Modeling Diffusely Invading Brain Tumors An Individualized Approach to Quantifying Glioma Evolution and Response to Therapy

  • Russell Rockne
  • Ellsworth C. AlvordJr.
  • Mindy Szeto
  • Stanley Gu
  • Gargi Chakraborty
  • Kristin R. Swanson
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Glioma Cell Glioblastoma Multiforme Gross Tumor Volume Gross Total Resection Glioma Growth 


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  1. 1.
    Alvord E.C. Jr.: Why do gliomas not metastasize. Arch. Neurol.,33, 73–75 (1976)Google Scholar
  2. 2.
    Alvord E.C. Jr., Shaw C.M.: Neoplasms affecting the nervous system in the elderly. In: Duckett S (ed), The Pathology of the Aging Human Nervous System. Lea – Febiger, Philadelphia (1991)Google Scholar
  3. 3.
    Alvord E.C. Jr., Swanson K.R.: Using mathematical modeling to predict survival of low-grade gliomas. Ann. Neurol.,61, 496; author reply 496–497 (2007)CrossRefGoogle Scholar
  4. 4.
    Anderson H., Price P.: What does positron emission tomography offer oncology? Euro. J. Cancer.,26, 2028–2035 (2000)CrossRefGoogle Scholar
  5. 5.
    Araujo R.P., McElwain D.L.: A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull. Math. Biol.,66, 1039–1091 (2004)CrossRefMathSciNetGoogle Scholar
  6. 6.
    B. Jones R.G.D.: Cell loss factors and the linear-quadratic model. Rad. Onc.,37, 136–139 (1995)CrossRefGoogle Scholar
  7. 7.
    Barker F.G. II, Prados M.D., Chang S.M., et al.: Radiation response and survival time in patients with glioblastoma multiforme. J. Neurosurg.,84, 442–448 (1996)Google Scholar
  8. 8.
    Bloor R., Templeton A.W., Quick R.S.: Radiation therapy in the treatment of intracranial tumors. Am J. Roentgenol. Radium Ther. Nucl. Med.,87, 463–472 (1962)Google Scholar
  9. 9.
    Brown M.A., Semelka R.C.: MRI: Basic Principles and Applications ed. 2. Wiley-Liss Inc., New York (1999)Google Scholar
  10. 10.
    Cocosco C.A., Kollokian V., et al.: Brainweb: online interface to a 3D simulated brain database. Neuroimage.,5, 425 (1997)Google Scholar
  11. 11.
    Collins D.L., Zijdenbos A.P., Kollokian V., et al.: Design and construction of a realistic digital brain phantom. IEEE T. Med. Imaging.,17, 463–468 (1998)CrossRefGoogle Scholar
  12. 12.
    Collins V.P., Loeffler R.K., Tivey H.: Observations on growth rates of human tumors. Am. J. Roentgenol. Radium. Ther. Nucl. Med.,76, 988–1000 (1956)Google Scholar
  13. 13.
    Concannon J.P., Kramer S., Berry R.: The extent of intracranial gliomata at autopsy and its relationship to techniques used in radiation therapy of brain tumors. Am. J. Roentgenol. Radium. Ther. Nucl. Med.,84, 99–107 (1960)Google Scholar
  14. 14.
    Dalrymple S.J., Parisi J.E., Roche P.C., et al.: Changes in proliferating cell nuclear antigen expression in glioblastoma multiforme cells along a stereotactic biopsy trajectory. Neurosurg.,35, 1036–1044; discussion 1044–1045 (1994)CrossRefGoogle Scholar
  15. 15.
    Enderling H., Anderson A.R., Chaplain M.A., et al.: Mathematical modelling of radiotherapy strategies for early breast cancer. J. Theor. Biol.,241, 158–171 (2006)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Fisher R.A.: The wave of advance of advantageous genes. Ann. Eugenics., Vol. 7 (1937)Google Scholar
  17. 17.
    Galanis E., Buckner J.: Chemotherapy for high-grade gliomas. Brit. J. Cancer,82, 1371–1380 (2000)Google Scholar
  18. 18.
