Diffusive modelling of glioma evolution: a review

Alexandros Roniotis, Kostas Marias, Vangelis Sakkalis, Michalis Zervakis

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DOI: 10.4236/jbise.2010.35070                

Abstract

Gliomas, the most aggressive form of brain cancer, are known for their widespread invasion into the tissue near the tumor lesion. Exponential models, which have been widely used in other types of cancers, cannot be used for the simulation of tumor growth, due to the diffusive behavior of glioma. Diffusive models that have been proposed in the last two decades seem to better approximate the expansion of gliomas. This paper covers the history of glioma diffusive modelling, starting from the simplified initial model in 90s and describing how this have been enriched to take into account heterogenous brain tissue, anisotropic migration of glioma cells and adjustable proliferation rates. Especially, adjustable proliferation rates are very important for modelling therapy plans and personalising therapy to different patients.

Keywords

Glioma; Brain Tumor; Diffusive Models; Proliferation; Invasion

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Silbergeld, D.L., Rostomily, R.C. and Alvord, E.C.Jr. (1991) The cause of death in patients with glioblastoma is multifactorial: Clinical factors and autopsy findings in 117 cases of suprantentorial glioblastoma in adults. Journal of Neuro-Oncology, 10(1), 179-185.
[2]	Swanson, K.R., True, L.D. and Murray, J.D. (2003) On the use of quantitative modeling to help understand PSA dynamics and other medical problems. American Journal of Clinical Pathology, 119(1), 14-17.
[3]	Tracqui, P. (1995) From passive diffusion to active cellular migration in mathematical models of tumour invasion. Acta Bibliotheoretica, 43(1), 443-464.
[4]	Swanson, K.R., Alvord, E.C. and Murray, J.D. (2000) A quantitative model for differential motility of gliomas in grey and white matter. Cell Proliferation, 33(5), 317-330.
[5]	Burgess, P.K., Kulesa, P.M., Murray, J.D. and Alvord, E.C, (1997) The interaction of growth rates and diffusion coefficients in a three-dimensional mathematical model of gliomas. Journal of Neuropathology & Experimental Neurology, 56(6), 704-713.
[6]	Wheldon, T.E. (1986) Mathematical models in experimental and clinical oncology. In: Ingrain, D. and Bloch, R.F., Eds., Mathematical Methods in Medicine, John Wiley & Sons, Chichester, 1-32.
[7]	Adam, J.A. and Maggelakis, S.A. (1990) Diffusion regulated growth characteristics of a spherical prevascular car- cinoma. Bulletin of Mathematical Biology, 52(4), 549- 582.
[8]	Lefever, R., Hiemaux, J. and Meyers, P. (1989) Evolution of tumours attacked by immune cytotoxic cells: The immune response dilemma. In: Goldbetor, A., Ed., Cell to Cell Signaling: From Experiments to Theoretical Models, Academic Press, Boston, 315-333.
[9]	Sherratt, J.A. and Nowa, M.A. (1992) Oneogenes, anti- oncogenes and the immune response to cancer a mathematical model. Proceeding of the Royal Society of London, B248(5), 261-271.
[10]	Dionysiou, D., Stamatakos, G.S., Uzunoglu, N.K., Nikita, K.S., Marioli, A. (2004) A four-dimensional simulation model of tumour response to radiotherapy in vivo: Parametric validation considering radiosensitivity, genetic pro- file and fractionation. Journal of Theoretical Biology, 230(1), 1-20. Uhttp://www.ncbi.nlm.nih.gov/entrez/query.fcgi? cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=15275995&query_hl=2U
[11]	Clatz, O., Sermesant, M., Bondiau, P., Delingette, H., Warfield, S.K., Malandain, G. and Ayache, N. (2005) Realistic simulation of the 3-D growth of brain tumours in MR images coupling diffusion with biomechanical deformation. IEEE Transactions on Medical Imaging, 24(3), 1334-1346.
[12]	Leighton, J. and Tchao R. (1984) The propagation of cancer, a process of tissue remodeling. Cancer and Metastasis Reviews, 28(3), 81-97.
[13]	Murray, J.D. (1989) Mathematical biology. Springer-Ver- lag, Heidelberg.
[14]	Marusic, M., Bajzer, Z., Freyer, J.P. and Vuk-Palovic, S. (1994) Analysis of growth of multicellular tumour spheroids by mathematical models. Cell Proliferation, 27(1), 73-94.
