Complutense University Library

Modelling vascular morphogenesis: current views on blood vessels development

Herrero, Miguel A. and Köhn Luque, Álvaro and Pérez-Pomares, José M. (2009) Modelling vascular morphogenesis: current views on blood vessels development. Mathematical Models & Methods In Applied Sciences, 19 . pp. 1483-1537. ISSN 0218-2025

[img] PDF
Restricted to Repository staff only until 31 December 2020.


Official URL:

View download statistics for this eprint

==>>> Export to other formats


In this work we present a comprehensive account of our current knowledge on vascular morphogenesis, both from a biological and a mathematical point of view. To this end, we first describe the basic steps in the known mechanisms of blood vessel morphogenesis, whose structure, function and unfolding properties are examined. We then provide a wide, although by no means exhaustive, account of mathematical models which are used to describe and discuss particular aspects of the overall biological process considered. We finally summarize the approaches presented, and suggest possible directions for future research. Details about some of the major signalling molecules involved are included in a first Appendix at the end of the paper. A second Appendix provides a brief overview of design principles for vascular nets, a subject that has deserved considerable attention over the years.

Item Type:Article
Uncontrolled Keywords:Mathematical modelling; blood vessels formation; vascular patterning; reaction-diffusion equations; individual-based models; design principles; endothelial growth-factor; biological pattern-formation; receptor tyrosine kinases; arterial-venous differentiation; extended potts-model; tree-shaped networks; smooth-muscle-cell; in-vitro; extracellular-matrix; signaling pathways
Subjects:Medical sciences > Biology > Biomathematics
Sciences > Mathematics > Differential equations
Sciences > Mathematics > Operations research
ID Code:16365

K. Abdi, L. Kobzik, X. Li and S. J. Mentzer, Expression of membrane glycoconjugates on sheep lung endothelium, Lab. Invest. 72 (1995) 445–452.

R. H. Adams, Vascular patterning by Eph receptor tyrosine kinases and ephrins, Semin. Cell Dev. Biol. 13 (2002) 55–60.

M. Affolter, S. Bellusci, N. Itoh, B. Shilo, J. P. Thiery and Z. Werb, Tube or not tube: Remodeling epithelial tissues by branching morphogenesis, Dev. Cell 4 (2003) 11–18.

R. Agah, K. S. Prasad, R. Linnemann, M. T. Firpo, T. Quertermous and D. A. Dichek, Cardiovascular overexpression of transforming growth factor-beta(1) causes abnormal yolk sac vasculogenesis and early embryonic death, Circ. Res. 84 (2006) 1024–1030.

T. Alarcón, H. M. Byrne and P. K. Maini, A design principle for vascular beds: The effect of complex rheology, J. Theor. Biol. 69 (2002) 156–172.

T. Alarcón, H. M. Byrne and P. K. Maini, A multiple scale model for tumor growth, Multiscale Model. Simul. 3 (2005) 440–474.

R. Alon, P. D. Kassner, M. W. Carr, E. B. Finger, M. E. Hemler and T. A. Springer, The integrin VLA-4 supports tethering and rolling in flow on VCAM-1, J. Cell Biol. 128 (1995) 1243–1253.

C. R. Altman and A. H. Brivanlou, Neural patterning in the vertebrate embryo, Int. Rev. Cytol. 203 (2001) 447–482.

D. Ambrosi, A. Gamba and G. Serini, Cell directionality and chemotaxis in vascular morphogenesis, Bull. Math. Biol. 66 (2004) 1851–1873.

D. Ambrosi, F. Bussolino and L. Preziosi, A review of vasculogenesis models, J. Theor. Med. 6 (2005) 1–19.

Eds. A. R. A. Anderson, M. A. J. Chaplain and K. A. Rejniak, Single-Cell-Based Models in Biology and Medicine (Birkhäuser, 2007).

A. Anderson-Berry, E. A. O'Brien, S. B. Bleyl, A. Lawson, N. Gundersen, D. Ryssman, J. Sweeley, M. J. Dahl, C. J. Drake, G. C. Schoenwolf and K. H. Albertine, Vasculogenesis drives pulmonary vascular growth in the developing chick embryo, Dev. Dyn. 233 (2005) 145–153.

D. Andreucci, M. A. Herrero and J. J. L. Velázquez, On the growth of filamentary structures in planar media, Math. Meth. Appl. Sci. 27 (2004) 1935–1968.

W. S. Argraves and C. J. Drake, Genes critical to vasculogenesis as defined by systematic analysis of vascular defects in knockout mice, Anat. Rec. 286 (2005) 875–884.

Aristotle: Parts of Animals, translator A. L. Peck (Harvard Univ. Press, 1961)

Aristotle: The generation of animals, Book II (Loeb Classical Library, 1963).

A. Armulik, A. Abramsson and C. Betsholtz, Endothelial/pericyte interactions, Circ. Res. 97 (2005) 512–523.

S. Artavanis-Tsakonas, M. D. Rand and R. J. Lake, Notch signaling: Cell fate control and signal integration in development, Science 284 (1999) 770–776.

J. Astorga and P. Carlsson, Hedgehog induction of murine vasculogenesis is mediated by Foxf1 and Bmp4, Development 134 (2007) 3753–3761.

P. Auguste, S. Javerzat and A. Bikfalvi, Regulation of vascular development by fibroblast growth factors, Cell Tissue Res. 314 (2003) 157–166.

Y. Azar and H. Eyal-Giladi, Marginal zone cells—the primitive streak-inducing component of the primary hypoblast in the chick, J. Embryol. Exp. Morphol. 52 (1979) 79–88.

R. G. Bagley, W. Weber, C. Rouleau and B. A. Teicher, Pericytes and endothelial precursor cells: Cellular interactions and contributions to malignancy, Cancer Res. 65 (2005) 9741–9750.

J. Bauer, M. Margolis, C. Schreiner, C. J. Edgell, J. Azizkhan, E. Lazarowski and R. L. Juliano, In vitro model of angiogenesis using a human endothelium-derived permanent cell line: Contributions of induced gene expression, G-proteins, and integrins, J. Cell Physiol. 153 (1992) 437–449.

L. Beck and P. A. D'Amore, Vascular development: Cellular and molecular regulation, FASEB J. 11 (1997) 365–373.

N. Bellomo, A. Bellouquid, J. Nieto and J. J. Soler, Multicellular growing systems: Hyperbolic limits towards macroscopic description, Math. Mod. Meth. Appl. Sci. 17 (2007) 1675–1693.

N. Bellomo and M. Delitala, From the mathematical kinetic and stochastic game theory to modeling mutations, onset, progression and innume competition of cancer cells, Phys. Life Rev. 5 (2008) 183–206.

N. Bellomo, N. K. Li and P. K. Maini, On the foundations of cancer modeling: Selected topics, speculations, and perspectives, Math. Mod. Meth. Appl. Sci. 18 (2008) 593–646.

