# American Institute of Mathematical Sciences

2013, 10(3): 729-742. doi: 10.3934/mbe.2013.10.729

## Hybrid discrete-continuous model of invasive bladder cancer

 1 School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Ramat Aviv, 69978, Israel 2 Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, 40700, Israel

Received  June 2012 Revised  November 2012 Published  April 2013

Bladder cancer is the seventh most common cancer worldwide. Epidemiological studies and experiments implicated chemical penetration into urothelium (epithelial tissue surrounding bladder) in the etiology of bladder cancer. In this work we model invasive bladder cancer. This type of cancer starts in the urothelium and progresses towards surrounding muscles and tissues, causing metastatic disease. Our mathematical model of invasive BC consists of two coupled sub-models: (i) living cycle of the urothelial cells (normal and mutated) simulated using discrete technique of Cellular Automata and (ii) mechanism of tumor invasion described by the system of reaction-diffusion equations. Numerical simulations presented here are in good qualitative agreement with the experimental results and reproduce in vitro observations described in medical literature.
Citation: Eugene Kashdan, Svetlana Bunimovich-Mendrazitsky. Hybrid discrete-continuous model of invasive bladder cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 729-742. doi: 10.3934/mbe.2013.10.729
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