Left Coronary Artery Tree Research Articles

Low-density lipoprotein concentration in the normal left coronary artery tree

BackgroundThe blood flow and transportation of molecules in the cardiovascular system plays a crucial role in the genesis and progression of atherosclerosis. This computational study elucidates the Low Density Lipoprotein (LDL) site concentration in the entire normal human 3D tree of the LCA.MethodsA 3D geometry model of the normal human LCA tree is constructed. Angiographic data used for geometry construction correspond to end-diastole. The resulted model includes the LMCA, LAD, LCxA and their main branches. The numerical simulation couples the flow equations with the transport equation applying realistic boundary conditions at the wall.ResultsHigh concentration of LDL values appears at bifurcation opposite to the flow dividers in the proximal regions of the Left Coronary Artery (LCA) tree, where atherosclerosis frequently occurs. The area-averaged normalized luminal surface LDL concentrations over the entire LCA tree are, 1.0348, 1.054 and 1.23, for the low, median and high water infiltration velocities, respectively. For the high, median and low molecular diffusivities, the peak values of the normalized LDL luminal surface concentration at the LMCA bifurcation reach 1.065, 1.080 and 1.205, respectively. LCA tree walls are exposed to a cholesterolemic environment although the applied mass and flow conditions refer to normal human geometry and normal mass-flow conditions.ConclusionThe relationship between WSS and luminal surface concentration of LDL indicates that LDL is elevated at locations where WSS is low. Concave sides of the LCA tree exhibit higher concentration of LDL than the convex sides. Decreased molecular diffusivity increases the LDL concentration. Increased water infiltration velocity increases the LDL concentration. The regional area of high luminal surface concentration is increased with increasing water infiltration velocity. Regions of high LDL luminal surface concentration do not necessarily co-locate to the sites of lowest WSS. The degree of elevation in luminal surface LDL concentration is mostly affected from the water infiltration velocity at the vessel wall. The paths of the velocities in proximity to the endothelium might be the most important factor for the elevated LDL concentration.

Non-Newtonian models for molecular viscosity and wall shear stress in a 3D reconstructed human left coronary artery

The capabilities and limitations of various molecular viscosity models, in the left coronary arterial tree, were analyzed via: molecular viscosity, local and global non-Newtonian importance factors, wall shear stress (WSS) and wall shear stress gradient (WSSG). The vessel geometry was acquired using geometrically correct 3D intravascular ultrasound (3D IVUS). Seven non-Newtonian molecular viscosity models, plus the Newtonian one, were compared. The WSS distribution yielded a consistent LCA pattern for nearly all non-Newtonian models. High molecular viscosity, low WSS and low WSSG values occured at the outer walls of the major bifurcation in proximal LCA regions. The Newtonian blood flow was found to be a good approximation at mid- and high-strain rates. The non-Newtonian Power Law, Generalized Power Law, Carreau and Casson and Modified Cross blood viscosity models gave comparable molecular viscosity, WSS and WSSG values. The Power Law and Walburn–Schneck models over-estimated the non-Newtonian global importance factor I G and under-estimated the area averaged WSS and WSSG values. The non-Newtonian Power Law and the Generalized Power Law blood viscosity models were found to approximate the molecular viscosity and WSS calculations in a more satisfactory way.

Flow parameters in normal left coronary artery tree. Implication to atherogenesis

The dominant haemodynamic flow parameters of wall pressure (WP), wall shear stress (WSS), molecular viscosity and the spatial gradients: wall pressure gradient (WPG) and wall shear stress gradient (WSSG) along the normal human left coronary artery (LCA) tree are numerically analyzed in relation to atheronegenesis. The LCA tree includes the left main coronary artery, the left anterior descending branch, the left circumflex branch and their major branches. Spatial differentiation indicates that low values of WP (locally), WPG, WSS, WSSG and high molecular viscosity appear opposite flow dividers and this probably correlates to atherosclerosis localization.

Molecular Viscosity in the Normal Left Coronary Arterial Tree. Is It Related to Atherosclerosis?