A. Bellouquid and M. Delitala, Mathematical Modeling of Complex Biological Systems, A Kinetic Theory Approach (Birkhäuser, 2006).

M. Bernot, V. Caselles and J. M. Morel, The structure of branched transportation networks, Calc. Var. 32 (2008) 279–317.

M. Bernot, V. Caselles and J. M. Morel, Optimal Transportation Networks: Models and Theory, to appear.

A. Bobik, Transforming growth factor-betas and vascular disorders. Arterioscler, Thromb. Vasc. Biol. 26 (2006) 1712–1720.

B. L. Bohnsack and K. K. Hirschi, Red light, green light: Signals that control endothelial cell proliferation during embryonic vascular development, Cell Cycle 3 (2004) 1506–1511.

B. L. Bohnsack, L. Lai, P. Dolle and K. K. Hirschi, Signaling hierarchy downstream of retinoic acid that independently regulates vascular remodeling and endothelial cell proliferation, Genes Dev. 18 (2004) 1345–1358.

R. C. Böttcher and C. Niehrs, Fibroblast growth factor signaling during early vertebrate development, Endocr. Rev. 26 (2005) 63–77.

M. Boudreau and N. J. Bissell, Extracellular matrix signaling: Integration of form and function in normal and malignant cells, Curr. Opin. Cell. Biol. 10 (1998) 640–646.

D. Bouïs, G. A. P. Hospers, C. Meijer, G. Molema and N. H. Mulder, Endothelium in vitro: A review of human vascular endothelial cell lines for blood-vessel-related research, Angiogenesis 4 (2001) 91–102.

B. Brand-Saberi, R. Seifert, M. Grim, J. Wilting, M. Kuhlewein and B. Christ, Blood vessel formation in the avian limb bud involves angioblastic and angiotrophic growth, Dev. Dyn. 202 (1995) 181–194.

G. Breier, U. Albrecht, S. Sterrer and W. Risau, Expression of vascular endothelial growth factor during embryonic angiogenesis and endothelial cell differentiation, Development 114 (1992) 521–532.

P. C. Brooks, R. A. Clark and D. A. Cheresh, Requirement of vascular integrin alpha v beta 3 for angiogenesis, Science 264 (1994) 569–571.

P. C. Brooks, S. Strömblad, L. C. Sanders, T. L. von Schalscha, R. T. Aimes, W. G. Stetler-Stevenson, J. P. Quigley and D. A. Cheresh, Localization of matrix metalloproteinase MMP-2 to the surface of invasive cells by interaction with integrin alpha v beta 3, Cell 85 (1996) 683–693.

R. Brusca and G. Brusca, Invertebrates (Sinauer Associates, 2003).

A. W. Burks, Ed., Essays on Cellular Automata, XXVI (University of Illinois Press, 1970).

L. A. Caffarelli and R. J. McCann, Free boundaries in optimal transport and Monge-Ampère obstacle problems, to appear in Ann. Math. (2009).

P. Carmeliet, M. G. Lampugnani, L. Moons, F. Breviario, V. Compernolle, F. Bono, G. Balconi, R. Spagnuolo, B. Oostuyse, M. Dewerchin, A. Zanetti, A. Angellilo, V. Mattot, D. Nuyens, E. Lutgens, F. Clotman, M. C. de Ruiter, A. Gittenberger-de Groot, R. Poelmann, F. Lupu, J. M. Herbert, D. Collen and E. Dejana, Targeted deficiency or cytosolic truncation of the VE-cadherin gene in mice impairs VEGF-mediated endothelial survival and angiogenesis, Cell 98 (1999) 147–157.

W. B. Chapman, The effect of the heart-beat upon the development of the vascular system in the chick, Am. J. Anat. 23 (1918) 175–203.

R. Chaturvedi, C. Huang, J. A. Izaguirre, S. A. Newman, J. A. Glazier and M. Alber, A Hybrid Discrete-Continuum Model for 3D Skeletogenesis of the Vertebrate Limb, Sloot P. M.A., eds. B. Chopard and Hoekstra ACRI 2004, LNCS 3305 (2004) 543–552.

T. Chihara and S. Hayashi, Control of tracheal tubulogenesis by wingless signaling, Development 127 (2000) 4433–4442.

D. E. Clark, S. K. Smith, Y. He, K. A. Day, D. R. Licence, A. N. Corps, R. Lammoglia and D. S. Charnock-Jones, Biol. Reprod. 6 (1998) 1540–1548.

J. D. Coffin and T. J. Poole, Endothelial cell origin and migration in embryonic heart and cranial blood vessel development, Anat. Rec. 231 (1991) 383–395.

J. F. Colas and G. C. Schoenwolf, Towards a cellular and molecular understanding of neurulation, Dev. Dyn. 221 (2001) 117–145.

F. Crick, Diffusion in embryogenesis, Nature 225 (1970) 420–422.

M. J. Cross, J. Dixelius, T. Matsumoto and L. Claesson-Welsh, VEGF-receptor signal transduction, Trends Biochem. Sci. 28 (2003) 488–494.

A. Czirók, P. A. Rupp, B. J. Rongish and C. D. Little, Multifield 3D scanning light microscopy of early embryogenesis, J. Microsci. 206 (2002) 209–217.

A. Czirók, E. A. Zamir, M. B. Filla, C. D. Little and B. J. Rongish, Extracellular matrix macroassembly dynamics in early vertebrate embryos, Curr. Top. Dev. Biol. 73 (2006) 237–258.

A. Czirók, E. A. Zamir, A. Szabo and C. D. Little, Multicellular sprouting during vasculogenesis, Curr. Top. Dev. Biol. 81 (2008) 269–289.

S. Davis, T. H. Aldrich, P. F. Jones, A. Acheson, D. L. Compton, V. Jain, T. E. Ryan, J. Bruno, C. Radziejewski, P. C. Maisonpierre and G. D. Yancopoulos, Isolation of angiopoietin-1, a ligand for the TIE2 receptor, by secretion-trap expression cloning, Cell 87 (1996) 1161–1169.

G. E. Davis and C. W. Camarillo, An alpha 2 beta 1 integrin-dependent pinocytic mechanism involving intracellular vacuole formation and coalescence regulates capillary lumen and tube formation in three-dimensional collagen matrix, Exp. Cell Res. 224 (1996) 39–51.

E. Deindl, I. Buschmann, I. E. Hoefer, T. Podzuweit, K. Boengler, S. Vogel, N. van Royen, B. Fernandez and W. Schaper, Role of ischemia and of hypoxia-inducible genes in arteriogenesis after femoral artery occlusion in the rabbit, Circ. Res. 89 (2001) 779–786.

P. J. Del Vecchio, A. Siflinger-Birnboim, P. N. Belloni, L. A. Holleran, H. Lum and A. B. Malik, Culture and characterization of pulmonary microvascular endothelial cells, In Vitro Cell. Dev. Biol. A 28 (1992) 711–715.

