scholarly journals Using Murray’s law to design artificial vascular microfluidic networks

2006 ◽  
Author(s):  
R. W. Barber ◽  
K. Cieślicki ◽  
D. R. Emerson
Keyword(s):  
Murray's Law ◽  
Murray’S Law ◽  
Microfluidic Networks

scholarly journals Murray’s law for discrete and continuum models of biological networks

2019 ◽  
Vol 29 (12) ◽  
pp. 2359-2376
Author(s):  
Jan Haskovec ◽  
Peter Markowich ◽  
Giulia Pilli
Keyword(s):  
Biological Networks ◽  
Discrete Model ◽  
Continuum Model ◽  
Transportation Network ◽  
Continuum Models ◽  
Scaling Relation ◽  
Murray's Law ◽  
Murray’S Law ◽  
Rectangular Mesh ◽  
The Continuum

We demonstrate the validity of Murray’s law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray’s law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray’s law for its linearly stable steady states.

scholarly journals Seeking minimum entropy production for a tree-like flow-field in a fuel cell

2020 ◽  
Vol 22 (13) ◽  
pp. 6993-7003 ◽  
Author(s):  
Marco Sauermoser ◽  
Signe Kjelstrup ◽  
Natalya Kizilova ◽  
Bruno G. Pollet ◽  
Eirik G. Flekkøy
Keyword(s):  
Fuel Cell ◽  
Flow Field ◽  
Entropy Production ◽  
Minimum Entropy ◽  
Murray's Law ◽  
Field Patterns ◽  
Murray’S Law ◽  
Minimum Entropy Production

We show how we can improve bio-inspired flow field patterns for use in PEMFCs by deviating from Murray's law.

Deviation from Murray's law is associated with a higher degree of calcification in coronary bifurcations

2012 ◽  
Vol 221 (1) ◽  
pp. 124-130 ◽  
Author(s):  
Andreas W. Schoenenberger ◽  
Nadja Urbanek ◽  
Stefan Toggweiler ◽  
Robert Seelos ◽  
Peiman Jamshidi ◽  
...  
Keyword(s):  
Murray's Law ◽  
Murray’S Law

scholarly journals Optimal fractal tree-like microchannel networks with slip for laminar-flow-modified Murray’s law

2018 ◽  
Vol 9 ◽  
pp. 482-489 ◽  
Author(s):  
Dalei Jing ◽  
Shiyu Song ◽  
Yunlu Pan ◽  
Xiaoming Wang
Keyword(s):  
Laminar Flow ◽  
Hydraulic Resistance ◽  
Slip Length ◽  
Diameter Ratio ◽  
Slip Condition ◽  
Channel Network ◽  
Murray's Law ◽  
Murray’S Law ◽  
Level Number ◽  
Optimal Diameter

The fractal tree-like branched network is an effective channel design structure to reduce the hydraulic resistance as compared with the conventional parallel channel network. In order for a laminar flow to achieve minimum hydraulic resistance, it is believed that the optimal fractal tree-like channel network obeys the well-accepted Murray’s law of βm = N −1/3 (βm is the optimal diameter ratio between the daughter channel and the parent channel and N is the branching number at every level), which is obtained under the assumption of no-slip conditions at the channel wall–liquid interface. However, at the microscale, the no-slip condition is not always reasonable; the slip condition should indeed be considered at some solid–liquid interfaces for the optimal design of the fractal tree-like channel network. The present work reinvestigates Murray’s law for laminar flow in a fractal tree-like microchannel network considering slip condition. It is found that the slip increases the complexity of the optimal design of the fractal tree-like microchannel network to achieve the minimum hydraulic resistance. The optimal diameter ratio to achieve minimum hydraulic resistance is not only dependent on the branching number, as stated by Murray’s law, but also dependent on the slip length, the level number, the length ratio between the daughter channel and the parent channel, and the diameter of the channel. The optimal diameter ratio decreases with the increasing slip length, the increasing level number and the increasing length ratio between the daughter channel and the parent channel, and decreases with decreasing channel diameter. These complicated relations were found to become relaxed and simplified to Murray’s law when the ratio between the slip length and the diameter of the channel is small enough.

Murray's law, the ‘Yarrum’ optimum, and the hydraulic architecture of compound leaves

2009 ◽  
Vol 184 (1) ◽  
pp. 234-244 ◽  
Author(s):  
Katherine A. McCulloh ◽  
John S. Sperry ◽  
Frederick C. Meinzer ◽  
Barbara Lachenbruch ◽  
Cristian Atala
Keyword(s):  
Hydraulic Architecture ◽  
Murray's Law ◽  
Murray’S Law

Investigating Murray's law in the chick embryo

2001 ◽  
Vol 34 (1) ◽  
pp. 121-124 ◽  
Author(s):  
Larry A Taber ◽  
Stella Ng ◽  
Alicia M Quesnel ◽  
Jennifer Whatman ◽  
Craig J Carmen
Keyword(s):  
Chick Embryo ◽  
Murray's Law ◽  
Murray’S Law

scholarly journals Lepidoptera demonstrate the relevance of Murray’s Law to circulatory systems with tidal flow

BMC Biology ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandra R. Schachat ◽  
C. Kevin Boyce ◽  
Jonathan L. Payne ◽  
David Lentink
Keyword(s):  
Predictive Power ◽  
Fluid Transport ◽  
Tidal Flow ◽  
Pupal Stage ◽  
Wing Venation ◽  
Structural Support ◽  
Murray's Law ◽  
Selective Pressures ◽  
Murray’S Law ◽  
Branching Architecture

Abstract Background Murray’s Law, which describes the branching architecture of bifurcating tubes, predicts the morphology of vessels in many amniotes and plants. Here, we use insects to explore the universality of Murray’s Law and to evaluate its predictive power for the wing venation of Lepidoptera, one of the most diverse insect orders. Lepidoptera are particularly relevant to the universality of Murray’s Law because their wing veins have tidal, or oscillatory, flow of air and hemolymph. We examined over one thousand wings representing 667 species of Lepidoptera. Results We found that veins with a diameter above approximately 50 microns conform to Murray’s Law, with veins below 50 microns in diameter becoming less and less likely to conform to Murray’s Law as they narrow. The minute veins that are most likely to deviate from Murray’s Law are also the most likely to have atrophied, which prevents efficient fluid transport regardless of branching architecture. However, the veins of many taxa continue to branch distally to the areas where they atrophied, and these too conform to Murray’s Law at larger diameters (e.g., Sesiidae). Conclusions This finding suggests that conformity to Murray’s Law in larger taxa may reflect requirements for structural support as much as fluid transport, or may indicate that selective pressures for fluid transport are stronger during the pupal stage—during wing development prior to vein atrophy—than the adult stage. Our results increase the taxonomic scope of Murray’s Law and provide greater clarity about the relevance of body size.

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