ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH, Mathematical Models and Methods in Applied Sciences, vol.12, issue.05, pp.734-754, 2002. ,
DOI : 10.1142/S0218202502001878
Cell adhesion mechanisms and stress relaxation in the mechanics of tumours, Biomechanics and Modeling in Mechanobiology, vol.2, issue.5, pp.397-413, 2009. ,
DOI : 10.1007/s10237-008-0145-y
An elasto-visco-plastic model of cell aggregates, J. Theor. Biol, vol.262, pp.35-47, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00554642
Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis, Bulletin of Mathematical Biology, vol.60, issue.5, pp.857-900, 1998. ,
DOI : 10.1006/bulm.1998.0042
Cancer Medicine, chapter Cell Proliferation, Differentiation, and Apoptosis, 2000. ,
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
A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation, SIAM Journal on Applied Mathematics, vol.65, issue.4, pp.1261-1284, 2005. ,
DOI : 10.1137/040607113
Sur les conditions hydrodynamiques au voisinage d'une interface milieu fluide-milieux poreux: application la convection naturelle, C.R. Acad. Sci. Paris II, vol.299, pp.1-4, 1984. ,
Die Methode der finiten Elemente f??r elliptische Gleichungen mit diskontinuierlichen Koeffizienten, Computing, vol.19, issue.3, pp.207-213, 1970. ,
DOI : 10.1007/BF02248021
PETSc users manual, 2008. ,
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.4493-4501, 2009. ,
DOI : 10.1158/0008-5472.CAN-08-3834
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2835777
A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions, Journal of Computational Physics, vol.197, issue.1, pp.364-386, 2004. ,
DOI : 10.1016/j.jcp.2003.12.003
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, pp.545-562, 2009. ,
DOI : 10.1016/j.jtbi.2009.06.026
URL : https://hal.archives-ouvertes.fr/inria-00440447
A finite element method for interface problems in domains with smooth boundaries and interfaces, Advances in Computational Mathematics, vol.58, issue.1, pp.109-138, 1996. ,
DOI : 10.1007/BF02127700
Computational Modeling of Solid Tumor Growth: The Avascular Stage, SIAM Journal on Scientific Computing, vol.32, issue.4, pp.2321-2344, 2009. ,
DOI : 10.1137/070708895
URL : https://hal.archives-ouvertes.fr/inria-00148610
Numerical studies on the effect of electric pulses on an egg-shaped cell with a spherical nucleus, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00477495
The Essential Physics of Medical Imaging, Medical Physics, vol.30, issue.7, 2001. ,
DOI : 10.1118/1.1585033
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
Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development, Mathematical and Computer Modelling, vol.23, issue.6, pp.47-87, 1996. ,
DOI : 10.1016/0895-7177(96)00019-2
Modeling cell movement in anisotropic and heterogeneous network tissues, Networks Heterogen. Media, pp.333-357, 2007. ,
DOI : 10.3934/nhm.2007.2.333
Finite element methods and their convergence for elliptic and parabolic interface problems, Numerische Mathematik, vol.79, issue.2, pp.175-202, 1998. ,
DOI : 10.1007/s002110050336
A coupling interface method for elliptic interface problems, Journal of Computational Physics, vol.225, issue.2, pp.2138-2174, 2007. ,
DOI : 10.1016/j.jcp.2007.03.012
Abstract, Communications in Computational Physics, vol.39, issue.05 ,
DOI : 10.1016/j.jcp.2006.02.014
SYSTEM IDENTIFICATION IN TUMOR GROWTH MODELING USING SEMI-EMPIRICAL EIGENFUNCTIONS, Mathematical Models and Methods in Applied Sciences, vol.22, issue.06, 2011. ,
DOI : 10.1142/S0218202512500030
A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type, Proc. Camb, pp.50-67, 1947. ,
Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching, Journal of Mathematical Biology, vol.67, issue.4-5, pp.723-763, 2009. ,
DOI : 10.1007/s00285-008-0215-x
Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics, vol.77, issue.2, pp.439-471, 1988. ,
DOI : 10.1016/0021-9991(88)90177-5
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, Journal of Computational Physics, vol.83, issue.1, pp.32-87, 1989. ,
DOI : 10.1016/0021-9991(89)90222-2
Cellular Automaton Modeling of Biological Pattern Formation, Birkhäuser, 2005. ,
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
URL : http://doi.org/10.1016/s0895-7177(03)00128-6
