Urinary bladder carcinoma also known as Bladder Cancer (BC) is the seventh most com-

mon cancer worldwide. According to existing statistics, 80% of BC patients had occupa-

tional 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 a_ect umbrella cells of the urothelium (epithelial tissue surrounding bladder) and

then subsequently penetrate 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 su_cient to trigger DNA mutations leading to the tumor develop-

ment.

In this talk, I propose a model of BC progression that includes the crucial processes

involved in tumor growth. My collaborator (Kashdan Eugene) and I simulated oxygen

di_usion, carcinogen penetration and angiogenesis within the framework of the urothelial

cell dynamics. The cell living cycle is modeled using discrete technique of Cellular Au-

tomata, while the continuous processes of carcinogen penetration and oxygen di_usion are

described by the nonlinear di_usion-absorption equations. Our model yields a theoretical

insight into all stages of BC development and growth with especial accent on two most

common types of urinary bladder carcinoma: bladder polyps and carcinoma in situ. Our

numerical simulations are in a good qualitative agreement with in vivo results reported

in the corresponding medical literature.