154 5.4. DIFFUSION ANISOTROPE 3D (a) terme source f -échelle : de -234, pp.238-283 ,
A cellular automaton model for tumour growth in inhomogeneous environment, Journal of Theoretical Biology, vol.225, issue.2, pp.257-274, 2003. ,
DOI : 10.1016/S0022-5193(03)00244-3
A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells, Journal of Theoretical Biology, vol.229, issue.3, pp.395-411, 2004. ,
DOI : 10.1016/j.jtbi.2004.04.016
ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH, Mathematical Models and Methods in Applied Sciences, vol.12, issue.05, p.737, 2002. ,
DOI : 10.1142/S0218202502001878
Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis, Bulletin of Mathematical Biology, vol.60, issue.5, pp.857-899, 1998. ,
DOI : 10.1006/bulm.1998.0042
Microenvironment driven invasion: a multiscale multimodel investigation, Journal of Mathematical Biology, vol.67, issue.19, pp.579-624, 2009. ,
DOI : 10.1007/s00285-008-0210-2
A penalization method to take into account obstacles in incompressible viscous flows, Numerische Mathematik, vol.81, issue.4, pp.497-520, 1999. ,
DOI : 10.1007/s002110050401
PETSc users manual, 2010. ,
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries, Modern Software Tools in Scientific Computing, pp.163-202, 1997. ,
DOI : 10.1007/978-1-4612-1986-6_8
Multiparameter Computational Modeling of Tumor Invasion, Cancer Research, vol.69, issue.10, pp.694493-4501, 2009. ,
DOI : 10.1158/0008-5472.CAN-08-3834
Exact-gradient shape optimization of a 2-d euler flow. Finite Elements in Analysis and Design, pp.281-302, 1992. ,
A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy, Journal of Theoretical Biology, vol.260, issue.4, 2009. ,
DOI : 10.1016/j.jtbi.2009.06.026
URL : https://hal.archives-ouvertes.fr/inria-00440447
A viscoelastic model for avascular tumor growth. Discrete and Continuous Dynamical Systems, Dynamical Systems, Differential Equations and Applications, 7th AIMS Conference, pp.101-108, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00267292
Computational Modeling of Solid Tumor Growth: The Avascular Stage, SIAM Journal on Scientific Computing, vol.32, issue.4, pp.2321-2344, 2010. ,
DOI : 10.1137/070708895
URL : https://hal.archives-ouvertes.fr/inria-00148610
Computerized tomographic and pathologic studies of the untreated, quiescent, and recurrent glioblastoma multiforme, Journal of Neurosurgery, vol.58, issue.2, pp.159-169, 1983. ,
DOI : 10.3171/jns.1983.58.2.0159
A two-phase model of solid tumour growth, Applied Mathematics Letters, vol.16, issue.4, pp.567-573, 2003. ,
DOI : 10.1016/S0893-9659(03)00038-7
Angiogenesis in cancer and other diseases, Nature, vol.407, issue.6801, pp.249-257, 2000. ,
DOI : 10.1038/35025220
Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design, Journal of Computational Physics, vol.228, issue.17, pp.6291-6315, 2009. ,
DOI : 10.1016/j.jcp.2009.05.017
URL : https://hal.archives-ouvertes.fr/hal-00385460
Realistic simulation of the 3-D growth of brain tumors in MR images coupling diffusion with biomechanical deformation, IEEE Transactions on Medical Imaging, vol.24, issue.10, pp.1334-1346, 2005. ,
DOI : 10.1109/TMI.2005.857217
A 3d model for glioblastoma, 2011. ,
Abstract, Journal of Inverse and Ill-posed Problems, vol.22, issue.6 ,
DOI : 10.1515/jip-2013-0009
SYSTEM IDENTIFICATION IN TUMOR GROWTH MODELING USING SEMI-EMPIRICAL EIGENFUNCTIONS, Mathematical Models and Methods in Applied Sciences, vol.22, issue.06 ,
