Medical Image Analysis
Volume 14, Issue 2 , Pages 111-125 , April 2010

Extrapolating glioma invasion margin in brain magnetic resonance images: Suggesting new irradiation margins

  • Ender Konukoglu

      Affiliations

    • Asclepios Research Project – INRIA, 2004 Route des Lucioles, 06902, Sophia Antipolis, France
    • Corresponding Author InformationCorresponding author. Address: 2004 Route des Lucioles, 06902 Sophia Antipolis, France. Tel.: +33 0 492 387 927.
    • Present address: 7 JJ Thomson Avenue, Cambridge CB3 0FB, United Kingdom. Tel.: +44 1223 479 884.
    • ,
  • Olivier Clatz

      Affiliations

    • Asclepios Research Project – INRIA, 2004 Route des Lucioles, 06902, Sophia Antipolis, France
    • ,
  • Pierre-Yves Bondiau

      Affiliations

    • Centre Antoine Lacassagne, 33, Ave. de Valombrosse, 06189, Nice, France
    • ,
  • Hervé Delingette

      Affiliations

    • Asclepios Research Project – INRIA, 2004 Route des Lucioles, 06902, Sophia Antipolis, France
    • ,
  • Nicholas Ayache

      Affiliations

    • Asclepios Research Project – INRIA, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

Received 22 December 2008 ,Revised 12 October 2009 ,Accepted 23 November 2009.

