Computational modeling of brain tumors: discrete, continuum or hybrid?

Open Access


In spite of all efforts, patients diagnosed with highly malignant brain tumors (gliomas), continue to face a grim prognosis. Achieving significant therapeutic advances will also require a more detailed quantitative understanding of the dynamic interactions among tumor cells, and between these cells and their biological microenvironment. Data-driven computational brain tumor models have the potential to provide experimental tumor biologists with such quantitative and cost-efficient tools to generate and test hypotheses on tumor progression, and to infer fundamental operating principles governing bidirectional signal propagation in multicellular cancer systems. This review highlights the modeling objectives of and challenges with developing such in silicobrain tumor models by outlining two distinct computational approaches: discrete and continuum, each with representative examples. Future directions of this integrative computational neuro-oncology field, such as hybrid multiscale multiresolution modeling are discussed.


Brain tumor Agent-based model Cellular automata Continuum Multi-scale 



Agent-based model


Cellular automata


Epidermal growth factor receptor


Extracellular matrix




Magnetic resonance imaging


Phopholipase Cγ


Region of interest






  1. 1.
    Al-Hajj M., Clarke M.F.: Self-renewal and solid tumor stem cells. Oncogene 23, 7274–7282 (2004)PubMedCrossRefGoogle Scholar
  2. 2.
    Albeck J.G., MacBeath G., White F.M., Sorger P.K., Lauffenburger D.A., Gaudet S.: Collecting and organizing systematic sets of protein data. Nat. Rev. Mol. Cell. Biol. 7, 803–812 (2006)PubMedCrossRefGoogle Scholar
  3. 3.
    Anderson A.R., Chaplain M.A.: Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60, 857–899 (1998)MATHPubMedCrossRefGoogle Scholar
  4. 4.
    Anderson A.R., Weaver A.M., Cummings P.T., Quaranta V.: Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127, 905–915 (2006)PubMedCrossRefGoogle Scholar
  5. 5.
    Athale C., Mansury Y., Deisboeck T.S.: Simulating the impact of a molecular ‘decision-process’ on cellular phenotype and multicellular patterns in brain tumors. J. Theor. Biol. 233, 469–481 (2005)PubMedCrossRefGoogle Scholar
  6. 6.
    Athale C.A., Deisboeck T.S.: The effects of EGF-receptor density on multiscale tumor growth patterns. J. Theor. Biol. 238, 771–779 (2006)PubMedCrossRefMathSciNetGoogle Scholar
  7. 7.
    Badruddoja M.A., Black K.L.: Improving the delivery of therapeutic agents to CNS neoplasms: a clinical review. Front. Biosci. 11, 1466–1478 (2006)PubMedCrossRefGoogle Scholar
  8. 8.
    Bailey A.M., Thorne B.C., Peirce S.M.: Multi-cell agent-based simulation of the microvasculature to study the dynamics of circulating inflammatory cell trafficking. Ann. Biomed. Eng. 35, 916–936 (2007)PubMedCrossRefGoogle Scholar
  9. 9.
    Ballman K.V., Buckner J.C., Brown P.D., Giannini C., Flynn P.J., LaPlant B.R., Jaeckle K.A.: The relationship between six-month progression-free survival and 12-month overall survival end points for phase II trials in patients with glioblastoma multiforme. Neuro. Oncol. 9, 29–38 (2007)PubMedCrossRefGoogle Scholar
  10. 10.
    Berg O.G., Paulsson J., Ehrenberg M.: Fluctuations and quality of control in biological cells: zero-order ultrasensitivity reinvestigated. Biophys. J. 79, 1228–1236 (2000)PubMedGoogle Scholar
  11. 11.
