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2009, 6(3): 451-467. doi: 10.3934/mbe.2009.6.451

Blasting neuroblastoma using optimal control of chemotherapy

Craig Collins 1, , K. Renee Fister 2, , Bethany Key 1, and  Mary Williams 1,

1. 

Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, United States, United States, United States
2. 

Department of Mathematics and Statistics, Murray State University, 6C Faculty Hall, Murray, KY 42071

Received  July 2007 Revised  January 2009 Published  June 2009

A mathematical model is used to investigate the effectiveness of the chemotherapy drug Topotecan against neuroblastoma. Optimal control theory is applied to minimize the tumor volume and the amount of drug utilized. The model incorporates a state constraint that requires the level of circulating neutrophils (white blood cells that form an integral part of the immune system) to remain above an acceptable value. The treatment schedule is designed to simultaneously satisfy this constraint and achieve the best results in fighting the tumor. Existence and uniqueness of the solution of the optimality system, which is the state system coupled with the adjoint system, is established. Numerical simulations are given to demonstrate the behavior of the tumor and the immune system components represented in the model.
Keywords: topotecan., optimal control, chemotherapy.
Mathematics Subject Classification: Primary: 49J15, 49K15; Secondary: 93C1.
Citation: Craig Collins, K. Renee Fister, Bethany Key, Mary Williams. Blasting neuroblastoma using optimal control of chemotherapy. Mathematical Biosciences & Engineering, 2009, 6 (3) : 451-467. doi: 10.3934/mbe.2009.6.451
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