Branching characteristics of human coronary arteries

Zamir, M.; Chee, Hyun Keun

doi:10.1139/y86-109

Cited by 82 publications

(71 citation statements)

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“…Hence, any accordance with a real arterial tree can be seen as a positive test for the parameters chosen and the method of constrained constructive optimization itself. In general, the distributions of branching angles obtained from the model resemble those found experimentally (Zamir and Chee, 1986). In particular the following similarities may be discussed 9…”

Section: Comparison Between Model Results and Branching Angles In Reasupporting

confidence: 54%

“…Second, one negative angle indicates that both daughter segments branch to the same side, relative to the parents' axis. If 01 is negative, it follows that the smaller branch aberrates more from the parent's axis Corosion Cast (Zamir, 1986) .... i .... , An interesting question is "why do we find negative branching angles at all ?" Obviously they are exceptional and seem to violate what we would expect to result from an optimization.…”

Section: Comparison Between Model Results and Branching Angles In Reamentioning

confidence: 99%

“…When comparing the branching angles in the model with measurements on corrosion casts, we have to bear in mind that no anatomical information whatsoever has been plugged into the model, and all structural features have solely emerged from the governing influence of the optimization principle under the constraint of appropriate Corosion Cast (Zamir, 1986) .... boundary conditions. Hence, any accordance with a real arterial tree can be seen as a positive test for the parameters chosen and the method of constrained constructive optimization itself.…”

Section: Comparison Between Model Results and Branching Angles In Reamentioning

confidence: 99%

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The branching angles in computer-generated optimized models of arterial trees.

Schreiner

Neumann

et al. 1994

The Journal of General Physiology

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The structure of a complex arterial tree model is generated on the computer using the newly developed method of "constrained constructive optimization." The model tree is grown step by step, at each stage of development fulfilling invariant boundary conditions for pressures and flows. The development of structure is governed by adopting minimum volume inside the vessels as target function. The resulting model tree is analyzed regarding the relations between branching angles and segment radii. Results show good agreement with morphometric measurements on corrosion casts of human coronary arteries reported in the literature.

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Section: Comparison Between Model Results and Branching Angles In Reasupporting

confidence: 54%

Section: Comparison Between Model Results and Branching Angles In Reamentioning

confidence: 99%

Section: Comparison Between Model Results and Branching Angles In Reamentioning

confidence: 99%

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The branching angles in computer-generated optimized models of arterial trees.

Schreiner

Neumann

et al. 1994

The Journal of General Physiology

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“…Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cube of the radii of the daughters, has been considered in various bifurcations of different organs (5,7,10,11,(13)(14)(15). On the basis of angiographic data of vascular tress, there has been important progress to establish more global relationships between morphological parameters in an entire tree and its subtrees (6).…”

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confidence: 99%

Vascular metabolic dissipation in Murray's law

Liu¹,

Kassab²

2007

American Journal of Physiology-Heart and Circulatory Physiology

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The metabolic dissipation in Murray's minimum energy hypothesis includes only the blood metabolism. The metabolic dissipation of the vascular tree, however, should also include the metabolism of passive and active components of the vessel wall. In this study, we extend the metabolic dissipation to include blood metabolism, as well as passive and active components of the vessel wall. The analysis is extended to the entire vascular arterial tree rather than a single vessel as in Murray's formulation. The calculations are based on experimentally measured morphological data of coronary artery network and the longitudinal distribution of blood pressure along the tree. Whereas the model includes multiple dissipation sources, the total metabolic consumption of a complex vascular tree is found to remain approximately proportional to the cumulative arterial volume of the unit. This implies that the previously described scaling relations for the various morphological features (volume, length, diameter, and flow) remain unchanged under the generalized condition of metabolic requirements of blood and blood vessel wall. vessel wall; vascular tree; scaling laws THE CIRCULATORY SYSTEM consists of complex vascular trees that distribute and collect blood in the various organs to maintain their functions. A typical vascular tree consists of millions of vessel segments, in series and parallel, with different diameters and lengths. Although there is a great deal of heterogeneity in morphological (diameters and lengths) and hemodynamic (pressure, flow, etc.) parameters, there is a prevailing hypothesis that the design of the vascular trees obeys some simple physiological and physical principle that optimizes the operation of the system.The best-recognized minimum dissipation principle was proposed by Murray (8), in which the metabolic consumption in a single vessel segment is proportional to the blood volume. Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cube of the radii of the daughters, has been considered in various bifurcations of different organs (5,7,10,11,(13)(14)(15). On the basis of angiographic data of vascular tress, there has been important progress to establish more global relationships between morphological parameters in an entire tree and its subtrees (6). Zhou et al. (16) (ZKM model) extended Murray's cost form to stem-crown units (SCU), and they deduced a set of scaling laws that describe the optimal structure-function relationships in vascular trees. Briefly, a vessel segment was defined as a stem, and the tree distal to the stem was defined as a crown. Although the form of these scaling laws has been validated in numerous trees (3), the theory only considers the metabolic consumption of the blood. There was no consideration of the metabolic requirements of the vessel wall (passive and active).At first glance, the volume of blood to the volume of vessel wall scales as R 2 L/2RHL or R/2H, where R and H are the radius of the vessel and wall thickness, respectively. F...

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“…Laws of the vascular systems organization are investigated with the help of special casts , radiographic, x -ray images and tinted preparations. The lengths The following statistical dependences between the measured parameters were obtained for the arterial [1][2][3][4]6], venous [1,2,3], respiratory [1,6,7] mammal systems, astrorhizal systems in sponge [1], tree trunks and shoots [8][9], plant leaves of different types [10- for respiratory systems) and the higher the animal's position at the evolutionary scale, the closer γ to 3 [12]. For the large vessels where flow is not laminar (aorta, respiratory trunk) 33 .…”

Section: Principles Of Transport Systems Constructionmentioning

confidence: 99%

Construction principles and control over transport systems organization in biological tissues

Kizilova¹

2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775)

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The main common principles of the long-range transport systems construction in animal and plant tissues are summarized. The results of measurement of conducting system geometry in Cotinus obovatus leaf are analyzed. It is shown that the principles of design of the conducting systems in animals and higher plants are the same and correspond to the model of optimal pipeline. The mathematical model of fluid motion in the conducting system of the leaf as a mo tion in a branching pipeline with permeable walls is investigated. The cost of a bifurcation of the vessels is analyzed. The hypothesis of the control principle of optimal transport system formation in the growing leaf is discussed. As an example the self-similar conducting system with loops is investigated and compared with some venation systems in plant leaves.

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Branching characteristics of human coronary arteries

Cited by 82 publications

References 0 publications

The branching angles in computer-generated optimized models of arterial trees.

The branching angles in computer-generated optimized models of arterial trees.

Vascular metabolic dissipation in Murray's law

Construction principles and control over transport systems organization in biological tissues

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