Development of a model of the coronary arterial tree for the 4D XCAT phantom

A detailed three-dimensional (3D) model of the coronary artery tree with cardiac motion has great potential for applications in a wide variety of medical imaging research areas. In this work, we first developed a computer-generated 3D model of the coronary arterial tree for the heart in the extended cardiac-torso (XCAT) phantom, thereby creating a realistic computer model of the human anatomy. The coronary arterial tree model was based on two datasets: (1) a gated cardiac dual-source computed tomography (CT) angiographic dataset obtained from a normal human subject and (2) statistical morphometric data of porcine hearts. The initial proximal segments of the vasculature and the anatomical details of the boundaries of the ventricles were defined by segmenting the CT data. An iterative rule-based generation method was developed and applied to extend the coronary arterial tree beyond the initial proximal segments. The algorithm was governed by three factors: (1) statistical morphometric measurements of the connectivity, lengths and diameters of the arterial segments; (2) avoidance forces from other vessel segments and the boundaries of the myocardium, and (3) optimality principles which minimize the drag force at the bifurcations of the generated tree. Using this algorithm, the 3D computational model of the largest six orders of the coronary arterial tree was generated, which spread across the myocardium of the left and right ventricles. The 3D coronary arterial tree model was then extended to 4D to simulate different cardiac phases by deforming the original 3D model according to the motion vector map of the 4D cardiac model of the XCAT phantom at the corresponding phases. As a result, a detailed and realistic 4D model of the coronary arterial tree was developed for the XCAT phantom by imposing constraints of anatomical and physiological characteristics of the coronary vasculature. This new 4D coronary artery tree model provides a unique simulation tool that can be used in the development and evaluation of instrumentation and methods for imaging normal and pathological hearts with myocardial perfusion defects.     

Morphometric Studies of Human Coronary Artery Trees in Healthy and Disease

Objective According to the report from American Heart Association(AHA),cardiovascular diseases(CVDs)are the leading causes of death globally,and coronary artery disease(CAD),known as coronary atherosclerotic plaques,accounts for over 30%of cardiovascular diseases.Therefore,it is of great clinical significance to study the relationship between coronary bifurcations morphometrical feature change and coronary artery disease.Although coronary atherosclerosis has been extensively investigated,there is a lack of in-deep study on the differences in morphometric features between optimal and realistic geometry of coronary arterial trees.The purpose of the present paper is to determine the morphological changes in patients with CAD lesion compared with non-coronary artery disease(non-CAD)subjects.Methods Due to the difficulty of studying the coronary bifurcations in vivo,image-based in vitro anatomical 3D models have been widely used as a noninvasive method for morphometric measurement and clinical diagnosis of the coronary bifurcations.With the development of coronary computed tomography angiography(CTA)hardware and software technologies,the CTA imaging technique has been shown a promising application in the characterization,visualization,and identification of coronary artery disease in recent decades.The CTA images used to reconstruct three-dimensional(3D)coronary arterial trees are from Asia populations(Southern Chinese populations),including five cadavers without CAD lesion and 102 patients with CAD lesion.The best fit artery diameter was calculated as twice the average radius between the points in the centerlines and the points on the coronary arterial inner wall.The bifurcation angles between larger daughter artery and smaller daughter artery were determined by the intersection angle of their centerlines.Murray's law was introduced to assess the deviation of the realistic vascular networks from its optimal state.Results Based on the morphometric analysis of coronary artery bifurcations in non-CAD subjects and patients with CAD lesion subjects,the most important finding is that morphological feature parameters of non-CAD subjects are closer to the optimal values than those of patients with CAD lesion.Moreover,by comparing the morphometric data between the left and right coronary arteries,the right coronary artery exhibits a structure closer to the optimal one in morphological feature than the left coronary artery.In addition,coronary arterial trees with CAD lesion have higher asymmetry and larger area expansion ratio(AER)than those of the coronary arterial trees without CAD lesion.Conclusions We morphologically found that the coronary arterial trees with CAD lesion and left are more likely to deviate from the optimal structure predicted by Murray's law than those without CAD lesion and right.The degree to which coronary arterial system deviating from their optimal state may directly affect the incidence of coronary artery disease.This computer morpho-logical analysis strategy is illustrated to be effective in the distinguishing of the geometric differences between the healthy and diseased coronary arteries,and the analysis method may have a large potential in cardiovascular disease earlier diagnosis.     

