A Hybrid Multiscale Approach in Cancer Modelling and Treatment Prediction

  • Gibin Powathil
  • Mark A. J. ChaplainEmail author
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Cancer is a complex multiscale disease involving inter-related processes across a wide range of temporal and spatial scales. Multiscale mathematical models can help in studying cancer progression and serve as an in silico test base for comparing and optimizing various multi-modality anticancer treatment protocols. Here, we discuss one such hybrid multiscale approach, interlinking individual cell behavior with the macroscopic tissue scale. Using this technique, we study the spatio-temporal dynamics of individual cells and their interactions with the tumor microenvironment. At the intracellular level, the internal cell-cycle mechanism is modelled using a system of coupled ordinary differential equations, which determine cellular growth dynamics for each individual cell. The evolution of these individual cancer cells are modelled using a cellular automaton approach. Moreover, we have also incorporated the effects of oxygen distribution into this multiscale model as it has been shown to affect the internal cell-cycle dynamics of the cancer cells. The hybrid multiscale model is then used to study the effects of cell-cycle-specific chemotherapeutic drugs, alone and in combination with radiotherapy, with a long-term goal of predicting an optimal multimodality treatment plan for individual patients.


Cancer Hybrid multiscale model Cell cycle Hypoxia Chemotherapy Radiotherapy 



The authors gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, M5CGS - From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread.


  1. 1.
    Z. Agur, R. Hassin, S. Levy, Optimizing chemotherapy scheduling using local search heuristics. Operat. Res. 54(5), 829–846 (2006)CrossRefzbMATHGoogle Scholar
  2. 2.
    M. Al-Tameemi, M. Chaplain, A. d’Onofrio, Evasion of tumours from the control of the immune system: consequences of brief encounters. Biol. Direct 7, 31 (2012)Google Scholar
  3. 3.
    T. Alarcon, H.M. Byrne, P.K. Maini, A cellular automaton model for tumour growth in inhomogeneous environment. J. Theor. Biol. 225, 257–274 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    T. Alarcon, H.M. Byrne, P.K. Maini, A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells. J. Theor. Biol. 229, 395–411 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    T. Alarcon, H.M. Byrne,, Maini,.: A multiple scale model for tumour growth. Multiscale Model. Sim. 3, 440–475 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Alper, T., Howard-Flanders, P.: Role of oxygen in modifying the radiosensitivity of E. coli B. Nature 178(4540), 978–979 (1956)Google Scholar
  7. 7.
    A. Altinok, F. Levi, A. Goldbeter, A cell cycle automaton model for probing circadian patterns of anticancer drug delivery. Adv. Drug Deliv. Rev. 59, 1036–1053 (2007)CrossRefGoogle Scholar
  8. 8.
    V. Andasari, A. Gerisch, G. Lolas, A.P. South, M.A. Chaplain, Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. J. Math. Biol. 63(1), 141–171 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    A.R. Anderson, M.A. Chaplain, Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60, 857–899 (1998)CrossRefzbMATHGoogle Scholar
  10. 10.
    J.C. Bailar, H.L. Gornik, Cancer undefeated. N. Engl. J. Med. 336, 1569–1574 (1997)CrossRefGoogle Scholar
  11. 11.
    F. Billy, B. Ribba, O. Saut, H. Morre-Trouilhet, T. Colin, D. Bresch, J.P. Boissel, E. Grenier, J.P. Flandrois, A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy. J. Theor. Biol. 260(4), 545–562 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    H.M. Byrne, Dissecting cancer through mathematics: from the cell to the animal model. Nat. Rev. Cancer 10, 221–230 (2010)CrossRefGoogle Scholar
  13. 13.
    H.M. Byrne, M.A. Chaplain, Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math. Biosci. 130(2), 151–181 (1995)CrossRefzbMATHGoogle Scholar
  14. 14.
    H.M. Byrne, M.A. Chaplain, Growth of necrotic tumors in the presence and absence of inhibitors. Math. Biosci. 135(2), 187–216 (1996)CrossRefzbMATHGoogle Scholar
  15. 15.
