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 a branch of discrete mathematics that is excellently suited to model vascular networks and to analyze their properties (invariants). 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 growth of the network 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 is given to support this conjecture.
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Cha, SH., Gargano, M.L., Quintas, L.V., Wahl, E.M. (2005). A Vascular Network Growth Estimation Algorithm Using Random Graphs. In: Brun, L., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2005. Lecture Notes in Computer Science, vol 3434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31988-7_5
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DOI: https://doi.org/10.1007/978-3-540-31988-7_5
Publisher Name: Springer, Berlin, Heidelberg
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