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

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.     

冠脉树三维重建中几何变换矩阵的优化

冠脉造影图像间的几何变换矩阵是实现冠脉树三维重建的关键。本研究分析了优化几何变换矩阵的必要性，提出利用分支点坐标、分支血管方向矢量和分支夹角三类数据优化几何变换矩阵的方法，并给出了kvenberg-Marquardt算法的优化步骤。最后利用两幅未标定的单面冠脉造影图像，实现冠脉树骨架的三维重建。重建的误差统计结果表明，优化方法有效地提高了冠状动脉树三维重建的精度。     

On the design of the coronary arterial tree: a generalization of Murray's law

Murray's law has been generalized to provide morphometric relationships among various subtrees as well as between a feeding segment and the subtree it perfuses. The equivalent resistance of each subtree is empirically determined to be proportional to the cube of a subtree's cumulative arterial length (L) and inversely proportional to a subtree's arterial volume (V) raised to a power of approximately 2.6. This relationship, along with a minimization of a cost function, and a linearity assumption between flow and cumulative arterial length, provides a power law relationship between V and L. These results, in conjunction with conservation of energy, yield relationships between the diameter of a segment and the length of its distal subtree. The relationships were tested based on a complete set of anatomical data of the coronary arterial trees using two models. The first model, called the truncated tree model, is an actual reconstruction of the coronary arterial tree down to 500 microm in diameter. The second model, called the symmetric tree model, satisfies all mean anatomical data down to the capillary vessels. Our results show very good agreement between the theoretical formulation and the measured anatomical data, which may provide insight into the design of the coronary arterial tree. Furthermore, the established relationships between the various morphometric parameters of the truncated tree model may provide a basis for assessing the extent of diffuse coronary artery disease.     

Patient-specific simulations of stenting procedures in coronary bifurcations: Two clinical cases

Computational simulations of stenting procedures in idealized geometries can only provide general guidelines and their use in the patient-specific planning of percutaneous treatments is inadequate. Conversely, image-based patient-specific tools that are able to realistically simulate different interventional options might facilitate clinical decision-making and provide useful insights on the treatment for each individual patient.The aim of this work is the implementation of a patient-specific model that uses image-based reconstructions of coronary bifurcations and is able to replicate real stenting procedures following clinical indications. Two clinical cases are investigated focusing the attention on the open problems of coronary bifurcations and their main treatment, the provisional side branch approach. Image-based reconstructions are created combining the information from conventional coronary angiography and computed tomography angiography while structural finite element models are implemented to replicate the real procedure performed in the patients.First, numerical results show the biomechanical influence of stents deployment in the coronary bifurcations during and after the procedures. In particular, the straightening of the arterial wall and the influence of two overlapping stents on stress fields are investigated here. Results show that a sensible decrease of the vessel tortuosity occurs after stent implantation and that overlapping devices result in an increased stress state of both the artery and the stents. Lastly, the comparison between numerical and image-based post-stenting configurations proved the reliability of such models while replicating stent deployment in coronary arteries.     

A Novel Simulation Strategy for Stent Insertion and Deployment in Curved Coronary Bifurcations: Comparison of Three Drug-Eluting Stents

The introduction of drug-eluting stents (DES) has reduced the occurrence of restenosis in coronary arteries. However, restenosis remains a problem in stented coronary bifurcations. This study investigates and compares three different second generation DESs when being implanted in the curved main branch of a coronary bifurcation with the aim of providing better insights into the related changes of the mechanical environment. The 3D bifurcation model is based on patient-specific angiographic data that accurately reproduce the in vivo curvatures of the vessel segments. The layered structure of the arterial wall and its anisotropic mechanical behavior are taken into account by applying a novel algorithm to define the fiber orientations. An innovative simulation strategy considering the insertion of a folded balloon catheter over a guide wire is proposed in order to position the stents within the curved vessel. Straightening occurs after implantation of all stents investigated. The resulting distributions of the wall stresses are strongly dependent on the stent design. Using a parametric modeling approach, two design modifications, which reduce the predicted maximum values of the wall stress, are proposed and analyzed.     

