A Multiscale Hybrid Cellular Automata Model of Tumor Growth: The Impact of Nutrient and Acidity on Tumor Growth

Cancer is the third leading cause of death in Iran after cardiac diseases and car accidents. Mathematical and computational models are great help to better understand cancer related phenomena. It may even improve common therapies or introduce new therapies. In this paper, a new multiscale cellular automata model of tumor growth based on the tumor micro-environment is introduced. Two separate square lattices are presumed for metabolic and cellular spaces. One of the following four states can be devoted to each cell in the cellular lattice: proliferating cancer, non- proliferating cancer, necrotic, and normal cells. Changing the cell's state and tumor growth is discussed in this lattice. However, production/consumption, and the diffusion of nutrients (oxygen and glucose) and also waste products including lactic acid are studied in the metabolic lattice. In this study, we determined the stochastic rules of altering the states of each cell based on the concentration rates of nutrients and lactic acid. The growth fraction and necrotic fraction were used as output parameters beside a 2-D graphical display of growth. The changes in the level of nutrients in the metabolic lattice and the effect of acidity on the growth of tumor have been reported in this paper. Our simulations faithfully reproduce the in vivo experimental observations reported for cholangiocarcinoma.