The Role of Nonconservative Interactions in the Asymptotic Limit of Thermostatted Kinetic Models

Brézin

2017

Int. J. Biomath.

The activation and the resulting response of the immune system to antigens comprise different complex processes and cells. This paper aims at modeling the processes of recognition and learning of the immune system by means of the thermostatted kinetic theory methods. Specifically, the thermostatted kinetic framework is firstly generalized for taking into account that in some processes of proliferation of the cells, the rate is also function of the degree of information exchanged amongst cells. In particular, within the new framework, a mathematical model is proposed for miming the recognition process of the immune system through the definition of interactions between the cytotoxic and humoral components of the adaptive immune system via T-and B-cells. The model validation is obtained by performing a sensitivity analysis on the parameters which depicts the main emerging phenomena and the different phases of the recognition and learning of the immune system.

Section: Critical Analysis and Research Perspectivesmentioning

confidence: 99%

Modeling the antigen recognition by B-cell and T-cell receptors through thermostatted kinetic theory methods

Brézin

2017

Int. J. Biomath.

“…Classically different kinds of scalings lead to different kinds of equations: parabolic and hyperbolic [172][173][174][175][176][177][178][179][180][181]. Specifically by defining a rescaling of time and space variables (low-field or high-field scaling), and under suitable technical assumptions, macroscopic equations typically of the mechanics continuum approach are derived.…”

Section: The Thermostatted Kinetic Theorymentioning

confidence: 99%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Physics of Life Reviews

2016

Pathological fibrosis is the result of a failure in the wound healing process. The comprehension and the related modeling of the different mechanisms that trigger fibrosis is a challenge of many researchers that work in the field of medicine and biology. The modern scientific analysis of a phenomenon generally consists of three major approaches: theoretical, experimental, and computational. Different theoretical tools coming from mathematics and physics have been proposed for the modeling of the physiological and pathological fibrosis. However a complete framework is missing and the development of a general theory is required. This review aims at finding a unified approach in the modeling of fibrosis diseases that takes into account the different phenomena occurring at each level: molecular, cellular and tissue. Specifically by means of a critical analysis of the different models that have been proposed in the mathematical, computational and physical biology, from molecular to tissue scales, a multiscale approach is proposed, an approach that has been strongly recommended by top level biologists in the past decades.

“…A model of competition between cancer cells and immune system cells should reflect these different interactions as well as the activation and learning processes. With the aim of building a minimal model, we consider a single type of immune system cells i, cancer cells c, and normal cells n. The learning process is reproduced by the increase of a so-called activity u carried by each cell [9,10,11,12,13,14]. Thermostatted kinetic theory appears as a suitable framework to model cancer and immune system competition at the cell scale [15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Thermostatted kinetic theory approach to the competition between cancer and immune system cells in an inhomogeneous system

Masurel

31st International Symposium on Rarefied Gas Dynamics: Rgd31

Lemarchand

2019

The competition between a cancer and the immune system are modelled at cell scale in the framework of thermostatted kinetic theory. Cell activation and learning are reproduced by the increase of cell activity during interactions. The fluctuations of system activity are controlled by a thermostat which reproduces the regulation of the learning process and memory loss through cell death. An algorithm, including spatial description and inspired from the direct simulation Monte Carlo (DSMC) method, is used to simulate stochastic trajectories for cell numbers and activities. We focus on the decisive role played by the thermostat. For inefficient thermalization, the divergence of the number of cancer cells is obtained in spite of favored production of immune system cells. Conversely, when the activity fluctuations are controlled, the development of cancer is contained even for weakened immune defenses. These results may be correlated to unexpected clinical observations in the case of different cancers, such as carcinoma, lymphoma, and melanoma.