{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T01:48:27Z","timestamp":1792115307567,"version":"4.4.0"},"reference-count":201,"publisher":"The Royal Society","issue":"7","license":[{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["Open Biol."],"published-print":{"date-parts":[[2020,7]]},"abstract":"<jats:p>\n            Fractal geometry (FG) is a branch of mathematics that instructively characterizes structural complexity. Branched structures are ubiquitous in both the physical and the biological realms. Fractility has therefore been termed nature's design. The fractal properties of the bronchial (airway) system, the pulmonary artery and the pulmonary vein of the human lung generates large respiratory surface area that is crammed in the lung. Also, it permits the inhaled air to intimately approximate the pulmonary capillary blood across a very thin blood\u2013gas barrier through which gas exchange to occur by diffusion. Here, the bronchial (airway) and vascular systems were simultaneously cast with latex rubber. After corrosion, the bronchial and vascular system casts were physically separated and cleared to expose the branches. The morphogenetic (Weibel's) ordering method was used to categorize the branches on which the diameters and the lengths, as well as the angles of bifurcation, were measured. The fractal dimensions (\n            <jats:italic>D<\/jats:italic>\n            <jats:sub>F<\/jats:sub>\n            ) were determined by plotting the total branch measurements against the mean branch diameters on double logarithmic coordinates (axes). The diameter-determined\n            <jats:italic>D<\/jats:italic>\n            <jats:sub>F<\/jats:sub>\n            values were 2.714 for the bronchial system, 2.882 for the pulmonary artery and 2.334 for the pulmonary vein while the respective values from lengths were 3.098, 3.916 and 4.041. The diameters yielded\n            <jats:italic>D<\/jats:italic>\n            <jats:sub>F<\/jats:sub>\n            values that were consistent with the properties of fractal structures (i.e. self-similarity and space-filling). The data obtained here compellingly suggest that the design of the bronchial system, the pulmonary artery and the pulmonary vein of the human lung functionally comply with the Hess\u2013Murray law or \u2018the principle of minimum work\u2019.\n          <\/jats:p>","DOI":"10.1098\/rsob.190249","type":"journal-article","created":{"date-parts":[[2020,7,7]],"date-time":"2020-07-07T23:05:12Z","timestamp":1594163112000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung"],"prefix":"10.1098","volume":"10","author":[{"given":"Montanna","family":"Essey","sequence":"first","affiliation":[{"name":"Department of Zoology, University of Johannesburg, Auckland Park Campus, Kingsway, Johannesburg 2006, South Africa"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7549-2861","authenticated-orcid":true,"given":"John N.","family":"Maina","sequence":"additional","affiliation":[{"name":"Department of Zoology, University of Johannesburg, Auckland Park Campus, Kingsway, Johannesburg 2006, South Africa"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2020,7,8]]},"reference":[{"key":"e_1_3_7_2_2","first-page":"1","article-title":"Mandelbrot's fractals and the geometry of life: a tribute to Benoit Mandelbrot on his 80th birthday","volume":"4","author":"Weibel E","year":"2005","unstructured":"Weibel E. 2005 Mandelbrot's fractals and the geometry of life: a tribute to Benoit Mandelbrot on his 80th birthday. Fractals Biol. Med. 4, 1-14.","journal-title":"Fractals Biol. Med."},{"key":"e_1_3_7_3_2","volume-title":"The fractal and geometry of nature","author":"Mandelbrot BB","year":"1977","unstructured":"Mandelbrot BB. 1977 The fractal and geometry of nature. San Francisco, CA: WH Freeman."