Cancer immunotherapy, mathematical modeling and optimal control

Journal of Theoretical Biology

Volumn 247, Issue 4, 2007, Pages 723-732

  Castiglione, F ^a   Piccoli, B ^a  

^a CNR   (Italy)

Author keywords

Autologous cells transfection; Cancer; Drug scheduling; Immunotherapy; Optimal control

Indexed keywords

IMMUNOMODULATING AGENT; VACCINE;

BIOMECHANICS; CANCER; DRUG; GENE TRANSFER; IMMUNE RESPONSE; IMMUNE SYSTEM; NUMERICAL MODEL;

ARTICLE; CANCER IMMUNOTHERAPY; IMMUNE RESPONSE; IMMUNE SYSTEM; IMMUNOGENICITY; IMMUNOSTIMULATION; MATHEMATICAL MODEL; PRIORITY JOURNAL; TUMOR IMMUNITY;

CANCER VACCINES; COMPUTER SIMULATION; DENDRITIC CELLS; DRUG ADMINISTRATION SCHEDULE; HUMANS; IMMUNOTHERAPY, ACTIVE; MODELS, IMMUNOLOGICAL; NEOPLASMS;

EID: 34447501892     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2007.04.003     Document Type: Article

References (20)

1. Acharya R., and Sundareshan M. Development of optimal drug administration strategies for cancer-chemotherapy in the framework of systems theory. Int. J. Biomed. Comput. 15 2 (1984) 139-150
2. Bressan, A., Piccoli, B., Introduction to mathematical control theory. Am. Inst. Math. Sci., to appear.
3. Bressan A. Hyper-impulsive motions and controllizable coordinates for Lagrangean systems. Atti Accd. Naz. Lincei, Memorie VIII XIX (1990) 197-246
4. Bensoussan, A., Lions, J.-L., 1984. Impulse control and quasivariational inequalities. Translated from the French by J.M. Cole. Gauthier-Villars, Montrouge, Heyden & Son, Inc., Philadelphia, PA.
5. Burden T., Ernstberger J., and Renee Fister K. Optimal control applied to immunotherapy. Discrete Contin. Dyn. S. B 4 1 (2004) 135-146
6. Cappuccio, A., Castiglione, F., Piccoli, B., 2006. Determination of the optimal therapeutic protocol in cancer immunotherapy. Mathematical Biosciences, Epub ahead of print 10.1016/j.mbs.2007.02.009.
7. Castiglione F., and Piccoli B. Optimal control in a model of dendritic cell transfection cancer immunotherapy. Bull. Math. Biol. 68 (2006) 255-274
8. Fister K.R., and Donnelly J.H. Immunotherapy: an optimal control theory approach. Math. Biosci. Eng. 2 3 (2005) 499-510
9. Garavello M., and Piccoli B. Hybrid necessary principle. SIAM J. Control Optimization 43 (2005) 1867-1877
10. Gilboa E., Nair S.K., and Lyerly H.K. Immunotherapy of cancer with dendritic-cell-based vaccines. Cancer Immunol. Immunother. 46 (1998) 82-87
11. Goldsby R.A., Kindt T.J., and Osborne B.A. Kuby Immunology. fourth ed (2000), Freeman, NY
12. Kirschner D., and Panetta J.C. Modeling immunotherapy of tumor-immune interaction. J. Math. Biol. 37 (1998) 235-252
13. Martin R.B. Optimal control drug scheduling of cancer chemotherapy. Automatica 28 (1992) 1113-1123
14. Piccoli B., and Castiglione F. Optimal vaccine scheduling in cancer immunotherapy. Physica A 370 2 (2006) 672-680
15. de Pillis L., and Radunskaya A. A mathematical tumor model with immune resistance and drug therapy: an optimal control approach. J. Theor. Med. 3 (2001) 79-100
16. Polak E. Optimization (1997), Springer, Berlin
17. Preziosi, L. (Ed.), 2003. Cancer Modeling and Simulation. Chapman & Hall, CRC Press, London, UK.
18. Schmidt W.H., Heier K., and Bittner L. Variational Calculus, Optimal Control and Applications (1998), Birkhäuser, Basel
19. Swan G. Role of optimal control theory in cancer chemotherapy. Math. Biosci. 101 2 (1990) 237-284
20. Swierniak A., Ledzewicz U., and Schattler H. Optimal control for a class of compartmental models in cancer chemotherapy. Int. J. Appl. Math. and Comp. Sci. 13 3 (2003) 357-368