The Physiological Principle of Minimum Work

Murray, Cecil D.

doi:10.1073/pnas.12.3.207

Cited by 1,790 publications

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“…The concept of an arterial homeostatic wall shear stress magnitude (ie, shear stress set point) at which vessels maintain a steady‐state luminal diameter72 arises from Murray's principle of minimum work 73. Outward collateral artery growth is therefore hypothesized to stop once normalization to the shear stress set point has been achieved 2, 3, 4, 5.…”

Section: Discussionmentioning

confidence: 99%

DNA Methyltransferase 1–Dependent DNA Hypermethylation Constrains Arteriogenesis by Augmenting Shear Stress Set Point

Heuslein

Gorick

Song

et al. 2017

JAHA

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BackgroundArteriogenesis is initiated by increased shear stress and is thought to continue until shear stress is returned to its original “set point.” However, the molecular mechanism(s) through which shear stress set point is established by endothelial cells (ECs) are largely unstudied. Here, we tested the hypothesis that DNA methyltransferase 1 (DNMT1)–dependent EC DNA methylation affects arteriogenic capacity via adjustments to shear stress set point.Methods and ResultsIn femoral artery ligation–operated C57BL/6 mice, collateral artery segments exposed to increased shear stress without a change in flow direction (ie, nonreversed flow) exhibited global DNA hypermethylation (increased 5‐methylcytosine staining intensity) and constrained arteriogenesis (30% less diameter growth) when compared with segments exposed to both an increase in shear stress and reversed‐flow direction. In vitro, ECs exposed to a flow waveform biomimetic of nonreversed collateral segments in vivo exhibited a 40% increase in DNMT1 expression, genome‐wide hypermethylation of gene promoters, and a DNMT1‐dependent 60% reduction in proarteriogenic monocyte adhesion compared with ECs exposed to a biomimetic reversed‐flow waveform. These results led us to test whether DNMT1 regulates arteriogenic capacity in vivo. In femoral artery ligation–operated mice, DNMT1 inhibition rescued arteriogenic capacity and returned shear stress back to its original set point in nonreversed collateral segments.ConclusionsIncreased shear stress without a change in flow direction initiates arteriogenic growth; however, it also elicits DNMT1‐dependent EC DNA hypermethylation. In turn, this diminishes mechanosensing, augments shear stress set point, and constrains the ultimate arteriogenic capacity of the vessel. This epigenetic effect could impact both endogenous collateralization and treatment of arterial occlusive diseases.

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Section: Discussionmentioning

confidence: 99%

DNA Methyltransferase 1–Dependent DNA Hypermethylation Constrains Arteriogenesis by Augmenting Shear Stress Set Point

Heuslein

Gorick

Song

et al. 2017

JAHA

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“…A classical result obtained by Murray 1926a prescribes a “cube law” relationship, namely q ∝ d 3 . The result is based on a compromise between the power required to drive steady flow through the vessel, which varies as d −4 , and the rate of expenditure of metabolic energy required to maintain the volume of blood filling the vessel, which varies as d 2 .…”

Section: Methodsmentioning

confidence: 99%

“…The great variety of vascular systems in biology, and the apparent similarity between the branching structure of such diverse systems as blood arteries (Murray 1926a,Murray 1926b), botanical plants (Prusinkiewicz and Lindenmayer 1990), neural systems (Berry and Pymm 1981), and rivers (Horton 1945), make the subject somewhat intractable when it comes to the study of form as it relates to function. For a meaningful discussion, the subject must clearly be narrowed.…”

Section: Introductionmentioning

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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“…The great depth of focus of the SEM, and the possibility to take stereopaired images for subsequent 3D morphometry (Malkusch et al, 1995;Minnich et al, 1999Minnich et al, , 2002, enables the measurement of parameters in the casted vasa vasorum required to calculate flow and pressure gradients within the vascular network. Additionally, it can provide the vascular parameters needed to define which optimality principle(s) (Murray, 1926a(Murray, , 1926bGössl et al, 2003) are applicable to the vasa vasorum of the aged human GSV.…”

mentioning

confidence: 99%

“…From these data, it is possible to calculate branching indexes of arterial, capillary, and venular bifurcations (mergings). These data can then be used to calculate optimum vessel diameters and optimum branching angles to find out which of the four optimality principles (minimum lumen volume, minimum pumping power, minimum lumen surface, minimum endothelial shear force) (Murray, 1926a(Murray, , 1926b) is achieved in the vasa vasorum network.…”

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confidence: 99%

Three‐dimensional arrangement of the vasa vasorum in explanted segments of the aged human great saphenous vein: Scanning electron microscopy and three‐dimensional morphometry of vascular corrosion casts

et al. 2004

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The vasa vasorum of skeletonized and nonskeletonized segments of five human great saphenous veins (GSVs), harvested during coronary bypass grafting, were cannulated, rinsed, and injected (casted) with the polymerizing resin Mercox-Cl-2B. After removal of the dry vascular tissue, the casts were examined using scanning electron microscopy. Stereopaired images (tilt angle, 6°) were taken, imported into a 3D morphometry system, and the 3D architecture of the vasa vasorum (arterial and venous vasa as well as capillaries) was studied qualitatively and quantitatively in terms of vasa diameters, intervascular and interbranching distances, and branching angles. Diameters of parent (d 0 ) and large (d 1 ) and small (d 2 ) daughter vessels of arterial and venous bifurcations served to calculate asymmetry ratios (␣) and area ratios (␤). Additionally, deviations of bifurcations and branching angles from optimal branches were calculated for selected arterial vasa. The arrangement of the vasa vasorum closely followed the longitudinally oriented connective tissue fibers in the adventitia and the circularly arranged smooth muscle cell layers within the outer layers of the media. Venous vasa by far outnumbered arterial vasa. Vasa vasorum changed their course several times in acute angles and revealed numerous circular constrictions, kinks, and outpouchings. Due to their spatial arrangement, the vasa vasorum are prone to tolerate vessel wall distension generated by acute increases in blood pressure or stretching of the vessel without severe impact on vessel functions. Preliminary comparisons of data from the bifurcations of cast arterial vasa vasorum, with calculated optimal bifurcations, do not yet give clear insights into the optimality principle(s) governing the design of arterial vasa vasorum bifurcations of the human GSVs.

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The Physiological Principle of Minimum Work

Abstract: sex of Chaetocladium was grown with either sex of Parasitella, both species acted as host to the other parasite and galls were produced characteristic of both Parasitella and Chaetocladium. The parasitic behavior of Chaetocladium has been described in detail by Burgeff.2

Cited by 1,790 publications

References 0 publications

DNA Methyltransferase 1–Dependent DNA Hypermethylation Constrains Arteriogenesis by Augmenting Shear Stress Set Point

DNA Methyltransferase 1–Dependent DNA Hypermethylation Constrains Arteriogenesis by Augmenting Shear Stress Set Point

Arterial Branching within the Confines of Fractal L-System Formalism

Three‐dimensional arrangement of the vasa vasorum in explanted segments of the aged human great saphenous vein: Scanning electron microscopy and three‐dimensional morphometry of vascular corrosion casts

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