},{"key":"e_1_3_7_4_2","doi-asserted-by":"publisher","DOI":"10.1006\/jtbi.1998.0723"},{"key":"e_1_3_7_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-7643-7412-8"},{"key":"e_1_3_7_6_2","doi-asserted-by":"publisher","DOI":"10.1152\/ajplung.1991.261.6.L361"},{"key":"e_1_3_7_7_2","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-4666-2077-3.ch002"},{"key":"e_1_3_7_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-8094-5_1"},{"key":"e_1_3_7_9_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2014.00009"},{"key":"e_1_3_7_10_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005615"},{"key":"e_1_3_7_11_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.12.5.299"},{"key":"e_1_3_7_12_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.12.3.207"},{"key":"e_1_3_7_13_2","doi-asserted-by":"publisher","DOI":"10.1085\/jgp.9.6.835"},{"key":"e_1_3_7_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02481813"},{"key":"e_1_3_7_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02477859"},{"key":"e_1_3_7_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02461198"},{"key":"e_1_3_7_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0092-8240(82)80001-3"},{"key":"e_1_3_7_18_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.2396104"},{"key":"e_1_3_7_19_2","doi-asserted-by":"publisher","DOI":"10.1161\/01.RES.77.5.1017"},{"key":"e_1_3_7_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.artres.2010.06.003"},{"key":"e_1_3_7_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.artres.2015.01.001"},{"key":"e_1_3_7_22_2","volume-title":"Trees and networks in biological models","author":"MacDonald N","year":"1983","unstructured":"MacDonald N. 1983. Trees and networks in biological models. New York, NY: Wiley."},{"key":"e_1_3_7_23_2","volume-title":"Encounters with chaos","author":"Gulick D","year":"1992","unstructured":"Gulick D. 1992. Encounters with chaos. New York, NY: McGraw Hill Inc."},{"key":"e_1_3_7_24_2","first-page":"571","volume-title":"Complexity in structure and function of the lung","author":"Glenny RW","year":"1998","unstructured":"Glenny RW. 1998 Heterogeneity in the lung: concepts and measures. In Complexity in structure and function of the lung (eds MP Hlastal, HT Robertsone), pp. 571-609. Seattle, WA: University of Washington."},{"key":"e_1_3_7_25_2","doi-asserted-by":"publisher","DOI":"10.1186\/s12968-015-0179-0"},{"key":"e_1_3_7_26_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1997.82.3.968"},{"key":"e_1_3_7_27_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1999.87.6.2207"},{"key":"e_1_3_7_28_2","volume-title":"The notebooks of Leonardo da Vinci","author":"Richter J","year":"1970","unstructured":"Richter J. 1970 The notebooks of Leonardo da Vinci. New York, NY: Dover."},{"key":"e_1_3_7_29_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.156.3775.636"},{"key":"e_1_3_7_30_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.72.10.3825"},{"key":"e_1_3_7_31_2","doi-asserted-by":"publisher","DOI":"10.1109\/42.14515"},{"key":"e_1_3_7_32_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-54508-8"},{"key":"e_1_3_7_33_2","doi-asserted-by":"publisher","DOI":"10.3109\/02713683.2013.779722"},{"key":"e_1_3_7_34_2","first-page":"1","article-title":"Quantification of tortuosity and fractal dimension of the lung vessels in pulmonary hypertension patients","volume":"9","author":"Helmberger M","year":"2014","unstructured":"Helmberger M, Pienn M, Urschler M, Kullnig P, Stollberger R, Kovacs G, Olschewski A, Olschewski H, B\u00e1lint Z. 2014 Quantification of tortuosity and fractal dimension of the lung vessels in pulmonary hypertension patients. Peer-Rev. Open Acc. Sci. J. 9, 1-9.","journal-title":"Peer-Rev. Open Acc. Sci. J."},{"key":"e_1_3_7_35_2","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/8.4.359"},{"key":"e_1_3_7_36_2","volume-title":"Fractal geometry: mathematical foundations and applications","author":"Falconer K","year":"2014","unstructured":"Falconer K. 2014 Fractal geometry: mathematical foundations and applications. New York, NY: Wiley."},{"key":"e_1_3_7_37_2","doi-asserted-by":"publisher","DOI":"10.1038\/nrclinonc.2015.108"},{"key":"e_1_3_7_38_2","first-page":"31","article-title":"Fractals: geometry between dimensions","volume":"105","author":"Michael B","year":"1985","unstructured":"Michael B. 1985 Fractals: geometry between dimensions. New Sci. 105, 31.","journal-title":"New Sci."