References 

  1. Araujo R, McElwain D. A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull. Math. Biol. 2004;66:1039–1091
  2. Aronson D, Weinberger H. Multidimensional nonlinear diffusion arising in population genetics. Adv. Math. 1978;30:33–76
  3. Athale C, Deisboeck T. The effects of EGF-receptor density on multiscale tumor growth patterns. J. Theor. Biol. 2006;238:771–779
  4. Breward C, Byrne H, Lewis C. A multiphase model describing vascular tumour growth. Bull. Math. Biol. 2003;65:609–640
  5. Burger P, Dubois P, Schold S, Smith K, Odom G, Crafts D, et al. Computerized tomographic and pathologic studies of the untreated, quiescent, and recurrent glioblastoma multiforme. J. Neurosurg. 1983;58:159–169
  6. Byrne H, Preziosi L. Modelling solid tumour growth using the theory of mixtures. Math. Med. Biol. 2003;20:341–366
  7. Byrne H, Owen M, Alarcon T, Murphy J, Maini P. Modelling the response of vascular tumours to chemotherapy: a multiscale approach. Math. Models Meth. Appl. Sci. 2006;16(7S):1219–1241
  8. Clatz O, Sermesant M, Bondiau P, Delingette H, Warfield S, Malandain G, et al. Realistic simulation of the 3D growth of brain tumors in mr images coupling diffusion with biomechanical deformation. IEEE TMI. 2005;24(10):1334–1346
  9. Cristini V, Lowengrub J, Nie Q. Nonlinear simulation of tumor growth. J. Math. Biol. 2003;46:191–224
  10. Cruywagen, G., Woodward, D., Tracqui, P., Bartoo, G., Murray, J., Alvord, E., 1995. The modelling of diffusive tumours. J. Biol. Syst. 3.
  11. Drasdo D, Höhme S. A single-cell-based model of tumor growth in vitro: monolayers and spheroids. Phys. Biol. 2005;2:133–147
  12. Ebert U, Saarlos WV. Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts. Physica D. 2000;146:1–99
  13. Fisher R. The wave of advance of advantegous genes. Ann. Eug. 1937;7:355–369
  14. Frieboes H, Lowengrub J, Wise S, Zheng X, Macklin P, Bearer E, et al. Computer simulation of glioma growth and morphology. NeuroImage. 2007;37:S59–S70
  15. Giese A, Kluwe L, Laube B, Meissner H, Berens M, Westphal M. Migration of human glioma cells on myelin. Neurosurgery. 1996;38(4):755–764
  16. Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Phil. Trans. R Soc. London. 1825;115:513–585
  17. Hogea C, Murray B, Sethian J. Simulating complex tumor dynamics from avascular to vascular growth using a general level-set method. J. Math. Biol. 2006;53(1):86–134
  18. Hogea, C., Davatzikos, C., Biros, G., 2007. Modeling glioma growth and mass effect in 3D mr images of the brain. In: Lecturer Notes in Computer Science, vol. 4791. Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007.
  19. Jbabdi S, Mandonnet E, Duffau H, Capelle L, Swanson K, Pélégrini-Issac M, et al. Simulation of anisotropic growth of low-grade gliomas using diffusion tensor imaging. Magnet. Reson. Med. 2005;54(3):616–624
  20. Kansal A, Torquato S, Harsh GR, Chiocca IA, Deisboeck TS. Simulated brain tumor growth dynamics using a three-dimensional cellular automaton. J. Theor. Biol. 2000;203:367–382
  21. Kantor G, Loiseau H, Vital A, Mazeron J. Descriptions of GTV and CTV for radiation therapy of adult glioma. Cancer Radiother. 2001;5(5):571–580
  22. Kaspari N, Michaelis B, Gademann G. Using an artificial neural network to define the planning target volume in radiotherapy. J. Med. Syst. 1997;21:389–401
  23. Konukoglu, E., Clatz, O., Bondiau, P.-Y., Delingette, H., Ayache, N., 2006. Extrapolating tumor invasion margins for physiologically determined radiotherapy regions. In: Proceedings of the 9th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI’06), Part I, No. 4190 in LNCS.
  24. Konukoglu, E., Sermesant, M., Clatz, O., Peyrat, J.-M., Delingette, H., Ayache, N., 2007. A recursive anisotropic fast marching approach to reaction diffusion equation: Application to tumor growth modeling. In: IPMI 2007, LNCS, vol. 4584.
  25. Konukoglu, E., Clatz, O., Menze, B., Stieltjes, B., Weber, M.-A., Mandonnet, E., Delingette, H., Ayache, N., 2009. Image guided personalization of reaction–diffusion type tumor growth models using modified anisotropic Eikonal equations. IEEE T. Med. Imaging, in press.
  26. Maini P, McElwain D, Leavesley D. Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng. 2004;10:475–482
  27. Mohamed, A., Davatzikos, C., 2005. Finite element modeling of brain tumor mass-effect from 3D medical images. In: Lecturer Notes Computer Science, vol. 3749. MICCAI.
  28. Murray J. Mathematical Biology. Springer-Verlag; 2002;
  29. Patel A, Gawlinski E, Lemieux S, Gatenby R. A cellular automaton model of early tumor growth and invasion. J. Theor. Biol. 2001;213(3):315–331
  30. Price S, Burnet N, Donovan T, Green H, na AP, Antoun N, et al. Diffusion tensor imaging of brain tumours at 3t: a potential tool for assessing white matter tract invasion?. Clin. Radiol. 2003;58:455–462
  31. Qian J, Zhang Y-T, Zhao H-K. A fast sweeping method for static convex Hamilton–Jacobi equations. J. Sci. Comp. 2007;31:237–271
  32. Sanga S, Frieboes H, Zheng X, Gatenby R, Bearer E, Cristini V. Predictive oncology: a review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth. NeuroImage. 2007;37:S120–S134
  33. Seither R, Jose B, Paris K, Lindberg R, Spanos W. Results of irradiation in patients with high-grade gliomas evaluated by magnetic resonance imaging. Am. J. Clin. Oncol. 1995;18:297–299
  34. Sethian J. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press; 1999;
  35. Sethian J, Vladimirsky A. Ordered upwind methods for static Hamilton–Jacobi equations: theory and algorithms. SIAM J. Numer. Anal. 2003;41(1):325–363
  36. Stamatakos G, Antipas V, Uzunoglu N. A spatiotemporal patient individualized simulation model of solid tumor response to chemotherapy in vivo: the paradigm of glioblastoma multiforme treated by temozolomide. IEEE Trans. Biol. Med. Eng. 2006;53(8):1467–1477
  37. Stamatakos G, Antipas V, Uzunoglu N, Dale R. 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. Radiat. 2006;79:389–400
  38. Stein A, Demuth T, Mobley D, Berens M, Sander L. A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment. Biophys. J. 2007;92:356–365
  39. Strauss W. Partial Differential Equations: An Introduction. New York: Wiley and Sons; 1992;
  40. Swanson K, Alvord E, Murray J. A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif. 2000;33(5):317–329
  41. Swanson K, Alvord E, Murray J. Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Brit. J. Cancer. 2002;86:14–18
  42. Swanson K, Alvord E, Murray J. Dynamics of a model for brain tumors reveals a small window for therapeutic intervention. Discrete Continous Dyn. Syst. B. 2004;4(1):289–295
  43. Swanson K, Rostomily R, Alvord E. A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle. Brit. J. Cancer. 2008;98:113–119
  44. Taylor M. Partial differential Eqs. 1: Basic Theory. Springer; 1996;
  45. Tovi M. Mr imaging in cerebral gliomas analysis of tumour tissue components. Acta Radiol. Suppl. 1993;384:1–24
  46. Tracqui P, Cruywagen G, Woodward D, Bartoo G, Murray J, Alvord E. A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth. Cell Prolif. 1995;28(1):17–31
  47. Verhulst P-F. Recherches matheématiques sur la loi d’accroissement de la population. Nouveau mémoires de l’Académie Royale des Sciences et Belles-Lettres de Bruxelles. 1845;18:1–41
  48. Watanabe M, Tanaka R, Takeda N, Wakabayashi K, Takahashi H. Correlation of computed tomography with the histopathology of primary malignant lymphoma of the brain. Neuroradiology. 1992;34:36–42
  49. Zizzari, A., Michaelis, B., Gademann, G., 2004. Simulation and modeling of brain tumors in computer-assisted radiotherapy. In: Proceedings of the IASTED Conference on Applied Simulation and Modelling.

PII: S1361-8415(09)00144-3

doi: 10.1016/j.media.2009.11.005

Medical Image Analysis
Volume 14, Issue 2 , Pages 111-125 , April 2010

Article Tools

* Image Usage & Resolution