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

  • Janet DysonEmail author
  • Glenn F. Webb
Chapter
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

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.

Keywords

Cell age Cell adhesion Non-local Reaction-diffusion Analytic semigroup Fractional power Existence Regularity Positivity 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Mansfield CollegeUniversity of OxfordOxfordUK
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA

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