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Fotso CT, Girel S, Anjuère F, Braud VM, Hubert F, Goudon T. A mixture-like model for tumor-immune system interactions. J Theor Biol 2024; 581:111738. [PMID: 38278343 DOI: 10.1016/j.jtbi.2024.111738] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 11/20/2023] [Accepted: 01/10/2024] [Indexed: 01/28/2024]
Abstract
We introduce a mathematical model based on mixture theory intended to describe the tumor-immune system interactions within the tumor microenvironment. The equations account for the geometry of the tumor expansion, and the displacement of the immune cells, driven by diffusion and chemotactic mechanisms. They also take into account the constraints in terms of nutrient and oxygen supply. The numerical investigations analyze the impact of the different modeling assumptions and parameters. Depending on the parameters, the model can reproduce elimination, equilibrium or escape phases and it identifies a critical role of oxygen/nutrient supply in shaping the tumor growth. In addition, antitumor immune cells are key factors in controlling tumor growth, maintaining an equilibrium while protumor cells favor escape and tumor expansion.
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Affiliation(s)
| | - Simon Girel
- Université Côte d'Azur, Inria, CNRS, LJAD, Parc Valrose, F-06108, Nice, France
| | - Fabienne Anjuère
- Université Côte d'Azur, CNRS, Institut de Pharmacologie Moléculaire et Cellulaire UMR 7275, 660 Route des Lucioles, F-06560, Valbonne, France
| | - Véronique M Braud
- Université Côte d'Azur, CNRS, Institut de Pharmacologie Moléculaire et Cellulaire UMR 7275, 660 Route des Lucioles, F-06560, Valbonne, France
| | - Florence Hubert
- I2M, Aix Marseille Université, CNRS, 39 rue F. Joliot-Curie, F-13453, Marseille, France
| | - Thierry Goudon
- Université Côte d'Azur, Inria, CNRS, LJAD, Parc Valrose, F-06108, Nice, France.
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Leschiera E, Al-Hity G, Flint MS, Venkataraman C, Lorenzi T, Almeida L, Audebert C. An individual-based model to explore the impact of psychological stress on immune infiltration into tumour spheroids. Phys Biol 2024; 21:026003. [PMID: 38266283 DOI: 10.1088/1478-3975/ad221a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Accepted: 01/24/2024] [Indexed: 01/26/2024]
Abstract
In recentin vitroexperiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol resulted in a decreased immune cell infiltration into the spheroids. Moreover, the presence of cortisol deregulated the normal levels of the pro- and anti-inflammatory cytokines IFN-γand IL-10. We present an individual-based model to explore the interaction dynamics between tumour and immune cells under psychological stress conditions. With our model, we explore the processes underlying the emergence of different levels of immune infiltration, with particular focus on the biological mechanisms regulated by IFN-γand IL-10. The set-up of numerical simulations is defined to mimic the scenarios considered in the experimental study. Similarly to the experimental quantitative analysis, we compute a score that quantifies the level of immune cell infiltration into the tumour. The results of numerical simulations indicate that the motility of immune cells, their capability to infiltrate through tumour cells, their growth rate and the interplay between these cell parameters can affect the level of immune cell infiltration in different ways. Ultimately, numerical simulations of this model support a deeper understanding of the impact of biological stress-induced mechanisms on immune infiltration.
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Affiliation(s)
- Emma Leschiera
- Léonard de Vinci Pôle Universitaire, Research Center, 92 916 Paris, La Défense, France
- Univ. Bordeaux, CNRS, INRIA, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France
| | - Gheed Al-Hity
- School of Applied Sciences, University of Brighton, Centre for Stress and Age-related Diseases, Moulsecoomb, Brighton BN2 4GJ, United Kingdom
| | - Melanie S Flint
- School of Applied Sciences, University of Brighton, Centre for Stress and Age-related Diseases, Moulsecoomb, Brighton BN2 4GJ, United Kingdom
| | - Chandrasekhar Venkataraman
- School of Mathematical and Physical Sciences, University of Sussex, Department of Mathematics, Falmer, Brighton BN1 9QH, United Kingdom
| | - Tommaso Lorenzi
- Department of Mathematical Sciences 'G. L. Lagrange', Politecnico di Torino, 10129 Torino, Italy
| | - Luis Almeida
- Sorbonne Université, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions UMR 7598, 75005 Paris, France
| | - Chloe Audebert
- Sorbonne Université, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions UMR 7598, 75005 Paris, France
- Sorbonne Université, CNRS, Institut de biologie Paris-Seine (IBPS), Laboratoire de Biologie Computationnelle et Quantitative UMR 7238, 75005 Paris, France
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Atsou K, Khou S, Anjuère F, Braud VM, Goudon T. Analysis of the Equilibrium Phase in Immune-Controlled Tumors Provides Hints for Designing Better Strategies for Cancer Treatment. Front Oncol 2022; 12:878827. [PMID: 35832538 PMCID: PMC9271975 DOI: 10.3389/fonc.2022.878827] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 05/02/2022] [Indexed: 11/13/2022] Open
Abstract
When it comes to improving cancer therapies, one challenge is to identify key biological parameters that prevent immune escape and maintain an equilibrium state characterized by a stable subclinical tumor mass, controlled by the immune cells. Based on a space and size structured partial differential equation model, we developed numerical methods that allow us to predict the shape of the equilibrium at low cost, without running simulations of the initial-boundary value problem. In turn, the computation of the equilibrium state allowed us to apply global sensitivity analysis methods that assess which and how parameters influence the residual tumor mass. This analysis reveals that the elimination rate of tumor cells by immune cells far exceeds the influence of the other parameters on the equilibrium size of the tumor. Moreover, combining parameters that sustain and strengthen the antitumor immune response also proves more efficient at maintaining the tumor in a long-lasting equilibrium state. Applied to the biological parameters that define each type of cancer, such numerical investigations can provide hints for the design and optimization of cancer treatments.
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Affiliation(s)
- Kevin Atsou
- Université Côte d’Azur, Inria, CNRS, LJAD, Nice, France
| | - Sokchea Khou
- Université Côte d’Azur, CNRS, Institut de Pharmacologie Moléculaire et Cellulaire UMR 7275, Valbonne, France
| | | | - Véronique M. Braud
- Université Côte d’Azur, CNRS, Institut de Pharmacologie Moléculaire et Cellulaire UMR 7275, Valbonne, France
- *Correspondence: Véronique M. Braud, ; Thierry Goudon,
| | - Thierry Goudon
- Université Côte d’Azur, Inria, CNRS, LJAD, Nice, France
- *Correspondence: Véronique M. Braud, ; Thierry Goudon,
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