A. Deutsch and S. Dormann, Cellular Automation Modeling of Biological Pattern Formation, Modeling and Simulation in Science Engineering and Technology (Birkhäuser, 2005).

V. C. Dodelet and E. B. Pasquale, Eph receptors and ephrin ligands: Embryogenesis to tumorigenesis, Oncogene 19 (2000) 5614–5619.

C. S. Dodson, A. V. Peresypkin, K. Rengarajan, S. Wu and J. M. Nickerson, Diffusion coefficients of retinoids, Curr. Eye Res. 24 (2002) 66–74.

C. J. Drake and C. D. Little, Exogenous vascular endothelial growth factor induces malformed and hyperfused vessels during embryonic neovascularization, Proc. Natl. Acad. Sci. USA 92 (1995) 7657–7661.

C. J. Drake, S. J. Brandt, T. C. Trusk and C. D. Little, TAL1/SCL is expressed in endothelial progenitor cells/angioblasts and defines a dorsal-to-ventral gradient of vasculogenesis, Dev. Biol. 192 (1997) 17–30.

C. J. Drake and C. D. Little, VEGF and vascular fusion: Implications for normal and pathological vessels, J. Histochem. Cytochem. 47 (1999) 1351–1356.

C. J. Drake, A. LaRue, N. Ferrara and C. D. Little, VEGF regulates cell behavior during vasculogenesis, Dev. Biol. 224 (2000) 178–188.

D. J. Dumont, G. H. Fong, M. C. Puri, G. Gradwohl, K. Alitalo and M. L. Breitman, Vascularization of the mouse embryo: A study of flk-1, tek, TIE, and vascular endothelial growth factor expression during development, Dev. Dyn. 203 (1995) 80–89.

R. Eckert and D. Randall, Animal Physiology: Mechanisms and Adaptations (W. H. Freeman & Co., 1988).

B. P. Eliceiri and D. A. Cheresh, The role of alpha v integrins during angiogenesis: Insights into potential mechanisms of action and clinical development, J. Clin. Invest. 103 (1999) 1227–1230.

V. P. Eswarakumar, I. Lax and J. Schlessinger, Cellular signaling by fibroblast growth factor receptors, Cytokine Growth Factor Rev. 16 (2005) 139–149.

R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics 7 (1937) 353–369.

J. Folkman and M. Klagsbrun, Angiogenic factors, Science 235 (1987) 442–447.

M. Friedlander, P. C. Brooks, R. W. Shaffer, C. M. Kincaid, J. A. Varner and D. A. Cheresh, Definition of two angiogenic pathways by distinct alpha v integrins, Science 270 (1995) 1500–1502.

V. V. Gafiychuk and L. A. Lubashevsky, On the principles of the vascular network branching, J. Theor. Biol. 212 (2001) 1–9.

A. Gamba, D. Ambrosi, A. Coniglio, A. de Candia, S. Di Talia, E. Giraudo, G. Serini, L. Preziosi and F. Bussolino, Percolation, morphogenesis and Burgers dynamics in blood vessels formation, Phys. Rev. Lett. 90 (2003) 1–4.

W. Gangbo and R. McCann, The geometry of optimal transportation, Acta Math. 177 (1996) 113–161.

E. Gazzerro and E. Canalis, Bone morphogenetic proteins and their antagonists, Rev. Endocr. Metab. Disord. 7 (2006) 51–65.

H. Gerhardt, M. Golding, M. Fruttiger, C. Ruhrberg, A. Lundkvist, A. Abramsson, M. Jeltsch, C. Mitchell, K. Alitalo, D. Shima and C. Betsholtz, VEGF guides angiogenic sprouting utilizing endothelial tip cell filopodia, J. Cell Biol. 161 (2003) 1163–1177.

A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetik 12 (1972) 30–39.

J. A. Glazier and F. Graner, Simulation of the differential adhesion driven rearrangement of biological cells, Phys. Rev. E 47 (1993) 2128–2154.

J. A. Glazier, A. Balter and N. J. Poplawski, Magnetization to morphogenesis: A brief history of the Glazier-Graner-Hogeweg model, in Single-Cell-Based Models in Biology and Medicine, eds. A. R. A. Anderson, M. A. J. Chaplain and K. A. Rejniak (Birkhäuser, 2007), pp. 79–106.

J. A. Glazier, Y. Zhang, M. Swat, B. Zaitlen and S. Schnell, Coordinated action of N-CAM, N-cadherin, EphA4 and ephrinB2 translates genetic prepatterns into structure during somitogenesis in chick, Curr. Top. Dev. Biol. 81 (2008) 2005–2247.

F. González-Crussi, Vasculogenesis in the chick embryo. An ultrastructural study, Am. J. Anat. 130 (1971) 441–460.

D. Gospodarowicz, G. M. Lui and J. Cheng, Purification in high yield of brain fibroblast growth factor by preparative isoelectric focusing at pH 9.6. J. Biol. Chem. 257 (1982) 12266–12276.

L. Gosselin and A. Bejan, Tree networks for minimal pumping power, Int. J. Thermal Sci. 44 (2005) 53–63.

M. J. Goumans, F. Lebrin and G. Valdimarsdottir, Controlling the angiogenic switch: A balance between two distinct TGF-b receptor signaling pathways, Trends Cardiovasc. Med. 13 (2003) 301–307.

F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett. 69 (1992) 2013–2016.

T. Gridley, Notch signaling is essential for vascular morphogenesis in mice, Genes Dev. 14 (2000) 1343–1352.

T. Gridley, Notch signaling in vascular development and physiology, Development 134 (2007) 2709–2718.

G. Grimmett, Percolation (Springer-Verlag, 1999).

J. A. Guadix, R. Carmona, R. Muñoz-Chapuli and J. M. Pérez-Pomares, In vivo and in vitro analysis of the vasculogenic potential of avian proepicardial and epicardial cells, Dev. Dyn. 235 (2006) 1014–1026.

D. Guo, Q. Jia, H. Y. Song, R. S. Warren and D. B. Donner, Vascular endothelial cell growth factor promotes tyrosine phosphorylation of mediators of signal transduction that contain SH2 domains. Association with endothelial cell proliferation, J. Biol. Chem. 270 (1995) 6729–6733.

H. Hatzikirou, G. Breier and A. Deutsch, Cellular automation models for tumor invasion. Encyclopedia of Complexity and Systems Science. Springer (to appear), preprint available at

M. Heil, I. Eitenmüller, T. Schmitz-Rixen and W. Schaper, Arteriogenesis versus angiogenesis: Similarities and differences, J. Cell Mol. Med. 10 (2006) 45–55.

M. Hellstrom, M. Kalen, P. Lindahl, A. Abramsson and C. Betsholtz, Role of PDGF-B and PDGFR-beta in recruitment of vascular smooth muscle cells and pericytes during embryonic blood vessel formation in the mouse, Development 126 (1997) 3047–3055.

