Estimating a vascular network growth using random graphs

Sung Hyuk Cha, Michael L. Gargano, Sukmoon Chang, Louis V. Quintas, Eric M. Wahl

Research output: Contribution to journalArticle

Abstract

Vascular networks develop by way of angiogenesis, a growth process that involves the biological mechanisms of vessel sprouting (budding) and splitting (intussusception). Graph theory is excellently suited to model vascular networks and to analyze their properties (invariants). In particular, a random graph process model can simulate the development of a vascular network that has been modeled using graph theory. The renal glomerulus is one example of such a vascular network. Here the correlation between the invariants of this vascular network modeled as a graph and the mechanisms of the network growth using a random graph process are studied. It is proposed that the relative frequencies of sprouting and splitting during the growth of a given renal glomerulus can be estimated by the invariants (root distance, radius, and diameter) of the graph representing the renal glomerulus network. Experimental evidence has been given to support this conjecture.

Original languageEnglish (US)
Pages (from-to)91-103
Number of pages13
JournalMachine Graphics and Vision
Volume17
Issue number1-2
StatePublished - Aug 21 2008

Fingerprint

Graph theory

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

Cite this

Cha, S. H., Gargano, M. L., Chang, S., Quintas, L. V., & Wahl, E. M. (2008). Estimating a vascular network growth using random graphs. Machine Graphics and Vision, 17(1-2), 91-103.
Cha, Sung Hyuk ; Gargano, Michael L. ; Chang, Sukmoon ; Quintas, Louis V. ; Wahl, Eric M. / Estimating a vascular network growth using random graphs. In: Machine Graphics and Vision. 2008 ; Vol. 17, No. 1-2. pp. 91-103.
@article{7d220a1622354128a469455669f3cf84,
title = "Estimating a vascular network growth using random graphs",
abstract = "Vascular networks develop by way of angiogenesis, a growth process that involves the biological mechanisms of vessel sprouting (budding) and splitting (intussusception). Graph theory is excellently suited to model vascular networks and to analyze their properties (invariants). In particular, a random graph process model can simulate the development of a vascular network that has been modeled using graph theory. The renal glomerulus is one example of such a vascular network. Here the correlation between the invariants of this vascular network modeled as a graph and the mechanisms of the network growth using a random graph process are studied. It is proposed that the relative frequencies of sprouting and splitting during the growth of a given renal glomerulus can be estimated by the invariants (root distance, radius, and diameter) of the graph representing the renal glomerulus network. Experimental evidence has been given to support this conjecture.",
author = "Cha, {Sung Hyuk} and Gargano, {Michael L.} and Sukmoon Chang and Quintas, {Louis V.} and Wahl, {Eric M.}",
year = "2008",
month = "8",
day = "21",
language = "English (US)",
volume = "17",
pages = "91--103",
journal = "Machine Graphics and Vision",
issn = "1230-0535",
publisher = "Polska Akademia Nauk",
number = "1-2",

}

Cha, SH, Gargano, ML, Chang, S, Quintas, LV & Wahl, EM 2008, 'Estimating a vascular network growth using random graphs', Machine Graphics and Vision, vol. 17, no. 1-2, pp. 91-103.

Estimating a vascular network growth using random graphs. / Cha, Sung Hyuk; Gargano, Michael L.; Chang, Sukmoon; Quintas, Louis V.; Wahl, Eric M.

In: Machine Graphics and Vision, Vol. 17, No. 1-2, 21.08.2008, p. 91-103.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Estimating a vascular network growth using random graphs

AU - Cha, Sung Hyuk

AU - Gargano, Michael L.

AU - Chang, Sukmoon

AU - Quintas, Louis V.

AU - Wahl, Eric M.

PY - 2008/8/21

Y1 - 2008/8/21

N2 - Vascular networks develop by way of angiogenesis, a growth process that involves the biological mechanisms of vessel sprouting (budding) and splitting (intussusception). Graph theory is excellently suited to model vascular networks and to analyze their properties (invariants). In particular, a random graph process model can simulate the development of a vascular network that has been modeled using graph theory. The renal glomerulus is one example of such a vascular network. Here the correlation between the invariants of this vascular network modeled as a graph and the mechanisms of the network growth using a random graph process are studied. It is proposed that the relative frequencies of sprouting and splitting during the growth of a given renal glomerulus can be estimated by the invariants (root distance, radius, and diameter) of the graph representing the renal glomerulus network. Experimental evidence has been given to support this conjecture.

AB - Vascular networks develop by way of angiogenesis, a growth process that involves the biological mechanisms of vessel sprouting (budding) and splitting (intussusception). Graph theory is excellently suited to model vascular networks and to analyze their properties (invariants). In particular, a random graph process model can simulate the development of a vascular network that has been modeled using graph theory. The renal glomerulus is one example of such a vascular network. Here the correlation between the invariants of this vascular network modeled as a graph and the mechanisms of the network growth using a random graph process are studied. It is proposed that the relative frequencies of sprouting and splitting during the growth of a given renal glomerulus can be estimated by the invariants (root distance, radius, and diameter) of the graph representing the renal glomerulus network. Experimental evidence has been given to support this conjecture.

UR - http://www.scopus.com/inward/record.url?scp=49549099777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549099777&partnerID=8YFLogxK

M3 - Article

VL - 17

SP - 91

EP - 103

JO - Machine Graphics and Vision

JF - Machine Graphics and Vision

SN - 1230-0535

IS - 1-2

ER -

Cha SH, Gargano ML, Chang S, Quintas LV, Wahl EM. Estimating a vascular network growth using random graphs. Machine Graphics and Vision. 2008 Aug 21;17(1-2):91-103.