Mathematical Biosciences and Engineering (MBE)

Hybrid discrete-continuous model of invasive bladder cancer

Pages: 729 - 742, Volume 10, Issue 3, June 2013      doi:10.3934/mbe.2013.10.729

       Abstract        References        Full Text (448.8K)       Related Articles       

Eugene Kashdan - School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Ramat Aviv, 69978, Israel (email)
Svetlana Bunimovich-Mendrazitsky - Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, 40700, Israel (email)

Abstract: 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.

Keywords:  Bladder cancer, metaloproteinases, cellular automata, reaction-diffusion equations.
Mathematics Subject Classification:  Primary: 92C42; Secondary: 35K57, 37B15.

Received: June 2012;      Accepted: November 2012;      Available Online: April 2013.