    M. Chaplain, A. Anderson, Mathematical modelling of tumour-induced angiogenesis: network growth and structure. Cancer Treat. Res. 117, 51–75 (2004)CrossRefGoogle Scholar
  16. 16.
    M.A. Chaudhry, Base excision repair of ionizing radiation-induced DNA damage in G1 and G2 cell cycle phases. Cancer Cell. Int. 7, 15 (2007)CrossRefGoogle Scholar
  17. 17.
    J. Clairambault, A step toward optimization of cancer therapeutics. Physiologically based modeling of circadian control on cell proliferation. IEEE Eng. Med. Biol. Mag. 27, 20–24 (2008)Google Scholar
  18. 18.
    A. Dasu, I. Toma-Dasu, M. Karlsson, Theoretical simulation of tumour oxygenation and results from acute and chronic hypoxia. Phys. Med. Biol. 48, 2829–2842 (2003)CrossRefGoogle Scholar
  19. 19.
    N.E. Deakin, M.A. Chaplain, Mathematical modeling of cancer invasion: the role of membrane-bound matrix metalloproteinases. Front. Oncol. 3, 70 (2013)CrossRefGoogle Scholar
  20. 20.
    T.S. Deisboeck, Z. Wang, P. Macklin, V. Cristini, Multiscale cancer modeling. Annu. Rev. Biomed. Eng. 13, 127–155 (2011)CrossRefGoogle Scholar
  21. 21.
    S. Dormann, A. Deutsch, Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. In Silico Biol. (Gedrukt) 2, 393–406 (2002)Google Scholar
  22. 22.
    H. Enderling, A.R. Anderson, M.A. Chaplain, A.J. Munro, J.S. Vaidya, Mathematical modelling of radiotherapy strategies for early breast cancer. J. Theor. Biol. 241(1), 158–171 (2006)MathSciNetCrossRefGoogle Scholar
  23. 23.
    K. Fister, J. Panetta, Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM J. Appl. Math. 60, 1059–1072 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    H.B Frieboes, M.E. Edgerton, J.P. Fruehauf, F.R. Rose, L.K. Worrall, R.A. Gatenby, M. Ferrari, V. Cristini, Prediction of drug response in breast cancer using integrative experimental/computational modeling. Cancer Res. 69, 4484–4492 (2009)Google Scholar
  25. 25.
    K. Fu, Biological basis for the interaction of chemotherapeutic agents and radiation therapy. Cancer 55(S9), 2123–2130 (1985)CrossRefGoogle Scholar
  26. 26.
    C. Gerard, A. Goldbeter, Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle. Proc. Natl. Acad. Sci. U.S.A. 106, 21,643–21,648 (2009)CrossRefGoogle Scholar
  27. 27.
    A. Gerisch, M.A. Chaplain, Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion. J. Theor. Biol. 250(4), 684–704 (2008)MathSciNetCrossRefGoogle Scholar
  28. 28.
    P. Gerlee, A.R. Anderson, An evolutionary hybrid cellular automaton model of solid tumour growth. J. Theor. Biol. 246, 583–603 (2007)MathSciNetCrossRefGoogle Scholar
  29. 29.
    N. Goda, H.E. Ryan, B. Khadivi, McNulty, W., Rickert, R.C., Johnson, R.S.: Hypoxia-inducible factor 1alpha is essential for cell cycle arrest during hypoxia. Mol. Cell. Biol. 23, 359–369 (2003)Google Scholar
  30. 30.
    A. Goldbeter, A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Natl. Acad. Sci. U.S.A. 88, 9107–9111 (1991)CrossRefGoogle Scholar
  31. 31.
    M. Guerrero, X.A. Li, Analysis of a large number of clinical studies for breast cancer radiotherapy: estimation of radiobiological parameters for treatment planning. Phys. Med. Biol. 48(20), 3307–3326 (2003)CrossRefGoogle Scholar
  32. 32.