M. A. Herrero and J. J. L. Velázquez, Chemotactic collapse for the Keller-Segel model, J. Math. Biol. 35 (1996) 177–196.

M. A. Herrero, Reaction-diffusion systems: A mathematical biology approach, in Cancer Modeling and Simulation, ed. L. Preziosi (Chapman and Hall, 2003), pp. 367–420.

M. A. Herrero, The Mathematics of Chemotaxis. Handbook of Differential Equations (Elsevier, 2007), pp. 137–191.

A. T. Hertig, Angiogenesis in the early human chorion and in the primary placenta of the macaque monkey, Contrib. Embryol. Carnegie Inst. 25 (1935) 37–81.

K. K. Hirschi, S. A. Rohovsky, L. H. Beck, S. R. Smith and P. A. D'Amore, Endothelial cells modulate the proliferation of mural cell precursors via platelet-derived growth factor-BB and heterotypic cell contact, Circ. Res. 84 (1999) 298–305.

A. L. Hodgkin and A. F. Huxley, A qualitative description of membrane current and its application to conduction and excitation in nerves, J. Physiol. (London) 117 (1952) 500–544.

J. J. Hofmann and M. L. Iruela-Arispe, Notch signaling in blood vessels: Who is talking to whom about what? Circ. Res. 100 (2007) 1556–1568.

B. L. Hogan and P. A. Kolodziej, Organogenesis: Molecular mechanisms of tubulogenesis, Nat. Rev. Genet. 3 (2002) 513–523.

P. Hogeweg, Evolving mechanisms of morphogenesis: On the interplay between differential adhesion and cell differentiation, J. Theor. Biol. 203 (2000) 317–333.

E. A. Holm, J. A. Glazier, D. J. Srolovitz and G. S. Grest, Effects of lattice anisotropy and temperature on domain growth in the two-dimensional Potts model, Phys. Rev. A 43 (1991) 2662–2668.

J. E. Hungerford and C. D. Little, Developmental biology of the vascular smooth muscle cell: Building a multilayered vessel wall, J. Vasc. Res. 36 (1999) 2–27.

E. Ising, Beitrag zur Theorie des Ferromagnetismus, Z. Phys. 31 (1925) 253–358.

N. Itoh and D. M. Ornitz, Evolution of the Fgf and Fgfr gene families, Trends Genet. 20 (2004) 563–569.

N. Itoh, The Fgf families in humans, mice, and zebrafish: Their evolutional processes and roles in development, metabolism, and disease, Biol. Pharm. Bull. 30 (2007) 1819–1825.

C. J. Jackson and M. Nguyen, Human microvascular endothelial cells differ from macrovascular endothelial cells in their expression of matrix metalloproteinases, Int. J. Biochem. Cell Biol. 29 (1997) 1167–1177.

Y. Jiang, J. Pjesivac-Grbovic, I. C. Cantrel and J. P. Freyer, A multiscale model for avascular tumor growth, Biophys. J. 89 (2005) 3884–3894.

E. A. V. Jones, F. le Noble and A. Eichmann, What determines blood vessel structure? Genetic prespecification vs. hemodynamics, Physiology 21 (2006) 388–395.

D. Kalderon, Similarities between the Hedgehog and Wnt signaling pathways, Trends Cell Biol. 12 (2002) 523–531.

A. R. Kallianpur, J. E. Jordan and S. J. Brandt, The SCL/TAL-1 gene is expressed in progenitors of both the hemopoietic and vascular systems during embryogenesis, Blood 83 (1994) 1200–1208.

L. Kantorovich, On the transfer of masses, Dokl. Acad. Nauk. USSR 37 (1942) 7–8 (in Russian).

P. Kastner, J. M. Grondona, M. Mark, A. Gansmuller, M. LeMeur, D. Decimo, J. L. Vonesch, P. Dollé and P. Chambon, Genetic analysis of RXR alpha developmental function: Convergence of RXR and RAR signaling pathways in heart and eye morphogenesis, Cell 78 (1994) 987–1003.

J. Kattan, R. W. Dettman and J. Bristow, Formation and remodeling of the coronary vascular bed in the embryonic avian heart, Dev. Dyn. 230 (2004) 34–43.

P. J. Keck, S. D. Hauser, G. Krivi, K. Sanzo, T. Warren, J. Feder and D. T. Connolly, Vascular permeability factor, an endothelial cell mitogen related to PDGF, Science 246 (1989) 1309–1312.

E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970) 399–415.

R. Kemler, Classical cadherins, Semin. Cell Biol. 3 (1992) 149–155.

J. Kessel and B. C. Fabian, The pluripotency of the extraembryonic mesodermal cells of the early chick blastoderm: Effects of the AP and AOV environments, Dev. Biol. 116 (1986) 319–327.

J. King, T. Hamil, J. Creighton, S. Wu, P. Bhat, F. McDonald and T. Stevens, Structural and functional characteristics of lung macro- and microvascular endothelial cell phenotypes, Microvasc. Res. 67 (2004) 139–151.

A. J. Koch and H. Meinhardt, Biological pattern-formation—from basis mechanisms to complex structures, Rev. Mod. Phys. 66 (1994) 1481–1507.

G. Y. Koh, I. Kim, H. J. Kwak, M. J. Yun and J. C. Leem, Biomedical significance of endothelial cell specific growth factor angiopoietin, Exp. Mol. Med. 34 (Korean Soc. of Medical Biochemistry and Molecular Biology, 2002) 1–11.

A. A. Kolmogorov, I. G. Petrovsky and N. N. Piskunov, Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem, Bul. Moskovskovo Gos. Univ. 17 1–26 (in Russian) (English Translation in The Dynamics of Curved Fronts, ed. P. Pelcé).

R. Kopan, Notch: A membrane-bound transcription factor, J. Cell Sci. 115 (2002) 1095–1097.

R. Kowalczyk, A. Gamba and L. Preziosi, On the stability of homogeneous solutions to some aggregation models, Discr. Cont. Dynam. Sys. Ser B 4 (2004) 203–220.

R. Kowalczyk, Preventing Blow-up in a Chemotaxis Model, J. Math. Anal. Appl. 305 (2005) 566–588.

K. Krah, V. Mironov, W. Risau and I. Flamme, Induction of vasculogenesis in quail blastodisc-derived embryoid bodies, Dev. Biol. 164 (1994) 123–132.

L. T. Krebs, Y. Xue, C. R. Norton, J. R. Shutter, M. Maguire, J. P. Sundberg, D. Gallahan, V. Closson, J. Kitajewski, R. Callahan, G. H. Smith, K. L. Stark and T. Gridley, Notch signaling is essential for vascular morphogenesis in mice, Genes Dev. 14 (2000) 1343–1352.

L. T. Krebs, J. R. Shutter, K. Tanigaki, T. Honjo, K. L. Stark and T. Gridley, Haploinsufficient lethality and formation of arteriovenous malformations in Notch pathway mutants, Genes Dev. 18 (2004) 2469–2473.

K. Kullander and R. Klein, Mechanisms and functions of Eph and ephrin signaling, Nat. Rev. Mol. Cell Biol. 3 (2002) 475–486.

