Modelling the formation of capillaries

[1]  Charles D. Little,et al.  Vascular Morphogenesis: In Vivo, In Vitro, In Mente , 2011, Cardiovascular Molecular Morphogenesis.

[2]  Luigi Preziosi,et al.  Exogenous control of vascular network formation in vitro: a mathematical model , 2006, Networks Heterog. Media.

[3]  L. Preziosi,et al.  Mechanics and Chemotaxis in the Morphogenesis of Vascular Networks , 2006, Bulletin of mathematical biology.

[4]  R. Kowalczyk,et al.  Preventing blow-up in a chemotaxis model , 2005 .

[5]  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..

[6]  Luigi Preziosi,et al.  A review of vasculogenesis models , 2005 .

[7]  Davide Carlo Ambrosi,et al.  Cell directional and chemotaxis in vascular morphogenesis , 2004 .

[8]  Roeland M. H. Merks,et al.  Cell-Oriented Modeling of In Vitro Capillary Development , 2004, ACRI.

[9]  P. Maini,et al.  Towards whole-organ modelling of tumour growth. , 2004, Progress in biophysics and molecular biology.

[10]  A. Coniglio,et al.  Percolation and Burgers' dynamics in a model of capillary formation. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[12]  L. Preziosi,et al.  On the stability of homogeneous solutions to some aggregation models , 2003 .

[13]  Antonio Fasano,et al.  Regression and regrowth of tumour cords following single-dose anticancer treatment , 2003, Bulletin of mathematical biology.

[14]  Luigi Preziosi,et al.  Cancer Modelling and Simulation , 2003 .

[15]  Federico Bussolino,et al.  Biological Aspects of Tumour Angiogenesis , 2003 .

[16]  L. Preziosi,et al.  Modeling the early stages of vascular network assembly , 2003, The EMBO journal.

[17]  L Preziosi,et al.  Percolation, morphogenesis, and burgers dynamics in blood vessels formation. , 2003, Physical review letters.

[18]  Holger Gerhardt,et al.  Spatially restricted patterning cues provided by heparin-binding VEGF-A control blood vessel branching morphogenesis. , 2002, Genes & development.

[19]  B. Sleeman,et al.  Tumour induced angiogenesis as a reinforced random walk: Modelling capillary network formation without endothelial cell proliferation , 2002 .

[20]  S. McDougall,et al.  Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies , 2002, Bulletin of mathematical biology.

[21]  D. Vittet,et al.  In Vitro Models of Vasculogenesis and Angiogenesis , 2001, Laboratory Investigation.

[22]  B. Sleeman,et al.  Mathematical modeling of the onset of capillary formation initiating angiogenesis , 2001, Journal of mathematical biology.

[23]  M. J. Holmes,et al.  A mathematical model of tumour angiogenesis incorporating cellular traction and viscoelastic effects. , 2000, Journal of theoretical biology.

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

[25]  J. Murray,et al.  A mechanical model for the formation of vascular networks in vitro , 1996, Acta biotheoretica.

[26]  Judah Folkman,et al.  Angiogenesis in vitro , 1980, Nature.

[27]  Hans Meinhardt,et al.  Models and Hypotheses , 1976 .

[28]  Davide Carlo Ambrosi,et al.  Cell directional persistence and chemotaxis in vascular morphogenesis , 2005 .

[29]  Léone Tranqui,et al.  The formation of tubular structures by endothelial cells is under the control of fibrinolysis and mechanical factors , 2004, Angiogenesis.

[30]  Luigi Preziosi,et al.  Multiscale modeling and mathematical problems related to tumor evolution and medical therapy. , 2003 .

[31]  B. Sleeman,et al.  Modelling Tumour-Induced Angiogenesis , 2003 .

[32]  Davide Carlo Ambrosi,et al.  Mechanical models in tumour growth , 2003 .

[33]  Hans Meinhardt,et al.  Biological Pattern Formation as a Complex Dynamic Phenomenon , 1997 .

[34]  James D. Murray,et al.  A Mechanical Theory of In Vitro Vascular Network Formation , 1996 .

[35]  H. Meinhardt Models of biological pattern formation , 1982 .

[36]  Andrew Ilachinski,et al.  Cellular automata , 1968 .