    S. Gupta, T. Koru-Sengul, S.M. Arnold, G.R. Devi, M. Mohiuddin, M.M. Ahmed, Low-dose fractionated radiation potentiates the effects of cisplatin independent of the hyper-radiation sensitivity in human lung cancer cells. Mol. Cancer Ther. 10(2), 292–302 (2011)CrossRefGoogle Scholar
  33. 33.
    C. Hennequin, V. Favaudon, Biological basis for chemo-radiotherapy interactions. European J. Cancer 38(2), 223–230 (2002)CrossRefGoogle Scholar
  34. 34.
    C. Hennequin, N. Giocanti, V. Favaudon, Interaction of ionizing radiation with paclitaxel (Taxol) and docetaxel (Taxotere) in HeLa and SQ20B cells. Cancer Res. 56(8), 1842–1850 (1996)Google Scholar
  35. 35.
    A.R. Kansal, S. Torquato, G.R. Harsh IV, E.A. Chiocca, T.S. Deisboeck, Cellular automaton of idealized brain tumor growth dynamics. BioSystems 55, 119–127 (2000)CrossRefGoogle Scholar
  36. 36.
    M.A. Konerding, W. Malkusch, B. Klapthor, C. van Ackern, E. Fait, S.A. Hill, C. Parkins, D.J. Chaplin, M. Presta, J. Denekamp, Evidence for characteristic vascular patterns in solid tumours: quantitative studies using corrosion casts. Br. J. Cancer 80, 724–732 (1999)CrossRefGoogle Scholar
  37. 37.
    F. Levi, A. Okyar, Circadian clocks and drug delivery systems: impact and opportunities in chronotherapeutics. Expert Opin. Drug Deliv. 8(12), 1535–1541 (2011)CrossRefGoogle Scholar
  38. 38.
    F. Levi, A. Okyar, S. Dulong, P.F. Innominato, J. Clairambault, Circadian timing in cancer treatments. Annu. Rev. Pharmacol. Toxicol. 50, 377–421 (2010)CrossRefGoogle Scholar
  39. 39.
    W. Liu, T. Hillen, H. Freedman, A mathematical model for m-phase specific chemotherapy including the g0-phase and immunoresponse. Math. Biosci. Eng. 4(2), 239 (2007)Google Scholar
  40. 40.
    J.S. Lowengrub, H.B. Frieboes, F. Jin, Y.L. Chuang, X. Li, P. Macklin, S.M. Wise, V. Cristini, Nonlinear modelling of cancer: bridging the gap between cells and tumours. Nonlinearity 23, R1–R9 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    P. Macklin, S. McDougall, A.R. Anderson, M.A. Chaplain, V. Cristini, J. Lowengrub, Multiscale modelling and nonlinear simulation of vascular tumour growth. J. Math. Biol. 58(4–5), 765–798 (2009)MathSciNetCrossRefGoogle Scholar
  42. 42.
    A. Maity, McKenna, W.G., Muschel, R.J.: The molecular basis for cell cycle delays following ionizing radiation: a review. Radiother. Oncol. 31(1), 1–13 (1994)Google Scholar
  43. 43.
    A. Matzavinos, M.A. Chaplain, V.A. Kuznetsov, Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour. Math. Med. Biol. 21(1), 1–34 (2004)CrossRefzbMATHGoogle Scholar
  44. 44.
    Matzavinos, A., Kao, C.Y., Green, J.E., Sutradhar, A., Miller, M., Friedman, A.: Modeling oxygen transport in surgical tissue transfer. Proc. Natl. Acad. Sci. U.S.A. 106, 12,091–12,096 (2009)Google Scholar
  45. 45.
    S.R. McDougall, A.R. Anderson, M.A. Chaplain, Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. J. Theor. Biol. 241(3), 564–589 (2006)MathSciNetCrossRefGoogle Scholar
  46. 46.
