AN IN VITRO CELL POPULATION DYNAMICS MODEL INCORPORATING CELL SIZE, QUIESCENCE, AND CONTACT INHIBITION-Reference-Cited by-同舟云学术

AN IN VITRO CELL POPULATION DYNAMICS MODEL INCORPORATING CELL SIZE, QUIESCENCE, AND CONTACT INHIBITION

Published:2011-04 Issue:supp01 Volume:21 Page:871-892
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

DUCROT ARNAUD¹,LE FOLL FRANK²,MAGAL PIERRE¹,MURAKAWA HIDEKI³,PASQUIER JENNIFER²,WEBB GLENN F.⁴

Affiliation:

1. Institut de Mathématiques de Bordeaux, UMR CNRS 5251 — Case 36, Université Victor Segalen Bordeaux 2, 3ter place de la Victoire 33000 Bordeaux Cedex, France

2. Laboratory of Ecotoxicology UPRES-EA 3222, IFRMP 23, University of Le Havre, 25 rue Philippe Lebon, 76058 Le Havre Cedex, France

3. Graduate School of Science and Engineering for Research, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan

4. Department of Mathematics, Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA

Abstract

In this paper, we construct a model to describe the spatial motion of a monolayer of cells occupying a two-dimensional dish. By taking care of nonlocal contact inhibition, quiescence phenomenon, and the cell cycle, we derive porous media-like equation with nonlocal reaction terms. The first part of this paper is devoted to the construction of the model. In the second part we study the well-posedness of the model. We conclude the paper by presenting some numerical simulations of the model and we observe the formation of colonies.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202511005404

Reference54 articles.

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2. A history of the study of solid tumour growth: the contribution of mathematical modelling

3. A continuum approach to modelling cell–cell adhesion

4. Adding Adhesion to a Chemical Signaling Model for Somite Formation

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