A graph theory model of the glomerular capillary network and its development

Eric M. Wahl; Frederick H. Daniels; E. F. Leonard; Cyrus Levinthal; Stanley Cortell

doi:10.1016/0026-2862(84)90044-X

A graph theory model of the glomerular capillary network and its development

Eric M. Wahl, Frederick H. Daniels, E. F. Leonard, Cyrus Levinthal, Stanley Cortell

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Abstract

Graph theory methods were used to analyze the topology of the renal glomerular capillary network using data both from a serial reconstruction of a rat glomerulus and from the literature. The graphs obtained were tested for planarity, and all but one were found to be nonplanar. This result indicated that the development of the glomerular capillary network must include a nonplanar growth process, and new growth models were proposed. In addition, the statistical properties of capillary branching patterns were analyzed, and a node degree distribution function estimate was obtained.

Original language	English
Pages (from-to)	96-109
Number of pages	14
Journal	Microvascular Research
Volume	27
Issue number	1
DOIs	https://doi.org/10.1016/0026-2862(84)90044-X
State	Published - Jan 1984
Externally published	Yes

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title = "A graph theory model of the glomerular capillary network and its development",

abstract = "Graph theory methods were used to analyze the topology of the renal glomerular capillary network using data both from a serial reconstruction of a rat glomerulus and from the literature. The graphs obtained were tested for planarity, and all but one were found to be nonplanar. This result indicated that the development of the glomerular capillary network must include a nonplanar growth process, and new growth models were proposed. In addition, the statistical properties of capillary branching patterns were analyzed, and a node degree distribution function estimate was obtained.",

author = "Wahl, \{Eric M.\} and Daniels, \{Frederick H.\} and Leonard, \{E. F.\} and Cyrus Levinthal and Stanley Cortell",

note = "Funding Information: {\textquoteright} This work was supported in part by grants from the National Institutes of Health (RR-00442) and the research funds of St. Luke{\textquoteright}s Hospital.",

year = "1984",

month = jan,

doi = "10.1016/0026-2862(84)90044-X",

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journal = "Microvascular Research",

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T1 - A graph theory model of the glomerular capillary network and its development

AU - Wahl, Eric M.

AU - Daniels, Frederick H.

AU - Leonard, E. F.

AU - Levinthal, Cyrus

AU - Cortell, Stanley

N1 - Funding Information: ’ This work was supported in part by grants from the National Institutes of Health (RR-00442) and the research funds of St. Luke’s Hospital.

PY - 1984/1

Y1 - 1984/1

N2 - Graph theory methods were used to analyze the topology of the renal glomerular capillary network using data both from a serial reconstruction of a rat glomerulus and from the literature. The graphs obtained were tested for planarity, and all but one were found to be nonplanar. This result indicated that the development of the glomerular capillary network must include a nonplanar growth process, and new growth models were proposed. In addition, the statistical properties of capillary branching patterns were analyzed, and a node degree distribution function estimate was obtained.

AB - Graph theory methods were used to analyze the topology of the renal glomerular capillary network using data both from a serial reconstruction of a rat glomerulus and from the literature. The graphs obtained were tested for planarity, and all but one were found to be nonplanar. This result indicated that the development of the glomerular capillary network must include a nonplanar growth process, and new growth models were proposed. In addition, the statistical properties of capillary branching patterns were analyzed, and a node degree distribution function estimate was obtained.

UR - https://www.scopus.com/pages/publications/0021321059

U2 - 10.1016/0026-2862(84)90044-X

DO - 10.1016/0026-2862(84)90044-X

M3 - Article

C2 - 6708827

AN - SCOPUS:0021321059

SN - 0026-2862

VL - 27

SP - 96

EP - 109

JO - Microvascular Research

JF - Microvascular Research

IS - 1

ER -

A graph theory model of the glomerular capillary network and its development

Abstract

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