    H.B. Mistry, D.E. MacCallum, R.C. Jackson, M.A. Chaplain, F.A. Davidson, Modeling the temporal evolution of the spindle assembly checkpoint and role of Aurora B kinase. Proc. Natl. Acad. Sci. U.S.A. 105(51), 20,215–20,220 (2008)CrossRefGoogle Scholar
  47. 47.
    B. Novak, J.J. Tyson, Modelling the controls of the eukaryotic cell cycle. Biochem. Soc. Trans. 31, 1526–1529 (2003)CrossRefGoogle Scholar
  48. 48.
    B. Novak, J.J. Tyson, A model for restriction point control of the mammalian cell cycle. J. Theor. Biol. 230, 563–579 (2004)MathSciNetCrossRefGoogle Scholar
  49. 49.
    M.R. Owen, T. Alarcon, P.K. Maini, H.M. Byrne, Angiogenesis and vascular remodelling in normal and cancerous tissues. J. Math. Biol. 58, 689–721 (2009)MathSciNetCrossRefGoogle Scholar
  50. 50.
    M.R. Owen, H.M. Byrne, C.E. Lewis, Mathematical modelling of the use of macrophages as vehicles for drug delivery to hypoxic tumour sites. J. Theor. Biol. 226, 377–391 (2004)MathSciNetCrossRefGoogle Scholar
  51. 51.
    J. Panetta, J. Adam, A mathematical model of cycle-specific chemotherapy. Math. Comput. Model.22(2), 67–82 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    A.A. Patel, E.T. Gawlinski, S.K. Lemieux, R.A. Gatenby, A cellular automaton model of early tumor growth and invasion. J. Theor. Biol. 213, 315–331 (2001)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Pawlik, T.M., Keyomarsi, K.: Role of cell cycle in mediating sensitivity to radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 59(4), 928–942 (2004)CrossRefGoogle Scholar
  54. 54.
    Perfahl, H., Byrne, H.M., Chen, T., Estrella, V., Alarcon, T., Lapin, A., Gatenby, R.A., Gillies, R.J., Lloyd, M.C., Maini, P.K., Reuss, M., Owen, M.R.: Multiscale modelling of vascular tumour growth in 3D: the roles of domain size and boundary conditions. PLoS ONE 6, e14,790 (2011)CrossRefGoogle Scholar
  55. 55.
    G. Powathil, M. Kohandel, M. Milosevic, S. Sivaloganathan, Modeling the spatial distribution of chronic tumor hypoxia: implications for experimental and clinical studies. Comput. Math. Meth. Med. 2012, 410,602 (2012)CrossRefGoogle Scholar
  56. 56.
    G.G. Powathil, D.J.A. Adamson, M.A.J. Chaplain, Towards predicting the response of a solid tumour to chemotherapy and radiotherapy treatments: Clinical insights from a computational model. PLOS Computational Biology (To appear) (2013). DOI 10.1371/journal.pcbi.1003120Google Scholar
  57. 57.
    G.G. Powathil, K.E. Gordon, L.A., Hill, M.A. Chaplain, Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: Biological insights from a hybrid multiscale cellular automaton model. J. Theor. Biol. 308, 1–9 (2012)Google Scholar
  58. 58.
    I. Ramis-Conde, M.A. Chaplain, A.R. Anderson, D. Drasdo, Multi-scale modelling of cancer cell intravasation: the role of cadherins in metastasis. Phys. Biol. 6(1), 016,008 (2009)Google Scholar
  59. 59.
    I. Ramis-Conde, D. Drasdo, A.R. Anderson, M.A. Chaplain, Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach. Biophys. J. 95(1), 155–165 (2008)CrossRefGoogle Scholar
  60. 60.
    B. Ribba, T. Alarcon, K. Marron, P. Maini, Z. Agur, The Use of Hybrid Cellular Automaton Models for Improving Cancer Therapy. Lect. Notes Comput. Sci 3305, 444–453 (2004)CrossRefGoogle Scholar
  61. 61.
