A size and space structured model describing interactions of tumor cells with immune cells reveals cancer persistent equilibrium states in tumorigenesis. (7th April 2020)

• Record Type: Journal Article
• Authors: Atsou, Kevin; Anjuère, Fabienne; Braud, Véronique M.; Goudon, Thierry
• Is Part Of: Journal of theoretical biology. Volume 490(2020)
• Publication Date: 2020-04-07
• Subjects: Tumor growth -- Immune system -- Equilibrium phase; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2020.110163
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: A new size and space structured model describing early interactions between tumor cells and cytotoxic effector immune cells. A model able to reproduce cancer persistent equilibrium phases. Interpretation of the equilibrium by means of eigenvalue problems. Numerical results illustrate the crucial role of space heterogeneities in the dynamics of the immune response. Abstract: The recent success of immunotherapies for the treatment of cancer has highlighted the importance of the interactions between tumor and immune cells. Mathematical models of tumor growth are needed to faithfully reproduce and predict the spatiotemporal dynamics of tumor growth. We introduce a mathematical model intended to describe by means of a system of partial differential equations the early stages of the interactions between effector immune cells and tumor cells. The model is structured in size and space, and it takes into account the migration of the tumor antigen-specific cytotoxic effector cells towards the tumor micro-environment by a chemotactic mechanism. We investigate on numerical grounds the role of the key parameters of the model such as the division and growth rates of the tumor cells, and the conversion and death rates of the immune cells. Our main findings are two-fold. Firstly, the model exhibits a possible control of the tumor growth by the immune response; nevertheless, the control is not complete in the sense that the asymptotic equilibrium states keep residual tumors and activated immune cells. Secondly, space heterogeneities of the source of immune cells can significantly reduce the efficiency of the control dynamics, making patterns of remission-recurrence appear.