Using either the principle of minimum energy or constant shear stress, a relation can be derived that predicts the diameters of branching vessels at a bifurcation. This relation, known as Murray's Law, has been shown to predict vessel diameters in a variety of cardiovascular 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 (Eln+/−). Elastin is one of the major proteins in the blood vessel wall and is organized in concentric rings, known as lamellae, with smooth muscle cells (SMCs) around the vessel lumen. Eln+/− 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, Eln+/− vessels would not follow Murray's Law. We examined vessel bifurcations in six different physiologic regions, including the brain, heart, epidermis, ceocum (or cecum), testes, and intestines, in Eln+/− mice and wild-type (WT) littermates. All vessels were between 40 and 300 μm in diameter. We found that the diameters of both Eln+/− and WT vessels have an average 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 Murray's Law, despite limitations on the proteins available for growth and remodeling of the vessel wall.
Murray's Law in Elastin Haploinsufficient (Eln+/−) and Wild-Type (WT) Mice
Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING Manuscript received June 25, 2012; final manuscript received November 15, 2012; accepted manuscript posted November 28, 2012; published online December 5, 2012. Assoc. Editor: Kevin D. Costa.
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Sather, B. A., Hageman, D., and Wagenseil, J. E. (December 5, 2012). "Murray's Law in Elastin Haploinsufficient (Eln+/−) and Wild-Type (WT) Mice." ASME. J Biomech Eng. December 2012; 134(12): 124504. https://doi.org/10.1115/1.4023093
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