    B. Ribba, T. Colin, S. Schnell, A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies. Theor. Biol. Med. Model. 3, 7 (2006)CrossRefGoogle Scholar
  62. 62.
    B. Ribba, K. Marron, Z. Agur, T. Alarcon, P.K. Maini, A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin’s lymphoma: investigation of the current protocol through theoretical modelling results. Bull. Math. Biol. 67(1), 79–99 (2005)MathSciNetCrossRefGoogle Scholar
  63. 63.
    B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier, J.P. Boissel, A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents. J. Theor. Biol. 243(4), 532–541 (2006)MathSciNetCrossRefGoogle Scholar
  64. 64.
    M. Richard, K. Kirkby, R. Webb, N. Kirkby, A mathematical model of response of cells to radiation. Nuclear Instruments and Meth. Phy. Res. Section B: Beam Interactions Mater. Atoms 255(1), 18–22 (2007)CrossRefGoogle Scholar
  65. 65.
    R.K. Sachs, P. Hahnfeld, D.J. Brenner, The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair. Int. J. Radiat. Biol. 72(4), 351–374 (1997)CrossRefGoogle Scholar
  66. 66.
    G.K. Schwartz, M.A. Shah, Targeting the cell cycle: a new approach to cancer therapy. J. Clin. Oncol. 23, 9408–9421 (2005)CrossRefGoogle Scholar
  67. 67.
    G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi, F. Bussolino, Modeling the early stages of vascular network assembly. EMBO J. 22, 1771–1779 (2003)CrossRefGoogle Scholar
  68. 68.
    E. Shochat, D. Hart, Z. Agur, Using computer simulations for evaluating the efficacy of breast cancer chemotherapy protocols. Math. Models Meth. Appl. Sci. 9(4), 599–615 (1999)CrossRefzbMATHGoogle Scholar
  69. 69.
    M. Sturrock, A.J. Terry, D.P. Xirodimas, A.M. Thompson, M.A. Chaplain, Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways. J. Theor. Biol. 273(1), 15–31 (2011)MathSciNetCrossRefGoogle Scholar
  70. 70.
    M. Sturrock, A.J. Terry, D.P. Xirodimas, A.M. Thompson, M.A. Chaplain, Influence of the nuclear membrane, active transport, and cell shape on the Hes1 and p53-Mdm2 pathways: insights from spatio-temporal modelling. Bull. Math. Biol. 74(7), 1531–1579 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  71. 71.
    I. Tannock, R. Hill, R. Bristow, L. Harrington, Basic Science of Oncology (MacGraw Hill, Boston 2005)Google Scholar
  72. 72.
    I. Turesson, J. Carlsson, A. Brahme, B. Glimelius, B. Zackrisson, B. Stenerlow, Biological response to radiation therapy. Acta Oncol 42(2), 92–106 (2003)CrossRefGoogle Scholar
  73. 73.
    S. Turner, J.A. Sherratt, Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts model. J. Theor. Biol. 216, 85–100 (2002)MathSciNetCrossRefGoogle Scholar
  74. 74.
    J.J. Tyson, B. Novak, Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions. J. Theor. Biol. 210, 249–263 (2001)CrossRefGoogle Scholar
  75. 75.
    B.G. Wouters, J.M. Brown, Cells at intermediate oxygen levels can be more important than the “hypoxic fraction” in determining tumor response to fractionated radiotherapy. Radiat. Res. 147(5), 541–550 (1997)CrossRefGoogle Scholar
  76. 76.
    M. Wu, H.B. Frieboes, S.R. McDougall, M.A. Chaplain, V. Cristini, J. Lowengrub, The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. J. Theor. Biol. 320, 131–151 (2013)MathSciNetCrossRefGoogle Scholar
  77. 77.
    L. Zhang, Z. Wang, J.A. Sagotsky, T.S. Deisboeck, Multiscale agent-based cancer modeling. J. Math. Biol. 58(4–5), 545–559 (2009)MathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Division of MathematicsUniversity of DundeeDundeeUK

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