Bifurcating distributive system using Monte Carlo method

Wang, C. Y.; Bassingthwaighte, James B.; Weissman, L.

doi:10.1016/0895-7177(92)90050-u

Cited by 23 publications

(19 citation statements)

References 8 publications

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“…Coronary arterial tree models have also been constructed based on the fractal principal, 18 constrained constructive optimization, 7 and Monte Carlo method. 25 Recently, Beard and Bassingthwaighte 1,2 have developed an avoidance algorithm which is based on the morphometric measurements of Kassab et al 11 They reconstructed the vascular branching pattern in a cylindrical model of the heart. Smith et al 20 also using Kassab's morphometric data, 11 have developed a similar algorithm to map the distribution of vascular elements in the myocardium as a nonlinear optimization of individual branch angles based on the minimum shear stress hypothesis and whole organ vessel distribution.…”

Section: Comparison With Other Tree Growth Algorithmsmentioning

confidence: 99%

A Computer Reconstruction of the Entire Coronary Arterial Tree Based on Detailed Morphometric Data

et al. 2005

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A rigorous analysis of blood flow must be based on the branching pattern and vascular geometry of the full vascular circuit of interest. It is experimentally difficult to reconstruct the entire vascular circuit of any organ because of the enormity of the vessels. The objective of the present study was to develop a novel method for the reconstruction of the full coronary vascular tree from partial measurements. Our method includes the use of data on those parts of the tree that are measured to extrapolate the data on those parts that are missing. Specifically, a two-step approach was employed in the reconstruction of the entire coronary arterial tree down to the capillary level. Vessels > 40 microm were reconstructed from cast data while vessels < 40 microm were reconstructed from histological data. The cast data were reconstructed one-bifurcation at a time while histological data were reconstructed one-sub-tree at a time by "cutting" and "pasting" of data from measured to missing vessels. The reconstruction algorithm yielded a full arterial tree down to the first capillary bifurcation with 1.9, 2.04 and 1.15 million vessel segments for the right coronary artery (RCA), left anterior descending (LAD) and left circumflex (LCx) trees, respectively. The node-to-node connectivity along with the diameter and length of every vessel segment was determined. Once the full tree was reconstructed, we automated the assignment of order numbers, according to the diameter-defined Strahler system, to every vessel segment in the tree. Consequently, the diameters, lengths, number of vessels, segments-per-element ratio, connectivity and longitudinal matrices were determined for every order number. The present model establishes a morphological foundation for future analysis of blood flow in the coronary circulation.

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Section: Comparison With Other Tree Growth Algorithmsmentioning

confidence: 99%

A Computer Reconstruction of the Entire Coronary Arterial Tree Based on Detailed Morphometric Data

et al. 2005

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“…The tree growing algorithm used was developed by Wang et al [38] and extended to three-dimensional volumes by Tawhai et al [39]. A schematic illustration of the area-filling branching algorithm of Wang et al [41] is given in figure 2.…”

Section: A23 Tree Growing Algorithmmentioning

confidence: 99%

“…(a) Schematic of the area-filling branching algorithm of Wang et al [38]. Initial placement of the umbilical arteries is assigned and seed points are split into two groups.…”

Section: Villous Vesselsmentioning

confidence: 99%

“…Seed points were defined on the chorionic surface, towards which an asymmetric tree was grown. Thirtytwo seed points, equally spaced over the chorionic surface, were defined and a Monte Carlo method described by Wang et al [38] was implemented in CMISS (www.cmiss.org) to generate an 'area-filling' bifurcating system of chorionic vessels. Details of seed point generation and the growing algorithm are given in appendix A.2, and the algorithm is schematically illustrated in figure 2.…”

Section: Chorionic Vesselsmentioning

confidence: 99%

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Multiscale modelling of the feto–placental vasculature

et al. 2015

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One contribution of 11 to a theme issue 'Multiscale modelling in biomechanics: theoretical, computational and translational challenges'. The placenta provides all the nutrients required for the fetus through pregnancy. It develops dynamically, and, to avoid rejection of the fetus, there is no mixing of fetal and maternal blood; rather, the branched placental villi 'bathe' in blood supplied from the uterine arteries. Within the villi, the feto-placental vasculature also develops a complex branching structure in order to maximize exchange between the placental and maternal circulations. To understand the development of the placenta, we must translate functional information across spatial scales including the interaction between macro-and micro-scale haemodynamics and account for the effects of a dynamically and rapidly changing structure through the time course of pregnancy. Here, we present steps towards an anatomically based and multiscale approach to modelling the feto-placental circulation. We assess the effect of the location of cord insertion on feto-placental blood flow resistance and flow heterogeneity and show that, although cord insertion does not appear to directly influence feto-placental resistance, the heterogeneity of flow in the placenta is predicted to increase from a 19.4% coefficient of variation with central cord insertion to 23.3% when the cord is inserted 2 cm from the edge of the placenta. Model geometries with spheroidal and ellipsoidal shapes, but the same volume, showed no significant differences in flow resistance or heterogeneity, implying that normal asymmetry in shape does not affect placental efficiency. However, the size and number of small capillary vessels is predicted to have a large effect on feto-placental resistance and flow heterogeneity. Using this new model as an example, we highlight the importance of taking an integrated multi-disciplinary and multiscale approach to understand development of the placenta.

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“…Several other classes of vascular models have been proposed for flow analysis based on various simplifications such as fractal geometry, 33 constrained constructive optimization, 21 and Monte Carlo simulation. 45 Simulations of partial or full coronary arterial trees based on measured morphometric data have also been presented. 26,41,44 Although these models were based on measured vascular morphometry, they lacked the 3-D branching structure or alternatively, were based on limited number of arterial branching generations.…”

Section: Introductionmentioning

confidence: 99%

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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Bifurcating distributive system using Monte Carlo method

Abstract: A new method to generate a bifurcating distributive system is presented. The method utilizes random points inside a given area and is sensitive to the global and local concentrations of the points. The algorithm is highly efficient compared to the current area-halving algorithms.

Cited by 23 publications

References 8 publications

A Computer Reconstruction of the Entire Coronary Arterial Tree Based on Detailed Morphometric Data

A Computer Reconstruction of the Entire Coronary Arterial Tree Based on Detailed Morphometric Data

Multiscale modelling of the feto–placental vasculature

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

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