The purpose of this study is to elucidate, probably for the first time, the distribution of molecular viscosity in the entire left coronary artery (LCA) tree. The governing mass, momentum, and energy flow equations were solved by using a previously validated 3-dimensional numerical (finite-element analysis) code. High-molecular-viscosity regions occur at bifurcations in regions opposite the flow dividers, which are anatomic sites predisposed for atherosclerotic development. Furthermore, high-molecular-viscosity values appear in the proximal regions of the LCA tree, where atherosclerosis frequently occurs. The effect of blood flow resistance, due to increased blood viscosity, gives rise to increased contact time between the atherogenic particles of the blood and the endothelium, probably promoting atherosclerosis. Observations suggest that, whole viscosity distribution within the coronary artery tree may represent a risk factor for the resulting atherosclerosis. This distribution can become a possible tool for the location of atherosclerotic lesions.

Wall pressure gradient in normal left coronary artery tree

The three-dimensional wall pressure gradient (WPG) of the normal human left coronary artery (LCA) tree is quantitatively analysed. A model LCA tree, based on averaged human data set extracted from angiographies was adopted for finite-element analysis. The LCA tree includes the left main coronary artery (LMCA), the left anterior descending (LAD), the left circumflex artery (LCxA) and their major branches. The WPG is calculated using 44,452 nodes throughout the tree extension. The governing flow equations were solved using a validated numerical code. WPG as well as wall shear stress gradient (WSSG) were calculated at all available bifurcation regions. In proximal LCA tree regions where atherosclerosis frequently occurs, low WPG appears. At distal segments, WPG increases substantially due to increased velocity resulted from increased vessel tapering. Low WPG occurs at bifurcations in regions opposite the apexes, which are anatomic sites predisposed for atherosclerotic development. Endothelial cells respond to the combined effects of locally low WPG and low WSSG and provide a mechanism promoting atherosclerosis. This computational work determines probably for the first time the topography of the WPG in the normal human LCA tree. Spatial WPG differentiation indicates that locally low values of this physical parameter probably correlate to atherosclerosis localization.

Wall shear stress in normal left coronary artery tree

Despite the fact that the role of wall shear stress (WSS) as a local mechanical factor in atherogenesis is well established, its distribution over the entire normal human left coronary artery (LCA) tree has not yet been studied. A three-dimensional computer generated model of the epicardial LCA tree, based on averaged human data set extracted from angiographies, was adopted for finite-element analysis of the Navier–Stokes flow equations treating blood as non-Newtonian fluid. The LCA tree includes the left main coronary artery (LMCA), the left anterior descending (LAD), the left circumflex artery (LCxA) and their major branches. In proximal LCA tree regions where atherosclerosis frequently occurs, low WSS appears. Low WSS regions occur at bifurcations in regions opposite the flow dividers, which are anatomic sites predisposed for atherosclerotic development. On the LMCA bifurcation, at regions opposite to the flow divider, dominant low WSS values occur ranging from 0.75 to 2.25 N/m 2. High WSS values are encountered at all flow dividers. This work determines, probably for the first time, the topography of the WSS in the entire normal human LCA epicardial tree. It is also the first work determining the spatial WSS differentiation between proximal and distal normal human LCA parts. The haemodynamic analysis of the entire epicardial LCA tree further verifies the implications of the WSS in atherosclerosis mechanisms.

Wall shear stress gradient topography in the normal left coronary arterial tree: possible implications for atherogenesis

SUMMARYObjective: Wall shear stress gradient (WSSG) in vitro has shown its importance in atherogenesis, probably as a local modulator of endothelial gene expression.The purpose of this study is to numerically analyse the WSSG distribution over the normal human left coronary artery (LCA) tree.Research design and methods: A three-dimensional computer generated model of the LCA tree, based on an averaged human data set extracted from angiographies, was adopted for finite-element analysis. The LCA tree includes the left main coronary artery (LMCA), the left anterior descending (LAD), the left circumflex artery (LCxA) and their major branches.Results: In proximal LCA tree regions where atherosclerosis frequently occurs, low WSSG appears. At distal segments, the WSSG increases substantially due to increased velocity resulting from increased vessel tapering. Low WSSG occurs at bifurcations in regions opposite the flow dividers, which are anatomic sites predisposed for atherosclerotic development.Conclusions: This computational work determines, probably for the first time, the topography of the WSSG in the normal human LCA tree. Spatial WSSG differentiation indicates that low values of this parameter probably correlate to atherosclerosis localization. However, further studies are needed to clarify the role of WSSG in atherogenesis.

