# Blood Vessel Branching: Beyond the Standard Calculus Problem

by John A. Adam (Old Dominion University)

Year of Award: 2012

Award: Allendoerfer

Publication Information: Mathematics Magazine, vol. 84, 2011, pp. 196-207

Summary: The author first lays the groundwork by discussing the underlying biological setting, specifying his simplifying assumptions, and introducing some necessary equations from fluid dynamics. He then develops a sequence of models for blood vessel branching based upon a series of ever more comprehensive "cost functionals." The most sophisticated of these models implies certain empirical laws for vascular branching proposed by Wilhelm Roux in 1878, and also yields estimates for the total length of the vascular system.