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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 3: 729-742. doi: 10.3934/mbe.2013.10.729
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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
  • Received: 01 June 2012 Accepted: 29 June 2018 Published: 01 April 2013

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

  • 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.

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

    Related Papers:

  • 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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  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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