Analysis of pig’s coronary arterial blood flow with detailed anatomical data

Blood flow to perfuse the muscle cells of the heart is distributed by the capillary blood vessels via the coronary arterial tree. Because the branching pattern and vascular geometry of the coronary vessels in the ventricles and atria are nonuniform, the flow in all of the coronary capillary blood vessels is not the same. This nonuniformity of perfusion has obvious physiological meaning, and must depend on the anatomy and branching pattern of the arterial tree. In this study, the statistical distribution of blood pressure, blood flow, and blood volume in all branches of the coronary arterial tree is determined based on the anatomical branching pattern of the coronary arterial tree and the statistical data on the lengths and diameters of the blood vessels. Spatial nonuniformity of the flow field is represented by dispersions of various quantities (SD/mean) that are determined as functions of the order numbers of the blood vessels. In the determination, we used a new, complete set of statistical data on the branching pattern and vascular geometry of the coronary arterial trees. We wrote hemodynamic equations for flow in every vessel and every node of a circuit, and solved them numerically. The results of two circuits are compared: oneasymmetric model satisfies all anatomical data (including the meanconnectivity matrix) and the other, asymmetric model, satisfies all mean anatomical data except the connectivity matrix. It was found that the mean longitudinal pressure drop profile as functions of the vessel order numbers are similar in both models, but the asymmetric model yields interesting dispersion profiles of blood pressure and blood flow. Mathematical modeling of the anatomy and hemodynamics is illustrated with discussions on its accuracy.     

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

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 degrees ) 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 (alpha) and area ratios (beta). 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.     

Generation of an Anatomically Based Geometric Coronary Model

A discrete anatomically accurate finite element model of the largest six generations of the coronary arterial network is developed. Using a previously developed anatomically accurate model of ventricular geometry the boundaries of the coronary mesh are defined from measured epicardial coronaries. Network topology is then generated stochastically from published anatomical data. Spatial information is added to this topological data using an avoidance algorithm accounting for global network geometry and optimal local branch angle properties. The generated vessel lengths, radii and connectivity are consistent with the published studies and a relativity even spatial distribution of vessels within the ventricular mesh is achieved. The local finite element coordinates of the coronary nodes within the ventricular mesh are calculated such that the coronary geometry can be recalculated within a deformed ventricular mesh. © 2000 Biomedical Engineering Society. PAC00: 8710+e, 8718Bb, 0270Dh     

Residual strain in human atherosclerotic coronary arteries and age related geometrical changes

The opening angles of 16 rings excised from human coronary arteries with different degrees of atherosclerosis were determined 10 hours after death. Atherosclerosis, as a chronic inflammatory response of arterial endothelium and intima, is defined by three degrees of its development. The opening angle decreases more or less linearly with the distance from the right coronary artery orifice. This is in accordance with the functional requirements posed on blood transport into the coronary arteries. A decrease of the opening angle with age is affected by hardening of the arterial wall, among other factors. This is in accordance with a stochastic model of age related changes in the initial modulus of elasticity of the coronary artery. A part of the free energy of smooth muscle cells, fibroblasts, collagen and elastic fibres is used not for creating residual strain but for remodeling the arterial wall structure. The opening angle is also considerably affected by the degree of atheroclerosis. The dependence on age of the external diameter and the thickness of the intact left and right coronary arteries in the vicinity of the aortic sinus was also analyzed in two female and two male subjects. To ensure the objectivity of the results it is necessary to carry out additional experiments and studies in vivo.     

