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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

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  • 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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  • This article has been cited by:

    1. Svetlana Bunimovich-Mendrazitsky, Vladimir Pisarev, Eugene Kashdan, Modeling and simulation of a low-grade urinary bladder carcinoma, 2015, 58, 00104825, 118, 10.1016/j.compbiomed.2014.12.022
    2. Alex Kiselyov, Svetlana Bunimovich-Mendrazitsky, Vladimir Startsev, Key signaling pathways in the muscle-invasive bladder carcinoma: Clinical markers for disease modeling and optimized treatment, 2016, 138, 00207136, 2562, 10.1002/ijc.29918
    3. Joao Carvalho, Valeria Lopes, Rui Travasso, Tumor cell invasiveness in the initial stages of bladder cancer development ‐ A computational study, 2021, 37, 2040-7939, 10.1002/cnm.3417
    4. Angelo Torelli, Fabian Siegel, Philipp Erben, Markus Gumbel, 2015, Chapter 37, 978-3-319-16479-3, 375, 10.1007/978-3-319-16480-9_37
    5. BING ZHAO, XIAOMENG LI, Altholactone induces reactive oxygen species-mediated apoptosis in bladder cancer T24 cells through mitochondrial dysfunction, MAPK-p38 activation and Akt suppression, 2014, 31, 1021-335X, 2769, 10.3892/or.2014.3126
    6. Jacques Demongeot, Pierre Magal, Population dynamics model for aging, 2023, 20, 1551-0018, 19636, 10.3934/mbe.2023870
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