Fractal analysis of vascular networks: insights from morphogenesis.

[1]  D. Zwillinger Handbook of differential equations , 1990 .

[2]  Edward A. Codling,et al.  Random walk models in biology , 2008, Journal of The Royal Society Interface.

[3]  Sylvie Lorthois,et al.  During vertebrate development, arteries exert a morphological control over the venous pattern through physical factors. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Francis Cassot,et al.  Morphometry of the human cerebral cortex microcirculation: General characteristics and space-related profiles , 2008, NeuroImage.

[5]  Laurent Risser,et al.  From Homogeneous to Fractal Normal and Tumorous Microvascular Networks in the Brain , 2007, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[6]  Bin Tean Teh,et al.  Two Distinct Types of Blood Vessels in Clear Cell Renal Cell Carcinoma Have Contrasting Prognostic Implications , 2007, Clinical Cancer Research.

[7]  Philipp Schneider,et al.  Hierarchical microimaging for multiscale analysis of large vascular networks , 2006, NeuroImage.

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

[9]  Vincent Fleury,et al.  Dynamics of vascular branching morphogenesis: the effect of blood and tissue flow. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Céline Fouard,et al.  A Novel Three‐Dimensional Computer‐Assisted Method for a Quantitative Study of Microvascular Networks of the Human Cerebral Cortex , 2006, Microcirculation.

[11]  Luigi Pannarale,et al.  Fractal and Fourier analysis of the hepatic sinusoidal network in normal and cirrhotic rat liver , 2005, Journal of anatomy.

[12]  Roeland M. H. Merks,et al.  Contact-Inhibited Chemotaxis in De Novo and Sprouting Blood-Vessel Growth , 2005, PLoS Comput. Biol..

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

[14]  B. Masters,et al.  Fractal analysis of the vascular tree in the human retina. , 2004, Annual review of biomedical engineering.

[15]  B Weyn,et al.  Determination of tumour prognosis based on angiogenesis-related vascular patterns measured by fractal and syntactic structure analysis. , 2004, Clinical oncology (Royal College of Radiologists (Great Britain)).

[16]  S. Hartley,et al.  Uses and abuses of fractal methodology in ecology , 2004 .

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

[18]  Li Yuan,et al.  Flow regulates arterial-venous differentiation in the chick embryo yolk sac , 2003, Development.

[19]  H. Schmid-Schönbein,et al.  MEASURING THE FRACTAL DIMENSION OF THE MICROVASCULAR NETWORK OF THE CHORIOALLANTOIC MEMBRANE , 2003 .

[20]  Heinz-Otto Peitgen,et al.  FRACTAL PROPERTIES, SEGMENT ANATOMY, AND INTERDEPENDENCE OF THE HUMAN PORTAL VEIN AND THE HEPATIC VEIN IN 3D , 2003 .

[21]  F Grizzi,et al.  Correspondence re: E. Sabo et al., Microscopic Analysis and Significance of Vascular Architectural Complexity in Renal Cell Carcinoma. Clin. Cancer Res., 7: 533-537, 2001. , 2001, Clinical cancer research : an official journal of the American Association for Cancer Research.

[22]  László Kocsis,et al.  Fractal Branching Pattern in the Pial Vasculature in the Cat , 2001, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[23]  Vincent Fleury,et al.  Branching in Nature , 2001, Centre de Physique des Houches.

[24]  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.

[25]  E. Sabo,et al.  Microscopic analysis and significance of vascular architectural complexity in renal cell carcinoma. , 2001, Clinical cancer research : an official journal of the American Association for Cancer Research.

[26]  Sybill Patan,et al.  Vasculogenesis and Angiogenesis as Mechanisms of Vascular Network Formation, Growth and Remodeling , 2000, Journal of Neuro-Oncology.

[27]  Vincent Fleury,et al.  MODELISATION OF 3-D MICROVASCULATURE BY INTERLACED DIFFUSION LIMITED AGGREGATION , 2000 .

