Blasting neuroblastoma using optimal control of chemotherapy
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Department of Mathematics and Statistics, Murray State University, Murray, KY 42071
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Department of Mathematics and Statistics, Murray State University, 6C Faculty Hall, Murray, KY 42071
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Received:
01 July 2007
Accepted:
29 June 2018
Published:
01 June 2009
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MSC :
Primary: 49J15, 49K15; Secondary: 93C15.
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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.
Citation: Craig Collins, K. Renee Fister, Bethany Key, Mary Williams. Blasting neuroblastoma using optimal control of chemotherapy[J]. Mathematical Biosciences and Engineering, 2009, 6(3): 451-467. doi: 10.3934/mbe.2009.6.451
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Abstract
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.
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