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

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...

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Published inMicrovascular research Vol. 27; no. 1; pp. 96 - 109
Main Authors Wahl, Eric M., Daniels, Frederick H., Leonard, E.F., Levinthal, Cyrus, Cortell, Stanley
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 1984
Elsevier
Subjects
Animals
Biological and medical sciences
Capillaries - growth & development
Fundamental and applied biological sciences. Psychology
Kidney Glomerulus - blood supply
Kidney Glomerulus - growth & development
Male
Mathematics
Microcirculation - growth & development
Microcomputers
Models, Cardiovascular
Rats
Rats, Inbred Strains
Vertebrates: urinary system
Renal glomerulus
Microcirculation
Vertebrata
Mammalia
Urinary system
Rat
Rodentia
Blood capillary
Models
Circulatory system
Kidney
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0026-2862
1095-9319
DOI:10.1016/0026-2862(84)90044-X