Arterial bifurcations in the cardiovascular system of a rat.

Zamir, M.; Wrigley, S.; Langille, B. Lowell

doi:10.1085/jgp.81.3.325

Cited by 82 publications

(65 citation statements)

References 15 publications

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Section: A Brief Summary Of Experimental Results and Of Other Allometmentioning

confidence: 99%

“…(a) Assuming thin-walled vessels, the external radius does not play any significant role, because it is-at the considered scales-negligibly larger than the internal radius [6]; (b) For 3-D branchings, the H-M still applies, because over 90% of the bifurcations are experimentally found to be coplanar [9]; (c) A different "optimal branching ratio" can be derived by using fractals [10,11]: however, even for the smallest pulmonary alveoli (for which values 0.4 < δ < 0.85 are found experimentally) its value is not in agreement with the H-M law; (d) Both experimental and numerical findings show that while the H-M law leads-under the above stated assumptions-to an optimal value of δ = 0.7937 for laminar flow, for turbulent flow in veins and arteries the result becomes 0.74 and for the largest arteries, 0.77. Moreover, contrary to Hess & Murray's result of an inverse scaling of the pressure gradient in successive branchings with δ (∆p/L = δ´1, see Equation (4)), radius-dependent slenderness factors are found experimentally: L/r = 15.75r 1.10 for arterioles with r ě 50 µm, 1.79r 0.47 for arterioles with r ď 50 µm, 14.54r for veins with r ď 2000 µm, [12,13].…”

Section: A Brief Summary Of Experimental Results and Of Other Allometmentioning

confidence: 99%

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A Critical Reassessment of the Hess–Murray Law

Sciubba

2016

Entropy

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Abstract:The Hess-Murray law is a correlation between the radii of successive branchings in bi/trifurcated vessels in biological tissues. First proposed by the Swiss physiologist and Nobel laureate Walter Rudolf Hess in his 1914 doctoral thesis and published in 1917, the law was "rediscovered" by the American physiologist Cecil Dunmore Murray in 1926. The law is based on the assumption that blood or lymph circulation in living organisms is governed by a "work minimization" principle that-under a certain set of specified conditions-leads to an "optimal branching ratio" of. This "cubic root of 2" correlation underwent extensive theoretical and experimental reassessment in the second half of the 20th century, and the results indicate that-under a well-defined series of conditions-the law is sufficiently accurate for the smallest vessels (r of the order of fractions of millimeter) but fails for the larger ones; moreover, it cannot be successfully extended to turbulent flows. Recent comparisons with numerical investigations of branched flows led to similar conclusions. More recently, the Hess-Murray law came back into the limelight when it was taken as a founding paradigm of the Constructal Law, a theory that employs physical intuition and mathematical reasoning to derive "optimal paths" for the transport of matter and energy between a source and a sink, regardless of the mode of transportation (continuous, like in convection and conduction, or discrete, like in the transportation of goods and people). This paper examines the foundation of the law and argues that both for natural flows and for engineering designs, a minimization of the irreversibility under physically sound boundary conditions leads to somewhat different results. It is also shown that, in the light of an exergy-based resource analysis, an amended version of the Hess-Murray law may still hold an important position in engineering and biological sciences.

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Section: A Brief Summary Of Experimental Results and Of Other Allometmentioning

confidence: 99%

Section: A Brief Summary Of Experimental Results and Of Other Allometmentioning

confidence: 99%

A Critical Reassessment of the Hess–Murray Law

Sciubba

2016

Entropy

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“…1,4,9,17 Arterial bifurcations are designed to maintain WSS and other hemodynamic forces at optimum levels, thereby minimizing energy expenditure. 1,25 The underlying mechanisms responsible for controlling this dynamic vasoregulatory process are thought to be impaired at aneurysm sites. Resulting alterations in bifurcation geometry, namely angle size and vessel radii, have been shown to create hemodynamic conditions that predispose to IA development and progression.…”

Section: Discussionmentioning

confidence: 99%

“…11 An optimal arrangement of branching and bifurcation sites in the cerebral vasculature is essential to preserve minimum energy expenditure along the network by maintaining constant wall shear stress (WSS) across daughter and parent vessels. 11,25 This vascular optimality principle has been shown to generally apply to the cerebral circulation 11,19,20 and implies a relative optimal bifurcation angle depending on the relative sizes of the daughter branches. Consequently, changes in vessel design at bifurcations are intrinsically linked to altered hemodynamic forces at the apex and, as such, to a possible increased risk of IA formation.…”