},{"key":"e_1_3_7_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2018.11.030"},{"key":"e_1_3_7_40_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.279.5347.39"},{"key":"e_1_3_7_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0270(99)00066-7"},{"key":"e_1_3_7_42_2","doi-asserted-by":"publisher","DOI":"10.1038\/213668a0"},{"key":"e_1_3_7_43_2","first-page":"1061","volume-title":"The lung: scientific foundations","author":"Weibel ER","year":"1997","unstructured":"Weibel ER. 1997 Design of airways and between the organism blood vessels considered as confluent tree. In The lung: scientific foundations (eds RD Crystal, JB West, ER Weibel, PJ Barnes), pp. 1061-1071. Philadelphia, PA: Lippincott-Raven."},{"key":"e_1_3_7_44_2","doi-asserted-by":"publisher","DOI":"10.1164\/rccm.201212-2260OE"},{"key":"e_1_3_7_45_2","doi-asserted-by":"publisher","DOI":"10.2307\/2445879"},{"key":"e_1_3_7_46_2","doi-asserted-by":"publisher","DOI":"10.1152\/japplphysiol.01293.2010"},{"key":"e_1_3_7_47_2","doi-asserted-by":"publisher","DOI":"10.3389\/fpls.2016.00149"},{"key":"e_1_3_7_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01681580"},{"key":"e_1_3_7_49_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-6419-9"},{"key":"e_1_3_7_50_2","doi-asserted-by":"publisher","DOI":"10.1085\/jgp.78.4.431"},{"key":"e_1_3_7_51_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(86)80081-9"},{"key":"e_1_3_7_52_2","doi-asserted-by":"publisher","DOI":"10.2307\/1542042"},{"key":"e_1_3_7_53_2","volume-title":"Introduction to fluid mechanics","author":"Nakayama Y","year":"2000","unstructured":"Nakayama Y. 2000 Introduction to fluid mechanics. Oxford, UK: Butterworth-Heinemann."},{"key":"e_1_3_7_54_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature01444"},{"key":"e_1_3_7_55_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511761348"},{"key":"e_1_3_7_56_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2011.0270"},{"key":"e_1_3_7_57_2","doi-asserted-by":"publisher","DOI":"10.3390\/e18080283"},{"key":"e_1_3_7_58_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/5284816"},{"key":"e_1_3_7_59_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7527-9_1"},{"key":"e_1_3_7_60_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0094837300010447"},{"key":"e_1_3_7_61_2","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.2009.0302"},{"key":"e_1_3_7_62_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.plrev.2011.05.010"},{"key":"e_1_3_7_63_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0116260"},{"key":"e_1_3_7_64_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87553-3"},{"key":"e_1_3_7_65_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.137.3530.577"},{"key":"e_1_3_7_66_2","volume-title":"Tracheobronchial geometry: human, dog, hamster","author":"Raabe OG","year":"1976","unstructured":"Raabe OG, Yeh HC, Shum GM, Phalen RF. 1976 Tracheobronchial geometry: human, dog, hamster. Albuquerque, NM: Lovelace Foundation."},{"key":"e_1_3_7_67_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3138469"},{"key":"e_1_3_7_68_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1994.76.2.882"},{"key":"e_1_3_7_69_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1990.68.2.457"},{"key":"e_1_3_7_70_2","first-page":"721","article-title":"Pulmonary airways and blood vessels considered as confluent trees","author":"Horsfield K","year":"1991","unstructured":"Horsfield K. 1991 Pulmonary airways and blood vessels considered as confluent trees. In The lung scientific foundations (eds RD Crystal, JB West, ER Weibel, PJ Barnes), pp. 721\u2013 727. New York, NY: Raven.","journal-title":"The lung scientific foundations"},{"key":"e_1_3_7_71_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1095-6433(01)00411-1"},{"key":"e_1_3_7_72_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01951755"},{"key":"e_1_3_7_73_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1994.77.2.660"},{"key":"e_1_3_7_74_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1996.81.5.2123"},{"key":"e_1_3_7_75_2","doi-asserted-by":"publisher","DOI":"10.1152\/japplphysiol.01033.2004"},{"key":"e_1_3_7_76_2","doi-asserted-by":"publisher","DOI":"10.1242\/dev.104794"},{"key":"e_1_3_7_77_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1986.60.3.1089"},{"key":"e_1_3_7_78_2","doi-asserted-by":"publisher","DOI":"10.1002\/ar.1091770207"},{"key":"e_1_3_7_79_2","first-page":"1733","article-title":"Microvascular corrosion casting of the lung: a state-of-the-art review","volume":"4","author":"Schraufnagel DE","year":"1987","unstructured":"Schraufnagel DE. 1987 Microvascular corrosion casting of the lung: a state-of-the-art review. Scanning Microsc. 4, 1733-1747.","journal-title":"Scanning Microsc."},{"key":"e_1_3_7_80_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02327080"},{"key":"e_1_3_7_81_2","doi-asserted-by":"publisher","DOI":"10.1002\/ar.1092220206"},{"key":"e_1_3_7_82_2","first-page":"287","article-title":"Scanning electron microscopy of styrene-methylethylketone casts of the airway and the arterial system of the lung","volume":"7","author":"Hojo T","year":"1993","unstructured":"Hojo T. 1993 Scanning electron microscopy of styrene-methylethylketone casts of the airway and the arterial system of the lung. Scanning Microsc. 7, 287.","journal-title":"Scanning Microsc."},{"key":"e_1_3_7_83_2","first-page":"1173","article-title":"Combined vascular-bronchoalveolar casting using formalin-fixed canine lungs and a low viscosity silicone rubber","volume":"10","author":"Nettum JA","year":"1996","unstructured":"Nettum JA. 1996 Combined vascular-bronchoalveolar casting using formalin-fixed canine lungs and a low viscosity silicone rubber. Scanning Microsc. 10, 1173-1179.","journal-title":"Scanning Microsc."},{"key":"e_1_3_7_84_2","doi-asserted-by":"publisher","DOI":"10.1080\/019021400269943"},{"key":"e_1_3_7_85_2","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(89)90854-2"},{"key":"e_1_3_7_86_2","doi-asserted-by":"publisher","DOI":"10.1016\/0968-4328(94)90057-4"},{"key":"e_1_3_7_87_2","first-page":"517","article-title":"Realization of the box-counting method for calculating the fractal dimension of the urban form based on remote sensing image","volume":"43","author":"Meiling G","year":"2007","unstructured":"Meiling G, Qizhong L, Wang L. 2007 Realization of the box-counting method for calculating the fractal dimension of the urban form based on remote sensing image. Acta Scientiarum Naturalium Universitatis Pekinensis 43, 517-522.","journal-title":"Acta Scientiarum Naturalium Universitatis Pekinensis"},{"key":"e_1_3_7_88_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2010.12.004"},{"key":"e_1_3_7_89_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.proeng.2012.01.715"},{"key":"e_1_3_7_90_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-3995-4_6"},{"key":"e_1_3_7_91_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2016.02.038"},{"key":"e_1_3_7_92_2","first-page":"78","article-title":"New approach to the calculation of the fractal dimension of the lungs","volume":"44","author":"Lamrini-Uahabi K","year":"2017","unstructured":"Lamrini-Uahabi K, Atounti M. 2017 New approach to the calculation of the fractal dimension of the lungs. Ann. of the Univ. Craiova: Math. Comput. Sci. Ser. 44, 78-86.","journal-title":"Ann. of the Univ. Craiova: Math. Comput. Sci. Ser."},{"key":"e_1_3_7_93_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1993.75.1.432"},{"key":"e_1_3_7_94_2","doi-asserted-by":"publisher","DOI":"10.1152\/japplphysiol.00604.2003"},{"key":"e_1_3_7_95_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.284.5420.1677"},{"key":"e_1_3_7_96_2","volume-title":"The pathway for oxygen: structure and function in the mammalian respiratory system","author":"Weibel ER","year":"1984","unstructured":"Weibel ER. 1984 The pathway for oxygen: structure and function in the mammalian respiratory system. Cambridge, MA: Harvard University Press."},{"key":"e_1_3_7_97_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1998.85.3.867"},{"key":"e_1_3_7_98_2","doi-asserted-by":"publisher","DOI":"10.1586\/17434440.2013.827506"},{"key":"e_1_3_7_99_2","doi-asserted-by":"publisher","DOI":"10.1002\/path.1711660414"},{"key":"e_1_3_7_100_2","doi-asserted-by":"publisher","DOI":"10.1109\/4233.992163"},{"key":"e_1_3_7_101_2","first-page":"29","article-title":"The fractal geometry of life","volume":"102","author":"Losa GA","year":"2009","unstructured":"Losa GA. 2009 The fractal geometry of life. Riv. Biol. 102, 29-59.","journal-title":"Riv. Biol."},{"key":"e_1_3_7_102_2","doi-asserted-by":"publisher","DOI":"10.1172\/JCI120693"},{"key":"e_1_3_7_103_2","first-page":"1","article-title":"Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA)","volume":"4","author":"Bhandari S","year":"2018","unstructured":"Bhandari S, Choudannavar S, Avery E, Sahay P, Pradhan P. 2018 Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA). Biomed. Phys. Eng. Exp. 4, 1-11.","journal-title":"Biomed. Phys. Eng. Exp."