Flow Strategy and Functional Design of the Coronary Network

Zamir, M.

doi:10.1007/978-4-431-68087-1_2

Cited by 11 publications

(7 citation statements)

References 39 publications

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“…THERE IS SIGNIFICANT VARIABILITY in the coronary anatomy at the level of large epicardial subnetworks, both "globally" (leftright dominance), as well as "locally" at the level of bifurcations (4,30). The vessel branches are characterized by highly irregular and asymmetric branching patterns (11,(12)(13)(14)(15)28).…”

mentioning

confidence: 98%

Diameter asymmetry of porcine coronary arterial trees: structural and functional implications

Kaimovitz¹,

Huo²,

Lanir³

et al. 2008

American Journal of Physiology-Heart and Circulatory Physiology

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The coronary vasculature is characterized by highly asymmetric diameters at bifurcations, which may be an important determinant of flow distribution. To facilitate accurate reconstruction of the coronary network for hemodynamic analysis, we introduce a statistical data set of the diameter asymmetry at bifurcations based on morphometric data of the porcine coronary arterial and venous trees. The bifurcation asymmetry data were represented by the diameter ratio of the daughters relative to mother vessel and by an area expansion ratio (AER) at each bifurcation. A novel asymmetry ratio matrix was introduced to describe the diameter asymmetry of daughters to mother vessels. The relations between AER and flow velocity, and asymmetry ratio matrix and flow distribution, were considered. The results indicate that the ratio of large daughter to mother vessel has a minimum value at order 5 (mean diameter of approximately 70 microm), whereas the ratio of small daughter to mother vessel decreases monotonically with increase in order number. The AER was found to be fairly uniform for larger vessels and to increase from order 5 toward the capillaries. At order 5, we observe a transition in asymmetric bifurcation pattern that may mark a hemodynamic transition from transmural to perfusion subnetworks. The functional implications of these structural transitions are considered.

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mentioning

confidence: 98%

Diameter asymmetry of porcine coronary arterial trees: structural and functional implications

Kaimovitz¹,

Huo²,

Lanir³

et al. 2008

American Journal of Physiology-Heart and Circulatory Physiology

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“…The selection of order 9 as the lower bound is based on the observed diameter (600-800 µm) of transmural vessels that perforate the myocardium at approximately right angles. 4,10,12,19,39,51 A similar epicardial-transmural transition was considered by Beard et al 3 and Karch et al 21 in their respective models. The transmural sub-networks are defined as vessels in the range of orders 8-5 to ensure their span over the heart wall thickness.…”

Section: Model Hierarchymentioning

confidence: 90%

“…4,10,12,19,39,51 Furthermore, this partitioning facilitates an efficient algorithm which can reconstruct each of the entities independently and hence is amenable to parallel computing.…”

Section: Model Hierarchymentioning

confidence: 99%

“…There is large variability in the coronary anatomy at the level of the large epicardial sub-networks, both "globally" (left-right dominance) as well as "locally" at the level of major branches. 6,51 The vessel branches are characterized by highly irregular and asymmetric branching patterns. 23,25,41 Due to the diverging nature of the coronary vasculature, 52,53 the number of vessels increases in a geometric fashion towards the capillary vessels, thus leading to an overwhelming number of vessels which precludes a description of the coronary anatomy deterministically.…”

Section: -D Reconstruction Of Coronary Arterial Systemmentioning

confidence: 99%

“…Distinction was made between RV and LV free wall, and interventricular septum branches in terms of the penetration angle of the transmural sub-networks: right angles for the LV versus oblique course for the RV branches. 4,10,12,19,39,51 The optimized transmural sub-networks were then selected in random and transformed to the prolate spheroidal surface through angular rotation, and concatenated to the epicardial branches. In the last phase, the procedure was repeated by generating a pool of perfusion sub-networks starting with order 4 down to order 0a.…”

Section: Implementation Stepsmentioning

confidence: 99%

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Large-Scale 3-D Geometric Reconstruction of the Porcine Coronary Arterial Vasculature Based on Detailed Anatomical Data

2005

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The temporal and spatial distribution of coronary blood flow, pressure, and volume are determined by the branching pattern and three-dimensional (3-D) geometry of the coronary vasculature, and by the mechanics of heart wall and vascular tone. Consequently, a realistic simulation of coronary blood flow requires, as a first step, an accurate representation of the coronary vasculature in a 3-D model of the beating heart. In the present study, a large-scale stochastic reconstruction of the asymmetric coronary arterial trees (right coronary artery, RCA; left anterior descending, LAD; and left circumflex, LCx) of the porcine heart has been carried out to set the stage for future hemodynamic analysis. The model spans the entire coronary arterial tree down to the capillary vessels. The 3-D tree structure was reconstructed initially in rectangular slab geometry by means of global geometrical optimization using parallel simulated annealing (SA) algorithm. The SA optimization was subject to constraints prescribed by previously measured morphometric features of the coronary arterial trees. Subsequently, the reconstructed trees were mapped onto a prolate spheroid geometry of the heart. The transformed geometry was determined through least squares minimization of the related changes in both segments lengths and their angular characteristics. Vessel diameters were assigned based on a novel representation of diameter asymmetry along bifurcations. The reconstructed RCA, LAD and LCx arterial trees show qualitative resemblance to native coronary networks, and their morphological statistics are consistent with the measured data. The present model constitutes the first most extensive reconstruction of the entire coronary arterial system which will serve as a geometric foundation for future studies of flow in an anatomically accurate 3-D coronary vascular model.

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Geometrical Features of the Vascular System

Kassab¹

2009

Computational Cardiovascular Mechanics

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Flow Strategy and Functional Design of the Coronary Network

Cited by 11 publications

References 39 publications

Diameter asymmetry of porcine coronary arterial trees: structural and functional implications

Diameter asymmetry of porcine coronary arterial trees: structural and functional implications

Large-Scale 3-D Geometric Reconstruction of the Porcine Coronary Arterial Vasculature Based on Detailed Anatomical Data

Geometrical Features of the Vascular System

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