[28]  Ghassan S. Kassab,et al.  The Coronary Vasculature and its Reconstruction , 2000, Annals of Biomedical Engineering.

[29]  Fleury Branching morphogenesis in a reaction-diffusion model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  James H. Brown,et al.  The fourth dimension of life: fractal geometry and allometric scaling of organisms. , 1999, Science.

[31]  Vincent Fleury,et al.  DIFFUSION LIMITED AGGREGATION FROM SHEAR STRESS AS A SIMPLE MODEL OF VASCULOGENESIS , 1999 .

[32]  S. Kyriacos,et al.  Dynamic study of the extraembryonic vascular network of the chick embryo by fractal analysis. , 1998, Journal of theoretical biology.

[33]  D L Bergman,et al.  Scaling properties of the placenta's arterial tree. , 1998, Journal of theoretical biology.

[34]  P. Parsons-Wingerter,et al.  A novel assay of angiogenesis in the quail chorioallantoic membrane: stimulation by bFGF and inhibition by angiostatin according to fractal dimension and grid intersection. , 1998, Microvascular research.

[35]  G. Berntson,et al.  Correcting for finite spatial scales of self–similarity when calculating fractal dimensions of real–world structures , 1997, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[36]  H. Honda,et al.  Formation of the branching pattern of blood vessels in the wall of the avian yolk sac studied by a computer simulation , 1997, Development, growth & differentiation.

[37]  H Kurz,et al.  Measuring fractal dimension and complexity — an alternative approach with an application , 1997, Journal of microscopy.

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

[39]  David R. Noble,et al.  Questions in Fluid Mechanics: Tortuous Micro-Flow in Large Disordered Packed Beds , 1996 .

[40]  G. Martiny-Baron,et al.  VEGF121 induces proliferation of vascular endothelial cells and expression of flk-1 without affecting lymphatic vessels of chorioallantoic membrane. , 1996, Developmental biology.

[41]  Biham,et al.  Apparent fractality emerging from models of random distributions. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[42]  J D Murray,et al.  Use and abuse of fractal theory in neuroscience , 1995, The Journal of comparative neurology.

[43]  P Sterling,et al.  Retinal neurons and vessels are not fractal but space‐filling , 1995, The Journal of comparative neurology.

[44]  Berk,et al.  Scale-invariant behavior and vascular network formation in normal and tumor tissue. , 1995, Physical review letters.

[45]  Daniel Platt,et al.  Diffusion Limited Aggregation , 1995 .

[46]  F. Pansera Fractals and cancer. , 1994, Medical hypotheses.

[47]  G S Kassab,et al.  Diameter-defined Strahler system and connectivity matrix of the pulmonary arterial tree. , 1994, Journal of applied physiology.

[48]  G S Kassab,et al.  Morphometry of the dog pulmonary venous tree. , 1993, Journal of applied physiology.

[49]  A. Pries,et al.  Blood flow in microvascular networks. Experiments and simulation. , 1990, Circulation research.

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

[51]  L. Pietronero,et al.  Fractal Dimension of Dielectric Breakdown , 1984 .

[52]  H. Duvernoy,et al.  Cortical blood vessels of the human brain , 1981, Brain Research Bulletin.

[53]  J. Bear Dynamics of Fluids in Porous Media , 1975 .

[54]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[55]  N. Bressloff,et al.  Blood flow in microvascular networks , 2009 .

[56]  Laurent Risser Analyse quantitative de réseaux micro-vasculaires intra-corticaux , 2007 .

[57]  V. Fleury,et al.  A Link Between Dendritic Growth and Remodeling of Blood Vessels , 2001 .

[58]  T. Jøssang,et al.  Branched Patterns in Geology: Rivers and Other Systems , 2001 .

[59]  D L T,et al.  Networks with Side Branching in Biology , 1998 .

[60]  S. Schmidt,et al.  Quantitation of angiogenesis in the chick chorioallantoic membrane model using fractal analysis. , 1996, Microvascular research.

[61]  T. Vicsek Fractal Growth Phenomena , 1989 .