DOI : 10.1142/S0218202512500030
Prediction of the evolution of thyroidal lung nodules using a mathematical model, ERCIM News, vol.82, pp.37-38, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-01038030
Design and construction of a realistic digital brain phantom, IEEE Transactions on Medical Imaging, vol.17, issue.3, pp.463-468, 2002. ,
DOI : 10.1109/42.712135
Multiscale Modeling of Cancer : An Integrated Experimental and Mathematical Modeling Approach, 2010. ,
DOI : 10.1017/CBO9780511781452
Individual-based approaches to birth and death in avascu1ar tumors, Mathematical and Computer Modelling, vol.37, issue.11, pp.1163-1175, 2003. ,
DOI : 10.1016/S0895-7177(03)00128-6
Error estimates of the finite volume scheme for the nonlinear tensor-driven anisotropic diffusion, Applied Numerical Mathematics, vol.59, issue.10, pp.2548-2570, 2009. ,
DOI : 10.1016/j.apnum.2009.05.010
Convergence Analysis of Finite Volume Scheme for Nonlinear Tensor Anisotropic Diffusion in Image Processing, SIAM Journal on Numerical Analysis, vol.46, issue.1, pp.37-60, 2007. ,
DOI : 10.1137/070685038
A Mathematical Model for the Effects of HER2 Overexpression on Cell Proliferation in Breast Cancer, Bulletin of Mathematical Biology, vol.2, issue.2, pp.1707-1729, 2008. ,
DOI : 10.1007/s11538-008-9315-4
Finite volume methods. Handbook of numerical analysis, pp.713-1018, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-00346077
Three-dimensional multispecies nonlinear tumor growth???II: Tumor invasion and angiogenesis, Journal of Theoretical Biology, vol.264, issue.4, pp.1254-1278, 2010. ,
DOI : 10.1016/j.jtbi.2010.02.036
Computer simulation of glioma growth and morphology, NeuroImage, vol.37, pp.37-59, 2007. ,
DOI : 10.1016/j.neuroimage.2007.03.008
Modeling the Effect of Deregulated Proliferation and Apoptosis on the Growth Dynamics of Epithelial Cell Populations In Vitro, Biophysical Journal, vol.88, issue.1, pp.62-75, 2005. ,
DOI : 10.1529/biophysj.104.041459
Hypoxia Inhibits G1/S Transition through Regulation of p27 Expression, Journal of Biological Chemistry, vol.276, issue.11, pp.2767919-7926, 2001. ,
DOI : 10.1074/jbc.M010189200
Why do cancers have high aerobic glycolysis?, Nature Reviews Cancer, vol.62, issue.11, pp.891-899, 2004. ,
DOI : 10.1038/nrc1478
Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion, Journal of Theoretical Biology, vol.250, issue.4, pp.684-704, 2008. ,
DOI : 10.1016/j.jtbi.2007.10.026
An evolutionary hybrid cellular automaton model of solid tumour growth, Journal of Theoretical Biology, vol.246, issue.4, pp.583-603, 2007. ,
DOI : 10.1016/j.jtbi.2007.01.027
Evolution of cell motility in an individual-based model of tumour growth, Journal of Theoretical Biology, vol.259, issue.1, pp.67-83, 2009. ,
DOI : 10.1016/j.jtbi.2009.03.005
URL : https://hal.archives-ouvertes.fr/hal-00554584
A Second-Order-Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains, Journal of Computational Physics, vol.176, issue.1, pp.205-227, 2002. ,
DOI : 10.1006/jcph.2001.6977
Glioma invasion ??? Pattern of dissemination by mechanisms of invasion and surgical intervention, pattern of gene expression and its regulatory control by tumorsuppressor p53 and proto-oncogene ETS-1, Acta Neurochir, vol.88, pp.153-162, 2003. ,
DOI : 10.1007/978-3-7091-6090-9_21
