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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
