Invariance-based analysis of cancer chemotherapy

Riah, Rachid; Fiacchini, Mirko; Alamir, Mazen

doi:10.1109/cca.2015.7320761

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…Herewith our strategies were cancerous cells (C) and healthy cells (H). The payoff matrix of the game is shown in [1].…”

Section: Evolutionary Game Model Of the Interaction Between Healthy Amentioning

confidence: 99%

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Modeling and Analyzing Stem-Cell Therapy toward Cancer: Evolutionary Game Theory Perspective

Veisi¹,

Khadem²,

Ravanshadi³

2020

ijph

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Background: Immunotherapy is a recently developed method of cancer therapy, aiming to strengthen a patient’s immune system in different ways to fight cancer. One of these ways is to add stem cells into the patient’s body. Methods: The study was conducted in Kermanshah, western Iran, 2016-2017. We first modeled the interaction between cancerous and healthy cells using the concept of evolutionary game theory. System dynamics were analyzed employing replicator equations and control theory notions. We categorized the system into separate cases based on the value of the parameters. For cases in which the system converged to undesired equilibrium points, “stem-cell injection” was employed as a therapeutic suggestion. The effect of stem cells on the model was considered by reforming the replicator equations as well as adding some new parameters to the system. Results: By adjusting stem cell-related parameters, the system converged to desired equilibrium points, i.e., points with no or a scanty level of cancerous cells. In addition to the theoretical analysis, our simulation results suggested solutions were effective in eliminating cancerous cells. Conclusion: This model could be applicable to different types of cancer, so we did not restrict it to a specific type of cancer. In fact, we were seeking a flexible mathematical framework that could cover different types of cancer by adjusting the system parameters.

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“…Herewith our strategies were cancerous cells (C) and healthy cells (H). The payoff matrix of the game is shown in [1].…”

Section: Evolutionary Game Model Of the Interaction Between Healthy Amentioning

confidence: 99%

“…Thousands of people are annual victims of cancer (1). The disease is caused by genetic and epigenetic alterations, which can disturb cells' growth and death rates (2,3).…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analyzing Stem-Cell Therapy toward Cancer: Evolutionary Game Theory Perspective

Veisi¹,

Khadem²,

Ravanshadi³

2020

ijph

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“…The uncertainties affecting the cancer models, either parametric [3], or additive are crucial for the analysis and control design in order to find the successful drug administration therapy. Therefore, the main objective of the paper, whose preliminary version is [19], consists in the development of a new method for chemotherapy design considering that the model is affected by state proportional uncertainties. The state proportional uncertainties are the uncertainties which affect proportionally the dynamic of each state of the model.…”

Section: Introductionmentioning

confidence: 99%

Domain of attraction estimation of cancer chemotherapy model affected by state proportional uncertainty

Riah¹,

Fiacchini²,

Alamir³

2016

2016 European Control Conference (ECC)

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This paper proposes an analytical method for the characterisation of the set of all initial tumor and normal states of a cancer dynamical model for which there exists a successful drug administration therapy. The dynamical model considered simulates the behaviour of the tumor and the normal cells populations growth in presence of a chemotherapy drug. This model is assumed to be affected by a state proportional uncertainty. The successful drug administration therapy is attained by respecting the tumor eradication and avoiding the lower admissible bound of the normal cells population which is viewed as an indicator of the patients health. The problem is posed in terms of domain of attraction computation and is solved by applying set theory and invariance tools.

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