A. Kusch, S. Tkachuk, S. Lutter, H. Haller, R. Dietz, M. Lipp and I. Dumler, Monocyte-expressed urokinase regulates human vascular smooth muscle cell migration in a coculture model, Biol. Chem. 383 (2002) 217–221.

V. Lanza, D. Ambrosi and L. Preziosi, Exogenous control of vascular network formation in vitro: A mathematical model, Netw. Heterog. Media 1 (2006) 621–637.

L. Lai, B. L. Bohnsack, K. Niederreither and K. K. Hirschi, Retinoic acid regulates endothelial cell proliferation during vasculogenesis, Development 130 (2003) 6465–6474.

M. G. Lampugnani, M. Corada, L. Caveda, F. Breviario, O. Ayalon, B. Geiger and E. Dejana, The molecular organization of endothelial cell to cell junctions: Differential association of plakoglobin, beta-catenin, and alpha-catenin with vascular endothelial cadherin (VE-cadherin), J. Cell Biol. 129 (1995) 203–217.

B. Larrivée and A. Karsan, Signaling pathways induced by vascular endothelial growth factor (review), Int. J. Mol. Med. 5 (2000) 447–456.

A. C. LaRue, W. S. Argraves, M. H. Zile and C. J. Drake, Critical role for retinol in the generation/differentiation of angioblasts required for embryonic blood vessel formation, Dev. Dyn. 230 (2004) 666–674.

S. K. Lemmon, M. C. Riley, K. A. Thomas, G. A. Hoover, T. Maciag and R. A. Bradshaw, Bovine fibroblast growth factor: Comparison of brain and pituitary preparations, J. Cell Biol. 95 (1982) 162–169.

F. le Noble, D. Moyon, L. Pardanaud, L. Yuan, V. Djonov, R. Matthijsen, C. Bréant, V. Fleury and A. Eichmann, Flow regulates arterial-venous differentiation in the chick embryo yolk sac, Development 131 (2004) 361–375.

F. le Noble, V. Fleury, A. Pries, P. Cosvol, A. Eichmann and R. S. Renemann, Control of arterial branching morphogenesis in embryogenesis: Go with the flow, Cardiovasc. Res. 65 (2005) 619–628.

J. Lewis, Notch signaling and the control of cell fate choices in vertebrates, Semin. Cell Dev. Biol. 9 (1998) 583–589.

W. H. Lien, O. Klezovitch and V. Vasioukhin, Cadherin-catenin proteins in vertebrate development, Curr. Opin. Cell Biol. 18 (2006) 499–506.

F. P. Limbourg, K. Takeshita, F. Radtke, R. T. Bronson, M. T. Chin and J. K. Liao, Essential role of endothelial Notch1 in angiogenesis, Circulation 111 (2005) 1826–1832.

S. Lorente, W. Wechsatol and A. Bejan, Tree-shaped flow structures designed by minimizing path lengths, Int. J. Heat Mass Transf. 45 (2002) 3299–3312.

J. Lough and Y. Sugi, Endoderm and heart development, Dev. Dyn. 217 (2000) 327–342.

J. C. Magee, A. E. Stone, K. T. Oldham and K. S. Guice, Isolation, culture, and characterization of rat lung microvascular endothelial cells, Am. J. Physiol. 267 (1994) L433–L441.

J. N. Maina, Comparative respiratory morphology: Themes and principles in the design and construction of the gas exchangers, Anat Rec. 261 (2000) 25–44.

P. C. Maisonpierre, C. Suri, P. F. Jones, S. Bartunkova, S. J. Wiegand, C. Radziejewski, D. Compton, J. McClain, T. H. Aldrich, N. Papadopoulos, T. J. Daly, S. Davis, T. N. Sato and G. D. Yancopoulos, Angiopoietin-2, a natural antagonist for Tie2 that disrupts in vivo angiogenesis, Science 277 (1997) 55–60.

F. P. Mall, Die Blut und Lymphewege in Dunndarm des Hundes, Abhand Math. Phys. Classe Kön. Sachsischen Gess. Wiss. 14 (1888) 131–200.

C. Mallet, D. Vittet, J. J. Feige and S. Bailly, TGFbetal induces vasculogenesis and inhibits angiogenic sprouting in an embryonic stem cell differentiation model: Respective contribution of ALK1 and ALK5, Stem Cells 24 (2006) 2420–2427.

D. Manoussaki, S. R. Lubkin, R. B. Vernon and J. D. Murray, A mechanical model for the formation of vascular networks in vitro, Acta Biotheor. 44 (1996) 271–282.

D. Manoussaki, A mechanochemical model of vasculogenesis and angiogenesis, Math. Model. Num. Anal. 37 (2004) 581–599.

A. F. M. Marée and P. Hogeweg, How amoeboids self-organize into a fruiting body: Multicellular coordination, in Dictyostelium Discoideum, Proc. Natl. Acad. Sci. 98 (2001) 3879–3883.

A. F. M. Marée and P. Hogeweg, Modeling Dictyostelium discoideum morphogenesis: The culmination, Bull Math. Biol. 64 (2002) 327–353.

J. Massagué and Y. G. Chen, Controlling TGF-beta signaling, Genes Dev. 14 (2000) 627–644.

J. Massagué and D. Wotton, Transcriptional control by the TGF-beta/Smad signaling system, EMBO J. 19 (2000) 1745–1754.

M. Mato, E. Aikawa and K. Kishi, Some observations on interstice between mesoderm and endoderm in the area vasculosa of chick blastoderm, Exp. Cell Res. 35 (1964) 426–428.

D. A. McDonald, Blood Flow in Arteries (Williams and Wilkins, 1960).

H. Meinhardt, Morphogenesis of lines and nets, Differentiation 6 (1976) 117–123.

H. Meinhardt, Models of Biological Pattern Formation (Academic Press, 1982).

H. Meinhardt, Biological Pattern Formation as a complex dynamic phenomenon, Int. J. Bif. Chaos 7 (1997) 1–26.

H. Meinhardt, Models for the formation of netlike structure, in Vascular Morphogenesis: In Vivo, In Vitro, In Mente, eds. C. D. Little, V. Mironov and E. H. Sage (Birkhäuser, 1998), pp. 147–172.

R. M. H. Merks, S. A. Newman and J. A. Glazier, Cell-oriented modeling of in vitro capillary development, in Cellular Automata: 6th Int. Conf. on Cellular Automata for Research and Industry, eds. P. M. A. Soot, B. Chopard, A. G. Hoekstra (Springer-Verlag, 2004), pp. 425–434.

R. M. H. Merks and J. A. Glazier, A cell-centered approach to developmental biology, Physica A 352 (2005) 113–130.

R. M. H. Merks, S. V. Brodsky, M. S. Goligorsky, S. A. Newman and J. A. Glazier, Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling, Dev. Biol. 289 (2006) 44–54.