    Giese A., Westphal M.: Glioma invasion in the central nervous system. Neurosurg.,39, 235–250; discussion 250-252 (1996)CrossRefGoogle Scholar
  19. 19.
    Hall E.: Radiobiology for the Radiologist, ed. 4. J.B. Lippincott Company, Philadelphia (1994)Google Scholar
  20. 20.
    Hammoud M.A., Sawaya R., Shi W., et al.: Prognostic significance of preoperative MRI scans in glioblastoma multiforme. J. Neuroonc.,27, 65–73 (1996)CrossRefGoogle Scholar
  21. 21.
    Harpold H., Alvord E.C. Jr., Swanson K.R.: The evolution of mathematical modeling of glioma proliferation and invasion. J. Neuropathol. Exp. Neurol.,66, 1–9 (2007)CrossRefGoogle Scholar
  22. 22.
    Jbabdi S., Mandonnet E., Duffau H., et al.: Simulation of anisotropic growth of low-grade gliomas using diffusion tensor imaging. Magn. Reson. Med.,54, 616–624 (2005)CrossRefGoogle Scholar
  23. 23.
    Kelly P.J.: Computed tomography and histologic limits in glial neoplasms: tumor types and selection for volumetric resection. Surg. Neurol.,39, 458–465 (1993)CrossRefGoogle Scholar
  24. 24.
    Kleihues P., Louis D.N., Scheithauer B.W., et al.: The WHO classification of tumors of the nervous system. J. Neuropathol. Exp. Neurol.,61, 215–225; discussion 226-229 (2002)Google Scholar
  25. 25.
    Koh W.J., Griffin T.W., Rasey J.S., et al.: Positron emission tomography. A new tool for characterization of malignant disease and selection of therapy. Acta. Oncol.,33, 323–327 (1994)CrossRefGoogle Scholar
  26. 26.
    Koh W.J., Rasey J.S., Evans M.L., et al.: Imaging of hypoxia in human tumors with [F-18]fluoromisonidazole. Int. J. Rad. Oncol. Biol. Phys.,22, 199–212 (1992)Google Scholar
  27. 27.
    Lacroix M., Abi-Said D., Fourney D.R., et al.: A multivariate analysis of 416 patients with glioblastoma multiforme: prognosis, extent of resection, and survival. J. Neurosurg.,95, 190–198 (2001)CrossRefGoogle Scholar
  28. 28.
    Mandonnet E., Delattre J.Y., Tanguy M.L., et al.: Continuous growth of mean tumor diameter in a subset of grade II gliomas. Ann. Neurol.,53, 524–528 (2003)CrossRefGoogle Scholar
  29. 29.
    Murray J.D.: Mathematical Biology II. Spatial Models and Biological Applications. ed. 3. Vol. 2. Springer-Verlag, New York (2003)Google Scholar
  30. 30.
    Pallud J., Mandonnet E., Duffau H., et al.: Prognostic value of initial magnetic resonance imaging growth rates forWorld Health Organization grade II gliomas. Ann. Neurol.,60, 380–383 (2006)CrossRefGoogle Scholar
  31. 31.
    Rockne R., Alvord E.C. Jr., Rockhill J.K.: A mathematical model for brain tumor response to radiation therapy, J. Math. Biol. (2008),in press Google Scholar
  32. 32.
    Swanson K.R., Rostomily R.C., Alvord E.C. Jr.: A mathematical modeling tool for predicting survival of individual patients following resection of glioblastoma. Brit. J. Cancer,98, 113–119 (2008)CrossRefGoogle Scholar
  33. 33.
    Sachs R.K., Hlatky L.R., Hahnfeldt P.: Simple ODE models of tumor growth and anti-angiogenic or radiation treatment. Math. Comp. Mod.,33, 1297–1305 (2001)MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Spence A.M., Mankoff D.A., Muzi M.: Positron emission tomography imaging of brain tumors. Neuroimag. Clin. N. Am.,13, 717–739 (2003)Google Scholar
  35. 35.