    Blume-Jensen P., Hunter T.: Oncogenic kinase signalling. Nature 411, 355–365 (2001)PubMedCrossRefADSGoogle Scholar
  12. 12.
    Bonabeau E.: Agent-based modeling: methods and techniques for simulating human systems. Proc. Natl. Acad. Sci. USA 99(Suppl 3), 7280–7287 (2002)PubMedCrossRefADSGoogle Scholar
  13. 13.
    Burgess P.K., Kulesa P.M., Murray J.D., Alvord E.C. Jr: The interaction of growth rates and diffusion coefficients in a three-dimensional mathematical model of gliomas. J. Neuropathol. Exp. Neurol. 56, 704–713 (1997)PubMedCrossRefGoogle Scholar
  14. 14.
    Chaplain M.A., McDougall S.R., Anderson A.R.: Mathematical modeling of tumor-induced angiogenesis. Annu. Rev. Biomed. Eng. 8, 233–257 (2006)PubMedCrossRefGoogle Scholar
  15. 15.
    Cheng J.Q., Lindsley C.W., Cheng G.Z., Yang H., Nicosia S.V.: The Akt/PKB pathway: molecular target for cancer drug discovery. Oncogene 24, 7482–7492 (2005)PubMedCrossRefGoogle Scholar
  16. 16.
    Clatz O., Sermesant M., Bondiau P.Y., Delingette H., Warfield S.K., Malandain G., Ayache N.: Realistic simulation of the 3-D growth of brain tumors in MR images coupling diffusion with biomechanical deformation. IEEE Trans. Med. Imaging 24, 1334–1346 (2005)PubMedCrossRefGoogle Scholar
  17. 17.
    Cristini V., Lowengrub J., Nie Q.: Nonlinear simulation of tumor growth. J. Math. Biol. 46, 191–224 (2003)MATHPubMedCrossRefMathSciNetGoogle Scholar
  18. 18.
    Cristini V., Frieboes H.B., Gatenby R., Caserta S., Ferrari M., Sinek J.: Morphologic instability and cancer invasion. Clin. Cancer Res. 11, 6772–6779 (2005)PubMedCrossRefGoogle Scholar
  19. 19.
    Deisboeck, T.S., Zhang, l., Yoon, J., Costa, J.: In silico cancer modeling: Is ready for primetime? Nat. Clin. Pract. Oncol. (in press)Google Scholar
  20. 20.
    Deisboeck T.S., Berens M.E., Kansal A.R., Torquato S., Stemmer-Rachamimov A.O., Chiocca E.A.: Pattern of self-organization in tumour systems: complex growth dynamics in a novel brain tumour spheroid model. Cell Prolif. 34, 115–134 (2001)PubMedCrossRefGoogle Scholar
  21. 21.
    Di Ventura B., Lemerle C., Michalodimitrakis K., Serrano L.: From in vivo to in silico biology and back. Nature 443, 527–533 (2006)PubMedCrossRefADSGoogle Scholar
  22. 22.
    Dionysiou D.D., Stamatakos G.S., Uzunoglu N.K., Nikita K.S., Marioli A.: A four-dimensional simulation model of tumour response to radiotherapy in vivo: parametric validation considering radiosensitivity, genetic profile and fractionation. J. Theor. Biol. 230, 1–20 (2004)PubMedCrossRefGoogle Scholar
  23. 23.
    Dittmar T., Husemann A., Schewe Y., Nofer J.R., Niggemann B., Zanker K.S., Brandt B.H.: Induction of cancer cell migration by epidermal growth factor is initiated by specific phosphorylation of tyrosine 1248 of c-erbB-2 receptor via EGFR. FASEB J. 16, 1823–1825 (2002)PubMedGoogle Scholar
  24. 24.
    Entschladen F., Drell T.L.t., Lang K., Joseph J., Zaenker K.S.: Tumour-cell migration, invasion, and metastasis: navigation by neurotransmitters. Lancet Oncol. 5, 254–258 (2004)PubMedCrossRefGoogle Scholar
  25. 25.
    Frieboes H.B., Zheng X., Sun C.H., Tromberg B., Gatenby R., Cristini V.: An integrated computational/experimental model of tumor invasion. Cancer Res. 66, 1597–1604 (2006)PubMedCrossRefGoogle Scholar
  26. 26.
    Frieboes H.B., Lowengrub J.S., Wise S., Zheng X., Macklin P., Bearer E.L., Cristini V.: Computer simulation of glioma growth and morphology. Neuroimage 37(Suppl 1), S59–S70 (2007)PubMedCrossRefGoogle Scholar
  27. 27.
