Optimal control model of tumor treatment in the context of cancer stem cell

Ghassen Haddad; Amira Kebir; Nadia Raissi; Amira Bouhali; Slimane Ben Miled; Ghassen Haddad; Amira Kebir; Nadia Raissi; Amira Bouhali; Slimane Ben Miled

doi:10.3934/mbe.2022214

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 5: 4627-4642. doi: 10.3934/mbe.2022214

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Optimal control model of tumor treatment in the context of cancer stem cell

1.
IPT-BIMSLab (LR16IPT09), Tunis El Manar University, 1002 Tunis, Tunisia
2.
Sorbonne Université, Laboratoire Jacques-Louis Lions, Paris, France
3.
IPEIT, Tunis University, Tunisia
4.
Mohammed V University of Rabat — um5a Department of Mathematics, Morocco

Academic Editor:Sophia Jang

Received: 09 November 2021 Revised: 23 December 2021 Accepted: 11 January 2022 Published: 07 March 2022

We consider cancer cytotoxic drugs as an optimal control problem to stabilize a heterogeneous tumor by attacking not the most abundant cancer cells, but those that are crucial in the tumor ecosystem. We propose a mathematical cancer stem cell model that translates the hierarchy and heterogeneity of cancer cell types by including highly structured tumorigenic cancer stem cells that yield low differentiated cancer cells. With respect to the optimal control problem, under a certain admissibility hypothesis, the optimal controls of our problem are bang-bang controls. These control treatments can retain the entire tumor in the neighborhood of an equilibrium. We simulate the bang-bang control numerically and demonstrate that the optimal drug scheduling should be administered continuously over long periods with short rest periods. Moreover, our simulations indicate that combining multidrug therapies and monotherapies is more efficient for heterogeneous tumors than using each one separately.
- optimal control theory,
- Pontryagin's maximum principle,
- cancer stem cell,
- cancer dynamics,
- cytotoxic treatment
Citation: Ghassen Haddad, Amira Kebir, Nadia Raissi, Amira Bouhali, Slimane Ben Miled. Optimal control model of tumor treatment in the context of cancer stem cell[J]. Mathematical Biosciences and Engineering, 2022, 19(5): 4627-4642. doi: 10.3934/mbe.2022214

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Abstract

We consider cancer cytotoxic drugs as an optimal control problem to stabilize a heterogeneous tumor by attacking not the most abundant cancer cells, but those that are crucial in the tumor ecosystem. We propose a mathematical cancer stem cell model that translates the hierarchy and heterogeneity of cancer cell types by including highly structured tumorigenic cancer stem cells that yield low differentiated cancer cells. With respect to the optimal control problem, under a certain admissibility hypothesis, the optimal controls of our problem are bang-bang controls. These control treatments can retain the entire tumor in the neighborhood of an equilibrium. We simulate the bang-bang control numerically and demonstrate that the optimal drug scheduling should be administered continuously over long periods with short rest periods. Moreover, our simulations indicate that combining multidrug therapies and monotherapies is more efficient for heterogeneous tumors than using each one separately.

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