3D Multiscale Modelling of Angiogenesis and Vascular Tumour Growth

[1]  Jon Dobson,et al.  Mathematical modeling predicts synergistic antitumor effects of combining a macrophage-based, hypoxia-targeted gene therapy with chemotherapy. , 2011, Cancer research.

[2]  Robert J. Gillies,et al.  Multiscale Modelling of Vascular Tumour Growth in 3D: The Roles of Domain Size and Boundary Conditions , 2011, PloS one.

[3]  Nick Jagiella,et al.  Modeling Steps from Benign Tumor to Invasive Cancer , 2010 .

[4]  Luigi Preziosi,et al.  Cell Mechanics. From single scale-based models to multiscale modeling , 2010 .

[5]  J. Glazier,et al.  3D Multi-Cell Simulation of Tumor Growth and Angiogenesis , 2009, PloS one.

[6]  P. Tracqui,et al.  Biophysical models of tumour growth , 2009 .

[7]  S. McDougall,et al.  Multiscale modelling and nonlinear simulation of vascular tumour growth , 2009, Journal of mathematical biology.

[8]  Philip K Maini,et al.  Angiogenesis and vascular remodelling in normal and cancerous tissues , 2009, Journal of mathematical biology.

[9]  Gábor Székely,et al.  A computational framework for modelling solid tumour growth , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[11]  S. McDougall,et al.  Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. , 2006, Journal of theoretical biology.

[12]  P. Maini,et al.  Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy , 2006 .

[13]  D-S Lee,et al.  Flow correlated percolation during vascular remodeling in growing tumors. , 2005, Physical review letters.

[14]  A. Anderson,et al.  A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion , 2005 .

[15]  Alexander R. A. Anderson,et al.  Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies , 2005, Math. Comput. Model..

[16]  G. Zocchi,et al.  Local cooperativity mechanism in the DNA melting transition. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  V. Cristini,et al.  Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method , 2005, Bulletin of mathematical biology.

[18]  M. Plank,et al.  Lattice and non-lattice models of tumour angiogenesis , 2004, Bulletin of mathematical biology.

[19]  P. Maini,et al.  A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells. , 2004, Journal of theoretical biology.

[20]  Gernot Schaller,et al.  Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  H. Othmer,et al.  Mathematical modeling of tumor-induced angiogenesis , 2004, Journal of mathematical biology.

[22]  P. Maini,et al.  A cellular automaton model for tumour growth in inhomogeneous environment. , 2003, Journal of theoretical biology.

[23]  Helen M Byrne,et al.  A multiphase model describing vascular tumour growth , 2003, Bulletin of mathematical biology.

[24]  M J Plank,et al.  A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. , 2003, Mathematical medicine and biology : a journal of the IMA.

[25]  P. Ratcliffe,et al.  Regulation of angiogenesis by hypoxia: role of the HIF system , 2003, Nature Medicine.

[26]  Nitzan Resnick,et al.  Fluid shear stress and the vascular endothelium: for better and for worse. , 2003, Progress in biophysics and molecular biology.

[27]  B. Reglin,et al.  Structural adaptation of microvascular networks: functional roles of adaptive responses. , 2001, American journal of physiology. Heart and circulatory physiology.

[28]  J. Tyson,et al.  Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions. , 2001, Journal of theoretical biology.

[29]  T. Secomb,et al.  Theoretical Simulation of Oxygen Transport to Brain by Networks of Microvessels: Effects of Oxygen Supply and Demand on Tissue Hypoxia , 2000, Microcirculation.

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

[31]  A. Pries,et al.  Structural adaptation and stability of microvascular networks: theory and simulations. , 1998, American journal of physiology. Heart and circulatory physiology.

[32]  W. Risau,et al.  Mechanisms of angiogenesis , 1997, Nature.

[33]  D A Lauffenburger,et al.  Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. , 1991, Journal of theoretical biology.

[34]  J. Folkman Tumor angiogenesis: therapeutic implications. , 1971, The New England journal of medicine.

[35]  J Folkman,et al.  Transplacental carcinogenesis by stilbestrol. , 1971, The New England journal of medicine.

[36]  Helen M. Byrne,et al.  A Multiple Scale Model for Tumor Growth , 2005, Multiscale Model. Simul..

[37]  Z. Agur,et al.  Vessel maturation effects on tumour growth: validation of a computer model in implanted human ovarian carcinoma spheroids. , 2005, European journal of cancer.

[38]  Z. Agur,et al.  A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth , 2004, Angiogenesis.

[39]  Eliot R. Clark,et al.  Studies on the growth of blood-vessels in the tail of the frog larva—by observation and experiment on the living animal , 1918 .