Cancer Research: Computer Simulation of Tumor Growth with Immune Response

Ankana Boondirek

Authors

Ankana Boondirek Department of Mathematics, Burapha University, Chonburi 20131, Thailand

Keywords:

Cancer modeling, Stochastic model, Cellular automaton model, Gompertz function, Immune response

Abstract

A discrete model for the growth of an avascular tumor on a threedimensional square lattice has been developed. A cellular automata method for tumor growth based on microscopic description of the immune system response, the cell proliferation, the cell death and its degradation is used to simulate the growth. The MonteCarlo method is be applied to this model. The results give a growth curve which is shown to qualitatively agree well with experimental result.

References

Qi, A.S., Zheng, X., Du, C. Y. & An, B. S. (1993). A

cellular automaton of cancerous growth. J. theor. Biol, 161, 112.

Kansal, A. R., Torquato, S., Harsh, G. R., Chiocca, E. A. & Deisboeck, T. S. (2000). Cellular automaton of idealized brain tumor growth dynamics .Biosystems, 55, 119127.

Kansal, A. R., Torquato, S., Harsh, G. R., Chiocca, E. A. & Deisboeck, T. S. (2000). Simulated brain tumor growth dynamics using a threedimensional cellular automaton. J. theor. Biol, 203, 367382.

Boondirek, A., Lenbury, Y., Woongekkabut, J., Triampo,

W., Tang, I. M., & Picha, P. A. (2006). Stochastic model of cancer growth with immune response. Korean Physical Society, 49(4), 16521666.

Kirschner, D. & Panetta, J. C. (1998). Modelling immunotherapy of the tumorimmune interaction. J. Math. Bio, 37, 235252.

Ferreira Jr, S. C., Martins, M. L. & Vilela, M. J. (1998). A growth model for promary cancer. Physica A, 261, 569 580.

Ferreira Jr, S.C., Martins, M. L. & Vilela, M. J. (1999). A growth model for primarycancer (II), New rules progress curves and morphology transitions. Physica A, 271, 245256.

Voitikova, M. V. (1998). Cellular automaton model for immunology of tumor growth.

Smolle, J., Soyer, H. P., SmolleJuettner, F. M., Stettner, H., & Kerl, H. (1990). Computer simulation of tumour cell motility and proliferation. Path. Res. Pract, 186, 467472.

Duchting, W. & Vogelsaenger, T. (1981). Three dimensional pattern generation applied to spheroidal tumor growth in a nutrient medium. Int. J. BioMedical Computing, 12, 377392.

Bellomo, N., & Preziosi, L. (2000). Modelling an mathematical problems related to tumor evolution and its interaction with the immune system. Math. Comput. Modelling, 32, 413452.

Galach, M. (2003). Dynamics of the tumorimmune system competitionthe effect of time delay. Int. J. Appl. Math. Comput. Sci, 13(3), 395406.

Alarcon, T., Byrne, H. M., & Maini, P. K. (2003). A cellular automaton model for tumour growth in inhomogeneous environment. J. theor. Biol, 225, 257 274.

Buric, N. & Todorovic, D. (2002). Dynamics of delaydifferential equations modelling immunology of tumor growth. Chaos, Solitons and Fractals, 13, 645 665.

Steel, G. G. (1977). Growth kinetics of tumours. NewYork: Clarendon press.

Matzavinos, A. & Chaplain, A. J. (2004). Travelling wave analysis of a model of the immune response to cancer. C.R .Biologies, 327, 9951008.

Kuznetsoov V. A. & Taylor M. A. (1994). Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis. Bull. Math. Biol, 56(2), 295321.

Bru, A., Albertos, S., Subiza, J. L., GarciaAsenjo, J. L., & Bru, I. (2003). The universal dynamics of tumor growth. Biophysic Journal, 85, 29482961.

Preziosi, L. (2003). Cancer modeling and simulation.

Chapman & Hall/CRC,

Waliszewski, P. & Konarski, J. (2002). The Gompertzian curve reveals fractal properties of tumor growth. Chaos, Solitons and Fractals, 16, 665674.