Section: ©Aans 2014mentioning

confidence: 99%

Widening of the basilar bifurcation angle: association with presence of intracranial aneurysm, age, and female sex

Tütüncü¹,

Schimansky²,

Baharoglu³

et al. 2014

JNS

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Object. Arterial bifurcations represent preferred locations for aneurysm formation, especially when they are associated with variations in divider geometry. The authors hypothesized a link between basilar apex aneurysms and basilar bifurcation (a) and vertebrobasilar junction (VBJ) angles.Methods. The a and VBJ angles were measured in 3D MR and rotational angiographic volumes using a coplanar 3-point technique. Angle a was compared between age-matched cohorts in 45 patients with basilar artery (BA) aneurysms, 65 patients with aneurysms in other locations (non-BA), and 103 nonaneurysmal controls. Additional analysis was performed in 273 nonaneurysmal controls. Computational fluid dynamics (CFD) simulations were performed on parametric BA models with increasing angles.Results. Angle a was significantly wider in patients with BA aneurysms (146.7° ± 20.5°) than in those with non-BA aneurysms (111.7° ± 18°) and in controls (103° ± 20.6°) (p < 0.0001), whereas no difference was observed for the VBJ angle. A wider angle a correlated with BA aneurysm neck width but not dome size, which is consistent with CFD results showing a widening of the impingement zone at the bifurcation apex. BA bifurcations hosting even small aneurysms (< 5 mm) had a significantly larger a angle compared with matched controls (p < 0.0001). In nonaneurysmal controls, a increased with age (p < 0.0001), with a threshold effect above 35 years of age and a steeper dependence in females (p = 0.002) than males (p = 0.04).Conclusions. The a angle widens with age during adulthood, especially in females. This angular widening is associated with basilar bifurcation aneurysms and may predispose individuals to aneurysm initiation by diffusing the flow impingement zone away from the protective medial band region of the flow divider. (http://thejns.org/doi/abs/10.3171/2014 key WorDS • vessel morphology • basilar bifurcation • vascular disorders • bifurcation aneurysms • vascular age dependencyAbbreviations used in this paper: AUC = area under the curve; BA = basilar artery; CFD = computational fluid dynamics; IA = intracranial aneurysm; MPR = multiplanar reconstruction; MRA = MR angiography; PCA = posterior cerebral artery; ROC = receiver operating characteristic; VBJ = vertebrobasilar junction; WSS = wall shear stress.

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“…A reasonably complete cast of the arterial system of a rat (Zamir et al 1983). Branching is highly nonuniform and is dictated by reasons of anatomy, local flow requirements, and other constraints.…”

Section: Figurementioning

confidence: 99%

Arterial Branching within the Confines of Fractal L-System Formalism

Zamir

2001

The Journal of General Physiology

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Parametric Lindenmayer systems (L-systems) are formulated to generate branching tree structures that can incorporate the physiological laws of arterial branching. By construction, the generated trees are de facto fractal structures, and with appropriate choice of parameters, they can be made to exhibit some of the branching patterns of arterial trees, particularly those with a preponderant value of the asymmetry ratio. The question of whether arterial trees in general have these fractal characteristics is examined by comparison of pattern with vasculature from the cardiovascular system. The results suggest that parametric L-systems can be used to produce fractal tree structures but not with the variability in branching parameters observed in arterial trees. These parameters include the asymmetry ratio, the area ratio, branch diameters, and branching angles. The key issue is that the source of variability in these parameters is not known and, hence, it cannot be accurately reproduced in a model. L-systems with a random choice of parameters can be made to mimic some of the observed variability, but the legitimacy of that choice is not clear.

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Arterial bifurcations in the cardiovascular system of a rat.

Cited by 82 publications

References 15 publications

A Critical Reassessment of the Hess–Murray Law

A Critical Reassessment of the Hess–Murray Law

Widening of the basilar bifurcation angle: association with presence of intracranial aneurysm, age, and female sex

Arterial Branching within the Confines of Fractal L-System Formalism

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