Abstract
We show that heterogeneity of cells that compose a tumor leads to its irregular growth. We model avascular tumor growth using cellular automata (CA). In our model, we take into account the composition of cells and intercellular adhesion in addition to processes involved in cell cycle—proliferation, quiescence, apoptosis and necrosis. More importantly, we consider cell mutation that gives rise to a different phenotype and therefore, a tumor with heterogeneous population of cells. A new phenotype is probabilistically chosen and has the ability to survive at lower levels of nutrient concentration and reproduce faster. We solve diffusion equation using central difference method to determine the concentration of nutrients, in particular, oxygen available to each cell during the growth process. We present the growth simulation and demonstrate similarity with theoretical findings.
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References
Hanahan, D., Weinberg, R.A.: The Hallmarks of Cancer. Cell 100, 57–70 (2000)
Sutherland, R.: Cell and environment interactions in tumor microregions: The multicell spheroid model. Science 240, 177–184 (1988)
Greenspan, H.P.: Models for the growth of a solid tumor by diffusion. Stud Appl Math. L1(4), 31–340 (1972)
Gatenby, R.A., Gawlinski, E.T.: A reaction diffusion model of cancer invasion. Cancer. Res. 56, 5745–5753 (1996)
Ward, J.P., King, J.R.: Mathematical modelling of avascular-tumour growth – I. IMA J. Math. Appl. Med. Biol. 14, 39–69 (1997)
Ferreira, S.C., Martins, M.L., Vilela, M.J.: Reaction-diffusion model for the growth of avascular tumor. Phys. Rev. E. 65, 021907 (2002)
Ambrosi, D., Mollica, F.: On the mechanics of a growing tumor. Int. J. Eng. Sci. 40, 1297–1316 (2002)
Byrne, H., Preziosi, L.: Modelling solid tumour growth using the theory of mixtures. Math. Med. Biol. 20, 341–366 (2003)
Cristini, V., Li, X., Lowengrub, J.S., Wise, S.M.: Nonlinear simulations of solid tumor growth using a mixture model—Invasion and branching. J. Math. Biol. 58, 723–763 (2009)
Araujo, R.P., McElwain, D.L.S.: A history of the study of solid tumour growth—The contribution of mathematical modelling. Bull. Math. Biol. 66, 1039–1091 (2004)
Qi, A., Zheng, X., Du, C., An, B.: A cellular automaton model of cancerous growth. J. Theor. Biol. 161, 1–12 (1993)
Dormann, S., Deutsch, A.: Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. In Silico Biol. 2, 393–406 (2002)
Wang, Z., Deisboeck, T.S.: Computational modeling of brain tumors—Discrete, continuum or hybrid. Sci. Model. Simul. 15, 381–393 (2008)
Anderson, A.R.A.: A hybrid mathematical model of solid tumor invasion: the importance of cell adhesion. Math. Med. Biol. 22, 163–186 (2005)
Alarcon, T., Byrne, H.M., Maini, P.K.: Towards whole-organ modelling of tumour growth. Prog. Biophys. Mol. Biol. 75, 451–472 (2004)
Sottoriva, A., Verhoeff, J.C., Borovski, T., McWeeney, S.K., Naumov, L., Medema, J.P., Sloot, P.M.A., Vermeulen, L.: Cancer stem cell tumour model reveals invasive morphology and increased phenotypical heterogeneity. Cancer Res. 1, 46–56 (2010)
Wolfram, S.: Theory and Applications of Cellular Automata. World Scientific, Singapore (1986)
Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign, IL (2002)
Kansal, A.R., Torquato, S., Chiocca, E.A., Deisboeck, T.S.: Emergence of a subpopulation in a computational model of tumor growth. J. Theor. Biol. 207, 431–441 (2000)
Vermeulen, L., Torado, M., Mello, F.S., Sprick, M.R., Kemper, K., Alea, M.P., Richel, D.J., Stassi, G., Medema, J.P.: Single-cell cloning of colon cancer stem cells reveals a multi-lineage differentiation capacity. Proc. Natl. Acad. Sci. USA 105(36), 13427–13432 (2008)
Sherwood, L.: Human physiology: From cells to systems. Brooks/Cole, Cengage Learning (2010), ISBN 9780495391845; ISBN 0495391840
Tomita, K., Plager, J.E.: In vivo cell cycle synchronization of the murine sarcoma 180 tumor following Alternating periods of hydroxyurea blockade and release. Cancer Res. 39, 4407–4411 (1979)
Gerlee, P., Anderson, A.R.A.: Stability analysis of a hybrid cellular automaton model of cell colony growth. Phys. Rev. E 75, 051911 (2007)
Casciari, J.J., Sotirchos, S.V., Sutherland, R.M.: Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH. J. Cell. Physiol. 151, 386–394 (1992)
Freyer, J.P., Tustanoff, E., Franko, A.J., Sutherland, R.M.: In situ oxygen consumption rates of cells in V-79 multicellular spheroids during growth. J. Cell. Physiol. 118, 53–61 (1984)
Acknowledgments
The first author was a SIRF scholar in Australia and was in receipt of the UIS scholarship during the completion of this research. The financial support of the National Health and Medical Research Council (Australia) Grant No.1006031 is gratefully acknowledged.
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Shrestha, S.M.B., Joldes, G., Wittek, A., Miller, K. (2012). Modeling Heterogeneous Tumor Growth Using Hybrid Cellular Automata. In: Nielsen, P., Wittek, A., Miller, K. (eds) Computational Biomechanics for Medicine. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3172-5_14
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DOI: https://doi.org/10.1007/978-1-4614-3172-5_14
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