P1727 Does wall shear stress correlate to wall shear stress gradient in left coronary artery tree? Implications to atherogenesis

P1727 Does wall shear stress correlate to wall shear stress gradient in left coronary artery tree? Implications to atherogenesis

Relation between zero-stress state and branching order of porcine left coronary arterial tree.

The left common coronary arterial trees of eight pig hearts were dissected. The zero-stress state (the state of the organ when the external loads are removed) of the coronary arteries was determined by first cutting the arteries into short, ring-shaped segments perpendicular to the longitudinal axis of the blood vessel and then making a radial cut. This procedure caused the ring to open into a sector whose opening angle (theta), internal and external lengths (circumferences), and wall thickness were measured. Morphometric and theta data were organized in the framework of a diameter-defined Strahler system. We investigated 4 rings from the left common coronary artery (LCCA), 185 from the left anterior descending artery (LAD) and its branches, and 159 from the left circumflex artery (LCX) and its branches. The inner circumferences of the rings ranged over six orders for the LAD arterial tree and five orders for the LCX arterial tree, corresponding to a diameter range of about one order of magnitude for both arteries. theta demonstrates viscoelastic behavior and was measured 30 min after cutting. Our results show that the inner and outer circumference and the wall thickness increase as geometric sequences with the order number. theta is found to decrease linearly toward the smaller orders with a slope of 7.3 degrees/order in the range of the six largest orders. Strain calculations showed that the inner part of the arterial wall is in compression, whereas the outer part of the wall is in tension in the no-load (zero transmural pressure) state. This study provides basic data on the zero-stress state that are necessary for understanding the mechanics of the coronary artery.

Measurement from arteriograms of regional myocardial bed size distal to any point in the coronary vascular tree for assessing anatomic area at risk

Objectives. To obtain the size of regional myocardial mass for individual coronary arteries in vivo.Background. The anatomic site of occlusion in a coronary artery does not predict the size of the risk area because location of the occlusion does not account for the size of the artery or of its dependent myocardial bed.Methods. Intracoronary radiolabeled microspheres were injected and coronary arteriograms were quantitatively analyzed by semiautomated methods. The coronary artery lumen areas and the sum of epicardial coronary artery branch lengths distal to the points where radiomicrospheres had been injected were determined from both in vivo and postmortem coronary arteriograms. Regional myocardial mass distal to the point of each microsphere injection was correlated with corresponding distal summed coronary branch lengths and with coronary artery lumen areas.Results. 1) Regional myocardial mass was closely and linearly related to sum of coronary artery branch lengths distal to any point in the coronary artery tree and therefore could be determined for any location on a coronary arteriogram. 2) The fraction of total left ventricular mass at risk distal to a stenosis could be determined from the corresponding fraction of total coronary artery tree length independently of the scale or X-ray magnification used to measure absolute branch lengths. 3) Cross-sectional lumen area at any point in the left coronary artery tree was closely related to the size of the dependent vascular bed with a curvilinear relation similar to that observed in humans with normal coronary arteriograms.Conclusions. On coronary arteriograms, the anatomic area at risk for myocardial infarction distal to any point in the coronary artery tree can be determined from the sum of distal coronary artery branch lengths. There is a curvilinear relation between coronary artery lumen area and dependent regional myocardial mass comparable to that in humans, reflecting fundamental physical principles underlying the structure of the coronary vascular tree.

