Diffusion-limited tumour growth: Simulations and analysis
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. I...
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AIMS Press
2010-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.385 |
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| author | Philip Gerlee Alexander R. A. Anderson |
| author_facet | Philip Gerlee Alexander R. A. Anderson |
| author_sort | Philip Gerlee |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a61e1eb6851a4e69b46908533e5828a5 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a61e1eb6851a4e69b46908533e5828a52025-01-24T02:00:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-03-017238540010.3934/mbe.2010.7.385Diffusion-limited tumour growth: Simulations and analysisPhilip Gerlee0Alexander R. A. Anderson1Center for Models of Life, Niels Bohr Institute, Blegdamsvej 17, 2200 Copenhagen OCenter for Models of Life, Niels Bohr Institute, Blegdamsvej 17, 2200 Copenhagen OThe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.385tumour morphology.diffusion-limited growth |
| spellingShingle | Philip Gerlee Alexander R. A. Anderson Diffusion-limited tumour growth: Simulations and analysis Mathematical Biosciences and Engineering tumour morphology. diffusion-limited growth |
| title | Diffusion-limited tumour growth: Simulations and analysis |
| title_full | Diffusion-limited tumour growth: Simulations and analysis |
| title_fullStr | Diffusion-limited tumour growth: Simulations and analysis |
| title_full_unstemmed | Diffusion-limited tumour growth: Simulations and analysis |
| title_short | Diffusion-limited tumour growth: Simulations and analysis |
| title_sort | diffusion limited tumour growth simulations and analysis |
| topic | tumour morphology. diffusion-limited growth |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.385 |
| work_keys_str_mv | AT philipgerlee diffusionlimitedtumourgrowthsimulationsandanalysis AT alexanderraanderson diffusionlimitedtumourgrowthsimulationsandanalysis |