The immersed finite volume element methods for the elliptic interface problems, Mathematics and Computers in Simulation, vol.50, issue.1-4, pp.63-76, 1999. ,
DOI : 10.1016/S0378-4754(99)00061-0
Coupling an Eulerian Fluid Calculation to a Lagrangian Solid Calculation with the Ghost Fluid Method, Journal of Computational Physics, vol.175, issue.1, pp.200-224, 2002. ,
DOI : 10.1006/jcph.2001.6935
A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), Journal of Computational Physics, vol.152, issue.2 ,
DOI : 10.1006/jcph.1999.6236
Cancer Medicine, chapter Tumor Angiogenesis, 2000. ,
Modeling tumor growth: from differential deformable models to growth prediction of tumors detected in PET images, Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No.03CH37439), pp.2687-2690, 2003. ,
DOI : 10.1109/IEMBS.2003.1280470
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
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
A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem, Journal of Computational Physics, vol.202, issue.2, pp.577-601, 2005. ,
DOI : 10.1016/j.jcp.2004.07.018
On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies, Philosophical Transactions of the Royal Society of London, vol.115, issue.0, pp.513-585 ,
DOI : 10.1098/rstl.1825.0026
Total variation diminishing Runge-Kutta schemes, Mathematics of Computation of the American Mathematical Society, vol.67, issue.221, pp.73-85, 1998. ,
DOI : 10.1090/S0025-5718-98-00913-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.105.4521
A fourth order accurate discretization for the laplace and heat equations on arbitrary domains, with applications to the stefan problem, SIAM Journal of Numerical Analysis, vol.39, pp.396-406, 1975. ,
The Convergence Rate for Difference Approximations to General Mixed Initial-Boundary Value Problems, SIAM Journal on Numerical Analysis, vol.18, issue.2, pp.179-190, 1981. ,
DOI : 10.1137/0718014
Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Research, vol.59, pp.4770-4775, 1999. ,
Uniformly high order accurate essentially non-oscillatory schemes, III, Journal of Computational Physics, vol.71, issue.2, p.231, 1987. ,
DOI : 10.1016/0021-9991(87)90031-3
A mortar element method for elliptic problems with discontinuous coefficients. A mortar element method for elliptic problems with discontinuous coefficients, pp.549-576, 2002. ,
Exact subgrid interface correction schemes for elliptic interface problems, Proceedings of the National Academy of Sciences of the United States of America, p.9874, 2008. ,
DOI : 10.1073/pnas.0707997105
A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains, Journal of Computational Physics, vol.147, issue.1, pp.60-85, 1998. ,
DOI : 10.1006/jcph.1998.5965
I: THEORETICAL DEVELOPMENT AND EARLY RESULTS, Mathematical Models and Methods in Applied Sciences, vol.17, issue.supp01, pp.1773-1798, 2007. ,
DOI : 10.1142/S0218202507002479
Dynamics of Tumor Growth, British Journal of Cancer, vol.18, issue.3, pp.490-502, 1964. ,
DOI : 10.1038/bjc.1964.55
The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources, SIAM Journal on Numerical Analysis, vol.31, issue.4, pp.1019-1044, 1994. ,
DOI : 10.1137/0731054
A Fast Iterative Algorithm for Elliptic Interface Problems, SIAM Journal on Numerical Analysis, vol.35, issue.1, pp.230-254, 1998. ,
DOI : 10.1137/S0036142995291329
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients, SIAM Journal on Scientific Computing, vol.23, issue.1, pp.339-361, 2001. ,
DOI : 10.1137/S1064827500370160
Cancer Medicine, chapter Invasion and Metastases, 2000. ,
A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains, Journal of Computational Physics, vol.160, issue.1, pp.151-178, 2000. ,
DOI : 10.1006/jcph.2000.6444
Probì emes Inverses pour les modèles de croissance tumorale, 2011. ,
Nonlinear modelling of cancer: bridging the gap between cells and tumours, Nonlinearity, vol.23, issue.1, pp.1-91, 2010. ,
DOI : 10.1088/0951-7715/23/1/R01
An improved geometry-aware curvature discretization for level set methods: Application to tumor growth, Journal of Computational Physics, vol.215, issue.2, pp.392-401, 2006. ,
DOI : 10.1016/j.jcp.2005.11.016
A fat boundary method for the poisson problem in a domain with holes, Journal of Scientific Computing, vol.16, issue.3, pp.319-339, 2001. ,
DOI : 10.1023/A:1012821728631
