Hybrid mathematical model of glioma progression

Objectives:  Gliomas are an important form of brain cancer, with high mortality rate. Mathematical models are often used to understand and predict their behaviour. However, using current modeling techniques one must choose between simulating individual cell behaviour and modeling tumours of clinically significant size.

[1]  R. Gruetter,et al.  Direct measurement of brain glucose concentrations in humans by 13C NMR spectroscopy. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[2]  C. Schaller,et al.  MATHEMATICAL MODELLING OF GLIOBLASTOMA TUMOUR DEVELOPMENT: A REVIEW , 2005 .

[3]  Michael Berens,et al.  A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment. , 2007, Biophysical journal.

[4]  B. Grammaticos,et al.  A cellular automaton model for the migration of glioma cells , 2006, Physical biology.

[5]  M. Westphal,et al.  Cost of migration: invasion of malignant gliomas and implications for treatment. , 2003, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[6]  R. Ganguly,et al.  Mathematical model for the cancer stem cell hypothesis , 2006, Cell proliferation.

[7]  J. Lowengrub,et al.  Nonlinear simulation of the effect of microenvironment on tumor growth. , 2007, Journal of theoretical biology.

[8]  E. B. Butler,et al.  Hypofractionated intensity-modulated radiotherapy for primary glioblastoma multiforme. , 2004, International journal of radiation oncology, biology, physics.

[9]  G A Ojemann,et al.  Glucose metabolism in human malignant gliomas measured quantitatively with PET, 1-[C-11]glucose and FDG: analysis of the FDG lumped constant. , 1998, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[10]  Conan K. N. Li The glucose distribution in 9l rat brain multicell tumor spheroids and its effect on cell necrosis , 1982, Cancer.

[11]  A. Kriegstein,et al.  Gap junction adhesion is necessary for radial migration in the neocortex , 2007, Nature.

[12]  T. Deisboeck,et al.  Development of a three-dimensional multiscale agent-based tumor model: simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. , 2006, Journal of theoretical biology.

[13]  J. Murray,et al.  Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion , 2003, Journal of the Neurological Sciences.

[14]  I. Puri,et al.  Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis , 2007, Cell proliferation.

[15]  T. Deisboeck,et al.  Simulating non-small cell lung cancer with a multiscale agent-based model , 2007, Theoretical Biology and Medical Modelling.

[16]  H. Frieboes,et al.  Computer simulation of glioma growth and morphology , 2007, NeuroImage.

[17]  L. Sander,et al.  Growth patterns of microscopic brain tumors. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Satoshi O. Suzuki,et al.  Dynamic analysis of glioma cells: Looking into “movement phenotypes” , 2005, Neuropathology : official journal of the Japanese Society of Neuropathology.

[19]  H. Frieboes,et al.  Predictive oncology: A review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth , 2007, NeuroImage.

[20]  Numerical simulation of tumor spheroid dynamics , 2004 .

[21]  M. Clarke,et al.  Self-renewal and solid tumor stem cells , 2004, Oncogene.

[22]  R. Stupp,et al.  Optimal role of temozolomide in the treatment of malignant gliomas , 2005, Current neurology and neuroscience reports.

[23]  Zhigang Xie Brain Tumor Stem Cells , 2009, Neurochemical Research.

[24]  N. Hynes,et al.  The ErbB receptors and their role in cancer progression. , 2003, Experimental cell research.

[25]  J. Olson,et al.  Nervous system cancer models: Medulloblastoma , 2006 .

[26]  R. Wechsler-Reya,et al.  Getting at the Root and Stem of Brain Tumors , 2004, Neuron.

[27]  M. Berens,et al.  Regulation of glioma cell migration by serine-phosphorylated P311. , 2005, Neoplasia.

[28]  Thomas S. Deisboeck,et al.  Computational modeling of brain tumors: discrete, continuum or hybrid? , 2009 .

[29]  Peter Canoll,et al.  Transplanted glioma cells migrate and proliferate on host brain vasculature: A dynamic analysis , 2006, Glia.

[30]  E. Holland,et al.  Glioblastoma multiforme: the terminator. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[31]  M. Clarke Neurobiology: At the root of brain cancer , 2004, Nature.

[32]  D. Silbergeld,et al.  Assessment of brain tumor cell motility in vivo and in vitro. , 1995, Journal of neurosurgery.

[33]  Alissa M. Weaver,et al.  Tumor Morphology and Phenotypic Evolution Driven by Selective Pressure from the Microenvironment , 2006, Cell.

[34]  P. Dirks,et al.  Brain tumor stem cells: identification and concepts. , 2007, Neurosurgery clinics of North America.

[35]  K. Aldape,et al.  Models of malignant glioma , 2006 .