title: A mathematical representation for vessel network III.
abstract: The loop vascular network is found frequently within biological tissue, but a schematic characterization of the loop vascular network is at present difficult to describe. The reason is that the topographical feature of vessel loop can change during maturation. In this article, we treat the mathematical representation of the loop vessel network, and discuss the application of this to the increased vascular resistance in hypertensive animals resulting from microvascular rarefaction. On the other hand, the number of regions into which the tissue plane is divided by n bifurcational tree branches is derived from recurrence relation.
mesh_terms: D001160:Arterioles / Q000502:physiology; D001808:Blood Vessels / Q000502:physiology*; D002196:Capillaries / Q000502:physiology; D006801:Humans; D008433:Mathematics; D008833:Microcirculation; D008955:Models, Cardiovascular; D014655:Vascular Resistance; D014699:Venules / Q000502:physiology