Space-velocity thermostatted kinetic theory model of tumor growth

The competition between cancer cells and immune system cells in inhomogeneous conditions is described at cell scale within the framework of the thermostatted kinetic theory. Cell learning is reproduced by increased cell activity during favorable interactions. The cell activity fluctuations are contr...

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Autores principales:	Léon Masurel, Carlo Bianca, Annie Lemarchand
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	thermostatted kinetic theory cancer immune system kinetic monte carlo simulations oscillations Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/34fbba8fd66d4ebda0a24c7c17b157b8
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id	oai:doaj.org-article:34fbba8fd66d4ebda0a24c7c17b157b8
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spelling	oai:doaj.org-article:34fbba8fd66d4ebda0a24c7c17b157b82021-11-09T02:20:58ZSpace-velocity thermostatted kinetic theory model of tumor growth10.3934/mbe.20212791551-0018https://doaj.org/article/34fbba8fd66d4ebda0a24c7c17b157b82021-06-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021279?viewType=HTMLhttps://doaj.org/toc/1551-0018The competition between cancer cells and immune system cells in inhomogeneous conditions is described at cell scale within the framework of the thermostatted kinetic theory. Cell learning is reproduced by increased cell activity during favorable interactions. The cell activity fluctuations are controlled by a thermostat. The direction of cell velocity is changed according to stochastic rules mimicking a dense fluid. We develop a kinetic Monte Carlo algorithm inspired from the direct simulation Monte Carlo (DSMC) method initially used for dilute gases. The simulations generate stochastic trajectories sampling the kinetic equations for the distributions of the different cell types. The evolution of an initially localized tumor is analyzed. Qualitatively different behaviors are observed as the field regulating activity fluctuations decreases. For high field values, i.e. efficient thermalization, cancer is controlled. For small field values, cancer rapidly and monotonously escapes from immunosurveillance. For the critical field value separating these two domains, the 3E's of immunotherapy are reproduced, with an apparent initial elimination of cancer, a long quasi-equilibrium period followed by large fluctuations, and the final escape of cancer, even for a favored production of immune system cells. For field values slightly smaller than the critical value, more regular oscillations of the number of immune system cells are spontaneously observed in agreement with clinical observations. The antagonistic effects that the stimulation of the immune system may have on oncogenesis are reproduced in the model by activity-weighted rate constants for the autocatalytic productions of immune system cells and cancer cells. Local favorable conditions for the launching of the oscillations are met in the fluctuating inhomogeneous system, able to generate a small cluster of immune system cells with larger activities than those of the surrounding cancer cells.Léon MasurelCarlo BiancaAnnie LemarchandAIMS Pressarticlethermostatted kinetic theorycancerimmune systemkinetic monte carlo simulationsoscillationsBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 5525-5551 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	thermostatted kinetic theory cancer immune system kinetic monte carlo simulations oscillations Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	thermostatted kinetic theory cancer immune system kinetic monte carlo simulations oscillations Biotechnology TP248.13-248.65 Mathematics QA1-939 Léon Masurel Carlo Bianca Annie Lemarchand Space-velocity thermostatted kinetic theory model of tumor growth
description	The competition between cancer cells and immune system cells in inhomogeneous conditions is described at cell scale within the framework of the thermostatted kinetic theory. Cell learning is reproduced by increased cell activity during favorable interactions. The cell activity fluctuations are controlled by a thermostat. The direction of cell velocity is changed according to stochastic rules mimicking a dense fluid. We develop a kinetic Monte Carlo algorithm inspired from the direct simulation Monte Carlo (DSMC) method initially used for dilute gases. The simulations generate stochastic trajectories sampling the kinetic equations for the distributions of the different cell types. The evolution of an initially localized tumor is analyzed. Qualitatively different behaviors are observed as the field regulating activity fluctuations decreases. For high field values, i.e. efficient thermalization, cancer is controlled. For small field values, cancer rapidly and monotonously escapes from immunosurveillance. For the critical field value separating these two domains, the 3E's of immunotherapy are reproduced, with an apparent initial elimination of cancer, a long quasi-equilibrium period followed by large fluctuations, and the final escape of cancer, even for a favored production of immune system cells. For field values slightly smaller than the critical value, more regular oscillations of the number of immune system cells are spontaneously observed in agreement with clinical observations. The antagonistic effects that the stimulation of the immune system may have on oncogenesis are reproduced in the model by activity-weighted rate constants for the autocatalytic productions of immune system cells and cancer cells. Local favorable conditions for the launching of the oscillations are met in the fluctuating inhomogeneous system, able to generate a small cluster of immune system cells with larger activities than those of the surrounding cancer cells.
format	article
author	Léon Masurel Carlo Bianca Annie Lemarchand
author_facet	Léon Masurel Carlo Bianca Annie Lemarchand
author_sort	Léon Masurel
title	Space-velocity thermostatted kinetic theory model of tumor growth
title_short	Space-velocity thermostatted kinetic theory model of tumor growth
title_full	Space-velocity thermostatted kinetic theory model of tumor growth
title_fullStr	Space-velocity thermostatted kinetic theory model of tumor growth
title_full_unstemmed	Space-velocity thermostatted kinetic theory model of tumor growth
title_sort	space-velocity thermostatted kinetic theory model of tumor growth
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/34fbba8fd66d4ebda0a24c7c17b157b8
work_keys_str_mv	AT leonmasurel spacevelocitythermostattedkinetictheorymodeloftumorgrowth AT carlobianca spacevelocitythermostattedkinetictheorymodeloftumorgrowth AT annielemarchand spacevelocitythermostattedkinetictheorymodeloftumorgrowth
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Space-velocity thermostatted kinetic theory model of tumor growth

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