  In this work, we present a mathematical model of the initiation and
progression of a low-grade urinary bladder carcinoma. We simulate the crucial
processes involved in tumor growth, such as oxygen diffusion, carcinogen
penetration, and angiogenesis, within the framework of the urothelial cell
dynamics. The cell dynamics are modeled using the discrete technique of
Cellular Automata, while the continuous processes of carcinogen penetration and
oxygen diffusion are described by nonlinear diffusion-absorption equations. As
the availability of oxygen is necessary for tumor progression, processes of
oxygen transport to the tumor growth site seem most important. Our model yields
a theoretical insight into the main stages of development and growth of urinary
bladder carcinoma with emphasis on two most common types: bladder polyps and
carcinoma {\it in situ}. Analysis of histological structure of bladder tumor is
important to avoid misdiagnosis and wrong treatment and we expect our model to
be a valuable tool in the prediction of tumor grade and progression patterns,
based on the exposure to carcinogens and an oxygen dependent expression of
genes promoting tumor growth. Our numerical simulations have good qualitative
agreement with {\it in vivo} results reported in the corresponding medical
literature.
