论文信息 - Simulating the Tumor Growth with Cellular Automata Models

Simulating the Tumor Growth with Cellular Automata Models

In this paper, two types of cellular automata are studied in order to describe the 2-dimensional free growth of an avascular tumor under the effect of a limited nutrient source. On one hand a deterministic cellular automata approach is used. On the other hand a stochastic one is presented. An existing reaction-diffusion model including cell proliferation, motility and death is used. Finally, a numerical simulations that show the difference between these approaches are discussed.

[1] M. L. Martins,et al. Reaction-diffusion model for the growth of avascular tumor. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2] A. Radunskaya,et al. Mixed Immunotherapy and Chemotherapy of Tumors: Modeling, Applications and Biological Interpretations , 2022 .

[3] J. Folkman,et al. SELF-REGULATION OF GROWTH IN THREE DIMENSIONS , 1973, The Journal of experimental medicine.

[4] S. El Yacoubi,et al. A mathematical method for control problems on cellular automata models , 2008, Int. J. Syst. Sci..

[5] L. D. de Pillis,et al. A cellular automata model of tumor-immune system interactions. , 2006, Journal of theoretical biology.

[6] H. Byrne. Mathematical biomedicine and modeling avascular tumor growth , 2012 .

[7] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[8] V. Kuznetsov. Basic Models of Tumor-Immune System Interactions Identification, Analysis and Predictions , 1997 .

[9] P. Maini,et al. A cellular automaton model for tumour growth in inhomogeneous environment. , 2003, Journal of theoretical biology.

[10] M. Chaplain. Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development , 1996 .

[11] Nicola Bellomo,et al. A Survey of Models for Tumor-Immune System Dynamics , 1996 .

[12] Helen M. Byrne,et al. USING MATHEMATICS TO STUDY SOLID TUMOUR GROWTH , 2001 .