A generalization of the optimal models of arterial branching

Optimal models of arterial branching angles are usually based on the assumption that the equation relating flow and radius is given byf=kr ³, as proposed by Murray in 1926. An exception is the model of Uylings (1977), in which he allowed the exponent ofr to vary from 2.33 to 3.0. Theoretical considerations coupled with empirical evidence suggest that the cubic flow equation may not be appropriate to describe the branching pattern of the arterial tree. The optimal models are modified to accommodate a more general flow equationf=kr ^x . Models that minimize a geometric feature such as surface or volume are sensitive to variations inx in a different way from those which minimize flow-related parameters, such as power loss due to friction and shear stress.