Grahp and automata in arterial vascular tree of the kidney

Abstract

"The renal vascular development is not known and occurs through two mechanisms that sometimes overlap: vasculogenesis and angiogenesis. Here we only consider growth through angiogenesis, i.e., the arterial vascular tree of the kidney. There are two types of vascular angiogenesis in development: sprouting and splitting an- giogenesis. We study these processes through mathematical tools. The graphs and automatas allow modeling the vascular growth, can generated tree structures by incorporating the physiological laws of the arterial branching. That is, the graph prescribes topology of the vascular tree and the automaton can include the rule of dynamics in the phenomena of vascularization."