The Fast Solution of Poisson???s and the Biharmonic Equations on Irregular Regions, SIAM Journal on Numerical Analysis, vol.21, issue.2, pp.285-299, 1984. ,
DOI : 10.1137/0721021
The rapid evaluation of volume integrals of potential theory on general regions, Journal of Computational Physics, vol.100, issue.2, pp.236-245, 1992. ,
DOI : 10.1016/0021-9991(92)90231-M
Fast Parallel Iterative Solution of Poisson???s and the Biharmonic Equations on Irregular Regions, SIAM Journal on Scientific and Statistical Computing, vol.13, issue.1, pp.101-118, 1992. ,
DOI : 10.1137/0913006
A Cartesian Grid Embedded Boundary Method for the Heat Equation on Irregular Domains, Journal of Computational Physics, vol.173, issue.2, pp.620-635, 2001. ,
DOI : 10.1006/jcph.2001.6900
The modelling of the immune competition by generalized kinetic (boltzmann) models: Review and research perspectives, Mathematical and Computer Modelling, vol.37, pp.65-86, 2003. ,
A sharp interface finite volume method for elliptic equations on Cartesian grids, Journal of Computational Physics, vol.228, issue.14, pp.5184-5206, 2009. ,
DOI : 10.1016/j.jcp.2009.04.018
Level Set Methods and Dynamic Implicit Surfaces, 2003. ,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, p.79, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
Aggregation, blowup and collapse: the abc's of taxis in reinforced random walks, SIAM J. Appl. Math, vol.57, issue.4, pp.1044-1081, 1997. ,
An immersed boundary framework for modelling the growth of individual cells: An application to the early tumour development, Journal of Theoretical Biology, vol.247, issue.1, pp.186-204, 2007. ,
DOI : 10.1016/j.jtbi.2007.02.019
A multiscale mathematical model of cancer, and its use in analizing irradiation therapies, Theoretical Biology and Medical Modelling, vol.3, issue.1, p.7, 2006. ,
DOI : 10.1186/1742-4682-3-7
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.523-541, 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
Solid stress generated by spheroid growth estimated using a linear poroelasticity model???, Microvascular Research, vol.66, issue.3, pp.204-212, 2003. ,
DOI : 10.1016/S0026-2862(03)00057-8
Sparskit a basic tool-kit for sparse matrix computations ,
The algebraic immersed interface and boundary method for elliptic equations with discontinuous coefficients, 2009. ,
A fast marching level set method for monotonically advancing fronts., Proc. Nat. Acad. Sci, pp.1591-1595, 1996. ,
DOI : 10.1073/pnas.93.4.1591
Level Set Methods and Fast Marching Methods, 1999. ,
Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science, 1999. ,
Evolution, Implementation, and Application of Level Set and Fast Marching Methods for Advancing Fronts, Journal of Computational Physics, vol.169, issue.2, pp.503-555, 2001. ,
DOI : 10.1006/jcph.2000.6657
On the order of accuracy for difference approximations of initial-boundary value problems, Journal of Computational Physics, vol.218, issue.1, pp.333-352, 2006. ,
DOI : 10.1016/j.jcp.2006.02.014
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
Simulating non-small cell lung cancer with a multiscale agent-based model, Theoretical Biology and Medical Modelling, vol.4, issue.1, p.50, 2007. ,
DOI : 10.1186/1742-4682-4-50
The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions, SIAM Journal on Numerical Analysis, vol.37, issue.3, pp.827-862, 2000. ,
DOI : 10.1137/S0036142997328664
Weighted Essentially Non-oscillatory Schemes, Journal of Computational Physics, vol.115, issue.1, pp.202-212, 1996. ,
DOI : 10.1006/jcph.1994.1187
Engineering and algorithm design for an image processing api: A technical report on itk -the insight toolkit, Proc. of Medicine Meets Virtual, pp.586-592, 2002. ,
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities, Journal of Computational Physics, vol.227, issue.1, pp.602-632, 2007. ,
DOI : 10.1016/j.jcp.2007.08.003
A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity, Journal of Computational Physics, vol.225, issue.1, pp.1066-1099, 2007. ,
DOI : 10.1016/j.jcp.2007.01.017
On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method, Journal of Computational Physics, vol.219, issue.1, pp.228-246, 2006. ,
DOI : 10.1016/j.jcp.2006.03.027
High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources, Journal of Computational Physics, vol.213, issue.1, pp.1-30, 2006. ,
DOI : 10.1016/j.jcp.2005.07.022