Eur. Phys. J. Plus (2016) 131: 41
https://doi.org/10.1140/epjp/i2016-16041-7

Regular Article

From cellular to tissue scales by asymptotic limits of thermostatted kinetic models

¹ Ecole Normale Supérieure, Laboratoire de Physique Statistique, 24, rue Lhomond, 75231, Paris cedex 05, France
² CNRS, UMR 8550, LPS, Paris, France
³ Sorbonne Universités, UPMC Univ Paris 06, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, 4, place Jussieu, case courrier 121, 75252, Paris cedex 05, France
⁴ CNRS, UMR 7600 LPTMC, Paris, France
⁵ Université de Caen, Department of Mathematics, LMNO, CNRS, UMR 6139, 14032, Caen Cedex, France

^* e-mail: bianca@lps.ens.fr

Received: 7 December 2015
Accepted: 5 January 2016
Published online: 23 February 2016

Abstract

Tumor growth strictly depends on the interactions occurring at the cellular scale. In order to obtain the linking between the dynamics described at tissue and cellular scales, asymptotic methods have been employed, consisting in deriving tissue equations by suitable limits of mesoscopic models. In this paper, the evolution at the cellular scale is described by thermostatted kinetic theory that include conservative, nonconservative (proliferation, destruction and mutations), stochastic terms, and the role of external agents. The dynamics at the tissue scale (cell-density evolution) is obtained by performing a low-field scaling and considering the related convergence of the rescaled framework when the scaling parameter goes to zero.