},{"key":"e_1_3_7_104_2","doi-asserted-by":"publisher","DOI":"10.1128\/JB.172.3.1180-1185.1990"},{"key":"e_1_3_7_105_2","first-page":"211","volume-title":"Fractals in biology and medicine","author":"Smith TG","year":"1994","unstructured":"Smith TG. 1994 A fractal analysis of morphological differentiation of spinal cord neurons in cell culture. In Fractals in biology and medicine (eds TF Nonnenmacher, GA Losa, ER Weibel), pp. 211-220. Basel, Switzerland: Birkh\u00e4user Press."},{"key":"e_1_3_7_106_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.bioeng.6.040803.140100"},{"key":"e_1_3_7_107_2","doi-asserted-by":"publisher","DOI":"10.1164\/rccm.200411-1463OC"},{"key":"e_1_3_7_108_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature02287"},{"key":"e_1_3_7_109_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ophtha.2008.05.029"},{"key":"e_1_3_7_110_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1549-8719.2010.00075.x"},{"key":"e_1_3_7_111_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2010.06.050"},{"key":"e_1_3_7_112_2","doi-asserted-by":"publisher","DOI":"10.1097\/00005382-199424000-00002"},{"key":"e_1_3_7_113_2","doi-asserted-by":"publisher","DOI":"10.1136\/hrt.2010.214130"},{"key":"e_1_3_7_114_2","doi-asserted-by":"publisher","DOI":"10.3348\/kjr.2011.12.3.289"},{"key":"e_1_3_7_115_2","first-page":"43","article-title":"Chaos and fractals in human physiology","author":"Goldberger AL","year":"1990","unstructured":"Goldberger AL, Rigney DR, West BJ. 1990 Chaos and fractals in human physiology. Sci. Am. (Feb.) 43-49.","journal-title":"Sci. Am."},{"key":"e_1_3_7_116_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.012579499"},{"key":"e_1_3_7_117_2","doi-asserted-by":"publisher","DOI":"10.1161\/01.RES.38.6.572"},{"key":"e_1_3_7_118_2","doi-asserted-by":"publisher","DOI":"10.1042\/cs1030111"},{"key":"e_1_3_7_119_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.atherosclerosis.2011.12.040"},{"key":"e_1_3_7_120_2","unstructured":"Calkins J. 2013 Fractal geometry and its correlation to the efficiency of biological structures. Honours project Grand Valley State University Allendale MI."},{"key":"e_1_3_7_121_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8501-0_9"},{"key":"e_1_3_7_122_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02476898"},{"key":"e_1_3_7_123_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.acthis.2011.03.010"},{"key":"e_1_3_7_124_2","doi-asserted-by":"crossref","unstructured":"Youlin H Lede N. 2016 Fractal studies for basin characteristics of three parallel rivers area based on GIS. In Intern. Conf. Robots & Intelligent Systems 27\u201328 August. Zhangji: China pp. 197-202.","DOI":"10.1109\/ICRIS.2016.41"},{"key":"e_1_3_7_125_2","doi-asserted-by":"publisher","DOI":"10.1002\/ar.1092200410"},{"key":"e_1_3_7_126_2","doi-asserted-by":"publisher","DOI":"10.1017\/S1431927613014050"},{"key":"e_1_3_7_127_2","first-page":"224","volume-title":"Pulmonary diseases and disorders","author":"Weibel E","year":"1980","unstructured":"Weibel E. 1980 Design and structure of the human lung. In Pulmonary diseases and disorders (ed. AP Fishman), pp. 224-271. New York, NY: McGraw-Hill."},{"key":"e_1_3_7_128_2","first-page":"25","article-title":"Chaos and order in the human body","volume":"9","author":"Goldberger AL","year":"1992","unstructured":"Goldberger AL, West BJ. 1992 Chaos and order in the human body. MD Comput. 9, 25-34.","journal-title":"MD Comput."},{"key":"e_1_3_7_129_2","doi-asserted-by":"publisher","DOI":"10.1016\/0034-5687(80)90050-X"},{"key":"e_1_3_7_130_2","doi-asserted-by":"publisher","DOI":"10.1164\/rccm.200809-1522ST"},{"key":"e_1_3_7_131_2","doi-asserted-by":"publisher","DOI":"10.1130\/0016-7606(1952)63[923:DBOG]2.0.CO;2"},{"key":"e_1_3_7_132_2","first-page":"345","article-title":"Revision of Horton's quantitative factors in erosional terrain","volume":"34","author":"Strahler AN","year":"1953","unstructured":"Strahler AN. 1953 Revision of Horton's quantitative factors in erosional terrain. Trans. Am. Geophys. Union 34, 