## 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) |
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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 |

## All Science Journal Classification (ASJC) codes

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