Multiscale mathematical modeling occurrence and growth of a tumour in an epithelial tissue

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1 : :57; MSC 21: 92D2.. 1,,.. 1,.. 2, 1 -,,, 61499,.,.,. 24 2,,, 32,. dmitribratsun@rambler.ru, pismen@technion.ac.il , - -, - -, -., , - -. :,,,,, Multiscale mathematical modeling occurrence and growth of a tumour in an epithelial tissue D. A. Bratsun 1, A. P. Zakharov 1, L.M. Pismen 2 1 Perm State Humanitarian Pedagogical University, 24 Sibirskaya str., Perm, 61499, Russia 2 Department of Chemical Engineering, Technion Israel Institute of Technology, 32 Haifa, Israel Abstract. In this paper we propose a mathematical model of cancer tumour occurrence in a quasi twodimensional epithelial tissue. Basic model of the epithelium growth describes the appearance of intensive movement and growth of tissue when it is damaged. The model includes the effects of division of cells and intercalation. It is assumed that the movement of cells is caused by the wave of mitogen-activated protein kinase (MAPK), which in turn activated by the chemo-mechanical signal propagating along tissue due to its local damage. In this paper it is assumed that cancer cells arise from local failure of spatial synchronization of circadian rhythms. The study of the evolutionary dynamics of the model could determine the chemo-physical properties of a tumour, and spatial relationship between the occurrence of cancer cells and development of the entire tissue parameters coordinating its evolution through the exchange of chemical and mechanical signals. Keywords: mathematical modeling, cancer growth, circadian rhythms, gene regulation, synchronization, complex systems Citation: Computer Research and Modeling, 214, vol. 6, no. 4, pp (Russian). ( -26/244), ( 31-) ( ). 214,,

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