The relative anatomy of the coronary arterial and venous systems

An anatomical understanding of human coronary arterial and venous systems is necessary for device development and therapy applications that utilize these vessels. We investigated the unique use of contrast‐CT scans from perfusion‐fixed human hearts for three‐dimensional visualization and analysis of anatomical features of the coronary systems. The coronary arterial and venous systems of eleven perfusion‐fixed human hearts were modeled using contrast‐CT and Mimics software. The coronary arteries that coursed near the major coronary veins, how close coronary arteries were to coronary veins, and the size of adjacent coronary arteries were recorded and analyzed. The majority of coronary veins were within 5 mm of a coronary artery somewhere along its length. Interventricular veins elicited the largest occurrence of overlaps. There was significant variability in the percentage of each vein that coursed within 0.5, 1, 2, and 5 mm of a nearby artery. The left marginal veins and anterior interventricular vein had the largest portion of the vein that coursed near a coronary artery. The right coronary artery most often coursed near the middle cardiac vein. The inferior veins of the left ventricle elicited the most variation in adjacent arteries. The left circumflex artery and/or branches of the circumflex artery coursed near the left marginal vein in all cases where there was an artery near the marginal vein. The wide variation of measurements reinforces the importance of a precise understanding of individualized cardiac anatomy in order to provide the highest quality care to cardiac patients. Clin. Anat. 27:1023–1029, 2014. © 2014 Wiley Periodicals, Inc.     

冠状动脉中氧输运的数值模拟研究

利用正常人的CT数据,通过图像分割和重建建立右侧冠状动脉的真实三维几何模型;利用专业的网格划分软件ICEM CFD 12.0对几何模型进行计算网格的划分;利用商用CFD软件Fluent12.0对模型中的血液流动和氧输运进行数值模拟,获得了在入口的平均速度为0.2m/s的定常流情况下,冠状动脉内的流线图、壁面切应力分布图、重要截面上的速度分布和氧浓度分布图。数值模拟结果发现,在血管曲率较大的区域和血管分叉区域的血液流动较为复杂,存在二次流、回流和死水区;在弯曲血管附近靠近内侧的区域的氧浓度显著降低、浓度梯度也降低。这些结果与临床上观察到的这些区域易形成冠状动脉粥样硬化斑块的结论相吻合。     

Knowledge-based system for the three-dimensional reconstruction of blood vessels from two angiographic projections

A knowledge-based system for the three-dimensional reconstruction of blood vessels from wide-angle coronary and stereoscopic cerebral angiographic projections is developed. For the reconstruction of the coronary vessels, the left coronary artery (LCA) is automatically labelled on standard RAO and LAO projections, using anatomical models of the LCA. The labelling system succeeds in giving the most important coronary arteries a correct anatomical label. These labelling results enable us to find corresponding segments in both images. In the case of the reconstruction of the cerebral vessels however, such an anatomical model is clearly unavailable. To find corresponding segments, small-angle projections must be relied on, resulting in very similar images. Owing to the small angular separation between both projections, the three-dimensional reconstruction will be less accurate. Once the corresponding segments in both projections are obtained, the three-dimensional artery trajectory is reconstructed with dynamic programming techniques. The three-dimensional reconstructed coronary vessels are also used for an automatic quantification of stenotic lesions.     

Coronary perfusion pressure and inflow resistance have different influence on intramyocardial flows during coronary sinus interventions

A mathematical model is used to represent the vascular bed of the left coronary circulation by an arterial, a capillary and a venous compartment. The model is first adjusted so as to reproduce arterial hemodynamics known from measurements during normal perfusion. Additionally, measurements under coronary sinus occlusion are used to assess the venous section of the model. While the calculated phasic shapes of epicardial flows are seen to agree with measurements, intramyocardial flows, which are inaccessable to measurement, are predicted from the model. The model is run under stepwise changes of coronary perfusion pressure and coronary artery resistance for both the normal state and coronary sinus occlusion. Intramyocardial flow between capillaries and veins, being the main determinant for a possible therapeutic effect of coronary sinus interventions, is estimated.     

