{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T14:38:01Z","timestamp":1772462281016,"version":"3.50.1"},"reference-count":74,"publisher":"Association for Research in Vision and Ophthalmology (ARVO)","issue":"3","license":[{"start":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T00:00:00Z","timestamp":1772409600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Trans. Vis. Sci. Tech."],"published-print":{"date-parts":[[2026,3,2]]},"DOI":"10.1167\/tvst.15.3.1","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T13:30:34Z","timestamp":1772458234000},"page":"1","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical Modeling of Human Retinal Vascular Pattern Around the Foveal Avascular Zone"],"prefix":"10.1167","volume":"15","author":[{"given":"Kotaro","family":"Yoshimura","sequence":"first","affiliation":[{"name":"Department of Anatomy and Cell Biology, Kyushu University Graduate School of Medical Sciences, Fukuoka, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kei","family":"Sugihara","sequence":"additional","affiliation":[{"name":"Department of Anatomy and Cell Biology, Kyushu University Graduate School of Medical Sciences, Fukuoka, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ichiro","family":"Maruko","sequence":"additional","affiliation":[{"name":"Department of Ophthalmology, Tokyo Women's Medical University, Tokyo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomohiro","family":"Iida","sequence":"additional","affiliation":[{"name":"Department of Ophthalmology, Tokyo Women's Medical University, Tokyo, Japan"},{"name":"Department of Ophthalmology, Ageo Central General Hospital, Ageo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takashi","family":"Miura","sequence":"additional","affiliation":[{"name":"Department of Anatomy and Cell Biology, Kyushu University Graduate School of Medical Sciences, Fukuoka, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"27","reference":[{"key":"bib1","doi-asserted-by":"publisher","first-page":"960","DOI":"10.1038\/nature04482","article-title":"Retinal angiogenesis in development and disease","volume":"438","author":"Gariano","year":"2004","journal-title":"Nature"},{"key":"bib2","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s10456-007-9065-1","article-title":"Development of the retinal vasculature","volume":"10","author":"Fruttiger","year":"2007","journal-title":"Angiogenesis"},{"key":"bib3","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1038\/332834a0","article-title":"Retinal astrocytes are immigrants from the optic nerve","volume":"332","author":"Watanabe","year":"1988","journal-title":"Nature"},{"key":"bib4","doi-asserted-by":"publisher","first-page":"4738","DOI":"10.1523\/JNEUROSCI.15-07-04738.1995","article-title":"Development of retinal vasculature is mediated by hypoxia-induced vascular endothelial growth factor (VEGF) expression by neuroglia","volume":"15","author":"Stone","year":"1995","journal-title":"J Neurosci"},{"key":"bib5","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1001\/archopht.1996.01100140419009","article-title":"Regulation of vascular endothelial growth factor by oxygen in a model of retinopathy of prematurity","volume":"114","author":"Pierce","year":"1996","journal-title":"Arch Ophthalmol"},{"key":"bib6","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1006\/exer.1997.0365","article-title":"Development of the human retinal vasculature: cellular relations and VEGF expression","volume":"65","author":"Provis","year":"1997","journal-title":"Exp Eye Res"},{"key":"bib7","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1083\/jcb.200302047","article-title":"VEGF guides angiogenic sprouting utilizing endothelial tip cell filopodia","volume":"161","author":"Gerhardt","year":"2003","journal-title":"J Cell Biol"},{"key":"bib8","doi-asserted-by":"publisher","first-page":"1855","DOI":"10.1242\/dev.01732","article-title":"Stabilization of the retinal vascular network by reciprocal feedback between blood vessels and astrocytes","volume":"132","author":"West","year":"2005","journal-title":"Development"},{"key":"bib9","doi-asserted-by":"publisher","first-page":"2499","DOI":"10.1242\/jcs.107.9.2499","article-title":"Astrocytes modulate retinal vasculogenesis: effects on fibronectin expression","volume":"107","author":"Jiang","year":"1994","journal-title":"J