{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,20]],"date-time":"2025-07-20T04:26:46Z","timestamp":1752985606441,"version":"3.37.3"},"reference-count":19,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>One of the fields of applied mathematics is related to model analysis. Biomedical systems are suitable candidates for this field because of their importance in life sciences including therapeutics. Here we deal with the analysis of a model recently proposed by Espinoza-Valdez et al. (2010) for the kidney vasculature developed via angiogenesis. The graph theory allows one to model quantitatively a vascular arterial tree of the kidney in sense that (1) the vertex represents a vessels bifurcation, whereas (2) each edge stands for a vessel including physiological parameters. The analytical model is based on the two processes of sprouting and splitting angiogeneses, the concentration of the vascular endothelial growth factor (VEGF), and the experimental data measurements of the rat kidneys. The fractal dimension depends on the probability of sprouting angiogenesis in the development of the arterial vascular tree of the kidney, that is, of the distribution of blood vessels in the morphology generated by the analytical model. The fractal dimension might determine whether a suitable renal vascular structure is capable of performing physiological functions under appropriate conditions. The analysis can describe the complex structures of the development vasculature in kidney.<\/jats:p>","DOI":"10.1155\/2013\/396486","type":"journal-article","created":{"date-parts":[[2013,7,2]],"date-time":"2013-07-02T17:01:54Z","timestamp":1372784514000},"page":"1-6","source":"Crossref","is-referenced-by-count":6,"title":["Analysis of a Model for the Morphological Structure of Renal Arterial Tree: Fractal Structure"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7185-077X","authenticated-orcid":true,"given":"Aurora","family":"Espinoza-Valdez","sequence":"first","affiliation":[{"name":"Departamento de Ciencias Computacionales, CUCEI, Universidad de Guadalajara, Avenida Revoluci\u00f3n 1500, CP 44430, Guadalajara, JAL, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2430-284X","authenticated-orcid":true,"given":"Francisco C.","family":"Ordaz-Salazar","sequence":"additional","affiliation":[{"name":"Universidad Polit\u00e9cnica de San Luis Potos\u00ed, Urbano Villal\u00f3n 500, CP 78363, La Ladrillera, SLP, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4450-932X","authenticated-orcid":true,"given":"Edgardo","family":"Ugalde","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica UASLP, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Avenida Manuel Nava No. 6., Zona Universitaria, CP 78200, SLP, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6817-3704","authenticated-orcid":true,"given":"Ricardo","family":"Femat","sequence":"additional","affiliation":[{"name":"Laboratorio para Biodin\u00e1mica y Sistemas Alineales, Divisi\u00f3n de Matem\u00e1ticas Aplicadas, IPICYT, Apartado Postal 3-90, CP 78231, Tangamanga, SLP, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"2001","key":"1"},{"doi-asserted-by":"publisher","key":"2","DOI":"10.1016\/j.mvr.2003.11.005"},{"doi-asserted-by":"publisher","key":"3","DOI":"10.1152\/ajpheart.00814.2005"},{"doi-asserted-by":"publisher","key":"4","DOI":"10.1085\/jgp.118.3.267"},{"doi-asserted-by":"publisher","key":"5","DOI":"10.1016\/j.mbs.2010.01.007"},{"year":"2000","key":"6"},{"doi-asserted-by":"publisher","key":"7","DOI":"10.1023\/A:1006493130855"},{"issue":"12","key":"8","doi-asserted-by":"crossref","first-page":"2433","DOI":"10.1139\/y87-386","volume":"65","year":"1987","journal-title":"Canadian Journal of Physiology and Pharmacology"},{"doi-asserted-by":"publisher","key":"9","DOI":"10.1103\/PhysRevLett.75.2428"},{"issue":"4","key":"10","doi-asserted-by":"crossref","first-page":"395","DOI":"10.3109\/10739689709146803","volume":"4","year":"1997","journal-title":"Microcirculation"},{"doi-asserted-by":"publisher","key":"11","DOI":"10.1002\/cne.903610311"},{"doi-asserted-by":"publisher","key":"12","DOI":"10.1006\/jtbi.1998.0810"},{"doi-asserted-by":"publisher","key":"13","DOI":"10.1142\/S0218348X03002087"},{"doi-asserted-by":"publisher","key":"14","DOI":"10.1016\/j.jtbi.2009.10.037"},{"issue":"3","key":"15","first-page":"533","volume":"7","year":"2001","journal-title":"Clinical Cancer Research"},{"issue":"4","key":"16","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1002\/path.1711700412","volume":"170","year":"1993","journal-title":"Journal of Pathology"},{"doi-asserted-by":"publisher","key":"17","DOI":"10.1097\/01.LAB.0000107160.81875.33"},{"doi-asserted-by":"publisher","key":"18","DOI":"10.1016\/j.chaos.2004.09.087"},{"year":"1988","key":"19"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/396486.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/396486.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/396486.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T11:37:53Z","timestamp":1498045073000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/396486\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":19,"alternative-id":["396486","396486"],"URL":"https:\/\/doi.org\/10.1155\/2013\/396486","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}