Regulatory muscular structures of the cerebral and renal arteries in different regimens of blood circulation

The aim of this study was to summarize the regularities of location and structure of regulatory muscular structures in cerebral and renal arterial vascular bed in different hemocirculation regimens. The arterial vessels of brain and kidneys were studied in 10 dogs of control group and in 20 animals with experimental hyper- and hypotension caused by the modeling of coarctation of the aorta. Histological, histochemical and histoenzymological methods were used. It was established that in the arteries of organs studied in different hemocirculation regimens resulting from a modeled defect, the complex of uniform muscular structures was formed that included polypoid cushions, muscular-elastic sphincters, bundles of intimal musculature. These structures have some peculiarities of localization in distributive and resistive vessels and are found in the areas of arterial bifurcations. The results obtained suggest that these structures play an active role in the regulation of cerebral and renal hemodynamics.     

Variations of the hepatobiliary vasculature including coexistence of accessory right hepatic artery with unusually arising double cystic arteries: case report and literature review

Familiarity with the different anatomical variations of the arterial supply of the gallbladder and liver is of great importance in all hepatobiliary surgical procedures. A complex anomaly of the hepatobiliary arterial system, which has never been reported before, was found during anatomical dissection of a 73-year-old male Caucasian cadaver. The accessory right hepatic artery (aRHA) took its origin from the gastroduodenal artery. Two cystic arteries were present, the first arising from the gastroduodenal artery (more distal than the aRHA) and the second directly from the aRHA. Potential clinical implications of this anomaly and embryology are discussed. Knowledge of the different anatomical variations of the arterial supply of the gallbladder and liver is of great importance in hepatobiliary surgical procedures.     

A Parametric Model for Studies of Flow in Arterial Bifurcations

Regional differences in hemodynamic loads on arterial walls have been associated with localized vascular disease such as atherosclerosis and cerebral aneurysms. Due to their intrinsic geometric relevance, three-dimensional (3D) reconstructions of arterial segments are frequently used in hemodynamic studies of these diseases. However, it is not possible to use them to systematically vary geometric features for parametric studies. Idealized vascular models are inherently suited for parametric studies, but are limited by their tendency to oversimplify the vessel geometry. In this work, a hierarchy of three parametric bifurcation models is introduced. The models are relatively simple, yet capture all geometric features identified as common to cerebral bifurcations in the complex transition from parent to daughter branches. While these models were initially designed for parametric studies, we also evaluate the possibility of using them for 3D reconstruction of cerebral arteries, with the future goal of improving reconstruction of poor quality clinical data. The lumen surface and vessel hemodynamics are compared between two reconstructed cerebral bifurcations and matched parametric models. Good agreement is found. The average and maximum geometric differences are less than 3.1 and 10%, respectively for all three parametric models. The maximum difference in wall shear stress is less than 8% for the most complex parametric model.     

Anatomical Variations in the Aortic Bifurcation in New Zealand White Rabbits on Arteriography

The radiologic anatomy of the aortic bifurcation in the rabbit has received little study but it is important as this anatomical area is widely used in atherosclerosis research. Thirty rabbits were used to study the aortic bifurcation and subsequent branching patterns on arteriography. Fifteen different arteries were identified. Mean arterial diameters of 2.88 ± 0.7 and 2.27 ± 0.55 mm were obtained for the aorta and external iliac arteries, respectively. The cranial and middle aspects at the seventh lumbar vertebra (L7) were the most frequent anatomical landmarks (53.3% of the cases) for aortic and common iliac bifurcations, respectively. The caudal aspect of L6 was the most frequent origin (50% of the cases) for the median sacral artery. Deep circumflex iliac arteries originated from common iliac arteries and not the abdominal aorta in the rabbit, showing anatomical asymmetry in 73.3% of the cases. No gender disparity was found in the anatomical location of any of the arteries of the study. Knowledge of normal vascular landmarks for the aortic bifurcation as well as anatomical variations should be helpful to future experimental studies. Anat Rec, 297:663–669, 2014. © 2014 Wiley Periodicals, