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Assessing Cell Viability and Death in 3D Spheroid Cultures of Cancer Cells
Published on: June 16, 2019
Analysis of a mathematical model for the growth of cancer cells
1Peter L. Reichertz Institute for Medical Informatics, University of Braunschweig, D-38106 Braunschweig, Germany. martin.kohlmann@plri.de
Abstract:
In this paper, a 2D model for the growth of multilayer tumours is presented. The model consists of a free boundary problem for the tumour cell membrane and the tumour is supposed to grow or shrink due to cell proliferation or cell dead. The growth process is caused by a diffusing nutrient concentration σ and is controlled by an internal cell pressure p. We assume that the tumour occupies a strip-like domain with a fixed boundary at y = 0 and a free boundary y = ρ(x), where ρ is a 2π-periodic function. First, we prove the existence of solutions (σ, p, ρ) on a scale of small Höolder spaces and show that our model allows for flat stationary solutions. As a main result, we establish that these equilibrium points are locally asymptotically stable under small perturbations.
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