    Friedl P., Wolf K.: Tumour-cell invasion and migration: diversity and escape mechanisms. Nat. Rev. Cancer 3, 362–374 (2003)PubMedCrossRefGoogle Scholar
  28. 28.
    Friedman A., Tian J.P., Fulci G., Chiocca E.A., Wang J.: Glioma virotherapy: effects of innate immune suppression and increased viral replication capacity. Cancer Res. 66, 2314–2319 (2006)PubMedCrossRefGoogle Scholar
  29. 29.
    Gatenby R.A., Maini P.K.: Mathematical oncology: cancer summed up. Nature 421, 321 (2003)PubMedCrossRefADSGoogle Scholar
  30. 30.
    Gevertz J.L., Torquato S.: Modeling the effects of vasculature evolution on early brain tumor growth. J. Theor. Biol. 243, 517–531 (2006)PubMedCrossRefMathSciNetGoogle Scholar
  31. 31.
    Gilbert D., Fuss H., Gu X., Orton R., Robinson S., Vyshemirsky V., Kurth M.J., Downes C.S., Dubitzky W.: Computational methodologies for modelling, analysis and simulation of signalling networks. Brief Bioinform. 7, 339–353 (2006)PubMedCrossRefGoogle Scholar
  32. 32.
    Gilbert N., Bankes S.: Platforms and methods for agent-based modeling. Proc. Natl. Acad. Sci. USA 99(Suppl 3), 7197–7198 (2002)PubMedCrossRefADSGoogle Scholar
  33. 33.
    Gilhuis H.J., Bernse H.J., Jeuken J.W., Wesselin P., Sprenger S.H., Kerstens H.M., Wiegant J., Boerman R.H.: The relationship between genetic aberrations as detected by comparative genomic hybridization and vascularization in glioblastoma xenografts. J. Neurooncol. 51, 121–127 (2001)PubMedCrossRefGoogle Scholar
  34. 34.
    Hendrix M.J., Seftor E.A., Seftor R.E., Kasemeier-Kulesa J., Kulesa P.M., Postovit L.M.: Reprogramming metastatic tumour cells with embryonic microenvironments. Nat. Rev. Cancer 7, 246–255 (2007)PubMedCrossRefGoogle Scholar
  35. 35.
    Holland E.C.: Glioblastoma multiforme: the terminator. Proc. Natl. Acad. Sci. USA 97, 6242–6244 (2000)PubMedCrossRefADSGoogle Scholar
  36. 36.
    Jain R.K., di Tomaso E., Duda D.G., Loeffler J.S., Sorensen A.G., Batchelor T.T.: Angiogenesis in brain tumours. Nat. Rev. Neurosci. 8, 610–622 (2007)PubMedCrossRefGoogle Scholar
  37. 37.
    Jemal A., Siegel R., Ward E., Murray T., Xu J., Thun M.J.: Cancer statistics 2007. CA Cancer J. Clin. 57, 43–66 (2007)PubMedGoogle Scholar
  38. 38.
    Kansal A.R., Torquato S., Chiocca E.A., Deisboeck T.S.: Emergence of a subpopulation in a computational model of tumor growth. J. Theor. Biol. 207, 431–441 (2000a)PubMedCrossRefGoogle Scholar
  39. 39.
    Kansal A.R., Torquato S., Harsh G.I., Chiocca E.A., Deisboeck T.S.: Simulated brain tumor growth dynamics using a three-dimensional cellular automaton. J. Theor. Biol. 203, 367–382 (2000b)PubMedCrossRefGoogle Scholar
  40. 40.
    Kansal A.R., Torquato S., Harsh I.G., Chiocca E.A., Deisboeck T.S.: Cellular automaton of idealized brain tumor growth dynamics. Biosystems 55, 119–127 (2000c)PubMedCrossRefGoogle Scholar
  41. 41.
    Kastan M.B., Bartek J.: Cell-cycle checkpoints and cancer. Nature 432, 316–323 (2004)PubMedCrossRefADSGoogle Scholar
  42. 42.
    Kitano H.: Computational systems biology. Nature 420, 206–210 (2002)PubMedCrossRefADSGoogle Scholar
  43. 43.
    Lefranc F., Brotchi J., Kiss R.: Possible future issues in the treatment of glioblastomas: special emphasis on cell migration and the resistance of migrating glioblastoma cells to apoptosis. J. Clin. Oncol. 23, 2411–2422 (2005)PubMedCrossRefGoogle Scholar
  44. 44.
    Mansury Y., Deisboeck T.S.: The impact of “search precision” in an agent-based tumor model. J. Theor. Biol. 224, 325–337 (2003)PubMedCrossRefMathSciNetGoogle Scholar
