Using Mathematical Modelling as a Virtual Microscope to Support Biomedical Research

  • Chiara Giverso
  • Luigi PreziosiEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 6)


This chapter will explain what kind of support mathematics can give to biology and medicine. In order to explain the concepts in practice cell migration is used as a specific example. This phenomenon is of great biomedical interest because it is a fundamental phenomenon both in physiological (e.g. wound healing, immune response) and pathological processes (e.g. chronic inflammation, detachment of metastasis and related tissue invasion). Also a key feature of any artificial system aimed atmimicking biological structures is to allow and enhance cellmigration on or inside it. At the same time anti-cancer treatment can become more efficient blocking cell’s capability to migrate towards distant sites and invade different organs.


Ovarian Cancer Cell Mesothelial Cell Biological Experiment Multiphase Model Ovary Cancer Invasion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ambrosi, D.: Cellular traction as an inverse problem. SIAM J. Appl. Math. 66, 2049–2060 (2006)CrossRefGoogle Scholar
  2. 2.
    Anderson, A.R.A., Chaplain, M.A.J., Rejniak, K.A.: Single-cell-based models in biology and medicine. Mathematics and Biosciences in Interaction. Birkhäuser-Verlag, Basel (2007)Google Scholar
  3. 3.
    Cohen, J.E.: Mathematics is biology’s next microscope, only better; Biology is mathematics’ next physics, only better. PLoS Biology 2, e439 (2004)CrossRefGoogle Scholar
  4. 4.
    Giverso, C., Scianna, M., Preziosi, L., Lo Buono, N., Funaro, A.: Individual cell-based model for in-vitro mesothelial invasion of ovarian cancer. Math. Model. Nat. Phenom. 5, 203–223 (2010)CrossRefGoogle Scholar
  5. 5.
    Giverso, C., Grillo, A., Preziosi, L.: Influence of nucleus deformability on cell movement into cylindrical structures, Biomech. Model. Mechanobiol. (2013). doi 10.1007/s10237-013-0510-3Google Scholar
  6. 6.
    Glazier, J.A., Graner, F.: Simulation of the differential adhesion driven rearrangement of biological cells. Physical. Rev. E 47, 2128–2154 (1993)CrossRefGoogle Scholar
  7. 7.
    Glazier, J. A., Balter, A., Poplawski, N.J.: Magnetization to morphogenesis: a brief history of the Glazier-Graner-Hogeweg model. In: Anderson, A.R.A., Chaplain, M.A.J., Rejniak, K.A.(eds.) Single-Cell-Based Models in Biology and Medicine. Mathematics and Biosciences in Interactions, pp. 79–106. Birkhäuser-Verlag, Basel (2007)CrossRefGoogle Scholar
  8. 8.
    Graner, F., Glazier, J.A.: Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Letters 69, 2013–2017 (1992)CrossRefGoogle Scholar
  9. 9.
    Hentschel, H.G.E., Glimm, T., Glazier, J.A., Newman S.A.: Dynamical mechanisms for skeletal pattern formation in the vertebrate limb. Proc. R. Soc. Lond. B 271, 1713–1722 (2004)CrossRefGoogle Scholar
  10. 10.
    Lo Buono, N., Parrotta, R., Morone, S., Bovino, R., Nacci, G., Ortolan, E., Horenstein, A.L., Inzhutova, A., Ferrero, E., Funaro, A.: The CD157-integrin partnership controls transendothelial migration and adhesion of human monocytes, J. Biol. Chem. 286, 18681–18691 (2011)CrossRefGoogle Scholar
  11. 11.
    Marée, A.F.M., Grieneisen, V.A., Hogeweg, P.: The Cellular Potts Model and biophysical properties of cells, tissues and morphogenesis. In: Anderson, A.R.A., Chaplain, M.A.J., Rejniak, K.A. (eds.) Single-Cell-Based Models in Biology and Medicine. Mathematics and Biosciences in Interactions, pp. 107–136. Birkhäuser-Verlag, Basel (2007)CrossRefGoogle Scholar
  12. 12.
    Merks, R.M.H., Glazier, J.A.: A cell-centered approach to developmental biology. Physica. A. 352, 113–130 (2005)CrossRefGoogle Scholar
  13. 13.
    Morone, S., Lo Buono, N., Parrotta, R., Giacomino, A., Nacci, G., Brusco, A., Larionov, A., Ostano, P., Mello-Grand, M., Chiorino, G., Ortolan, E., Funaro, A.: Overexpression of CD157 contributes to epithelial ovarian cancer progression by promoting mesenchymal differentiation. PLoS ONE (2012). doi:10.1371/journal.pone.0043649Google Scholar
  14. 14.
    Preziosi, L., Tosin, A.: Multiphase and multiscale trends in cancer modelling, Math. Model. Nat. Phenom. 4, 1–11 (2009).CrossRefGoogle Scholar
  15. 15.
    Rolli, C.G., Seufferlein, T., Kemkemer, R., Spatz, J.P., Impact of tumor cell cytoskeleton organization on invasiveness and migration: A microchannel-based approach. PLos ONE 5, e8726 (2010)CrossRefGoogle Scholar
  16. 16.
    Savill, N.J., Hogeweg, P.: Modelling morphogenesis: from single cells to crawling slugs, J. Theor. Biol. 184, 118–124 (1997)CrossRefGoogle Scholar
  17. 17.
    Scianna, M, Preziosi, L.: Multiscale developments of cellular Potts models. Multiscale Model. Simul. 10, 342–382 (2012)CrossRefGoogle Scholar
  18. 18.
    Scianna, M, Preziosi, L.: Cellular Potts Models: Multiscale Developments and Biological Applications, Chapman & Hall/CRC Press (2013)Google Scholar
  19. 19.
    Scianna, M., Preziosi, L.: Modelling the influence of nucleus elasticity on cell invasion in fiber networks and microchannels, J. Theor. Biol. 317, 394–406 (2013)CrossRefGoogle Scholar
  20. 20.
    Scianna, M., Preziosi, L., Wolf, K.: A cellular potts model: simulating cell-and extracellular matrix-derived determinants for cell migration on and in matrix environments, Math. Biosci. Eng. 10, 235–261 (2013)CrossRefGoogle Scholar
  21. 21.
    Vitale, G., Preziosi, L., Ambrosi, D.: A numerical method for the inverse problem of cell traction in 3D. Inv. Prob. 28, 095013 (2012)Google Scholar
  22. 22.
    Wolf, K., Wu, Y.I., Liu, Y., Geiger, J., Tam, E., Overall, C., Stack, M.S., Friedl, P.: Multistep pericellular proteolysis controls the transition from individual to collective cancer cell invasion. Nat. Cell. Biol. 9, 893–904 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Dipartimento di Scienze MatematichePolitecnico di TorinoTorinoItaly

Personalised recommendations