Bending and twisting of an in vivo coronary artery at a bifurcation

Dynamic changes in the geometric shape and dimensions of a left coronary artery tree were extracted from the computer-tomographically reconstructed three-dimensional images of an in situ beating heart of an anesthetized dog. Wireframe models of the left coronary artery tree at 16 different instants of a cardiac cycle were constructed for the study of its flexing motion. For quantifying the local bending and twisting of the left coronary artery tree, the anatomic landmarks of the bifurcation points are selected as focussed locations. At these points, the space curves of the tree at different cardiac instants were first derived in parametric forms. Curvature and torsion expressions are next obtained in terms of the derivatives with respect to the parameter. This analysis revealed that during the initial contraction of the heart wall, a 2% reduction per millisecond in the radius of curvature occurred near the bifurcation point where the left circumflex coronary artery descends toward the apex of the heart. When the left ventricular chamber reached a maximum value, the radius of curvature was found to decrease at a rate of 2.3% ms −1. At the end of diastole, an increase in the radius of curvature at a rate of 5.7% ms −1 was observed. The twisting rates per unit length of artery near the bifurcation point of the selected artery were found to range from −0.62 to 0.63° ms −1.

Modeling sound generation in stenosed coronary arteries

Acoustic measurements obtained from sensitive microphones placed on the chest are being used in a procedure to noninvasively diagnose coronary artery disease. Utilizing specially developed signal processing techniques, the spectral content of isolated diastolic heart sounds has been estimated and usually shows an increase in high-frequency components in patients with occlusive coronary arteries. In order to establish a theory for the origin of these spectral features, a sound source model has been developed which combines an incremental network model of the left coronary artery tree with a transfer function model describing arterial chamber resonant characteristics. The network model predicts flow in both normal and stenosed coronary arteries. From this flow information, the arterial chamber transfer function model predicts the development of acoustic signals from the chamber resonant characteristics. The transfer function of a segment of coronary artery demonstrates two resonance frequencies. These resonance frequencies depend upon the length and diameter of the chamber segment, as well as upon the distal hydraulic impedance loading the segment. The lower resonance frequency can be excited by the usual flow fluctuations (low frequency) in the coronary artery. In cases of stenosis, the wideband spectral characteristics of the turbulence produced by the stenosis excites both the low and high resonance frequencies. In a small sample of patients, the spectra obtained from isolated diastolic acoustic signals recorded by a chest microphone agree well with those predicted by this theory.

Epicardial surface estimation from coronary angiograms

We describe a system for estimating the epicardial surface of the heart using data obtained from biplane coronary cinéangiograms. The 3-dimensional (3D) geometry of the left coronary arterial tree at an instant in time is interactively reconstructed as an ensemble of 3D Bézier cubics. This provides a compact representation of the tree structure, incorporating the 3D location of the bifurcation points and their connectivity as well as the locii of the connecting vessels. A finite element model for the surface is defined using bicubic Hermite basis functions to interpolate prolate spheroidal geometric parameters. As the arteries are not uniformly distributed around the left ventricular epicardium, weighted spline-type smoothness constraints are incorporated into the error function along with the least squares error estimate. A trial fit to data describing the superficial arteries of an isolated dog heart was compared to a uniform and dense data set covering the entire epicardial surface obtained from the same heart. Good agreement was found in elements containing coronary data, with the error increasing in a controlled manner in the remaining elements. Results with angiographic data are also given. The model is readily extended to fit time-varying surfaces with the inclusion of a time basis function and is intended for use in subsequent vessel tracking algorithms.

Three-dimensional reconstruction of myocardial contrast perfusion from biplane cineangiograms by means of linear programming techniques.