  45. 45.
    Mansury Y., Kimura M., Lobo J., Deisboeck T.S.: Emerging patterns in tumor systems: simulating the dynamics of multicellular clusters with an agent-based spatial agglomeration model. J. Theor. Biol. 219, 343–370 (2002)PubMedCrossRefMathSciNetGoogle Scholar
  46. 46.
    Mellinghoff I.K., Wang M.Y., Vivanco I., Haas-Kogan D.A., Zhu S., Dia E.Q., Lu K.V., Yoshimoto K., Huang J.H., Chute D.J., Riggs B.L., Horvath S., Liau L.M., Cavenee W.K., Rao P.N., Beroukhim R., Peck T.C., Lee J.C., Sellers W.R., Stokoe D., Prados M., Cloughesy T.F., Sawyers C.L., Mischel P.S.: Molecular determinants of the response of glioblastomas to EGFR kinase inhibitors. N. Engl. J. Med. 353, 2012–2024 (2005)PubMedCrossRefGoogle Scholar
  47. 47.
    Miners J.O., Smith P.A., Sorich M.J., McKinnon R.A., Mackenzie P.I.: Predicting human drug glucuronidation parameters: application of in vitro and in silico modeling approaches. Annu. Rev. Pharmacol. Toxicol. 44, 1–25 (2004)PubMedCrossRefGoogle Scholar
  48. 48.
    Mischel P.S., Cloughesy T.F.: Targeted molecular therapy of GBM. Brain Pathol. 13, 52–61 (2003)PubMedGoogle Scholar
  49. 49.
    Mohamed A., Zacharaki E.I., Shen D., Davatzikos C.: Deformable registration of brain tumor images via a statistical model of tumor-induced deformation. Med. Image Anal. 10, 752–763 (2006)PubMedCrossRefGoogle Scholar
  50. 50.
    Morrison P.F., Laske D.W., Bobo H., Oldfield E.H., Dedrick R.L.: High-flow microinfusion: tissue penetration and pharmacodynamics. Am. J. Physiol. 266, R292–R305 (1994)PubMedGoogle Scholar
  51. 51.
    Nathoo N., Chahlavi A., Barnett G.H., Toms S.A.: Pathobiology of brain metastases. J. Clin. Pathol. 58, 237–242 (2005)PubMedCrossRefGoogle Scholar
  52. 52.
    Pallud J., Mandonnet E., Duffau H., Kujas M., Guillevin R., Galanaud D., Taillandier L., Capelle L.: Prognostic value of initial magnetic resonance imaging growth rates for World Health Organization grade II gliomas. Ann. Neurol. 60, 380–383 (2006)PubMedCrossRefGoogle Scholar
  53. 53.
    Sanga S., Sinek J.P., Frieboes H.B., Ferrari M., Fruehauf J.P., Cristini V.: Mathematical modeling of cancer progression and response to chemotherapy. Expert Rev. Anticancer Ther. 6, 1361–1376 (2006)PubMedCrossRefGoogle Scholar
  54. 54.
    Sanga S., Frieboes H.B., Zheng X., Gatenby R., Bearer E.L., Cristini V.: Predictive oncology: a review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth. Neuroimage 37(Suppl 1), S120–S134 (2007)PubMedCrossRefGoogle Scholar
  55. 55.
    Schmitz J., Kansal A.R., Torquato S.: A cellular automaton model of brain tumor treatment and resistance. J. Theor. Med. 4, 223–239 (2002)MATHCrossRefGoogle Scholar
  56. 56.
    Sinek J., Frieboes H., Zheng X., Cristini V.: Two-dimensional chemotherapy simulations demonstrate fundamental transport and tumor response limitations involving nanoparticles. Biomed. Microdevices 6, 297–309 (2004)PubMedCrossRefGoogle Scholar
  57. 57.
    Stamatakos G.S., Antipas V.P., Uzunoglu N.K.: A spatiotemporal, patient individualized simulation model of solid tumor response to chemotherapy in vivo: the paradigm of glioblastoma multiforme treated by temozolomide. IEEE Trans. Biomed. Eng. 53, 1467–1477 (2006a)PubMedCrossRefGoogle Scholar
  58. 58.
    Stamatakos G.S., Antipas V.P., Uzunoglu N.K., Dale R.G.: A four-dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme: studies on the effect of clonogenic cell density. Br. J. Radiol. 79, 389–400 (2006b)PubMedCrossRefGoogle Scholar
