A graph theory analysis of renal glomerular microvascular networks

Eric M. Wahl; Louis V. Quintas; Lorraine L. Lurie; Michael L. Gargano

doi:10.1016/j.mvr.2003.11.005

A graph theory analysis of renal glomerular microvascular networks

Eric M. Wahl, Louis V. Quintas, Lorraine L. Lurie, Michael L. Gargano

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

A graph theory model and its invariants are used to compare previously published renal glomerular networks of six adult rats, one adult uremic rat, and one newborn rat. Invariants calculated include order, size, cycle rank, eccentricity, root distance, planarity, and vertex degree distribution. These invariants enabled the differentiation of six normal adult glomerular microvascular networks from that of the uremic glomerulus and from that of the normal newborn glomerulus. These invariants might then be used to differentiate between normal and pathological vascular networks. Also proposed are graph theory invariants that might be used to develop a quantitative model for angiogenesis.

Original language	English
Pages (from-to)	223-230
Number of pages	8
Journal	Microvascular Research
Volume	67
Issue number	3
DOIs	https://doi.org/10.1016/j.mvr.2003.11.005
State	Published - May 2004
Externally published	Yes

Keywords

Angiogenesis
Glomerulus
Graph theory
Microvasculature
Renal glomerular network
Uremia
Vascular branching patterns

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10.1016/j.mvr.2003.11.005

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title = "A graph theory analysis of renal glomerular microvascular networks",

abstract = "A graph theory model and its invariants are used to compare previously published renal glomerular networks of six adult rats, one adult uremic rat, and one newborn rat. Invariants calculated include order, size, cycle rank, eccentricity, root distance, planarity, and vertex degree distribution. These invariants enabled the differentiation of six normal adult glomerular microvascular networks from that of the uremic glomerulus and from that of the normal newborn glomerulus. These invariants might then be used to differentiate between normal and pathological vascular networks. Also proposed are graph theory invariants that might be used to develop a quantitative model for angiogenesis.",

keywords = "Angiogenesis, Glomerulus, Graph theory, Microvasculature, Renal glomerular network, Uremia, Vascular branching patterns",

author = "Wahl, {Eric M.} and Quintas, {Louis V.} and Lurie, {Lorraine L.} and Gargano, {Michael L.}",

note = "Funding Information: This work was supported in part by The Dyson College of Arts and Sciences and The School of Computer Science and Information Systems, Pace University.",

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AU - Wahl, Eric M.

AU - Quintas, Louis V.

AU - Lurie, Lorraine L.

AU - Gargano, Michael L.

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PY - 2004/5

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AB - A graph theory model and its invariants are used to compare previously published renal glomerular networks of six adult rats, one adult uremic rat, and one newborn rat. Invariants calculated include order, size, cycle rank, eccentricity, root distance, planarity, and vertex degree distribution. These invariants enabled the differentiation of six normal adult glomerular microvascular networks from that of the uremic glomerulus and from that of the normal newborn glomerulus. These invariants might then be used to differentiate between normal and pathological vascular networks. Also proposed are graph theory invariants that might be used to develop a quantitative model for angiogenesis.

KW - Angiogenesis

KW - Glomerulus

KW - Graph theory

KW - Microvasculature

KW - Renal glomerular network

KW - Uremia

KW - Vascular branching patterns

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JO - Microvascular Research

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A graph theory analysis of renal glomerular microvascular networks

Abstract

Keywords

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