Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies.

[1]  S. McDougall,et al.  Mathematical modeling of tumor-induced angiogenesis. , 2006, Annual review of biomedical engineering.

[2]  Alexander R. A. Anderson,et al.  Mathematical modelling of the influence of blood rheological properties upon adaptative tumour-induced angiogenesis , 2006, Math. Comput. Model..

[3]  M. Chaplain,et al.  Mathematical modelling of cancer cell invasion of tissue , 2005, Math. Comput. Model..

[4]  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..

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

[6]  K. Hellmann,et al.  Recognition of tumor blood vessel normalization as a new antiangiogenic concept , 2004, Nature Medicine.

[7]  R. Jain Reply to 'Recognition of tumor blood vessel normalization as a new antiangiogenic concept' , 2004, Nature Medicine.

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

[9]  K. Alitalo,et al.  Gene transfer as a tool to induce therapeutic vascular growth , 2003, Nature Medicine.

[10]  P. Carmeliet Angiogenesis in health and disease , 2003, Nature Medicine.

[11]  D. Melton,et al.  Endothelial signaling during development , 2003, Nature Medicine.

[12]  N. Ferrara,et al.  The biology of VEGF and its receptors , 2003, Nature Medicine.

[13]  Rakesh K Jain,et al.  Molecular regulation of vessel maturation , 2003, Nature Medicine.

[14]  Shahin Rafii,et al.  Therapeutic stem and progenitor cell transplantation for organ vascularization and regeneration , 2003, Nature Medicine.

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

[16]  Howard A. Levine,et al.  A Mathematical Model for the Role of Cell Signal Transduction in the Initiation and Inhibition of Angiogenesis , 2003, Growth factors.

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

[18]  Christopher A. Dawson,et al.  Vessel distensibility and flow distribution in vascular trees , 2002, Journal of mathematical biology.

[19]  Rakesh K Jain,et al.  Abnormalities in pericytes on blood vessels and endothelial sprouts in tumors. , 2002, The American journal of pathology.

[20]  B. Reglin,et al.  Structural Adaptation of Vascular Networks: Role of the Pressure Response , 2001, Hypertension.

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

[22]  Rakesh K. Jain,et al.  Normalizing tumor vasculature with anti-angiogenic therapy: A new paradigm for combination therapy , 2001, Nature Medicine.

[23]  R M Nerem,et al.  Endothelial cellular response to altered shear stress. , 2001, American journal of physiology. Lung cellular and molecular physiology.

[24]  B. Sleeman,et al.  Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma , 2001 .

[25]  H Kurz,et al.  Structural and biophysical simulation of angiogenesis and vascular remodeling , 2001, Developmental dynamics : an official publication of the American Association of Anatomists.

[26]  S. Maxwell,et al.  Matrix metalloproteinase-1 and -9 activation by plasmin regulates a novel endothelial cell-mediated mechanism of collagen gel contraction and capillary tube regression in three-dimensional collagen matrices. , 2001, Journal of cell science.

[27]  M. Hidalgo,et al.  Development of matrix metalloproteinase inhibitors in cancer therapy. , 2001, Journal of the National Cancer Institute.

[28]  Donald E. Ingber,et al.  Adhesion-dependent control of matrix metalloproteinase-2 activation in human capillary endothelial cells. , 2000, Journal of cell science.

[29]  E F Leonard,et al.  Model of structural and functional adaptation of small conductance vessels to arterial hypotension. , 2000, American journal of physiology. Heart and circulatory physiology.

[30]  Alfio Quarteroni,et al.  Computational vascular fluid dynamics: problems, models and methods , 2000 .

[31]  D. Walsh,et al.  Angiogenesis and arthritis. , 1999, Rheumatology.

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

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

[34]  A. Tedgui,et al.  Signal transduction of mechanical stresses in the vascular wall. , 1998, Hypertension.

[35]  E. Keshet,et al.  A plasticity window for blood vessel remodelling is defined by pericyte coverage of the preformed endothelial network and is regulated by PDGF-B and VEGF. , 1998, Development.

[36]  P. Maini,et al.  A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis. , 1997, IMA journal of mathematics applied in medicine and biology.

