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A Cell Population Model Structured by Cell Age Incorporating Cell–Cell Adhesion

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Mathematical Oncology 2013

Abstract

An analysis is given of a continuum model of a proliferating cell population, which incorporates cell movement in space and cell progression through the cell cycle. The model consists of a nonlinear partial differential equation for the cell density in the spatial position and the cell age coordinates. The equation contains a diffusion term corresponding to random cell movement, a nonlocal dispersion term corresponding to cell–cell adhesion, a cell age-dependent boundary condition corresponding to cell division, and a nonlinear logistic term corresponding to constrained population growth. Basic properties of the solutions are proved, including existence, uniqueness, positivity, and long-term behavior dependent on parametric input. The model is illustrated by simulations applicable to in vitro wound closure experiments, which are widely used for experimental testing of cancer therapies.

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Authors and Affiliations

  1. Mansfield College, University of Oxford, Oxford, OX1 3TF, UK

    Janet Dyson

  2. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Glenn F. Webb

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  1. Janet Dyson
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  2. Glenn F. Webb
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Correspondence to Janet Dyson .

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Editors and Affiliations

  1. International Prevention Research Institute, Lyon, France

    Alberto d'Onofrio

  2. Istituto di Analisi dei Sistemi ed Informatica "Antonio Ruberti"—CNR, Rome, Italy

    Alberto Gandolfi

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Dyson, J., Webb, G.F. (2014). A Cell Population Model Structured by Cell Age Incorporating Cell–Cell Adhesion. In: d'Onofrio, A., Gandolfi, A. (eds) Mathematical Oncology 2013. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-0458-7_4

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