Optimal control of drug therapy in cancer treatment

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 12, 2009, Pages

  Itik, Mehmet ^a   Salamci, Metin U ^b   Banks, Stephen P ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b GAZI UNIVERSITY   (Turkey)

Author keywords

Mathematical modelling; Optimal control; Time varying approximations; Tumour growth

Indexed keywords

APPROXIMATION TECHNIQUES; CANCER CELLS; CANCER TREATMENT; EQUILIBRIUM POINT; GLOBAL DYNAMICS; IMMUNE SYSTEMS; LINEAR TIME VARYING; MATHEMATICAL MODELLING; OPTIMAL CONTROL METHODS; OPTIMAL CONTROL STRATEGY; OPTIMAL CONTROLS; SIMULATED MODEL; SIMULATION RESULT; SMALL PERTURBATIONS; SYSTEM OF EQUATIONS; TUMOUR CELLS; TUMOUR GROWTH;

DRUG THERAPY; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; SIMULATORS;

TUMORS;

EID: 72149090879     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.01.214     Document Type: Article

References (15)

1. Murray J.M. Optimal control for a cancer chemotherapy problem with general growth and loss fuctions. Mathematical Biosciences 98 (1990) 273-287
2. Swanson K.R., and Alvord E.C. A quantitative model for differential motility of gliomas in grey and white matter. Cell Proliferation 33 5 (2000) 317-329
3. Kansal A.R., Torquato S., et al. Simulated brain tumor growth dynamics using a three-dimensional cellular automaton. Journal of Theoretical Biology 203 4 (2000) 367-382
4. Kansal A.R., Torquato S., et al. Cellular automaton of idealized brain tumor growth dynamics. Biosystems 55 1-3 (2000) 119-127
5. Gerlee P., and Anderson A.R.A. An evolutionary hybrid cellular automaton model of solid tumour growth. Journal of Theoretical Biology 246 4 (2007) 583-603
6. Anderson A.R.A., and Chaplain M.A.J. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bulletin of Mathematical Biology 60 5 (1998) 857-899
7. Enderling H., and Anderson A.R.A. Mathematical modelling of radiotherapy strategies for early breast cancer. Journal of Theoretical Biology 241 1 (2006) 158-171
8. de Pillis L.G., and Radunskaya A.E. The dynamics of an optimally controlled tumor model: A case study. Mathematical and Computer Modelling 37 (2003) 1221-1244
9. de Pillis L.G., Gu W., and Radunskaya A.E. Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations. Journal of Theoretical Biology 238 4 (2006) 841-862
10. de Pillis L.G., Gu W., Fister K.R., Head T., Maples K., Murugan A., Neal T., and Yoshida K. Chemotherapy for tumors: An analysis of the dynamics and a study of quadratic and linear optimal controls. Mathematical Biosciences 209 (2007) 292-315
11. Banks S.P., and Dinesh K. Approximate optimal control and stability of nonlinear finite- and infinite-dimensional systems. Annals of Operations Research 98 (2000) 19-44
12. Salamci M.U., Ozgoren M.K., and Banks S.P. Sliding mode control with optimal sliding surfaces for missile autopilot design. AIAA Journal of Guidance, Control, and Dynamics 23 4 (2000) 719-727
13. Pinch E.R. Optimal Control and the Calculus of Variations (1993), Oxford University Press
14. Cimen T., and Banks S.P. Nonlinear optimal tracking control with application to super-tankers for autopilot design. Automatica 40 (2004) 1845-1863
15. Swierniak A., Ledzewicz U., and Schattler H. Optimal control for a class of compartmental models in cancer chemotherapy. International Journal of Applied Mathematics and Computer Science 13 (2003) 357-368