Cell Sci"},{"key":"bib10","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1172\/JCI25964","article-title":"Tlx acts as a proangiogenic switch by regulating extracellular assembly of fibronectin matrices in retinal astrocytes","volume":"116","author":"Uemura","year":"2006","journal-title":"J Clin Invest"},{"key":"bib11","doi-asserted-by":"publisher","first-page":"4451","DOI":"10.1242\/dev.071381","article-title":"Integrin-dependent and -independent functions of astrocytic fibronectin in retinal angiogenesis","volume":"138","author":"Stenzel","year":"2011","journal-title":"Development"},{"key":"bib12","first-page":"3500","article-title":"Retinal vascular development is mediated by endothelial filopodia, a preexisting astrocytic template and specific R-cadherin adhesion","volume":"43","author":"Dorrell","year":"2002","journal-title":"Invest Ophthalmol Vis Sci"},{"key":"bib16","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1016\/S1350-9462(01)00012-X","article-title":"Development of the primate retinal vasculature","volume":"20","author":"Provis","year":"2001","journal-title":"Prog Retinal Eye Res"},{"key":"bib18","doi-asserted-by":"publisher","first-page":"3771","DOI":"10.1523\/JNEUROSCI.23-09-03771.2003","article-title":"A Retinotopic map of primate striate cortex generated from the representation of angioscotomas","volume":"23","author":"Adams","year":"2003","journal-title":"J Neurosci"},{"key":"bib19","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.preteyeres.2018.03.006","article-title":"The primate fovea: structure, function and development","volume":"66","author":"Bringmann","year":"2018","journal-title":"Prog Retinal Eye Res"},{"key":"bib20","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1038\/eye.2009.324","article-title":"Special features of human retinal angiogenesis","volume":"24","author":"Gariano","year":"2010","journal-title":"Eye"},{"key":"bib21","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1002\/cne.903330111","article-title":"Glia cells of the monkey retina. I. Astrocytes","volume":"333","author":"Distler","year":"1993","journal-title":"J Comp Neurol"},{"key":"bib22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.preteyeres.2017.11.003","article-title":"Optical coherence tomography angiography","volume":"64","author":"Spaide","year":"2018","journal-title":"Prog Retinal Eye Res"},{"key":"bib23","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1006\/bulm.1998.0042","article-title":"Continuous and discrete mathematical models of tumor-induced angiogenesis","volume":"60","author":"Anderson","year":"1998","journal-title":"Bull Math Biology"},{"key":"bib24","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/S0022-5193(05)80201-2","article-title":"Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis","volume":"152","author":"Stokes","year":"1991","journal-title":"J Theoret Biol"},{"key":"bib25","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/0025-5564(96)00044-2","article-title":"A model of wound-healing angiogenesis in soft tissue","volume":"136","author":"Pettet","year":"1996","journal-title":"Math Biosci"},{"key":"bib26","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1006\/mvre.2000.2282","article-title":"Numerical simulations of angiogenesis in the cornea","volume":"61","author":"Tong","year":"2001","journal-title":"Microvasc Res"},{"key":"bib27","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1093\/imammb\/20.2.135","article-title":"A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies","volume":"20","author":"Plank","year":"2003","journal-title":"Math Med Biol"},{"key":"bib28","doi-asserted-by":"publisher","first-page":"1137","DOI":"10.1016\/j.mcm.2005.05.008","article-title":"Mathematical modelling of flow in 2D and 3D vascular networks: applications to anti-angiogenic and chemotherapeutic drug strategies","volume":"41","author":"St\u00e9phanou","year":"2005","journal-title":"Math Computer Model"},{"key":"bib29","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1016\/j.jtbi.2005.12.022","article-title":"Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies","volume":"241","author":"McDougall","year":"2006","journal-title":"J Theoret Biol"},{"key":"bib30","doi-asserted-by":"publisher","first-page":"2272","DOI":"10.1007\/s11538-012-9754-9","article-title":"Chaplain