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.
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December 2012
In-Brief
Murray's Law in Elastin Haploinsufficient (Eln+/−) and Wild-Type (WT) Mice
Bradley A. Sather,
Bradley A. Sather
Department of Biomedical Engineering,
Saint Louis University
,3507 Lindell Blvd.
,Saint Louis, MO 63103
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Daniel Hageman,
Daniel Hageman
Department of Biomedical Engineering,
Case Western Reserve University
,Cleveland, OH 44106
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Jessica E. Wagenseil
Jessica E. Wagenseil
1
Department of Biomedical Engineering,
e-mail: jwagense@slu.edu
Saint Louis University
,3507 Lindell Blvd.
,Saint Louis, MO 63103
e-mail: jwagense@slu.edu
1Corresponding author.
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Bradley A. Sather
Department of Biomedical Engineering,
Saint Louis University
,3507 Lindell Blvd.
,Saint Louis, MO 63103
Daniel Hageman
Department of Biomedical Engineering,
Case Western Reserve University
,Cleveland, OH 44106
Jessica E. Wagenseil
Department of Biomedical Engineering,
e-mail: jwagense@slu.edu
Saint Louis University
,3507 Lindell Blvd.
,Saint Louis, MO 63103
e-mail: jwagense@slu.edu
1Corresponding author.
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.
J Biomech Eng. Dec 2012, 134(12): 124504 (3 pages)
Published Online: December 5, 2012
Article history
Received:
June 25, 2012
Revision Received:
November 6, 2012
Accepted:
November 28, 2012
Citation
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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