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

Primary: 92C42; Secondary: 35K57, 37B15.

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Hybrid discrete-continuous model of invasive bladder cancer

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

Bladder cancer is the seventh most common cancer worldwide.Epidemiological studies and experiments implicated chemicalpenetration into urothelium (epithelial tissue surrounding bladder) inthe etiology of bladder cancer.In this workwe model invasive bladder cancer. This type of cancer starts in theurothelium and progresses towards surroundingmuscles and tissues, causing metastatic disease.Our mathematical model of invasive BC consists of two coupledsub-models: (i) living cycle of the urothelial cells (normal and mutated) simulatedusing discrete technique of Cellular Automata and (ii) mechanism oftumor invasion described by the system of reaction-diffusionequations. Numerical simulations presented here are in good qualitative agreementwith the experimental results and reproduce in vitroobservations described in medical literature.
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Keywords cellular automata; Bladder cancer; reaction-diffusion equations.; metaloproteinases

Citation: Eugene Kashdan, Svetlana Bunimovich-Mendrazitsky. Hybrid discrete-continuous model of invasive bladder cancer. Mathematical Biosciences and Engineering, 2013, 10(3): 729-742. doi: 10.3934/mbe.2013.10.729

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