345.","journal-title":"Trans. Am. Geophys. Union"},{"key":"e_1_3_7_133_2","doi-asserted-by":"publisher","DOI":"10.1029\/TR038i006p00913"},{"key":"e_1_3_7_134_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02713917"},{"key":"e_1_3_7_135_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02368246"},{"key":"e_1_3_7_136_2","doi-asserted-by":"publisher","DOI":"10.1152\/ajpheart.1994.267.6.H2100"},{"key":"e_1_3_7_137_2","first-page":"230","volume-title":"Proc. Symp. Pulmonary Circulation, Sicily, 16\u201321 July","author":"Cumming G","year":"1970","unstructured":"Cumming G, Harding LK, Horsfield K, Prowse K, Singhal SS, Woldenberg MJ. 1970 Morphological aspects of the pulmonary circulation and of the airway. In Proc. Symp. Pulmonary Circulation, Sicily, 16\u201321 July (eds G Cumming, G Bonsignore), pp. 230-236. New York, NY: Springer."},{"key":"e_1_3_7_138_2","unstructured":"Shah V. 2007 A user friendly multiscale lung modelling suite and application. Master of science thesis Drexel University."},{"key":"e_1_3_7_139_2","first-page":"253","article-title":"The pulmonary artery seen as a convergent tree","author":"Horsfield K","year":"1994","unstructured":"Horsfield K. 1994 The pulmonary artery seen as a convergent tree. In The pulmonary circulation and gas exchange (eds WW Wagner, EK Weir), pp. 253\u2013 264. Armonk, NY: Futura Publishing.","journal-title":"The pulmonary circulation and gas exchange"},{"key":"e_1_3_7_140_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1971.31.2.207"},{"key":"e_1_3_7_141_2","doi-asserted-by":"publisher","DOI":"10.1161\/01.STR.24.3.371"},{"key":"e_1_3_7_142_2","doi-asserted-by":"publisher","DOI":"10.1002\/ar.23994"},{"key":"e_1_3_7_143_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8502(90)90288-9"},{"key":"e_1_3_7_144_2","doi-asserted-by":"publisher","DOI":"10.1089\/jam.1990.3.27"},{"key":"e_1_3_7_145_2","first-page":"275","volume-title":"Lung Development and Regeneration","author":"Schittny JC","year":"2004","unstructured":"Schittny JC, Burri PH. 2004 Morphogenesis of the mammalian lung: aspects of structure and extracellular matrix. In Lung Development and Regeneration (eds DJ Massaro, GD Massaro, P Chambon), pp. 275-317. New York, NY: Marcel Dekker."},{"key":"e_1_3_7_146_2","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0177(2000)9999:9999<::AID-DVDY1053>3.3.CO;2-8"},{"key":"e_1_3_7_147_2","volume-title":"Principles of animal design","author":"Weibel ER","year":"1998","unstructured":"Weibel ER, Taylor CR, Bolis L (eds). 1998 Principles of animal design. Cambridge, UK: Cambridge University Press."},{"key":"e_1_3_7_148_2","volume-title":"Symmorphosis: on form and function in shaping life","author":"Weibel ER","year":"2000","unstructured":"Weibel ER. 2000 Symmorphosis: on form and function in shaping life. Cambridge, MA: Harvard University Press."},{"key":"e_1_3_7_149_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-597203-1.50010-5"},{"key":"e_1_3_7_150_2","volume-title":"Shape and structure from engineering to nature","author":"Bejan A","year":"2000","unstructured":"Bejan A. 2000 Shape and structure from engineering to nature. Cambridge, UK: Cambridge University Press."},{"key":"e_1_3_7_151_2","volume-title":"Design in nature: how the constructal law governs evolution in biology, physics, technology and social organizations","author":"Bejan A","year":"2012","unstructured":"Bejan A, Zane JP. 2012 Design in nature: how the constructal law governs evolution in biology, physics, technology and social organizations. New York, NY: Doubleday."},{"key":"e_1_3_7_152_2","volume-title":"The latest on the best: essays on evolution and optimality","author":"Dupre J","year":"1987","unstructured":"Dupre J. (ed.) 1987 The latest on the best: essays on evolution and optimality. Cambridge, MA: MIT Press."},{"key":"e_1_3_7_153_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01920238"},{"key":"e_1_3_7_154_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.284.5420.1635"},{"key":"e_1_3_7_155_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature07005"},{"key":"e_1_3_7_156_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0070-2153(07)81010-6"},{"key":"e_1_3_7_157_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0070-2153(10)90003-3"},{"key":"e_1_3_7_158_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.devcel.2009.12.010"},{"key":"e_1_3_7_159_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-44153-5_5"},{"key":"e_1_3_7_160_2","doi-asserted-by":"publisher","DOI":"10.1186\/1742-9994-9-16"},{"key":"e_1_3_7_161_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20395-4"},{"key":"e_1_3_7_162_2","doi-asserted-by":"publisher","DOI":"10.1002\/path.1711690316"},{"key":"e_1_3_7_163_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0966-6362(00)00094-1"},{"key":"e_1_3_7_164_2","doi-asserted-by":"publisher","DOI":"10.1183\/09031936.00135909"},{"key":"e_1_3_7_165_2","doi-asserted-by":"publisher","DOI":"10.4187\/respcare.01411"},{"key":"e_1_3_7_166_2","volume-title":"Life