R. M. H. Merks and J. A. Glazier, Dynamic mechanisms of blood vessel growth, Nonlinearity 19 (2006) C1–C10.

R. M. H. Merks, E. D. Perryn, A. Shirinifard and J. A. Glazier, Contact-inhibited chemotactic motility in de novo and sprouting blood vessel growth, PLoS Comput. Biol. 4 (2008) e1000163.

B. Millauer, S. Wizigmann-Voos, H. Schnurch, R. Martinez, N. P. Moller, W. Risau and A. Ullrich, High affinity VEGF binding and developmental expression suggest Flk-1 as a major regulator of vasculogenesis and angiogenesis, Cell 72 (1993) 835–846.

T. Miura and K. Shiota, TGF-beta2 acts as an "activator" molecule in reaction-diffusion model and is involved in cell sorting phenomenon in mouse limb micromass culture, Dev. Dyn. 217 (2000) 241–249.

K. Miyazawa, M. Shinozaki, T. Hara, T. Furuya and K. Miyazono, Two major Smad pathways in TGF-beta superfamily signaling, Genes Cells 7 (2002) 1191–1204.

G. Monge, Mémoire sur le Theorie des Déblais et de Remblais (Hist. de l'Academie Royale des Sciences de Paris, 1781), pp. 666–704.

T. M. Moore, G. H. Brough, P. Babal, J. J. Kelly, M. Li and T. Stevens, Store-operated calcium entry promotes shape change in pulmonary endothelial cells expressing Trp1, Am. J. Physiol.: Lung Cell Mol. Physiol. 275 (1998) L574–L582.

S. J. Morrison, S. E. Perez, Z. Qiao, J. M. Verdi, C. Hicks, G. Weinmaster and D. J. Anderson, Transient Notch activation initiates an irreversible switch from neurogenesis to gliogenesis by neural crest stem cells, Cell 101 (2000) 499–510.

M. Moser and C. Patterson, Bone morphogenetic proteins and vascular differentiation: BMPing up vasculogenesis, Thromb. Haemost. 94 (2005) 713–718.

D. Moyon, L. Pardanaud, L. Yuan, C. Breant and A. Eichmann, Plasticity of endothelial cells during arterial-venous differentiation in the avian embryo, Development 128 (2001) 3359–3370.

C. D. Murray, The physiological principle of minimum work. I The vascular system and the cost of blood volume, Proc. Natl. Acad. Sci. USA 12 (1926) 207–214.

C. D. Murray, The physiological principle of minimum work applied to the angle of branching of arteries, J. Gen. Physiol. 9 (1926) 835–841.

J. D. Murray and G. F. Oster, Cell traction models for generation of pattern and form in morphogenesis, J. Math. Biol 19 (1984) 265–279.

J. D. Murray and G. F. Oster, Generation of biological pattern and form, J. Math. Appl. Med. Biol. 1 (1984) 51–75.

J. D. Murray, Mathematical Biology, Vols. I and II (Springer, 2000).

T. Mustonen and K. Alitalo, Endothelial receptor tyrosine kinases involved in angiogenesis. J. Cell Biol. 129 (1995) 895–898.

P. Namy, J. Ohayon and P. Traqui, Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields, J. Theor. Biol. 227 (2004) 103–120.

G. Neufeld, T. Cohen, H. Gitay-Goren, Z. Poltorak, S. Tessler, R. Sharon, S. Gengrinovitch and B. Z. Levi, Similarities and differences between the vascular endothelial growth factor (VEGF) splice variants, Cancer Metastasis Rev. 15 (1992) 153–158.

K. Niederreither, J. Vermot, B. Schuhbaur, P. Chambon and P. Dollé, Embryonic retinoic acid synthesis is required for forelimb growth and anteroposterior patterning in the mouse, Development 129 (2002) 3563–3574.

D. M. Noden, Origins and assembly of avian embryonic blood vessels, Ann. NY Acad. Sci. 588 (1990) 236–249.

D. M. Noden, Development of craniofacial blood vessels, in The Development of the Vascular System, eds. R. N. Feinberg, G. K. Sherer, R. Auerbach (Karger, 1991), pp. 1–24.

A. Nohe, E. Keating, P. Knaus and N. O. Petersen, Signal transduction of bone morphogenetic protein receptors, Cell Signal. 16 (2004) 291–299.

S. V. Nolte, H. O. Rennekampff and H. P. Rodemann, Diversity of fibroblasts—A review on implications for skin tissue engineering, Cells Tissues Organs 187 (2008) 165–176.

Y. Oike, Y. Ito, K. Hamada, X. Q. Zhang, K. Miyata, F. Arai, T. Inada, K. Araki, N. Nakagata, M. Takeya, Y. Y. Kisanuki, M. Yanagisawa, N. W. Gale and T. Suda, Regulation of vasculogenesis and angiogenesis by EphB/ephrin-B2 signaling between endothelial cells and surrounding mesenchymal cells, Blood 100 (2002) 1326–1333.

L. Onsager, Crystal statistics I. A two-dimensional model with an order-disorder transition, Phys. Rev. 65 (1944) 117–149.

D. M. Ornitz, FGFs, heparan sulfate and FGFRs: Complex interactions essential for development, Bioessays 22 (2000) 108–112.

D. M. Ornitz and N. Itoh, Fibroblast growth factors, Genome Biol. 2 (2001) R3005–1-12.

M. R. Owen, T. Alarcón, P. K. Maini and H. M. Byrne, Angiogenesis and vascular remodeling in normal and cancerous tissues, J. Math. Biol., to appear. DOI: 10.1007/s00285-008-0213-z.

K. J. Painter and T. Hillen, Volume-filling and quorum-sensing in models for chemosensitive movement, Can. Appl. Maths. Quart. 10 (2002) 501–543.

E. B. Pasquale, Eph receptor signaling casts a wide net on cell behavior, Nat. Rev. Mol. Cell Biol. 6 (2005) 462–475.

J. M. Pérez-Pomares, R. Carmona, M. González-Iriarte, G. Atencia, A. Wessels and R. Mu~noz-Chápuli, Origin of coronary endothelial cells from epicardial mesothelium in avian embryos, Int. J. Dev. Biol. 46 (2002) 1005–1013.

J. M. Pérez-Pomares and R. Mu~noz-Chápuli, Epithelial-mesenchymal transitions: A mesodermal cell strategy for evolutive innovation in Metazoans, Anat. Rec. 268 (2002) 343–351.

J. M. Pérez-Pomares and R. A. Foty, Tissue fusion and cell sorting in embryonic development and disease: Biomedical implications, Bioessays 28 (2006) 809–821.

E. D. Perryn, A. Czirok and C. D. Little, Vascular sprout formation entails tissue deformations and VE-cadherin-dependent cell-autonomous motility, Dev. Biol. 313 (2008) 545–555.

E. F. Plow, T. A. Haas, L. Zhang, J. Loftus, J. W. Smith, Ligand binding to integrins, J. Biol. Chem. 275 (2000) 21785–21788.

