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An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix

  • Received: 01 March 2012 Accepted: 29 June 2018 Published: 01 December 2012
  • MSC : 65C20, 74B99, 74C99, 74D99, 92C05, 92C10, 74L15.

  • The basement membrane (BM) and extracellular matrix (ECM) play critical roles in developmental and cancer biology, and are of great interest in biomathematics. We introduce a model of mechanical cell-BM-ECM interactions that extends current (visco)elastic models (e.g. [8,16]), and connects to recent agent-based cell models (e.g. [2,3,20,26]). We model the BM as a linked series of Hookean springs, each with time-varying length, thickness, and spring constant. Each BM spring node exchanges adhesive and repulsive forces with the cell agents using potential functions. We model elastic BM-ECM interactions with analogous ECM springs. We introduce a new model of plastic BM and ECM reorganization in response to prolonged strains, and new constitutive relations that incorporate molecular-scale effects of plasticity into the spring constants. We find that varying the balance of BM and ECM elasticity alters the node spacing along cell boundaries, yielding a nonuniform BM thickness. Uneven node spacing generates stresses that are relieved by plasticity over long times. We find that elasto-viscoplastic cell shape response is critical to relieving uneven stresses in the BM. Our modeling advances and results highlight the importance of rigorously modeling of cell-BM-ECM interactions in clinically important conditions with significant membrane deformations and time-varying membrane properties, such as aneurysms and progression from in situ to invasive carcinoma.

    Citation: Gianluca D'Antonio, Paul Macklin, Luigi Preziosi. An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix[J]. Mathematical Biosciences and Engineering, 2013, 10(1): 75-101. doi: 10.3934/mbe.2013.10.75

    Related Papers:

  • The basement membrane (BM) and extracellular matrix (ECM) play critical roles in developmental and cancer biology, and are of great interest in biomathematics. We introduce a model of mechanical cell-BM-ECM interactions that extends current (visco)elastic models (e.g. [8,16]), and connects to recent agent-based cell models (e.g. [2,3,20,26]). We model the BM as a linked series of Hookean springs, each with time-varying length, thickness, and spring constant. Each BM spring node exchanges adhesive and repulsive forces with the cell agents using potential functions. We model elastic BM-ECM interactions with analogous ECM springs. We introduce a new model of plastic BM and ECM reorganization in response to prolonged strains, and new constitutive relations that incorporate molecular-scale effects of plasticity into the spring constants. We find that varying the balance of BM and ECM elasticity alters the node spacing along cell boundaries, yielding a nonuniform BM thickness. Uneven node spacing generates stresses that are relieved by plasticity over long times. We find that elasto-viscoplastic cell shape response is critical to relieving uneven stresses in the BM. Our modeling advances and results highlight the importance of rigorously modeling of cell-BM-ECM interactions in clinically important conditions with significant membrane deformations and time-varying membrane properties, such as aneurysms and progression from in situ to invasive carcinoma.


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    [1]  Advances in Molecular and Cell Biology, 6 (1993), 183-206.
    [2]  PLoS Comput. Biol., 7 (2011), e1001045.
    [3]  FEBS J. (2012, in press).
    [4]  Chemistry and Biology, 3 (1996), 895-904.
    [5]  Cell, 103 (2000), 481-490.
    [6]  J. Theor. Biol., 231 (2004), 203-222.
    [7]  in preparation (2012).
    [8]  J. Theor. Biol., 298 (2012), 82-91.
    [9]  Math. Med. Biol., 20 (2003), 277-308.
    [10]  J. Theor. Biol., 232 (2005), 523-543.
    [11]  Phys. Biol., 6 (2009).
    [12]  Phys. Rev. E, 47 (1993), 2128-2154.
    [13]  Phys. Rev. Lett., 69 (1992), 2013-2016.
    [14]  Carcinogenesis, 25 (2004), 1543-1549.
    [15]  Cancer and Metastasis Review, 25 (2006), 35-43.
    [16]  Progress in Biophysics and Molecular Biology, 106 (2011), 353-379.
    [17]  Natural Structural Biology, 8 (2001), 573-574.
    [18]  in "Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach'' (eds. V. Cristini and J. S. Lowengrub), Cambridge University Press (2010), 8-23.
    [19]  in "Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach'' (eds. V. Cristini and J. S. Lowengrub), Cambridge University Press (2010), 88-122.
    [20]  J. Theor. Biol., 301 (2012), 122-140.
    [21]  in "Computational Biology: Issues and Applications in Oncology'' (ed. T. Pham), Springer (2009), 77-112.
    [22]  in "Multiscale Computer Modeling in Biomechanics and Biomedical Engineering'' (ed. A. Gefen), Springer (2013), in press.
    [23]  J. Theor. Biol., 263 (2010), 393-406.
    [24]  Bull. Math. Biol., 71 (2009), 1189-1227.
    [25]  J. Theor. Biol., 262 (2010), 35-47.
    [26]  Math. Comp. Model., 47 (2006), 533-545.
    [27]  J. Theor. Biol., 243 (2006), 532-541.
    [28]  Phys. Biol., 5 (2008), 015002.
    [29]  Phys. Biol., 8 (2011), 045007.
    [30]  Multiscale Model. Sim., 10 (2012), 342-382.
    [31]  CRC/Academic Press, 2012.
    [32]  Math. Biosci. Eng., (2013, in press).
    [33]  Comptes Rendus Physique, 10 (2009), 790-811.
    [34]  Carcinogenesis, 20 (1999), 749-755.
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