in moving fluids: the physical biology of flow","author":"Vogel S","year":"1981","unstructured":"Vogel S. 1981 Life in moving fluids: the physical biology of flow. Princeton, NJ: Princeton University Press."},{"key":"e_1_3_7_167_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0034-5687(96)02506-6"},{"key":"e_1_3_7_168_2","volume-title":"Invention and evolution design in nature and engineering","author":"French MJ","year":"1988","unstructured":"French MJ. 1988 Invention and evolution design in nature and engineering. Cambridge, UK: Cambridge University Press."},{"key":"e_1_3_7_169_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325852"},{"key":"e_1_3_7_170_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02301268"},{"key":"e_1_3_7_171_2","first-page":"54","article-title":"The design of fluid transport systems in organisms","volume":"70","author":"LaBarbera M","year":"1982","unstructured":"LaBarbera M, Vogel S. 1982 The design of fluid transport systems in organisms. Am. Sci. 70, 54-70.","journal-title":"Am. Sci."},{"key":"e_1_3_7_172_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.4033966"},{"key":"e_1_3_7_173_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(84)80089-2"},{"key":"e_1_3_7_174_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02476705"},{"key":"e_1_3_7_175_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0092-8240(74)80030-3"},{"key":"e_1_3_7_176_2","doi-asserted-by":"publisher","DOI":"10.1085\/jgp.67.2.213"},{"key":"e_1_3_7_177_2","doi-asserted-by":"publisher","DOI":"10.1139\/y86-109"},{"key":"e_1_3_7_178_2","doi-asserted-by":"publisher","DOI":"10.1085\/jgp.69.4.449"},{"key":"e_1_3_7_179_2","first-page":"109","article-title":"Factors of safety in the structure of animals","volume":"67","author":"Alexander RMcN","year":"1981","unstructured":"Alexander RMcN. 1981 Factors of safety in the structure of animals. Sci. Prog. 67, 109-130.","journal-title":"Sci. Prog."},{"key":"e_1_3_7_180_2","first-page":"28","volume-title":"Principles of animal design: the optimization and symmorphosis debate","author":"Alexander RMCN","year":"1998","unstructured":"Alexander RMCN. 1998 Symmorphosis and safety factors. In Principles of animal design: the optimization and symmorphosis debate (eds ER Weibel, CR Taylor, L Bolis), pp. 28-35. Cambridge, UK: Cambridge University Press."},{"key":"e_1_3_7_181_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2015.10.027"},{"key":"e_1_3_7_182_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-5049-8_2"},{"key":"e_1_3_7_183_2","doi-asserted-by":"publisher","DOI":"10.1130\/0016-7606(1945)56[275:EDOSAT]2.0.CO;2"},{"key":"e_1_3_7_184_2","first-page":"45","article-title":"Studies of longitudinal stream profiles in Virginia and Maryland","volume":"294","author":"Hack JT","year":"1957","unstructured":"Hack JT. 1957 Studies of longitudinal stream profiles in Virginia and Maryland. US Geol. Surv. Prof. Pap. 294B, 45-97.","journal-title":"US Geol. Surv. Prof. Pap."},{"key":"e_1_3_7_185_2","volume-title":"Fractal river basins","author":"Rodriguez-Iturbe I","year":"1997","unstructured":"Rodriguez-Iturbe I, Rinaldo A. 1997 Fractal river basins. New York, NY: Cambridge University Press."},{"key":"e_1_3_7_186_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomorph.2012.01.002"},{"key":"e_1_3_7_187_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfluidstructs.2009.11.004"},{"key":"e_1_3_7_188_2","unstructured":"Sochi T. 2013 Fluid flow at branching junctions. arXiv : 1309.0227vl."