### 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 language | English (US) |
---|---|

Pages (from-to) | 91-103 |

Number of pages | 13 |

Journal | Machine Graphics and Vision |

Volume | 17 |

Issue number | 1-2 |

State | Published - Aug 21 2008 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Machine Graphics and Vision*,

*17*(1-2), 91-103.

}

*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.

Research output: Contribution to journal › Article

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.

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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 -