Optimal control synthesis in therapy of solid tumor growth

Computational Mathematics and Mathematical Physics

Volumn 48, Issue 6, 2008, Pages 892-911

  Bratus', A S ^a   Chumerina, E S ^a  

^a RUSSIAN UNIVERSITY OF TRANSPORT   (Russian Federation)

Author keywords

Avascular tumor; Dynamic programming method; Optimal control synthesis; Optimal therapy

Indexed keywords

EID: 45749142472     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: 10.1134/S096554250806002X     Document Type: Article

References (15)

1. R. P. Aranjo and D. L. Mcelwain, "A History of the Study of Solid Tumor Growth: The Contribution of Mathematical Modeling," Bull. Math. Biol. 66, 1039-1091 (2004).
2. H. M. Byrne, "Using Mathematics to Investigate Solid Tumor Growth," in Proceedings of 9th International Meeting of European Women in Mathematics (1999), pp. 81-107.
3. H. M. Byrne, "A Weakly Nonlinear Analysis of a Model of Avascular Solid Tumor Growth," J. Math. Biol. 39, 151-181 (1999).
4. A. Matzavinos, M. Chaplain, and V. Kuznetsov, "Mathematical Modeling of the Spatiotemporal Response of Cytotoxic T-Lymphocytes to a Solid Tumor," Math. Medicine and Biology 21, 1-34 (2004).
5. C. Guiot, P. G. Degiorgis, P. P. Delsanto, et al., "Does Tumor Growth Follow a 'Universal Law'," J. Theor. Biol. 225, 147-151 (2003).
6. J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications (Springer-Verlag, Berlin, 2003).
7. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Graylock, Rochester, N.Y., 1957/1961; Nauka, Moscow, 1968).
8. M. I. Costa, J. L. Boldini, and R. C. Bassanezi, "Drug Kinetics and Drug Resistance in Optimal Chemotherapy," Math. Biosciences 125, 191-209 (1995).
9. M. I. Costa, J. L. Boldini, and R. C. Bassanezi, "Chemotherapeutic Treatments Involving Drug Resistance and Level of Normal Cells as a Criterion of Toxicity," Math. Biosciences 125, 211-228 (1995).
10. J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems (Cambridge Univ. Press, New York, 1988).
11. W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control (Springer-Verlag, Berlin, 1975).
12. F. L. Chernous'ko, "Self-Similar Solutions to the Bellman Equation for Optimal Correction of Random Disturbances," Prikl. Mat. Mekh. 35, 333-342 (1971).
13. A. S. Bratus' and K. A. Volosov, "Exact Solutions to Hamilton-Jacoby-Bellman Equation for Problems of Optimal Correction with a Constrained Overall Control Resource," Prikl. Mat. Mekh. 68, 819-832 (2004).
14. D. Kirschner and J. C. Panetta, "Modeling Immunotherapy of the Tumor-Immune Interaction," J. Math. Biol. 37, 235-252 (1998).
15. T. N. Burden, J. Ernstberger, and K. R. Fister, "Optimal Control Applied to Immunotherapy," J. Discrete Continuous Dyn. Syst. Ser. 4, 135-146 (2004).