On a multiobjective optimal control of a tumor growth model with immune response and drug therapies

Rocha, Ana Maria A. C.; Costa, M. Fernanda P.; Fernandes, Edite Manuela da G. P.

doi:10.1111/itor.12345

Cited by 8 publications

(8 citation statements)

References 24 publications

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“…Although tumor-immune dynamics occur at various scales, models have traditionally focused on one of these scales due to the complexities involved. In particular, a prey-predator approach is commonly used to describe numerous biological processes and is suited for representing the actions of individual cells (d'Onofrio et al, 2010;Letellier et al, 2013;Rocha et al, 2018;Singh et al, 2017). For example, a cell-by-cell approach may be useful for strategies in which Natural Killer cells or Cytotoxic T Lymphocytes "prey" on tumor cells.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Mathematical modeling of tumor-immune cell interactions

Mahlbacher

Reihmer

Frieboes

2019

Journal of Theoretical Biology

114

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The anti-tumor activity of the immune system is increasingly recognized as critical for the mounting of a prolonged and effective response to cancer growth and invasion, and for preventing recurrence following resection or treatment. As the knowledge of tumor-immune cell interactions has advanced, experimental investigation has been complemented by mathematical modeling with the goal to quantify and predict these interactions. This succinct review offers an overview of recent tumor-immune continuum modeling approaches, highlighting spatial models. The focus is on work published in the past decade, incorporating one or more immune cell types and evaluating immune cell effects on tumor progression. Due to their relevance to cancer, the following immune cells and their combinations are described: macrophages, Cytotoxic T Lymphocytes, Natural Killer cells, dendritic cells, T regulatory cells, and CD4+ T helper cells. Although important insight has been gained from a mathematical modeling perspective, the development of models incorporating patient-specific data remains an important goal yet to be realized for potential clinical benefit.

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Section: Mathematical Modelingmentioning

confidence: 99%

Mathematical modeling of tumor-immune cell interactions

Mahlbacher

Reihmer

Frieboes

2019

Journal of Theoretical Biology

114

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“…Thus, it is of interest to consider that radiation may have relevant eects on bone cells as for the cancer cell population (Vakaet and Boterberg, 2004). Based on works like Swierniak (2007), Ghaari et al (2016) and Rocha et al (2018), we incorporate the radiation eect into the death rates of the cancer cell populations and bone cells. Taking into account such hypotheses, we proposed the following model for radiotherapy (Camacho and Jerez, 2019):…”

Section: Radiotherapy Modelmentioning

confidence: 99%

“…In regards to the treatment duration per session, , some works based on mathematical modeling of cancer radiotherapy use instantaneous or a short radiation duration of the order of minutes (Ergun, 2003;Bachman and Hillen, 2013;Hong et al, 2021). Other authors assume duration of radiotherapy sessions of the order of hours or days (Ghaari et al, 2016;Rocha et al, 2018).…”

Section: Fractionated Radiotherapy Simulationsmentioning

confidence: 99%

“…Some relevant works based on this focal point are: In Ergun (2003) and Ledzewicz et al (2019), they studied optimization of radiotherapy in combination with anti-angiogenic therapy. Rocha et al (2018) proposed an optimization scheduling for a combination of radiotherapy, chemotherapy and immunotherapy. In Ledzewicz et al (2011) the authors analyzed a sub-optimization approach to obtain more clinically relevant chemotherapy treatment delivering.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control for a bone metastasis with radiotherapy model using a linear objective functional

Camacho¹,

Diaz-Ocampo²,

Jerez³

2022

Math. Model. Nat. Phenom.

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Radiation is known to cause genetic damage to highly proliferative cells such as cancer cells. However, the radiotherapy effects to bone cells is not completely known. In this work we present a mathematical modeling framework to test hypotheses related to the radiation-induced effects on bone metastasis. Thus, we pose an optimal control problem based on a Komarova model describing the interactions between cancer cells and bone cells at a single site of bone remodeling. The radiotherapy treatment is included in the form of a functional which minimizes the use of radiation using a penalty function. Moreover, we are interested to model the 'on' and the 'off' time states of the radiation schedules; so we propose an optimal control problem with a L1-type objective functional. Bang-bang or singular arc solutions are the obtained optimal control solutions. We characterize both solutions types and explicitly give necessary optimality conditions for them. We present numerical simulations to analyze the different possible radiation effects on the bone and cancer cells. We also evaluate the more significant parameters to shift from a bang-bang solution to a singular arc solution and vice versa. Additionally, we study a fractionated radiotherapy model.

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“…In [7], a metamodel for tumor-immune system interactions has been proposed, where the treatment has been formulated as an optimal control problem by cytotoxic agents and immunostimulations. In [8], a multi-objective optimal control of a tumor growth model with the immune response and drug therapies has been presented, so that the average number of tumor cells and immuno and chemotherapeutic drugs administration are minimized at the same time. In [9], a comparison has been made by means of an optimal strategy to control the dynamics of three tumor growth models that consist of an immune system and drug administration therapy.…”

Section: Introductionmentioning

confidence: 99%

A dual approach for positive T–S fuzzy controller design and its application to cancer treatment under immunotherapy and chemotherapy

Ahmadi

Zarei

Razavi–Far

et al. 2020

Biomedical Signal Processing and Control

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This study proposes an effective positive control design strategy for cancer treatment by resorting to the combination of immunotherapy and chemotherapy. The treatment objective is to transfer the initial number of tumor cells and immune-competent cells from the malignant region into the region of benign growth where the immune system can inhibit tumor growth. In order to achieve this goal, a new modeling strategy is used that is based on Takagi-Sugen. A Takagi-Sugeno fuzzy model is derived based on the Stepanova nonlinear model that enables a systematic design of the controller.Then, a positive Parallel Distributed Compensation controller is proposed based on a linear copositive Lyapunov Function so that the tumor volume and administration of the chemotherapeutic and immunotherapeutic drugs is reduced, while the density of the immune-competent cells is reached to an acceptable level. Thanks to the proposed strategy, the entire control design is formulated as a Linear Programming problem, which can be solved very efficiently. Finally, the simulation results show the effectiveness of the proposed control approach for the cancer treatment.

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On a multiobjective optimal control of a tumor growth model with immune response and drug therapies

Cited by 8 publications

References 24 publications

Mathematical modeling of tumor-immune cell interactions

Mathematical modeling of tumor-immune cell interactions

Optimal control for a bone metastasis with radiotherapy model using a linear objective functional

A dual approach for positive T–S fuzzy controller design and its application to cancer treatment under immunotherapy and chemotherapy

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