Mathematical Biosciences and Engineering, 2010, 7(2): 385-400. doi: 10.3934/mbe.2010.7.385.

Primary: 82B24; Secondary: 37B15.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Diffusion-limited tumour growth: Simulations and analysis

1. Center for Models of Life, Niels Bohr Institute, Blegdamsvej 17, 2200 Copenhagen O
2. H. Lee Moffitt Cancer Center & Research Institute, Integrated Mathematical Oncology, 12902 Magnolia Drive, Tampa, FL 33612

   

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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Tumour morphology.; Diffusion-limited growth

Citation: Philip Gerlee, Alexander R. A. Anderson. Diffusion-limited tumour growth: Simulations and analysis. Mathematical Biosciences and Engineering, 2010, 7(2): 385-400. doi: 10.3934/mbe.2010.7.385

 

This article has been cited by

  • 1. Benjamin Werner, David Dingli, Tom Lenaerts, Jorge M. Pacheco, Arne Traulsen, Natalia L. Komarova, Dynamics of Mutant Cells in Hierarchical Organized Tissues, PLoS Computational Biology, 2011, 7, 12, e1002290, 10.1371/journal.pcbi.1002290
  • 2. Alexei T. Skvortsov, Alexander M. Berezhkovskii, Leonardo Dagdug, Trapping of diffusing particles by spiky absorbers, The Journal of Chemical Physics, 2018, 148, 8, 084103, 10.1063/1.5011060
  • 3. Evgeniy Khain, Mark Katakowski, Nicholas Charteris, Feng Jiang, Michael Chopp, Migration of adhesive glioma cells: Front propagation and fingering, Physical Review E, 2012, 86, 1, 10.1103/PhysRevE.86.011904
  • 4. Stefan Burén, Ana L. Gomes, Ana Teijeiro, Mohamad-Ali Fawal, Mahmut Yilmaz, Krishna S. Tummala, Manuel Perez, Manuel Rodriguez-Justo, Ramón Campos-Olivas, Diego Megías, Nabil Djouder, Regulation of OGT by URI in Response to Glucose Confers c-MYC-Dependent Survival Mechanisms, Cancer Cell, 2016, 30, 2, 290, 10.1016/j.ccell.2016.06.023
  • 5. Shannon M. Mumenthaler, Jasmine Foo, Nathan C. Choi, Nicholas Heise, Kevin Leder, David B. Agus, William Pao, Franziska Michor, Parag Mallick, The Impact of Microenvironmental Heterogeneity on the Evolution of Drug Resistance in Cancer Cells, Cancer Informatics, 2015, 14s4, CIN.S19338, 10.4137/CIN.S19338
  • 6. Jan Poleszczuk, Paul Macklin, Heiko Enderling, , Stem Cell Heterogeneity, 2016, Chapter 346, 335, 10.1007/7651_2016_346
  • 7. Youness Azimzade, Abbas Ali Saberi, Muhammad Sahimi, Role of the Interplay Between the Internal and External Conditions in Invasive Behavior of Tumors, Scientific Reports, 2018, 8, 1, 10.1038/s41598-018-24418-8
  • 8. Philip Gerlee, Eunjung Kim, Alexander R.A. Anderson, Bridging scales in cancer progression: Mapping genotype to phenotype using neural networks, Seminars in Cancer Biology, 2015, 30, 30, 10.1016/j.semcancer.2014.04.013
  • 9. Vipin Narang, James Decraene, Shek-Yoon Wong, Bindu S. Aiswarya, Andrew R. Wasem, Shiang Rong Leong, Alexandre Gouaillard, Systems immunology: a survey of modeling formalisms, applications and simulation tools, Immunologic Research, 2012, 53, 1-3, 251, 10.1007/s12026-012-8305-7
  • 10. Marta Panuszewska, Bartosz Minch, Rafał Wcisło, Witold Dzwinel, , Cellular Automata, 2018, Chapter 4, 42, 10.1007/978-3-319-99813-8_4
  • 11. Hang Xie, Yang Jiao, Qihui Fan, Miaomiao Hai, Jiaen Yang, Zhijian Hu, Yue Yang, Jianwei Shuai, Guo Chen, Ruchuan Liu, Liyu Liu, Nils Cordes, Modeling three-dimensional invasive solid tumor growth in heterogeneous microenvironment under chemotherapy, PLOS ONE, 2018, 13, 10, e0206292, 10.1371/journal.pone.0206292
  • 12. Peng Feng, Zhewei Dai, Dorothy Wallace, On a 2D Model of Avascular Tumor with Weak Allee Effect, Journal of Applied Mathematics, 2019, 2019, 1, 10.1155/2019/9581072
  • 13. Woo Kyung Moon, Hong-Hao Chen, Sung Ui Shin, Wonshik Han, Ruey-Feng Chang, Evaluation of TP53/PIK3CA mutations using texture and morphology analysis on breast MRI, Magnetic Resonance Imaging, 2019, 63, 60, 10.1016/j.mri.2019.08.026

Reader Comments

your name: *   your email: *  

Copyright Info: 2010, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved