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Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver

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  • Iman Alimirzaei
  • Alaeddin Malek
  • Kolade M. Owolabi

Abstract

This paper proposes a real-life volume reduction for cancer cells using optimal doses of radiation and an anti-angiogenic drug. A generalized dynamical system based on the diffusion-consumption equation along with stimulation and inhibition factors is proposed. To achieve continuous and low-dose therapy, the related problem is simulated by an optimal regulator problem mathematically. By combining steepest descent, conjugate gradient, and Armijo techniques, a novel hybrid indirect iterative solver is designed. For accuracy and execution speed, the current solver is compared with an interior-point optimizer and sequential quadratic Hamiltonian methods. Cancer therapy under two different treatment strategies and 24 various versions of the general dynamical system is considered numerically. A comprehensive analysis of the corresponding outcomes is presented. Numerical results and related diagrams are provided.

Suggested Citation

  • Iman Alimirzaei & Alaeddin Malek & Kolade M. Owolabi, 2023. "Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver," Journal of Mathematics, Hindawi, vol. 2023, pages 1-19, September.
    • Handle: RePEc:hin:jjmath:5554420
    DOI: 10.1155/2023/5554420
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