G. J. Podgorski, M. Bansal and N. S. Flann, Regular mosaic pattern development: A study of the interplay between lateral inhibition, apoptosis and differential adhesion, Theor. Biol. Med. Modl. 4 (2007) 1–19.

R. Pola, L. E. Ling, M. Silver, M. J. Corbley, M. Kearney, R. Blake-Pepinsky, R. Shapiro, F. R. Taylor, D. P. Baker, T. Asahara and J. M. Isner, The morphogen Sonic hedgehog is an indirect angiogenic agent upregulating two families of angiogenic growth factors, Nat. Med. 7 (2001) 706–711.

T. J. Poole and J. D. Coffin, Vasculogenesis and angiogenesis: Two distinct morphogenetic mechanisms establish embryonic vascular pattern, J. Exp. Zool. 251 (1989) 224–231.

T. J. Poole, E. B. Finkelstein and C. M. Cox, The role of FGF and VEGF in angioblast induction and migration during vascular development, Dev. Dyn. 220 (2001) 1–17.

N. J. Poplawski, M. Swat, J. S. Gens and J. A. Glazier, Adhesion between cells, diffusion of growth factors and elasticity of the AER produce the paddle shape of the chick limb, Phys. Stat. Mech. Appl. C 373 (2007) 521–532.

N. J. Poplawski, A. Shirinifard, M. Swat and J. A. Glazier, Simulation of single-species bacterial-biofilm growth using the Glazier-Graner-Hogeweg model and the Compu-Cell3D modeling environment, Math. Biosci. Engrg. 5 (2008) 255–288.

R. B. Potts, Some generalized order-disorder transformations, Proc. Camb. Phil. Soc. 48 (1952) 106–109.

A. R. Pries, T. W. Secomb and P. Gaehtgens, Design principles of vascular beds, Circ. Res. 77 (1995) 1017–1023.

A. Raya, Y. Kawakami, C. Rodríguez-Esteban, M. Iba~nes, D. Rasskin-Gutman, J. Rodríguez-León, D. Büscher, J. Feijó and J. C. Izpisúa Belmonte, Notch activity acts as a sensor for extracellular calcium during vertebrate left-right determination, Nature 427 (2004) 121–128.

N. Resnick, H. Yehav, A. S. Salit, M. Sushy, S. Schubert, L. C. M. Zilberman and E. Wolfowitz, Fluid shear stress and the vascular endothelium: For better or worse, Progr. Biophys. Molec. Biol. 81 (2003) 177–199.

W. Risau and V. Lemmon, Changes in the vascular extracellular matrix during embryonic vasculogenesis and angiogenesis, Dev. Biol. 125 (1988) 441–450.

W. Risau, H. Sariola, H. G. Zerwes, J. Sasse, P. Ekblom, R. Kemler and T. Doetschman, Vasculogenesis and angiogenesis in embryonic-stem-cell-derived embryoid bodies, Development 102 (1988) 471–478.

W. Risau, Differentiation of endothelium, FASEB J. 9 (1995) 926–933.

W. Risau and I. Flamme, Vasculogenesis, Annu. Rev. Cell. Dev. Biol. 11 (1995) 73–91.

W. Risau, Mechanisms of angiogenesis, Nature 386 (1997) 671–674.

C. Roca and R. H. Adams, Regulation of vascular morphogenesis by Notch signaling, Development 21 (2007) 2511–2524.

F. Rothe, Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Mathematics, Vol. 1072 (Springer, 1984).

P. A. Rupp, A. Czirók and C. D. Little, Alphavbeta3 integrin-dependent endothelial cell dynamics in vivo, Development 131 (2004) 2887–2897.

H. E. Ryan, J. Lo and R. S. Johnson, HIF-1 alpha is required for solid tumor formation and embryonic vascularization, EMBO J. 17 (1998) 3005–3015.

K. Saha and D. V. Schaffer, Signal dynamics in Sonic hedgehog tissue patterning, Development 133 (2006) 889–900.

Y. Sasai and E. M. De Robertis, Ectodermal patterning in vertebrate embryos, Dev. Biol. 182 (1997) 5–20.

T. N. Sato, Y. Tozawa, U. Deutsch, K. Wolburg-Buchholz, Y. Fujiwara, M. Gendron-Maguire, T. Gridley, H. Wolburg, W. Risau and Y. Qin, Distinct roles of the receptor tyrosine kinases Tie-1 and Tie-2 in blood vessel formation, Nature 376 (1995) 70–74.

N. J. Savill and P. Hogeweg, Modeling morphogenesis: From single cells to crawling slugs, J. Theor. Biol. 184 (1997) 229–235.

N. J. Savill and J. A. Sherratt, Control of epidermal stem cell clusters by Notch-mediated lateral induction, Dev. Biol. 258 (2003) 141–153.

G. Schlosser and G. P. Wagner eds., Modularity in Development and Evolution (The University of Chicago Press, 2004).

G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi, F. Bussolino, Modeling the early stages of vascular network assembly, EMBO J. 22 (2003) 1771–1779.

G. K. Sherer, Vasculogenic mechanisms and epithelio-mesenchymal specificity in endodermal organs, in The Development of the Vascular System, eds. R. N. Feinberg, G. K. Sherer and R. Auerbach (Karger, 1991), pp. 37–57.

T. F. Sherman, On connecting large vessels to small, J. Gen. Physiol. 78 (1981) 431–453.

D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, 1994).

M. S. Steinberg, Differential adhesion in morphogenesis: A modern view, Curr. Opin. Genet. Dev. 17 (2007) 281–286.

S. Suchting, C. Freitas, F. le Noble, R. Benedito, C. Bréant, A. Duarte and A. Eichmann, The Notch ligand delta-like 4 negatively regulates endothelial tip cell formation and vessel branching, Proc. Natl. Acad. Sci. USA 104 (2007) 3225–3230.

H. M. Sucov, E. Dyson, C. L. Gumeringer, J. Price, K. R. Chien and R. M. Evans, RXR alpha mutant mice establish a genetic basis for vitamin A signaling in heart morphogenesis, Genes Dev. 8 (1994) 1007–1018.

Y. Sugi and J. Lough, Anterior endoderm is a specific effector of terminal cardiac myocyte differentiation of cells from the embryonic heart forming region, Dev. Dyn. 200 (1994) 155–162.

Y. Sugi and J. Lough, Activin-A and FGF-2 mimic the inductive effects of anterior endoderm on terminal cardiac myogenesis in vitro, Dev. Biol. 168 (1995) 567–574.

C. Suri, P. F. Jones, S. Patan, S. Bartunkova, P. C. Maisonpierre, S. Davis, T. N. Sato and G. D. Yancopoulos, Requisite role of angiopoietin-1, a ligand for the TIE2 receptor, during embryonic angiogenesis, Cell 87 (1996) 1171–1180.

