Multiscale Modelling of Solid Tumour Growth

  • Helen M. Byrne
  • I.M.M. van Leeuwen
  • Markus R. Owen
  • Tomás Alarcón
  • Philip K. Maini
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Vascular Endothelial Growth Factor Wall Shear Stress Vascular Endothelial Growth Factor Level Multiscale Modelling Quiescent Cell 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ad96]
    Adam, J.A.: Mathematical models of perivascular spheriod development and catastrophe-theoretic description of rapid metastatic growth/tumor remission, Invasion Metastasis,16, 247–267 (1996).Google Scholar
  2. [ABM03]
    Alarcón, T., Byrne, H.M., and Maini, P.K.: A cellular automaton model for tumour growth in inhomogeneous environment, J. Theor. Biol.,225, 257–274 (2003).CrossRefGoogle Scholar
  3. [ABM04b]
    Alarcón, T., Byrne, H.M., and Maini, P.K.: Towards whole-organ modelling of tumour growth, Prog. Biophys. Mol. Biol.,85, 451–472 (2004).CrossRefGoogle Scholar
  4. [ABM05a]
    Alarcón, T., Byrne, H.M., and Maini, P.K.: A multiple scale model for tumour growth, Multiscale Mod. Sim.,3, 440–475 (2005).MATHGoogle Scholar
  5. [ABM05b]
    Alarcón, T., Byrne, H.M., and Maini, P.K.: A design principle for vascular beds: the effects of complex blood rheology, Microvasc. Res.,69, 156–172 (2005).Google Scholar
  6. [AOBM06]
    Alarcón, T., Owen, M.R., Byrne, H.M., and Maini, P.K.: Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy, Comp. Math. Methods Med.,7, 85–119 (2006).CrossRefMATHGoogle Scholar
  7. [AC98]
    Anderson, A.R.A., and Chaplain, M.A.J.: Continuous and discrete mathematical models of tumour-induced angiogenesis, Bull. Math. Biol.,60, 857–899 (1998).CrossRefMATHGoogle Scholar
  8. [AWCQ06]
    Anderson, A.R.A., Weaver, A.M., Cummings, T.M., and Quaranta, V.: Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment, Cell,127, 905–915 (2006).CrossRefGoogle Scholar
  9. [AMcE]
    Araujo, R.P., and McElwain, D.L.S.: A history of the study of solid tumor growth: the contribution of mathematical modelling, Bull. Math. Biol.,66, 1039–1091 (2004).CrossRefMathSciNetGoogle Scholar
  10. [Armi54]
    Armitage, P., and Doll, R.: The age distribution of cancer and a multistage theory of carcinogenesis, Br. J. Cancer,8, 1–12 (1954).Google Scholar
  11. [Brod04]
    Brodland, G.W.: Computational modeling of cell sorting, tissue engulfment, and related phenomena: a review, Appl. Mech. Rev.,57, 47–76 (2004).CrossRefGoogle Scholar
  12. [BAOMM]
    Byrne, H.M., Alarcón, T., Owen, M.R., Murphy, J., and Maini, P.K.: Modelling the response of vascular tumours to chemotherapy: a multiscale approach, Math. Mod. Meth. Appl. Sci.,16, 1219–1241 Suppl S (2006).CrossRefMATHGoogle Scholar
  13. [Cram04]
    Crampin, E.J., Halstead, M., Hunter, P., Nielsen, P., Noble, D., Smith, N., and Tawhai, M.: Computational physiology and the Physiome project, Exp. Physiol.,89, 21–26 (2004).CrossRefGoogle Scholar
  14. [Dras01]
    Drasdo, D., and Loeffler, M.: Individual-based models to growth and folding in one-layered tissues: intestinal crypts and early development, Nonlinear Analysis,47, 245–256 (2001).CrossRefMathSciNetMATHGoogle Scholar
  15. [Edwa07]