    Stamatakos G.S., Antipas V.P., Uzunoglu N.K., et al.: A four-dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme: studies on the effect of clonogenic cell density. Brit. J. Rad.,79, 389–400 (2006)CrossRefGoogle Scholar
  36. 36.
    Swanson K.R.: Mathematical modeling of the growth and control of tumors. PhD Thesis, University of Washington, Seattle, Washington (1999)Google Scholar
  37. 37.
    Swanson K.R., Alvord E.C. Jr. (eds): A biomathematical and pathological analysis of an untreated glioblastoma. NeuroPath. Annual Meeting. Helsinki, Finland. (2002)Google Scholar
  38. 38.
    Swanson K.R., Alvord E.C. Jr.: Serial imaging observations and postmortem examination of an untreated glioblastoma: A traveling wave of glioma growth and invasion. Neuro-Oncol.,4, 340 (2002)Google Scholar
  39. 39.
    Swanson K.R., Alvord E.C. Jr., Murray J.: Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Brit. J. Cancer.,86, 14–18 (2002)CrossRefGoogle Scholar
  40. 40.
    Swanson K.R., Alvord E.C. Jr., Murray J.: Dynamics of a model for brain tumors reveals a small window for therapeutic intervention. Disc. Con. Dyn. Sys.-Series. B.,4, 289–295 (2004)MATHMathSciNetGoogle Scholar
  41. 41.
    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)CrossRefGoogle Scholar
  42. 42.
    Swanson K.R., Alvord E.C. Jr., Murray J.D.: Quantifying efficacy of chemotherapy of brain tumors with homogeneous and heterogeneous drug delivery. Acta. Biotheoretica,50, 223–237 (2002)CrossRefGoogle Scholar
  43. 43.
    Swanson K.R., Chakraborty G., Rockne R., et al.: A mathematical model for glioma growth and invasion links biological aggressiveness assessed by MRI with hypxoia assessed by FMISO-PET. 53rd Annual Meeting of the Soc. Nuc. Med., 48–115 (2007)Google Scholar
  44. 44.
    Swanson K.R., Murray J.D., Alvord E.C. Jr.: Combining radiological observations with a three-dimensional model to predict behavior of brain tumors in real patients. SIAM Life Sci. Imag. Sci. Conference. Boston, MA. (2002)Google Scholar
  45. 45.
    Swanson K.R., Rockne R., Rockhill J.K., et al.: Mathematical modeling of radiotherapy in individual glioma patients: quantifying and predicting response to radiation therapy. AACR Annual Meeting. Los Angeles, CA. (2007)Google Scholar
  46. 46.
    Tracqui P., Cruywagen G.C., Woodward D.E., et al.: A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth. Cell. Prolif.,28, 17–31 (1995)CrossRefGoogle Scholar
  47. 47.
    Valk P.E., Mathis C.A., Prados M.D., et al.: Hypoxia in human gliomas: demonstration by PET with fluorine-18-fluoromisonidazole. J. Nucl. Med.,33, 2133– 2137 (1992)Google Scholar
  48. 48.
    Vos M.J., Uitdehaag B.M.J., Barkhof F., et al.: Interobserver variability in the radiological assessment of response to chemotherapy in glioma. Neurology60, 826–830 (2003)Google Scholar
  49. 49.
    Weltens C., Menten J., Feron M., et al.: Interobserver variations in gross tumor volume delineation of brain tumors on computed tomography and impact of magnetic resonance imaging. Radiother Oncol.,60, 49–59 (2001)CrossRefGoogle Scholar
  50. 50.
    Woodward D.E., Cook J., Tracqui P., et al.: A mathematical model of glioma growth: the effect of extent of surgical resection. Cell. Prolif.,29, 269–288 (1996)CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Russell Rockne
    • 1
  • Ellsworth C. AlvordJr.
    • 1
  • Mindy Szeto
    • 1
  • Stanley Gu
    • 1
  • Gargi Chakraborty
    • 1
  • Kristin R. Swanson
    • 1
  1. 1.Department of PathologyUniversity of WashingtonUSA

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