[37]  M. Chaplain,et al.  Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. , 1997, IMA journal of mathematics applied in medicine and biology.

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

[39]  A. Pries,et al.  Biophysical aspects of blood flow in the microvasculature. , 1996, Cardiovascular research.

[40]  R. Jain,et al.  Role of tumor vascular architecture in nutrient and drug delivery: an invasion percolation-based network model. , 1996, Microvascular research.

[41]  L. G. Harrison On growth and form , 1995, Nature.

[42]  Steven Robert McDougall,et al.  The application of network modelling techniques to multiphase flow in porous media , 1995, Petroleum Geoscience.

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

[44]  R K Jain,et al.  Determinants of tumor blood flow: a review. , 1988, Cancer research.

[45]  R K Jain,et al.  Transport of molecules in the tumor interstitium: a review. , 1987, Cancer research.

[46]  Ferguson Gp,et al.  Mechanisms of neovascularization. Vascular sprouting can occur without proliferation of endothelial cells. , 1984 .

[47]  R. Auerbach,et al.  Tumor-induced neovascularization in the mouse eye. , 1982, Journal of the National Cancer Institute.

[48]  J. Folkman,et al.  Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumor angiogenesis. , 1977, Microvascular research.

[49]  J. Folkman,et al.  Tumor growth and neovascularization: an experimental model using the rabbit cornea. , 1974, Journal of the National Cancer Institute.

[50]  K. Hellmann,et al.  Metastases and the Normalization of Tumour Blood Vessels by ICRF 159: A New Type of Drug Action , 1972, British medical journal.

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

[52]  K. Hellmann,et al.  Inhibition of Metastatic Spread by I.C.R.F. 159: Selective Deletion of a Malignant Characteristic , 1970, British medical journal.

[53]  A. Anderson,et al.  A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. , 2005, Mathematical medicine and biology : a journal of the IMA.

[54]  J. Folkman,et al.  Endostatin inhibits angiogenesis by stabilization of newly formed endothelial tubes , 2004, Angiogenesis.

[55]  K. Hellmann Dynamics of tumour angiogenesis: Effect of razoxane-induced growth rate slowdown , 2004, Clinical & Experimental Metastasis.

[56]  Michael D Feldman,et al.  Tumor vessel development and maturation impose limits on the effectiveness of anti-vascular therapy. , 2003, The American journal of pathology.

[57]  Z. Werb,et al.  How matrix metalloproteinases regulate cell behavior. , 2001, Annual review of cell and developmental biology.

[58]  B. Sleeman,et al.  Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma , 2001, Bulletin of mathematical biology.

[59]  Sysi-Aho Marko,et al.  The Finite Difference Method in Partial Differential Equations , 2001 .

[60]  M. W. Collins,et al.  Nanoscale fluid dynamics in physiological processes : a review study , 1999 .

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

[62]  L A Taber,et al.  An optimization principle for vascular radius including the effects of smooth muscle tone. , 1998, Biophysical journal.

[63]  T. Secomb,et al.  Theoretical models for drug delivery to solid tumors. , 1997, Critical reviews in biomedical engineering.

[64]  J. Folkman Angiogenesis in cancer, vascular, rheumatoid and other disease , 1995, Nature Medicine.

[65]  T. Secomb,et al.  Mechanics of blood flow in the microcirculation. , 1995, Symposia of the Society for Experimental Biology.

[66]  N Paweletz,et al.  Tumor-related angiogenesis. , 1989, Critical reviews in oncology/hematology.

[67]  J. Folkman,et al.  Angiogenic factors. , 1987, Science.

[68]  T. Togawa,et al.  Adaptive regulation of wall shear stress optimizing vascular tree function. , 1984, Bulletin of mathematical biology.

[69]  J. Wilson,et al.  Mechanisms of neovascularization. Vascular sprouting can occur without proliferation of endothelial cells. , 1984, Laboratory investigation; a journal of technical methods and pathology.

[70]  R. A. ANDERSONa,et al.  Mathematical Modelling of Tumour Invasion and Metastasis , 2022 .