Murray's Law in Elastin Haploinsufficient (Eln+/−) and Wild-Type (WT) Mice

Using either the principle of minimum energy or constant shear stress, a relation can be derived that predicts the diameters of branch-ing vessels at a bifurcation. This relation, known as Murray’s Law, has been shown to predict vessel diameters in a variety of cardiovas-cular systems from adult humans to developing chicks. The goal of this study is to investigate Murray’s Law in vessels from mice that are haploinsufficient for the elastin protein (Elnþ/). Elastin is one of the major proteins in the blood vessel wall and is organized in con-centric rings, known as lamellae, with smooth muscle cells (SMCs) around the vessel lumen. Elnþ/ mice have an increased number of lamellae, as well as smaller, thinner vessels. It is possible that due to decreased amounts of elastin available for vessel wall remodeling during development and in adulthood, Elnþ/ vessels would not fol-low Murray’s Law. We examined vessel bifurcations in six different physiologic regions, including the brain, heart, epidermis, ceocum (or cecum), testes, and intestines, in Elnþ/ mice and wild-type (WT) littermates. All vessels were between 40 and 300lm in diameter. We found that the diameters of both Elnþ/ and WT vessels have an av-erage of 13 % error from the diameters predicted by Murray’s Law, with no significant differences between genotypes or physiologic regions. The data suggest that vessels are optimized to follow Mur-ray’s Law, despite limitations on the proteins available for growth and remodeling of the vessel wall. [DOI: 10.1115/1.4023093