MAJ. A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature","volume":"74","author":"McDougall","year":"2012","journal-title":"Bull Math Biol"},{"key":"bib31","article-title":"Modelling of retinal vasculature based on genetically tuned parametric L-system","volume":"5","author":"Aghamirmohammadali","year":"2018","journal-title":"Roy Soc Open Sci"},{"key":"bib32","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/s13160-021-00493-9","article-title":"Pattern formation of vascular network in a mathematical model of angiogenesis","volume":"39","author":"Mada","year":"2022","journal-title":"Japan J Indust Appl Math"},{"key":"bib33","doi-asserted-by":"publisher","first-page":"2351","DOI":"10.1098\/rsif.2012.0067","article-title":"Dynamics of angiogenesis during murine retinal development: a coupled in vivo and in silico study","volume":"9","author":"Watson","year":"2012","journal-title":"J Roy Soc Interface"},{"key":"bib34","doi-asserted-by":"publisher","first-page":"2169","DOI":"10.1038\/sj.onc.1201380","article-title":"p38 MAP kinase activation by vascular endothelial growth factor mediates actin reorganization and cell migration in human endothelial cells","volume":"15","author":"Rousseau","year":"1997","journal-title":"Oncogene"},{"issue":"4","key":"bib35","doi-asserted-by":"publisher","first-page":"1044","DOI":"10.1137\/S0036139995288976","article-title":"Aggregation, blowup, and collapse: the ABC's of taxis in reinforced random walks","volume":"57","author":"Stevens","year":"1997","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"bib36","first-page":"223","article-title":"A Two-dimensional growth process","volume":"4","author":"Eden","year":"1961","journal-title":"Dynamics of fractal surfaces"},{"key":"bib37","doi-asserted-by":"publisher","first-page":"1331","DOI":"10.1046\/j.1460-9568.2000.00029.x","article-title":"Developmental changes in astrocyte density in the macaque perifoveal region","volume":"12","author":"Distler","year":"2000","journal-title":"Eur J Neurosci"},{"issue":"7825","key":"bib39","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","article-title":"Array programming with NumPy","volume":"585","author":"Harris","year":"2020","journal-title":"Nature"},{"key":"bib40","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: fundamental algorithms for scientific computing in Python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nat Meth"},{"key":"bib42","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1002\/cyto.a.20022","article-title":"Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images","volume":"58A","author":"Meijering","year":"2004","journal-title":"Cytometry Part A"},{"key":"bib43","doi-asserted-by":"publisher","first-page":"2219","DOI":"10.1007\/s10792-022-02221-9","article-title":"Comparison of retinal vascular arcade trajectory between eyes with an idiopathic macular hole and the healthy fellow eye","volume":"42","author":"Nowroozzadeh","year":"2022","journal-title":"Int Ophthalm"},{"key":"bib44","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1038\/nmeth.2019","article-title":"Fiji: an open-source platform for biological-image analysis","volume":"9","author":"Schindelin","year":"2012","journal-title":"Nat Meth"},{"key":"bib45","doi-asserted-by":"publisher","first-page":"1519","DOI":"10.1114\/B:ABME.0000049036.08817.44","article-title":"Green's function methods for analysis of oxygen delivery to tissue by microvascular networks","volume":"32","author":"Secomb","year":"2004","journal-title":"Ann Biomed Engineer"},{"key":"bib46","doi-asserted-by":"publisher","first-page":"111432","DOI":"10.1016\/j.jtbi.2023.111432","article-title":"The Mathematical modeling of cancer growth and angiogenesis by an individual based interacting system","volume":"562","author":"Flandoli","year":"2023","journal-title":"J Theoret Biol"},{"key":"bib47","doi-asserted-by":"publisher","first-page":"4298","DOI":"10.1167\/iovs.09-4905","article-title":"The cellular expression of antiangiogenic factors in fetal primate macula","volume":"51","author":"Kozulin","year":"2010","journal-title":"Invest Ophthalmol Vis Sci"},{"key":"bib48","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1126\/science.285.5425.245","article-title":"Pigment epithelium-derived factor: a potent inhibitor of