  59. 59.
    Stamatakos G.S., Zacharaki E.I., Makropoulou M.I., Mouravliansky N.A., Marsh A., Nikita K.S., Uzunoglu N.K.: Modeling tumor growth and irradiation response in vitro–a combination of high-performance computing and web-based technologies including VRML visualization. IEEE Trans. Inf. Technol. Biomed. 5, 279–289 (2001)PubMedCrossRefGoogle Scholar
  60. 60.
    Stupp R., Hegi M.E., van den Bent M.J., Mason W.P., Weller M., Mirimanoff R.O., Cairncross J.G.: Changing paradigms–an update on the multidisciplinary management of malignant glioma. Oncologist 11, 165–180 (2006)PubMedCrossRefGoogle Scholar
  61. 61.
    Swanson K.R., Alvord E.C. Jr, Murray J.D.: A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif. 33, 317–329 (2000)PubMedCrossRefGoogle Scholar
  62. 62.
    Swanson K.R., Alvord E.C. Jr, Murray J.D.: Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Br. J. Cancer 86, 14–18 (2002a)PubMedCrossRefGoogle Scholar
  63. 63.
    Swanson K.R., Alvord E.C. Jr, Murray J.D.: Quantifying efficacy of chemotherapy of brain tumors with homogeneous and heterogeneous drug delivery. Acta Biotheor. 50, 223–237 (2002)PubMedCrossRefGoogle Scholar
  64. 64.
    Swanson K.R., Bridge C., Murray J.D., Alvord E.C. Jr: Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J. Neurol. Sci. 216, 1–10 (2003)PubMedCrossRefGoogle Scholar
  65. 65.
    Tracqui P., Cruywagen G.C., Woodward D.E., Bartoo G.T., Murray J.D., Alvord E.C. Jr: A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth. Cell Prolif. 28, 17–31 (1995)PubMedCrossRefGoogle Scholar
  66. 66.
    Walker D.C., Hill G., Wood S.M., Smallwood R.H., Southgate J.: Agent-based computational modeling of wounded epithelial cell monolayers. IEEE Trans. Nanobioscience 3, 153–163 (2004)PubMedCrossRefGoogle Scholar
  67. 67.
    Wang Z., Zhang L., Sagotsky J., Deisboeck T.S.: Simulating non-small cell lung cancer with a multiscale agent-based model. Theor. Biol. Med. Model 4, 50 (2007)PubMedCrossRefGoogle Scholar
  68. 68.
    Wein L.M., Wu J.T., Ianculescu A.G., Puri R.K.: A mathematical model of the impact of infused targeted cytotoxic agents on brain tumours: implications for detection, design and delivery. Cell Prolif. 35, 343–361 (2002)PubMedCrossRefGoogle Scholar
  69. 69.
    Wessels J.T., Busse A.C., Mahrt J., Dullin C., Grabbe E., Mueller G.A.: In vivo imaging in experimental preclinical tumor research—a review. Cytometry A 71, 542–549 (2007)PubMedGoogle Scholar
  70. 70.
    Wishart D.S., Yang R., Arndt D., Tang P., Cruz J.: Dynamic cellular automata: an alternative approach to cellular simulation. In Silico Biol. 5, 139–161 (2005)PubMedGoogle Scholar
  71. 71.
    Wolfram S.: A New Kind of Science. Wolfram Media, Champaign, IL (2002)MATHGoogle Scholar
  72. 72.
    Zhang L., Athale C.A., Deisboeck T.S.: Development of a three-dimensional multiscale agent-based tumor model: simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J. Theor. Biol. 244, 96–107 (2007)PubMedCrossRefMathSciNetGoogle Scholar
  73. 73.
    Zheng X., Wise S.M., Cristini V.: Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Bull. Math. Biol. 67, 211–259 (2005)PubMedCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Complex Biosystems Modeling LaboratoryHarvard-MIT (HST) Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital-EastCharlestownUSA

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