C. Suri, J. McClain, G. Thurston, D. M. McDonald, H. Zhou, E. H. Oldmixon, T. N. Sato and G. D. Yancopoulos, Increased vascularization in mice overexpressing angiopoietin-1, Science 282 (1998) 468–471.

A. Szabo, E. D. Perryn and A. Czirok, Network formation of tissue cells via preferential attraction to elongated structures, Phys. Rev. Lett. 98 (2007) 038102.

A. Szabo, E. Mehes, E. Kosa and A. Czirók, Multicellular sprouting in vitro, Biophys. J. 95 (2008) 2702–2710.

L. A. Taber, An optimization principle for vascular radius including the effects of smooth muscle tone, Biophysical J. 74 (1998) 109–114.

L. A. Timmerman, J. Grego-Bessa, A. Raya, E. Bertran, J. M. Pérez-Pomares, J. Diez, S. Aranda, S. Palomo, F. McCormick, J. C. Izpisua-Belmonte and J. L. de la Pompa, Notch promotes epithelial-mesenchymal transition during cardiac development and oncogenic transformation, Genes Dev. 18 (2004) 99–115.

B. Thisse and C. Thisse, Functions and regulations of fibroblast growth factor signaling during embryonic development, Dev. Biol. 287 (2005) 390–402.

J. P. Thiery, Cell adhesion in development: A complex signaling network, Curr. Opin. Genet. Dev. 13 (2003) 365–371.

D. W. Thompson, On Growth and Form (Dover, 1992).

C. Tickle, A. Crawley and J. Farrar, Retinoic acid application to chick wing buds leads to a dose-dependent reorganization of the apical ectodermal ridge that is mediated by the mesenchyme, Development 106 (1989) 691–705.

R. J. Tomanek, H. K. Hansen and E. I. Dedkov, Vascular patterning of the quail coronary system during development, Anat. Rec. A Discov. Mol. Cell. Evol. Biol. 288 (2006) 989–999.

A. Tosin, D. Ambrosi and L. Preziosi, Mechanics and chemotaxis in the morphogenesis of vascular networks, Bull. Math. Biol. 68 (2006) 1819–1836.

L. Tranqui and P. Tracqui, Mechanical signaling and angiogenesis. The integration of cell-extracellular matrix couplings, C. R. Acad. Sci. Paris, Science de la Vie 323 (2000) 31–47.

A. Tufro, V. F. Norwood, R. M. Carey and R. A. Gomez, Vascular endothelial growth factor induces nephrogenesis and vasculogenesis, J. Am. Soc. Nephrol. 10 (1999) 2125–2134.

A. M. Turing, The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. London 237 (1952) 37–72.

S. Turner and J. A. Sherratt, Intercellular adhesion and cancer invasion: A discrete simulation using the extended Potts model, J. Theor. Biol. 216 (2002) 85–100.

H. Uyttendaele, J. Ho, J. Rossant and J. Kitajewski, Vascular patterning defects associated with expression of activated Notch4 in embryonic endothelium, Proc. Natl. Acad. Sci. USA 98 (2001) 5643–5648.

B. van Wijk, A. F. Moorman and M. J. van den Hoff, Role of bone morphogenetic proteins in cardiac differentiation, Cardiovasc. Res. 74 (2007) 244–255.

D. Vittet, T. Buchou, A. Schweitzer, E. Dejana and P. Huber, Targeted null-mutation in the vascular endothelial-cadherin gene impairs the organization of vascular-like structures in embryoid bodies, Proc. Natl. Acad. Sci. USA 94 (1997) 6273–6278.

K. Vleminckx and R. Kemler, Cadherins and tissue formation: Integrating adhesion and signaling, Bioessays 21 (1999) 211–220.

S. A. Vokes and P. A. Krieg, Endoderm is required for vascular endothelial tube formation, but not for angioblast specification, Development 129 (2002) 775–785.

S. A. Vokes, T. A. Yatskievych, R. L. Heimark, J. McMahon, A. P. McMahon, P. B. Antin and P. A. Krieg, Hedgehog signaling is essential for endothelial tube formation during vasculogenesis, Development 131 (2004) 4371–4380.

G. von Dassow, E. Meir, E. M. Munro and G. M. Odell, The segment polarity network is a robust developmental module, Nature 406 (2000) 188–192.

J. von Neumann, The Theory of Self-Reproducing Automata, ed. A. W. Burks (University of Illinois Press, 1966).

H. W. Wang, Z. F. Chen and D. J. Anderson, Molecular distinction and angiogenic interaction between embryonic arteries and veins revealed by ephrin-B2 and its receptor Eph-B4, Cell 93 (1998) 741–753.

P. W. A. Willems, K. S. Han and B. Hillen, Evaluation by solid vascular costs of arterial geometric optimisation and the influence of ageing, J. Anat. 196 (2000) 160–171.

J. G. Wilson and J. Warkany, Aortic-arch and cardiac anomalies in the offspring of vitamin A deficient rats, Am. J. Anat. 85 (1949) 113–155.

F. H. Wilt, Erythropoiesis in the chick embryo: The role of the endoderm, Science 147 (1965) 1588–1590.

W. Wechsatol, S. Lorente and A. Bejan, Optimal tree-shaped networks for fluid flow in a disc-shaped body, Int. J. Heat Mass Transf. 45 (2002) 4911–4924.

W. Wechsatol, S. Lorente and A. Bejan, Tree-shaped networks with loops, Int. J. Heat Mass Transf. 48 (2005) 573–583.

Q. Xia, Optimal paths related to transport problems, Commun. Contemp. Math. 5 (2003) 251–259.

T. Young, On the functions of the heart and arteries, Philos. Trans. R. Soc. London (1809) 1–31.

M. Zajac, G. L. Jones and J. A. Glazier, Simulating convergent extension by way of anisotropic differential adhesion, J. Theor. Biol. 222 (2003) 247–259.

M. Zamir, On shear forces and blood vessel radii in the cardiovascular system, J. Gen. Physiology 69 (1977) 449–461.

M. Zamir, The Physics of Pulsatile Flow (Springer, 2000).

E. A. Zamir, A. Czirók, C. Cui, C. D. Little and B. J. Rongish, Mesodermal cell displacements during avian gastrulation are due to both individual cell-autonomous and convective tissue movements, Proc. Natl. Acad. Sci. USA 103 (2006) 19806–19811.

X. Q. Zhang, N. Takakura, Y. Oike, T. Inada, N. W. Gale and G. D. Yancopoulos and T. Suda, Stromal cells expressing ephrin-B2 promote the growth and sprouting of ephrin-B2(+) endothelial cells, Blood 98 (2001) 1028–1037.

H. Zhang and A. C. Issekutz, Down-modulation of monocyte transendothelial migration and endothelial adhesion molecule expression by fibroblast growth factor: Reversal by the anti-angiogenic agent SU6668, Am. J. Pathol. 160 (2002) 2219–2230.

Deposited On:17 Sep 2012 09:25
Last Modified:07 Feb 2014 09:28

Repository Staff Only: item control page