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Mathematical Biosciences and Engineering

2009, Volume 6, Issue 3: 451-467. doi: 10.3934/mbe.2009.6.451
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Blasting neuroblastoma using optimal control of chemotherapy

  • 1.
    Department of Mathematics and Statistics, Murray State University, Murray, KY 42071
  • 2.
    Department of Mathematics and Statistics, Murray State University, 6C Faculty Hall, Murray, KY 42071
  • Received: 01 July 2007 Accepted: 29 June 2018 Published: 01 June 2009

  • MSC : Primary: 49J15, 49K15; Secondary: 93C15.

  • 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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  • 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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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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