A size and space structured model describing interactions of tumor cells with immune cells reveals cancer persistent equilibrium states in tumorigenesis.

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.

Analysis of the Equilibrium Phase in Immune-Controlled Tumors Provides Hints for Designing Better Strategies for Cancer Treatment.

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.

A size and space structured model of tumor growth describes a key role for protumor immune cells in breaking equilibrium states in tumorigenesis.

Switching from the healthy stage to the uncontrolled development of tumors relies on complicated mechanisms and the activation of antagonistic immune responses, that can ultimately favor the tumor growth. We introduce here a mathematical model intended to describe the interactions between the immune system and tumors. The model is based on partial differential equations, describing the displacement of immune cells subjected to both diffusion and chemotactic mechanisms, the strength of which is driven by the development of the tumors. The model takes into account the dual nature of the immune response, with the activation of both antitumor and protumor mechanisms. The competition between these antagonistic effects leads to either equilibrium or escape phases, which reproduces features of tumor development observed in experimental and clinical settings. Next, we consider on numerical grounds the efficacy of treatments: the numerical study brings out interesting hints on immunotherapy strategies, concerning the role of the administered dose, the role of the administration time and the interest in combining treatments acting on different aspects of the immune response. Such mathematical model can shed light on the conditions where the tumor can be maintained in a viable state and also provide useful hints for personalized, efficient, therapeutic strategies, boosting the antitumor immune response, and reducing the protumor actions.