NDLI: Murray’s law and the bifurcation angle in the arterial micro-circulation system and their application to the design of microfluidics

Content Provider	Springer Nature Link
Author	Lee, Jung Yeop Lee, Sang Joon
Copyright Year	2009
Abstract	Murray’s law which is related to the bifurcations of vascular blood vessels states that the cube of a parent vessel’s diameter equals the sum of the cubes of the daughter vessels’ diameters $$ D_{0}^{3} = D_{1}^{3} + D_{2}^{3} ,\,\alpha = D_{0}^{3} /\left( {D_{1}^{3} + D_{2}^{3} } \right) = 1, $$ where D 0, D 1, and D 2 are the diameters of the parent and two daughter vessels, respectively and α is the ratio). The structural characteristics of the vessels are crucial in the development of the cardiovascular system as well as for the proper functioning of an organism. In order to understand the vascular circulation system, it is essential to understand the design rules or scaling laws of the system under a homeostatic condition. In this study, Murray’s law in the extraembryonic arterial bifurcations and its relationship with the bifurcation angle (θ) using 3-day-old chicken embryos in vivo has been investigated. Bifurcation is an important geometric factor in biological systems, having a significant influence on the circulation in the vascular system. Parameters such as diameter and bifurcation angle of all the 140 vessels tested were measured using image analysis softwares. The experimental results for α (= 1.053 ± 0.188) showed a good agreement with the ratio of 1 for Murray’s law. Furthermore, the diameter relation α approached the theoretical value of 1 as the diameter of parent vessel D 0 decreased below 100 μm. The bifurcation angle θ decreased as D 0 increased and vice versa. For the arterial bifurcations of chicken embryos tested in this study, the bifurcation pattern appears to be symmetric (D 1 = D 2). The bifurcation angle exhibited a nearly constant value of 77°, close to the theoretical value of 75° for a symmetric bifurcation.
Starting Page	85
Ending Page	95
Page Count	11
File Format	PDF
ISSN	16134982
Journal	Microfluidics and Nanofluidics
Volume Number	8
Issue Number	1
e-ISSN	16134990
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-05-16
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Murray’s law Cubic relationship Arterial bifurcation Micro-circulation Bifurcation angle Minimum work principle Design rule Biomedical Engineering Engineering Fluid Dynamics
Content Type	Text
Resource Type	Article
Subject	Nanoscience and Nanotechnology Materials Chemistry Condensed Matter Physics Electronic, Optical and Magnetic Materials

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