angiogenesis","volume":"285","author":"Dawson","year":"1999","journal-title":"Science"},{"key":"bib49","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1002\/cne.10705","article-title":"VEGF expression by ganglion cells in central retina before formation of the foveal depression in monkey retina: evidence of developmental hypoxia","volume":"462","author":"Sandercoe","year":"2003","journal-title":"J Comp Neurol"},{"key":"bib50","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1038\/385313a0","article-title":"A tension-based theory of morphogenesis and compact wiring in the central nervous system","volume":"385","author":"Essen","year":"1997","journal-title":"Nature"},{"key":"bib51","first-page":"2367","article-title":"Development of astrocytes and their relation to blood vessels in fetal monkey retina","volume":"37","author":"Gariano","year":"1996","journal-title":"Invest Ophthalmol Vis Sci"},{"key":"bib52","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.preteyeres.2017.11.001","article-title":"Retinal vasculature development in health and disease","volume":"63","author":"Selvam","year":"2018","journal-title":"Prog Retinal Eye Res"},{"key":"bib53","article-title":"Astrocytes and blood vessels define the foveal rim during primate retinal development","volume":"41","author":"Provis","year":"2000","journal-title":"Invest Ophthalm Vis Sci"},{"key":"bib54","first-page":"522","article-title":"Development of the mouse retinal vasculature: angiogenesis versus vasculogenesis","volume":"43","author":"Fruttiger","year":"2002","journal-title":"Invest Ophthalmol Vis Sci"},{"key":"bib55","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1002\/cne.902550104","article-title":"Relationship between astrocytes, ganglion cells and vasculature of the retina","volume":"255","author":"Stone","year":"1987","journal-title":"J Comp Neurol"},{"key":"bib56","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1002\/cne.902860305","article-title":"Origin of retinal astrocytes in the rat: evidence of migration from the optic nerve","volume":"286","author":"Ling","year":"1989","journal-title":"J Comp Neurol"},{"key":"bib57","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1016\/S0301-0082(97)00079-8","article-title":"Ontogeny of the primate fovea: a central issue in retinal development","volume":"54","author":"Provis","year":"1998","journal-title":"Prog in Neurobiol"},{"key":"bib58","first-page":"2649","article-title":"Gradients of Eph-A6 expression in primate retina suggest roles in both vascular and axon guidance","volume":"15","author":"Kozulin","year":"2009","journal-title":"Mol Vis"},{"key":"bib59","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.devcel.2017.05.024","article-title":"Fgf8 expression and degradation of retinoic acid are required for patterning a high-acuity area in the retina","volume":"42","author":"da Silva","year":"2017","journal-title":"Dev Cell"},{"key":"bib60","doi-asserted-by":"publisher","first-page":"1697","DOI":"10.1002\/glia.23189","article-title":"Astrocytes follow ganglion cell axons to establish an angiogenic template during retinal development","volume":"65","author":"O'Sullivan","year":"2017","journal-title":"Glia"},{"key":"bib61","doi-asserted-by":"crossref","DOI":"10.1001\/jamaophthalmol.2019.2165","article-title":"Capturing macular vascular development in an infant with retinopathy of prematurity","volume":"137","author":"Chen","year":"2019","journal-title":"JAMA Ophthalmol"},{"key":"bib62","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1001\/archopht.126.4.507","article-title":"The foveal avascular region of developing human retina","volume":"126","author":"Provis","year":"2008","journal-title":"Arch Ophthalmol"},{"key":"bib63","doi-asserted-by":"publisher","first-page":"e51","DOI":"10.1016\/j.ophtha.2021.05.031","article-title":"International classification of retinopathy of prematurity, third edition","volume":"128","author":"Chiang","year":"2021","journal-title":"Ophthalmology"},{"key":"bib64","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.mcn.2013.06.001","article-title":"Hyperoxia causes reduced density of retinal astrocytes in the central avascular zone in the mouse model of oxygen-induced retinopathy","volume":"56","author":"Bucher","year":"2013","journal-title":"Mol Cell Neurosci"},{"key":"bib65","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1136\/bjo.51.2.115","article-title":"Radial