Optimal control of drug therapy in cancer treatment

We present an optimal control strategy for nonlinear systems with application to the drug therapy of cancer. The tumour growth model is represented by a system of equations from population dynamics which is based on the competition between normal cells and tumour cells. The effect of the immune syst...

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Bibliographic Details
Published in:Nonlinear analysis 2009-12, Vol.71 (12), p.e1473-e1486
Main Authors: Itik, Mehmet, Salamci, Metin U., Banks, Stephen P.
Format: Article
Language:English
Subjects:
Cancer
Drugs
Dynamical systems
Mathematical modelling
Mathematical models
Nonlinear dynamics
Optimal control
Therapy
Time varying approximations
Tumour growth
Tumours
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Summary:We present an optimal control strategy for nonlinear systems with application to the drug therapy of cancer. The tumour growth model is represented by a system of equations from population dynamics which is based on the competition between normal cells and tumour cells. The effect of the immune system in the presence of cancer is also included in the model. A linear time varying approximation technique is proposed to construct an optimal control strategy for the nonlinear system which is valid not only within small perturbations around the equilibrium point, but also for global dynamics of the system. The optimal control method is applied to eliminate the tumour cells whilst minimizing the amount of drug in the simulated model. Simulation results show that cancer cells can be ‘eradicated’ 1 1 Of course, this work is based on a simulated model, so one should be careful in referring it to real patients. in a very short time with a small amount of drug using an optimal administration of the therapy.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.01.214