Using Reaction-Diffusion Equations, MSc Thesis, Oxford University, 2002.
14. J.D.Murray, Mathematical Biology I: An Introduction, Springer, New York, 2002.
15. J.D.Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, Springer, New York, 2003.
16. K.R. Swanson, Mathematical Modeling of the Growth and Control of Tumors, PhD Thesis, University of Washington, 1999.
17. C-H. Wang and J. Li, "Three dimensional simulation of IgG delivery to tumors," Chem. Engineering Sci., vol. 53, pp. 3579-3600, 1998.
18. C-H. Wang, J. Li, C.S. Teo and T. Lee, "The delivery of BCNU to brain tumors," J. Controlled Release, vol. 61, pp. 21-41, 1999.
19. J. J. Westman, B. R. Fabijonas, D. L. Kern and F. B. Hanson, "Probabilistic rate compartment cancer model: Alternate versus traditional chemotherapy dcheduling," in Stochastic Theory and Control, Lecture Notes in Control and Information Sciences, vol. 280, B. Pasik-Duncan (Editor), Springer-Verlag, New York, pp. 491-506, 2002.
20. D.E.Woodward, J.Cook, P.Tracqui, G.C.Cruywagen, J. D Murray, E.C.Alvord, Jr., "A mathematical model of glioma growth: the effect of extent of surgical resection," Cell Proliferation, vol. 29, pp. 269-288, 1996.