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2011, 2011(Special): 803-812. doi: 10.3934/proc.2011.2011.803

Multi-scale model of bladder cancer development

Eugene Kashdan 1, and  Svetlana Bunimovich-Mendrazitsky 2,

1. 

School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Ramat Aviv
2. 

Ariel University Centerof of Samaria, Mathematics Department, Ariel

Received  July 2010 Revised  April 2011 Published  October 2011

Bladder Cancer (BC) is the seventh most common cancer worldwide. Etiology of BC is well known. According to existing statistics, 80% of BC patients had occupational exposure to chemical carcinogens (rubber, dye, textile, or plant industry) or/and were smoking regularly during long periods of time. The carcinogens from the bladder lumen affect umbrella cells of the urothelium (epithelial tissue surrounding bladder) and then subsequently pen- etrate to the deeper layers of the tissue (intermediate and basal cells). It is a years-long process until the carcinogenic substance will accumulate in the tissue in the quantity necessary to trigger DNA mutations leading to the tumor development. We address carcinogen penetration (modeled as a nonlinear diffusion equation with variable coefficient and source term) within the cellular automata (CA) framework of the urothelial cell living cycle. Our approach combines both discrete and continuous models of some of the crucial biological and physical processes inside the urothelium and yields a first theoretical insight on the initial stages of the BC development and growth.
Keywords: Bladder Cancer, Cellular Automata, Carcinogen Penetration, Porous Medium Equation.
Mathematics Subject Classification: Primary: 92C42; Secondary: 92C17, 35K55.
Citation: Eugene Kashdan, Svetlana Bunimovich-Mendrazitsky. Multi-scale model of bladder cancer development. Conference Publications, 2011, 2011 (Special) : 803-812. doi: 10.3934/proc.2011.2011.803
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