Mathematical model of tumor invasion along linear or tubular structures
We examine a mathematical model of a population of cells distributed over a linear or tubular structure. Growth of cells is regulated by a growth factor, which can diffuse over the structure. Aside from this, production of cells and of the growth factor is governed by a pair of ordinary differential...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
17 October 2005
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| In: |
Mathematical and computer modelling
Year: 2005, Volume: 41, Issue: 10, Pages: 1097-1108 |
| DOI: | 10.1016/j.mcm.2005.05.005 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1016/j.mcm.2005.05.005 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0895717705001688 
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| Author Notes: | A. Marciniak-Czochra, M. Kimmel |
| Summary: | We examine a mathematical model of a population of cells distributed over a linear or tubular structure. Growth of cells is regulated by a growth factor, which can diffuse over the structure. Aside from this, production of cells and of the growth factor is governed by a pair of ordinary differential equations. We find conditions under which diffusion causes destabilization of the spatially homogeneous steady state, leading to exponential growth and apparently chaotic spatial patterns, following a period of almost constancy. This phenomenon may serve as a mathematical explanation of “unexpected” rapid growth and invasion of temporarily stable structures composed of cancer cells. |
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| Item Description: | Gesehen am 20.07.2018 |
| Physical Description: | Online Resource |
| DOI: | 10.1016/j.mcm.2005.05.005 |