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Diffusion-limited tumour growth: Simulations and analysis.

Artikel i vetenskaplig tidskrift
Författare Philip Gerlee
Alexander R.A. Anderson
Publicerad i Mathematical biosciences and engineering
Volym 7
Nummer/häfte 2
Sidor 385-400
ISSN 1547-1063
Publiceringsår 2010
Publicerad vid
Sidor 385-400
Språk en
Ämnesord Diffusion-limited growth, Tumour morphology
Ämneskategorier Tumörbiologi, Numerisk analys

Sammanfattning

The morphology of solid tumours is known to be affected by the background oxygen concentration of the tissue in which the tumour grows, and both computational and experimental studies have suggested that branched tumour morphology in low oxygen concentration is caused by diffusion-limited growth. In this paper we present a simple hybrid cellular automaton model of solid tumour growth aimed at investigating this phenomenon. Simulation results show that for high consumption rates (or equivalently low oxygen concentrations) the tumours exhibit branched morphologies, but more importantly the simplicity of the model allows for an analytic approach to the problem. By applying a steady-state assumption we derive an approximate solution of the oxygen equation, which closely matches the simulation results. Further, we derive a dispersion relation which reveals that the average branch width in the tumour depends on the width of the active rim, and that a smaller active rim gives rise to thinner branches. Comparison between the prediction of the stability analysis and the results from the simulations shows good agreement between theory and simulation.

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