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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 2: 263-277. doi: 10.3934/mbe.2011.8.263
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Modeling and simulation of some cell dispersion problems by a nonparametric method

  • 1.
    ICAM, WWU Münster, Einsteinstr. 62, 48149 Münster
  • Received: 01 February 2010 Accepted: 29 June 2018 Published: 01 April 2011

  • MSC : Primary: 92C17, 82C31, 60H10; Secondary: 60K40, 65C20, 62G07.

  • Starting from the classical descriptions of cell motion we propose some ways to enhance the realism of modeling and to account for interesting features like allowing for a random switching between biased and unbiased motion or avoiding a set of obstacles. For this complex behavior of the cell population we propose new models and also provide a way to numerically assess the macroscopic densities of interest upon using a nonparametric estimation technique. Up to our knowledge, this is the only method able to numerically handle the entire complexity of such settings.

    Citation: Christina Surulescu, Nicolae Surulescu. Modeling and simulation of some cell dispersion problems by a nonparametric method[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 263-277. doi: 10.3934/mbe.2011.8.263

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  • Starting from the classical descriptions of cell motion we propose some ways to enhance the realism of modeling and to account for interesting features like allowing for a random switching between biased and unbiased motion or avoiding a set of obstacles. For this complex behavior of the cell population we propose new models and also provide a way to numerically assess the macroscopic densities of interest upon using a nonparametric estimation technique. Up to our knowledge, this is the only method able to numerically handle the entire complexity of such settings.


  • This article has been cited by:

    1. Christian Engwer, Thomas Hillen, Markus Knappitsch, Christina Surulescu, Glioma follow white matter tracts: a multiscale DTI-based model, 2015, 71, 0303-6812, 551, 10.1007/s00285-014-0822-7
    2. Thomas Lorenz, Christina Surulescu, On a class of multiscale cancer cell migration models: Well-posedness in less regular function spaces, 2014, 24, 0218-2025, 2383, 10.1142/S0218202514500249
    3. Gülnihal Meral, Christian Stinner, Christina Surulescu, On a multiscale model involving cell contractivity and its effects on tumor invasion, 2015, 20, 1553-524X, 189, 10.3934/dcdsb.2015.20.189
    4. Christina Surulescu, Nicolae Surulescu, 2013, Chapter 9, 978-3-319-03079-1, 269, 10.1007/978-3-319-03080-7_9
    5. Sandesh Hiremath, Christina Surulescu, A stochastic multiscale model for acid mediated cancer invasion, 2015, 22, 14681218, 176, 10.1016/j.nonrwa.2014.08.008
    6. JAN KELKEL, CHRISTINA SURULESCU, A MULTISCALE APPROACH TO CELL MIGRATION IN TISSUE NETWORKS, 2012, 22, 0218-2025, 1150017, 10.1142/S0218202511500175
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  • © 2011 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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