Fundamental principles of vascular network topology

The vascular system is arguably the most important biological system in many organisms. Although the general principles of its architecture are simple, the growth of blood vessels occurs under extreme physical conditions. Optimization is an important aspect of the development of computational models of the vascular branching structures. This review surveys the approaches used to optimize the topology and estimate different geometrical parameters of the vascular system. The review is focused on optimizations using complex cost functions based on the minimum total energy principle and the relationship between the laws of growth and precise vascular network topology. Experimental studies of vascular networks in different species are also discussed.