Improving the time‐machine: estimating date of birth of grade II gliomas

Objectives:  Here we present a model aiming to provide an estimate of time from tumour genesis, for grade II gliomas. The model is based on a differential equation describing the diffusion–proliferation process. We have applied our model to situations where tumour diameter was shown to increase linearly with time, with characteristic diametric velocity.

[1]  H. Duffau,et al.  Evidence for the genesis of WHO grade II glioma in an asymptomatic young adult using repeated MRIs , 2011, Acta Neurochirurgica.

[2]  B. Grammaticos,et al.  Modelling intercellular communication and its effects on tumour invasion , 2010, Physical biology.

[3]  M. L. Tanaka,et al.  Coupled mathematical model of tumorigenesis and angiogenesis in vascular tumours , 2010, Cell proliferation.

[4]  R. Guillevin,et al.  Natural history of incidental world health organization grade II gliomas , 2010, Annals of neurology.

[5]  M. Primeau,et al.  Management of diffuse low-grade cerebral gliomas. , 2010, Neurologic clinics.

[6]  K Hendrickson,et al.  Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach , 2010, Physics in medicine and biology.

[7]  C. Daumas-Duport,et al.  Diffuse low-grade oligodendrogliomas extend beyond MRI-defined abnormalities , 2010, Neurology.

[8]  F. Ducray,et al.  Prolonged response without prolonged chemotherapy: a lesson from PCV chemotherapy in low-grade gliomas. , 2010, Neuro-oncology.

[9]  J. Honnorat,et al.  Predictive value of multimodality MRI using conventional, perfusion, and spectroscopy MR in anaplastic transformation of low-grade oligodendrogliomas , 2010, Journal of Neuro-Oncology.

[10]  I. Puri,et al.  Hybrid mathematical model of glioma progression , 2009, Cell proliferation.

[11]  Luc Taillandier,et al.  Prognostic significance of imaging contrast enhancement for WHO grade II gliomas. , 2009, Neuro-oncology.

[12]  Christophe Deroulers,et al.  Modeling tumor cell migration: From microscopic to macroscopic models. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Luc Taillandier,et al.  Inter- and intrapatients comparison of WHO grade II glioma kinetics before and after surgical resection , 2009, Neurosurgical Review.

[14]  M. Berger,et al.  GLIOMA EXTENT OF RESECTION AND ITS IMPACT ON PATIENT OUTCOME , 2008, Neurosurgery.

[15]  Luc Taillandier,et al.  Computational modeling of the WHO grade II glioma dynamics: principles and applications to management paradigm , 2008, Neurosurgical Review.

[16]  Olivier Clatz,et al.  Biocomputing: numerical simulation of glioblastoma growth using diffusion tensor imaging , 2008, Physics in medicine and biology.

[17]  M. A. J. Chaplainb.  Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion , 2008 .

[18]  M Aubert,et al.  A model for glioma cell migration on collagen and astrocytes , 2008, Journal of The Royal Society Interface.

[19]  B. Scheithauer,et al.  The 2007 WHO classification of tumours of the central nervous system , 2007, Acta Neuropathologica.

[20]  G Powathil,et al.  Mathematical modeling of brain tumors: effects of radiotherapy and chemotherapy , 2007, Physics in medicine and biology.

[21]  Pier Paolo Delsanto,et al.  Physical aspects of cancer invasion , 2007, Physical biology.

[22]  Laurent Capelle,et al.  Dynamic history of low‐grade gliomas before and after temozolomide treatment , 2007, Annals of neurology.

[23]  Kristin R. Swanson,et al.  The Evolution of Mathematical Modeling of Glioma Proliferation and Invasion , 2007, Journal of neuropathology and experimental neurology.

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

[25]  Luc Taillandier,et al.  Prognostic value of initial magnetic resonance imaging growth rates for World Health Organization grade II gliomas , 2006, Annals of neurology.

[26]  L. Liau,et al.  Current status of clinical trials for glioblastoma. , 2006, Reviews on recent clinical trials.

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

[28]  H. Frieboes,et al.  An integrated computational/experimental model of tumor invasion. , 2006, Cancer research.

[29]  R. Guillevin,et al.  Simulation of anisotropic growth of low‐grade gliomas using diffusion tensor imaging , 2005, Magnetic resonance in medicine.

[30]  C. Daumas-Duport,et al.  Oligodendrogliomas. Part I: Patterns of growth, histological diagnosis, clinical and imaging correlations: A study of 153 cases , 1997, Journal of Neuro-Oncology.

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

[32]  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.

[33]  Laurent Capelle,et al.  Continuous growth of mean tumor diameter in a subset of grade II gliomas , 2003, Annals of neurology.

[34]  M. Berger,et al.  Low-grade hemispheric gliomas in adults: a critical review of extent of resection as a factor influencing outcome. , 2001, Journal of neurosurgery.

[35]  J. Murray,et al.  A quantitative model for differential motility of gliomas in grey and white matter , 2000, Cell proliferation.

[36]  M. Chaplain,et al.  Continuous and discrete mathematical models of tumor-induced angiogenesis , 1998, Bulletin of mathematical biology.

[37]  J. Murray,et al.  The interaction of growth rates and diffusion coefficients in a three-dimensional mathematical model of gliomas. , 1997, Journal of neuropathology and experimental neurology.

[38]  J. Murray,et al.  A mathematical model of glioma growth: the effect of extent of surgical resection , 1996, Cell proliferation.

[39]  Philippe Tracqui,et al.  THE MODELLING OF DIFFUSIVE TUMOURS , 1995 .

[40]  J. Murray,et al.  A mathematical model of glioma growth: the effect of chemotherapy on spatio‐temporal growth , 1995, Cell proliferation.

[41]  B A Kall,et al.  Imaging-based stereotaxic serial biopsies in untreated intracranial glial neoplasms. , 1987, Journal of neurosurgery.

[42]  R. Barnard,et al.  The classification of tumours of the central nervous system. , 1982, Neuropathology and applied neurobiology.

[43]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[44]  G. B. Hassin.  THE RISE OF NEUROPATHOLOGY , 1942 .