The assessment of coronary flow reserve from the instantaneous distribution of the contrast agent within the coronary vessels and myocardial muscle at the control state and at maximal flow has been limited by the superimposition of myocardial regions of interest in the two-dimensional images. To overcome these limitations, we are in the process of developing a three-dimensional (3D) reconstruction technique to compute the contrast distribution in cross sections of the myocardial muscle from two orthogonal cineangiograms. To limit the number of feasible solutions in the 3D-reconstruction space, the 3D-geometry of the endo- and epicardial boundaries of the myocardium must be determined. For the geometric reconstruction of the epicardium, the centerlines of the left coronary arterial tree are manually or automatically traced in the biplane views. Next, the bifurcations are detected automatically and matched in these two views, allowing a 3D-representation of the coronary tree. Finally, the circumference of the left ventricular myocardium in a selected cross section can be computed from the intersection points of this cross section with the 3D coronary tree using B-splines. For the geometric reconstruction of the left ventricular cavity, we envision to apply the elliptical approximation technique using the LV boundaries defined in the two orthogonal views, or by applying more complex 3D-reconstruction techniques including densitometry. The actual 3D-reconstruction of the contrast distribution in the myocardium is based on a linear programming technique (Transportation model) using cost coefficient matrices. Such a cost coefficient matrix must contain a maximum amount of a priori information, provided by a computer generated model and updated with actual data from the angiographic views. We have only begun to solve this complex problem. However, based on our first experimental results we expect that the linear programming approach with advanced cost coefficient matrices and computed model will lead to acceptable solutions in the 3D-reconstruction of the myocardial contrast distribution from biplane cineangiograms.

Anomalous origin of the left coronary arterial tree through three stems — one from the pulmonary trunk

In an 18-year-old asymptomatic male athlete, the left anterior descending coronary artery was found to arise from the pulmonary trunk. The remainder of the left coronary arterial tree arose through two stems from the aorta. Collateral retrograde filling of the left anterior descending coronary artery from the right coronary artery and the left circumflex coronary artery was demonstrated, but we found no evidence of left-to-right shunting into the pulmonary trunk. The patient has chosen conservative treatment, thus offering an unusual opportunity to follow the natural course of this lesion, which may increase understanding of its natural history.

EFFICACY OF THE LEFT ANTERIOR OBLIQUE (LAO) VIEW OF THE LEFT CORONARY ARTERY WITH CRANIAL ANGULATION

To assess the efficacy of cranial angulation of the X-ray beam in studying the left coronary artery (LCA) tree during coronary cineangiography (CCA), 975 CCAs were reviewed retrospectively. In 297 cases, the study included a cranially angulated left coronary arteriogram in the LAO projection (LAO-C). Results: In 121 of the 297 cases (41%), the LAO-C view significantly enhanced coronary artery imaging. Among these 121, this view provided 204 specific instances of additional diagnostic information, which in turn could be divided into 5 different types: (a) In 92 instances, the LAO-C projection provided the clearest view of a lesion so that its severity could be graded with confidence. (b) In 47 instances, the anatomy of the proximal LCA tree was clarified so that it became more apparent in which branch a lesion was located. (c) In 29 instances, the LAO-C projection revealed that a lesion was significantly more severe than had been suspected on the standard views. (d) In 18 instances, the LAO-C projection allowed exclusion of a lesion which had been initially suspected on the standard views. (e) In the final 18 instances, the LAO-C projection was the only view to demonstrate a lesion. Among these 204 instances, the affected vessels were the left anterior descending artery (LAD) in 84 cases, a ramus medianus or diagonal branch of the LAD in 90 cases, the proximal circumflex artery or one of its obtuse marginal branches in 23 cases, and the main LCA in 7 cases. Conclusions: (1) The LAO-C projection should be routinely obtained on all CCAs. (2) If the LAO-C projection of the LCA can be quickly and simply obtained (depending upon the equipment available), it should be the first view obtained and can in most cases replace the standard LAO projection. (3) If only a single view of the LCA can be obtained (e.g. in a critically ill patient with unstable angina or suspected main LCA stenoses), it should be the LAO-C view. (4) A major explanation for the finding in earlier studies that CCA underestimates the severity of coronary disease is that many lesions were suboptimally demonstrated before the introduction of angulated views.

A Simulation of the Dynamics of Counterpulsation

An open-loop, lumped parameter, digital computer model of the left heart, coronary artery, and aortic tree is discussed. Introduction of an external flow source (counterpulsation pump system) at any of the eight major nodal points located along the aorta is permitted. The model is run for a variety of conditions to assess the effects of counterpulsation pump timing, stroke volume, infusion/aspiration rate and pump cannula location on selected indices of cardiac performance. Simulation results are compared to appropriate data from two series of animal experiments using a thin-walled cannula and a pneumatically driven, nonhemolytic counterpulsation pump system.