    Edwards, C.M., and Chapman, J.S.: Biomechanical modelling of colorectal crypt budding and fission, Bull. Math. Biol.,69, 1927–1942, (2007).CrossRefMathSciNetMATHGoogle Scholar
  16. [Ferl07]
    Ferlay, F., Autier, P., Boniol, M., Heanue, M., Colombet, M., and Boyle, P.: Estimates of the cancer incidence and mortality in Europe in 2006, Ann. Oncol.,18, 581–592 (2007).CrossRefGoogle Scholar
  17. [F93]
    Fung, Y.C.: Biomechanics, Springer, New York (1993).Google Scholar
  18. [GG96]
    Gatenby, R.A., and Gawlinski, E.T.: A reaction-diffusion model of cancer invasion, Cancer Res.,56, 5745–5753 (1996).Google Scholar
  19. [GG04]
    Gatenby, R.A., and Gillies, R.J.: Why do cancers have high aerobic glycolysis? Nature Rev. Cancer,4, 891–899 (2004).CrossRefGoogle Scholar
  20. [GM03]
    Gatenby, R.A., and Maini, P.K.: Mathematical oncology: cancer summed up, Nature,421, 321 (2003).CrossRefGoogle Scholar
  21. [GS07]
    Gatenby, R.A., Smallbone, K., Maini, P.K., Rose, F., Averill, J., Nagel, R.B., Worrall, L., and Gillies, R.J.: Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer, Brit. J. Cancer,97, 646–653 (2007).CrossRefGoogle Scholar
  22. [Gava05]
    Gavaghan, D.J., Simpson, A.C., Lloyd, S., MacRandal, D.F., and Boyd, D.R.: Towards a Grid infrastructure to support integrative approaches to biological research, Philos. Transact. A Math. Phys. Eng. Sci.,363, 1829–1841 (2005).CrossRefGoogle Scholar
  23. [GA07]
    Gerlee, P., and Anderson, A.R.A.: An evolutionary hybrid cellular automaton model of solid tumour growth, J. Theor. Biol.,246, 583–603 (2007).CrossRefMathSciNetGoogle Scholar
  24. [GLB94]
    Gillies, R.J., Liu, Z., and Bhujwalla, Z.: 31P-MRS measurements of extracellular pH of tumors using 3-aminopropylphosphonate, Am. J. Physiol.,267, 195–203 (1994).Google Scholar
  25. [GRM89]
    Grinstein, S., Rotin, D., and Mason, M.J.: Na+/H+ exchange and growth factor-induced cytosolic pH changes: role in cellular proliferation, Biochim. Biophys. Acta,988, 73–97 (1989).Google Scholar
  26. [HSR91]
    Haberkorn, U., Strauss, L.G., Reisser, C., Hagg, D., Dimitrakopoulu, A., Ziegler, S., Oberdorfe, F., Rudat, V., and van Kaick, G.: Glucose uptake, perfusion, and cell proliferation in head and neck tumours: relation to positron emission tomography and other whole-body applications, Semin. Nuc. Med.,22, 268–284 (1991).Google Scholar
  27. [HW00]
    Hanahan, D., and Weinberg, R.A.: The hallmarks of cancer, Cell,100, 57–70 (2000).CrossRefGoogle Scholar
  28. [Ilya05]
    Ilyas, M.: Wnt signalling and the mechanistic basis of tumour development, J. Pathol.,205, 130–144 (2005).CrossRefGoogle Scholar
  29. [Jain88]
    Jain, R.K.: Determinants of tumour blood flow: a review, Cancer Res.,48, 2641–2658 (1988).Google Scholar
  30. [JPCF]
    Jiang, Y., Pjseivac-Grbovic, J., Cantrell, C., and Freyer, J.P.: A multiscale model for avascular tumour growth, Biophys. J.,89, 3884–3894 (2005).CrossRefGoogle Scholar
  31. [JEBMC]
    Johnston, M.D., Edwards, C.M., Bodmer, W.F., Maini, P.K., and Chapman, S.J.: Mathematical modelling of cell population dynamics in the colonic crypt, Proc. Natl. Acad. Sci.,104, 4008–4013 (2007).CrossRefGoogle Scholar
  32. [Koma04]
    Komarova, N.L., and Wang, L.: Initiation of colorectal cancer: where do the two hits hit?, Cell Cycle,3, 1558–1565 (2004).Google Scholar