[15]	Kreth, F.W., Warnke, P.C., Scheremet, R., et al. (1993) Surgical resection and radiation therapy versus biopsy and radiation therapy in the treatment of glioblastoma multiforme. Journal of Neurosurgery, 78(5), 762-766.
[16]	Woodward, D.E., Cook, J., Tracqui, P., et al. (1996) A mathematical model of glioma growth: The effect of extent of surgical resection. Cell Proliferation, 29(6), 269-288.
[17]	Mandonnet, E., Delattre, J.Y., Tanguy, M.L., et al. (2003) Continuous growth of mean tumour diameter in a subset of grade II gliomas. Annals of Neurology, 53(4), 524-528.
[18]	Cocosco, C.A., Kollokian, V., Evans, A.C., et al. (1997) Brainweb: Online interface to a 3D simulated brain database. Neuroimage, 5(4), S425.
[19]	Jbabdi, S., Mandonnet, E., Duffau, H., et al. (2005) Simulation of anisotropic growth of low-grade gliomas using diffusion tensor imaging. Magnetic Resonance in Medicine, 54(3), 616-624.
[20]	Belien, A.T., Paganetti, P.A. and Schwab, M.E. (1999) Membrane-type 1 matrix metalloprotease (mt1-mmp) en- ables migration of glioma cells in central nervous system white matter. Journal of Cell Biology, 144(2), 373-384.
[21]	Giese, A., Bjerkvig, R., Berens, M.E. and Westphal, M., (2003) Cost of migration: Invasion of malignant gliomas and implications for treatment. Journal of Clinical Oncology, 21(8), 1624-1636.
[22]	Harpold, H.L.P., Alvord, E.C. and Swanson, K.R.Jr. (2007) Visualizing beyond the tip of the iceberg: The evolution of mathematical modeling of glioma growth and invasion. Journal of Neuropathology and Experimental Neurology, 66(1), 1-9.
[23]	Powathil, G., Kohandel, M., Oza, A. and Milosevic, M. (2007) Mathematical modeling of brain tumours: Effects of radiotherapy and chemotherapy. Physics in Medicine and Biology, 52(11), 3291-3306.
[24]	Cook, J., Woodward, D.E., Tracqui, P. and Murray, J.D. (1995) Resection of gliomas and life expectancy. Journal of Neuro-Oncology, 24(4), 131-135.
[25]	Murray, J. D. (2003) Mathematical biology I and II interdisciplinary applied mathematics. 3rd Edition, Springer, Berlin.
[26]	Stupp, R., et al. (2005) Radiotherapy plus concomitant and adjuvant Temozolomide for glioblastoma. The New England Journal of Medicine, 352(10), 987-996.
[27]	Walker, M.D., Strike, T.A and Sheline, G.E (1979) An analysis of dose-effect relationship in the radiotherapy of malignant Gliomas. International Journal of Radiation Oncology • Biology • Physics, 5(10), 1725-1731.
[28]	Werner-Wasik, M., Scott, C.B., Nelson, D.F., Gaspar, L.E., Murray, K.J., Fischbach, J.A., Nelson, J.S., Weinstein, A.S. and Curran, W.J.Jr. (1996) Final report of a phase I/II trial of hyperfractionated and accelerated hyperfractionated radiation therapy with carmustine for adults with supratentorial malignant gliomas (radiation therapy oncology group study 83-02). Cancer, 77(88), 1535-1543.
[29]	Shibamoto, Y., Nishimura, Y., Tsutsui, K., Sasai, K., Takahashi, M. and Abe, M. (1997) Comparison of accelerated hyperfractionated radiotherapy and conventional radiotherapy for supratentorial malignant glioma, Japan. Journal of Clinical Oncology, 27(1), 31-36.
[30]	Nieder, C., Nestle, U., Niewald, M., Walter, K. and Schnabel, K. (1999) Hyperfractionated reirradiation for malignant glioma. Frontiers of Radiation Therapy and Oncology, 33(3), 150-157.
[31]	Blakenberg, F.G., Teplitz, R.L., Ellis, W., Salamat, M.S., Min, B.H., Hall, L., et al. (1995) The influence of volumetric tumor doubling time, DNA ploidy, and histologic grade on the survival of patients with interracial astrocytomas. American Journal of Neuroradiology, 16(1), 1001- 1012.
[32]	Roniotis, A. (2010) Glioma growth modeling (internal report-submitted for review in the IEEE transactions on information and technology in biomedicine: Spectroscope issue on biomedicine information). FORTH-ICS, Heraklion.
[33]	Marias, K., Sakkalis, V., Roniotis, A., Farmaki, C., Stamatakos, G., et al. (2009) Clinically oriented translational cancer multilevel modeling: The contracancrum project. World Congress on Medical Physics and Biomedical Engineering, Munich.
[34]	Roniotis, A., Marias, K., Sakkalis, V., Tsibidis, G. and Zervakis, M. (2009) A complete mathematical study of a 3D model of heterogeneous and anisotropic glioma evolution. IEEE Engineering in Medicine and Biology Society, 1(185), 2807-2810.