Incorporating topological derivatives into shape derivatives based level set methods, Journal of Computational Physics, vol.225, issue.1, pp.891-909, 2007. ,
DOI : 10.1016/j.jcp.2007.01.003
An image-driven parameter estimation problem for a reaction???diffusion glioma growth model with mass effects, Journal of Mathematical Biology, vol.10, issue.3, pp.793-825, 2008. ,
DOI : 10.1007/s00285-007-0139-x
Weighted ENO Schemes for Hamilton--Jacobi Equations, SIAM Journal on Scientific Computing, vol.21, issue.6, pp.2126-2143, 2000. ,
DOI : 10.1137/S106482759732455X
Efficient Implementation of Weighted ENO Schemes, Journal of Computational Physics, vol.126, issue.1, pp.202-228, 1996. ,
DOI : 10.1006/jcph.1996.0130
A mathematical model for pattern formation of glioma cells outside the tumor spheroid core, Journal of Theoretical Biology, vol.260, issue.3, pp.359-371, 2009. ,
DOI : 10.1016/j.jtbi.2009.06.025
Image Guided Personalization of Reaction-Diffusion Type Tumor Growth Models Using Modified Anisotropic Eikonal Equations, IEEE Transactions on Medical Imaging, vol.29, issue.1, pp.77-95, 2010. ,
DOI : 10.1109/TMI.2009.2026413
URL : https://hal.archives-ouvertes.fr/inria-00616100
Extrapolating glioma invasion margin in brain magnetic resonance images: Suggesting new irradiation margins, Medical Image Analysis, vol.14, issue.2, pp.111-125, 2010. ,
DOI : 10.1016/j.media.2009.11.005
URL : https://hal.archives-ouvertes.fr/inria-00616107
Personalization of reactiondiffusion tumor growth models in mr images : Application to brain gliomas characterization and radiotherapy planning, Multiscale Cancer Modeling, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00616111
Inhibition of Glioblastoma Angiogenesis and Invasion by Combined Treatments Directed Against Vascular Endothelial Growth Factor Receptor-2, Epidermal Growth Factor Receptor, and Vascular Endothelial-Cadherin, Clinical Cancer Research, vol.11, issue.13, pp.114934-4940, 2005. ,
DOI : 10.1158/1078-0432.CCR-04-2270
Invasion as limitation to anti-angiogenic glioma therapy, Acta Neurochir, vol.88, pp.169-177, 2003. ,
DOI : 10.1007/978-3-7091-6090-9_23
A mathematical model for m-phase specific chemotherapy including the g0-phase and immunoresponse, Math Biosci Eng, vol.4, issue.2, pp.239-259, 2007. ,
Weighted Essentially Non-oscillatory Schemes, Journal of Computational Physics, vol.115, issue.1, pp.200-212, 1994. ,
DOI : 10.1006/jcph.1994.1187
The 2007 WHO Classification of Tumours of the Central Nervous System, Acta Neuropathologica, vol.64, issue.2, pp.97-109, 2007. ,
DOI : 10.1007/s00401-007-0243-4
Multiscale modelling and nonlinear simulation of vascular tumour growth, Journal of Mathematical Biology, vol.67, issue.2, pp.765-798, 1007. ,
DOI : 10.1007/s00285-008-0216-9
Emerging Patterns in Tumor Systems: Simulating the Dynamics of Multicellular Clusters with an Agent-based Spatial Agglomeration Model, Journal of Theoretical Biology, vol.219, issue.3, pp.343-370, 2002. ,
DOI : 10.1006/jtbi.2002.3131
Mathematical modeling of tumorinduced angiogenesis, Journal of Mathematical Biology, vol.49, pp.111-187, 2004. ,
Adjoint Equation and Analysis of Complex Systems, Number 295 in Mathematics and its Applications, 1995. ,
DOI : 10.1007/978-94-017-0621-6
Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications, Journal of Mathematical Biology, vol.114, issue.4, pp.625-656, 2009. ,
DOI : 10.1007/s00285-008-0218-7
Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow, Journal of Computational Physics, vol.230, issue.4, pp.863-889, 2011. ,
DOI : 10.1016/j.jcp.2010.04.037
Modeling the Influence of the E-Cadherin-??-Catenin Pathway in Cancer Cell Invasion: A Multiscale Approach, Biophysical Journal, vol.95, issue.1, pp.155-165, 2008. ,
DOI : 10.1529/biophysj.107.114678
A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies, Theoretical Biology and Medical Modelling, vol.3, issue.1, p.7, 2006. ,
DOI : 10.1186/1742-4682-3-7
URL : https://hal.archives-ouvertes.fr/hal-00756367
A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents, Journal of Theoretical Biology, vol.243, issue.4, pp.532-541, 2006. ,
DOI : 10.1016/j.jtbi.2006.07.013
URL : https://hal.archives-ouvertes.fr/hal-00428053
Mathematical Models of Avascular Tumor Growth, SIAM Review, vol.49, issue.2, pp.179-208, 2007. ,
DOI : 10.1137/S0036144504446291
A Remark on Computing Distance Functions, Journal of Computational Physics, vol.163, issue.1, pp.51-67, 2000. ,
DOI : 10.1006/jcph.2000.6553
Predictive Pharmacokinetic-Pharmacodynamic Modeling of Tumor Growth Kinetics in Xenograft Models after Administration of Anticancer Agents, Cancer Research, vol.64, issue.3, pp.1094-1101, 2004. ,
DOI : 10.1158/0008-5472.CAN-03-2524
Mathematical modelling of tumour acidity, Journal of Theoretical Biology, vol.255, issue.1, pp.106-112, 2008. ,
DOI : 10.1016/j.jtbi.2008.08.002
The role of acidity in solid tumour growth and invasion, Journal of Theoretical Biology, vol.235, issue.4, pp.476-484, 2005. ,
DOI : 10.1016/j.jtbi.2005.02.001
Hypoxia-driven selection of the metastatic phenotype, Cancer and Metastasis Reviews, vol.23, issue.Pt 13, pp.319-331, 2007. ,
DOI : 10.1007/s10555-007-9062-2
Quantifying glioma cell growth and invasion in vitro, Mathematical and Computer Modelling, vol.47, issue.5-6, pp.638-648, 2008. ,
DOI : 10.1016/j.mcm.2007.02.024
Virtual resection of gliomas: Effect of extent of resection on recurrence, Mathematical and Computer Modelling, vol.37, issue.11, pp.1177-1190, 2003. ,
DOI : 10.1016/S0895-7177(03)00129-8
Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion, Journal of the Neurological Sciences, vol.216, issue.1, pp.1-10, 2003. ,
DOI : 10.1016/j.jns.2003.06.001
Mechanisms of glioma cell invasion, Acta Neurochir, vol.88, pp.163-167, 2003. ,
DOI : 10.1007/978-3-7091-6090-9_22
Three-dimensional multispecies nonlinear tumor growth???I, Journal of Theoretical Biology, vol.253, issue.3, pp.524-543, 2008. ,
DOI : 10.1016/j.jtbi.2008.03.027
Domaine public, source MedlinePlus (http://upload.wikimedia.org/wikipedia ,
Source : JDifool, licence CC-BY-SA-3.0-2.5-2.0-1.0 (www.creativecommons.org/licenses/by-sa/3.0), via Wikimedia Commons (http://commons.wikimedia.org/wiki/File:Neuron_ glial_cells_diagram_dumb.svg), p.20 ,
Par LadyofHats, domaine public, via Wikimedia Commons, File:Complete_neuron_cell_diagram_en.svg), vol.21 ,
Source : service radiologie, Quelques IRMs de tumeurs cérébrales, p.26 ,
La première ligne représente la croissance obtenue avec anisotropie, la seconde lorsque le cerveau est considéré comme étant un milieu isotrope (les plus hautes densités de cellules proliférantes sont en blanc ,
La première ligne représente la croissance obtenue avec anisotropie, la seconde sans (les plus hautes densités sont en blanc, les plus basses en noir), p.99 ,
Croissance de glioblastome : temps nécessaire à l'invasion d'une portion donnée, p.106 ,