  33. [Lee03]
    Lee, E., Salic, A., Kruger, R., Heinrich, R., and Kirschner, M.W.: The roles of APC and Axin derived from experimental and theoretical analysis of the Wnt pathway, PLoS Biol.,1, E10 (2003).CrossRefGoogle Scholar
  34. [vLBJK06]
    van Leeuwen, I.M.M., Byrne, H.M., Jensen, O.E., and King, J.R.: Crypt dynamics and colorectal cancer: advances in mathematical modelling, Cell Prolif.,39, 157–181 (2006).CrossRefGoogle Scholar
  35. [vLBJK07]
    van Leeuwen, I.M.M., Byrne, H.M., Jensen, O.E., and King, J.R.: Elucidating the interactions between the adhesive and transcriptional functions of beta-catenin in normal and cancerous cells, J. Theor. Biol.,247, 77–102 (2007).CrossRefGoogle Scholar
  36. [vLEIB]
    van Leeuwen, I.M.M., Edwards, C.M., Ilyas, M., and Byrne, H.M.: Towards a multiscale model of colorectal cancer, W. J. Gastroenterol.,13, 1399–1407 (2007).Google Scholar
  37. [Loef86]
    Loeffler, M., Stein, R., Wichmann, H.E., Potten, C.S., Kaur, P., and Chwalinski, S.: Intestinal crypt proliferation. I. A comprehensive model of steady-state proliferation in the crypt, Cell Tissue Kinetics,19, 627– 645 (1986).Google Scholar
  38. [MACS02]
    McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., and Sherratt, J.A.: Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies, Bull. Math. Biol.,64, 673–702 (2002).CrossRefGoogle Scholar
  39. [MAC06]
    McDougall, S.R., Anderson, A.R.A., and Chaplain, M.A.J.: Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. Bull. Math. Biol.,241, 564–589 (2006).MathSciNetGoogle Scholar
  40. [ML07]
    Macklin, P., and Lowengrub, J.: Nonlinear simulation of the effect of microenvironment on tumor growth, J. Theor. Biol.,245, 677–704 (2007).CrossRefMathSciNetGoogle Scholar
  41. [Mein01]
    Meineke, F.A., Potten, C.S., and Loeffler, M.: Cell migration and organization in the intestinal crypt using a lattice-free model, Cell Prolif.,34, 253–266 (2001).CrossRefGoogle Scholar
  42. [Nath04]
    Näthke, I.S.: The adenomatous polyposis coli protein: the Achilles heel of the gut epithelium, Annu. Rev. Dev. Biol.,20, 337–366 (2004).CrossRefGoogle Scholar
  43. [Nobl06]
    Noble, D.: Systems biology and the heart, Biosystems,83, 75–80 (2005).CrossRefGoogle Scholar
  44. [dOno07]
    dónofrio, A., and Tomlinson, I.P.: A nonlinear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt, J. Theor. Biol.,244, 367–374 (2007).CrossRefGoogle Scholar
  45. [OAMB08]Owen,
    [OAMB08]Owen, M.R., Alarcón, T., Maini, P.K., and Byrne, H.M.: Angiogenesis and vascular remodelling in normal and cancerous tissues, J. Math. Biol., in press.Google Scholar
  46. [Pan97]
    Panetta, J.C.: A mathematical model of breast and ovarian cancer treated with paclitaxel, Math. Biosci.,146, 89–113 (1997).CrossRefMathSciNetMATHGoogle Scholar
  47. [PGLG]
    Patel, A.A., Gawlinsky, E.T., Lemieux, S.K., and Gatenby, R.A.: Cellular automaton model of early tumour growth and invasion: the effects of native tissue vascularity and increased anaerobic tumour metabolism, J. Theor. Biol.,213, 315–331 (2001).CrossRefGoogle Scholar
  48. [Paul93]
