Summary
Glioblastoma is the most malignant form of brain cancer. It is extremely invasive; the mechanisms that govern invasion are not well understood. To better understand the process of invasion, we conducted an in vitro experiment in which a 3D tumor spheroid is implanted into a collagen gel. The paths of individual invasive cells were tracked. These cells were modeled as radially biased, persistent random walkers. The radial velocity bias was found to be 19.6 μm/hr.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
CBTRUS: Primary brain tumors in the United States statistical report 1995–1999. Technical report (2002–2003).
Crocker, J.C., Grier, D.G.: Methods of digital viedo microscopy for colloidal studies. J. Coll. and Interf. Sci., 179, 298–310 (1996).
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 tumor spheroid model. Cell Proliferation, 34, 115–134 (2001).
Demuth, T., Berens, M.E.: Molecular mechanisms of glioma cell migration and invasion. J. Neuro-Oncol., 70, 217–228 (2004).
Demuth, T., Hopf, N.J., Kempski, O., Sauner, D., Herr, M., Giese, A., Perneczky, A.: Migratory activity of human glioma cell lines in vitro assessed by continuous single cell observation. Clin. and Exper. Metast., 18, 589–597 (2001).
Dunn, G.A., Brown, A.F.: A unified approach to analysing cell motility. J. Cell Sci. Suppl., 8, 81–102 (1987).
Hegedus, B., Zach, J., Czirok, A., Lpvey, J., Vicsek, T.: Irradiation and taxol treatment result in non-monotonous, dose-dependent changes in the motility of glioblastoma cells. J. of Neuro-Oncol., 67, 147–57 (2004).
Ionides, E.L., Fang, K.S., Oster, G.F.: Stochastic models for cell motion and taxis. J. Math. Biol., 48, 23–37 (2004).
Kanda, T., Sullivan, K.F., Wahl, G.M.: Histone-gfp fusion protein enables sensitive analysis of chromosome dynamics in living mammalian cells. Curr. Biol., 8, 377–385 (1998).
Kelm, J., Timmins, N., Brown, C., Fussenegger, M., Nielson, L.: Method for generation of homogeneous multicellular tumor spheroids applicable to a wide variety of cell types. Biotechn. and Bioeng., 83, 173–80 (2003).
Stokes, C.L., Lauffenburger, D.A., Williams, S.K.: Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. J. Cell Sci., 99, 419–430 (1991).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 springer
About this chapter
Cite this chapter
Stein, A.M., Vader, D.A., Sander, L.M., Weitz, D.A. (2007). A Stochastic Model of Glioblastoma Invasion. In: Deutsch, A., Brusch, L., Byrne, H., Vries, G.d., Herzel, H. (eds) Mathematical Modeling of Biological Systems, Volume I. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4558-8_19
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4558-8_19
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4557-1
Online ISBN: 978-0-8176-4558-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)