},{"key":"e_1_3_7_189_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2009.10.037"},{"key":"e_1_3_7_190_2","doi-asserted-by":"publisher","DOI":"10.1620\/tjem.79.168"},{"key":"e_1_3_7_191_2","first-page":"241","volume-title":"Principles of animal design: the optimization and symmorphosis debate","author":"Jones JH","year":"1998","unstructured":"Jones JH. 1998 Symmorphosis and the mammalian respiratory system: what is optimal design and does it exist? In Principles of animal design: the optimization and symmorphosis debate (eds ER Weibel, CR Taylor, L Bolis), pp. 241-248. Cambridge, UK: Cambridge University Press."},{"key":"e_1_3_7_192_2","first-page":"1","volume-title":"Principles of animal design: the optimization and symmorphosis debate","author":"Weibel ER","year":"1998","unstructured":"Weibel ER. 1998 Symmorphosis and optimization of biological design: Introduction and questions. In Principles of animal design: the optimization and symmorphosis debate (eds ER Weibel, CR Taylor, L Bolis), pp. 1-10. Cambridge, UK: Cambridge University Press."},{"key":"e_1_3_7_193_2","first-page":"21","volume-title":"Principles of animal design: the optimization and symmorphosis debate","author":"Diamond JD","year":"1998","unstructured":"Diamond JD 1998 Evolution of biological safety factors: a cost-benefit analysis. In Principles of animal design: the optimization and symmorphosis debate (eds ER Weibel, CR Taylor, L Bolis), pp. 21-27. Cambridge, UK: Cambridge University Press."},{"key":"e_1_3_7_194_2","volume-title":"Biometry: the principles and practices of statistics in biological research","author":"Sokal RR","year":"1994","unstructured":"Sokal RR, Roff FJ. 1994 Biometry: the principles and practices of statistics in biological research, 3rd edn. New York, NY: WH Freeman.","edition":"3"},{"key":"e_1_3_7_195_2","volume-title":"Statistics at square One","author":"Swinscow TDV","year":"2002","unstructured":"Swinscow TDV, Campbell MJ. 2002 Statistics at square One, 10th edn. London, UK: BMJ Publishing Group.","edition":"10"},{"key":"e_1_3_7_196_2","volume-title":"Respiratory physiology: the essentials","author":"West JB","year":"2000","unstructured":"West JB. 2000 Respiratory physiology: the essentials, 6th edn. Baltimore, MD: Lippincott Williams & Wilkins.","edition":"6"},{"key":"e_1_3_7_197_2","first-page":"100","volume-title":"Introduction to molecular biology: from physiology to pathophysiology","author":"Gosney JR","year":"1998","unstructured":"Gosney JR. 1998 Pulmonary hypertension. In Introduction to molecular biology: from physiology to pathophysiology (eds A Halliday, BJ Hunt, L Poston, M Schachter), pp. 100-111. Cambridge, UK: Cambridge University Press."},{"key":"e_1_3_7_198_2","volume-title":"A textbook of histology","author":"Bloom W","year":"1975","unstructured":"Bloom W, Fawcett DW. 1975 A textbook of histology, 10th edn. New York, NY: Chapman and Hall.","edition":"10"},{"key":"e_1_3_7_199_2","volume-title":"Text\/atlas of histology","author":"Leeson TS","year":"1988","unstructured":"Leeson TS, Leeson CR, Paparo AA 1988 Text\/atlas of histology. Philadelphia, PA: WB Saunders Company."},{"key":"e_1_3_7_200_2","volume-title":"Applied veterinary histology","author":"Banks WJ","year":"1986","unstructured":"Banks WJ 1986 Applied veterinary histology, 2nd edn. Baltimore, MD: Williams & Wilkins.","edition":"2"},{"key":"e_1_3_7_201_2","doi-asserted-by":"publisher","DOI":"10.1152\/jappl.1993.75.4.1877"},{"key":"e_1_3_7_202_2","doi-asserted-by":"publisher","DOI":"10.1002\/ar.1091900202"}],"container-title":["Open Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsob.190249","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rsob.190249","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsob.190249","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,23]],"date-time":"2022-11-23T14:13:37Z","timestamp":1669212817000},"score":1,"resource":{"primary":{"URL":"https:\/\/royalsocietypublishing.org\/doi\/10.1098\/rsob.190249"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7]]},"references-count":201,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["10.1098\/rsob.190249"],"URL":"https:\/\/doi.org\/10.1098\/rsob.190249","relation":{},"ISSN":["2046-2441"],"issn-type":[{"value":"2046-2441","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7]]},"assertion":[{"value":"2019-10-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-06-12","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-07-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"190249"}}