    Paulus, U., Loeffler, M., Zeidler, J., Owen, G., and Potten, C.S.: The differentiation and lineage development of goblet cells in the murine small intestinal crypt: experimental and modelling studies, J. Cell Sci.,106, 473–484 (1993).Google Scholar
  49. [Pott94]
    Potten, C.S., Merritt, A., Hickman, J., Hall, P., and Faranda, A.: Characterization of radiation-induced apoptosis in the small intestine and its biological implications, Int. J. Radiat. Biol.,65, 71–78 (1994).CrossRefGoogle Scholar
  50. [PSG98]
    Pries, A.R., Secomb, T.W., and Gaehtgens, P.: Structural adaptation and stability of microvascular networks: theory and simulations, Am. J. Physiol.,275, H349–H360 (1998).Google Scholar
  51. [RMZAM]
    Ribba, B., Marron, K., Agur, Z., Alarcón, T., and Maini, P.K.: 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, 79–99 (2005).CrossRefMathSciNetGoogle Scholar
  52. [RCS06]
    Ribba, B., Colin, T., and Schnell, S.: A multiscale mathematical model of cancer and its use in analyzing irradiation therapies, Theor. Biol. Med. Model.,3, 7 (2006).CrossRefGoogle Scholar
  53. [RCM07]
    Roose, T., Chapman, S.J., and Maini, P.K.: Mathematical models of avascular tumour growth, SIAM Review,49, 179–208 (2007).CrossRefMathSciNetMATHGoogle Scholar
  54. [Sans04]
    Sansom, O.J., Reed, K.R., Hayes, A.J., Ireland, H., Brinkmann, H., Newton, I.P., Batlle, E., Simon-Assman, P., Clevers, H., Nathke, I.S., Clarke, A.R., and Winton, D.J.: Loss of Apcin vivo immediately perturbs Wnt signaling, differentiation, and migration, Genes Dev,18, 1385–1390 (2004).CrossRefGoogle Scholar
  55. [Sha06]
    Shaked, Y., Ciarrocchi, A., Franco, M., Lee, C.R., Man, S., Cheung, A.M., Kicklin, D.J., Chaplin, D., Foster, F.S., Benezra, R., and Kerbel, R.S.: Therapy-induced acute recruitment of circulating endothelial progenitor cells to tumours. Science,313, 1785–1787 (2006).CrossRefGoogle Scholar
  56. [SGGMG07]
    Smallbone, K., Gatenby, R.A., Gillies, R.J., Maini, P.K., and Gavaghan, D.J.: Metabolic changes during carcinogenesis: potential impact on invasiveness. J. Theor. Biol.,244, 703–713 (2007).CrossRefMathSciNetGoogle Scholar
  57. [Swat04]
    Swat, M., Kel, A., and Herzel, H.: Bifurcation analysis of the regulatory modules of the mammalian G1/S transition, Bioinformatics,20, 1506– 1511 (2004).CrossRefGoogle Scholar
  58. [TN01]
    Tyson, J.J., and Novak, B.: Regulation of the eukariotic cell-cycle: molecular anatagonism, hysteresis, and irreversible transitions, J. Theor. Biol.,210, 249–263 (2001).CrossRefGoogle Scholar
  59. [W30]
    Warburg, O.: The Metabolism of Tumours, Constable Press, L1ondon (1930).Google Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Helen M. Byrne
    • 1
  • I.M.M. van Leeuwen
    • 1
  • Markus R. Owen
    • 2
  • Tomás Alarcón
    • 3
  • Philip K. Maini
    • 4
  1. 1.Centre for Mathematical Medicine and Biology School of Mathematical SciencesUniversity of NottinghamNottingham NG7 2RDUK
  2. 2.Department of Surgery and Molecular Oncology Ninewells HospitalUniversity of DundeeDundee DD1 9SYUK
  3. 3.Department of MathematicsImperial College180 Queen’s GateUK
  4. 4.Centre for Mathematical Biology Mathematical Institute Department of BiochemistryUniversity of OxfordSouth Parks RoadUK

Personalised recommendations