peripapillary capillaries of the retina. I. Anatomy: human and comparative","volume":"51","author":"Henkind","year":"1967","journal-title":"Br J Ophthalmolo"},{"key":"bib66","doi-asserted-by":"publisher","first-page":"OCT504","DOI":"10.1167\/iovs.15-18877","article-title":"Radial peripapillary capillary network visualized using wide-field montage optical coherence tomography angiography","volume":"57","author":"Mase","year":"2016","journal-title":"Invest Opthalmol Vis Sci"},{"key":"bib67","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0092-8674(95)90425-5","article-title":"In vitro guidance of retinal ganglion cell axons by RAGS, a 25 kDa tectal protein related to ligands for Eph receptor tyrosine kinases","volume":"82","author":"Drescher","year":"1995","journal-title":"Cell"},{"key":"bib68","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/0092-8674(95)90426-3","article-title":"Complementary gradients in expression and binding of ELF-1 and Mek4 in development of the topographic retinotectal projection map","volume":"82","author":"Cheng","year":"1995","journal-title":"Cell"},{"key":"bib69","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1016\/S0092-8674(00)80150-6","article-title":"Topographically specific effects of ELF-1 on retinal axon guidance in vitro and retinal axon mapping in vivo","volume":"86","author":"Nakamoto","year":"1996","journal-title":"Cell"},{"key":"bib70","doi-asserted-by":"publisher","first-page":"e0235373","DOI":"10.1371\/journal.pone.0235373","article-title":"Remodeling mechanisms determine size distributions in developing retinal vasculature","volume":"15","author":"Iizuka","year":"2020","journal-title":"PLoS One"},{"key":"bib71","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1242\/dev.108.3.515","article-title":"The early development of retinal ganglion cells with uncrossed axons in the mouse: retinal position and axonal course","volume":"108","author":"Colello","year":"1990","journal-title":"Development"},{"key":"bib72","doi-asserted-by":"publisher","first-page":"926","DOI":"10.1016\/0002-9394(66)91920-9","article-title":"The temporal raphe of the human retina","volume":"62","author":"Vrabec","year":"1966","journal-title":"Am J Ophthalmol"},{"key":"bib73","doi-asserted-by":"publisher","first-page":"4044","DOI":"10.1523\/JNEUROSCI.4794-08.2009","article-title":"FGF8 signaling regulates growth of midbrain dopaminergic axons by inducing semaphorin 3F","volume":"29","author":"Yamauchi","year":"2009","journal-title":"J Neurosci"},{"key":"bib74","doi-asserted-by":"publisher","first-page":"3432","DOI":"10.1523\/JNEUROSCI.4938-04.2005","article-title":"Sonic Hedgehog has a dual effect on the growth of retinal ganglion axons depending on its concentration","volume":"25","author":"Kolpak","year":"2005","journal-title":"J Neurosci"},{"key":"bib13","volume-title":"System of Ophthalmology, Vol. I. The eye in evolution","author":"Duke-Elder","year":"1958"},{"key":"bib14","volume-title":"System of ophthalmology, Vol. III, Normal and abnormal development, part 2, congenital deformities","author":"Duke-Elder","year":"1963"},{"key":"bib15","first-page":"22","volume-title":"Development of the retinal vasculature","author":"Chan-Ling","year":"2010"},{"key":"bib17","volume-title":"System of ophthalmology, Vol. II. The anatomy of the visual system","author":"Duke-Elder","year":"1961"},{"key":"bib38","volume-title":"Python 3 Reference Manual","author":"van Rossum","year":"2009"},{"key":"bib41","first-page":"120","article-title":"The OpenCV Library","volume-title":"Dr Dobb's Journal of Software Tools","author":"Bradski","year":"2000"}],"container-title":["Translational Vision Science & Technology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/tvst.arvojournals.org\/article.aspx?doi=10.1167\/tvst.15.3.1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T13:30:37Z","timestamp":1772458237000},"score":1,"resource":{"primary":{"URL":"http:\/\/tvst.arvojournals.org\/article.aspx?doi=10.1167\/tvst.15.3.1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,2]]},"references-count":74,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,3,2]]}},"URL":"https:\/\/doi.org\/10.1167\/tvst.15.3.1","relation":{},"ISSN":["2164-2591"],"issn-type":[{"value":"2164-2591","type":"print"}],"subject":[],"published":{"date-parts":[[2026,3,2]]}}}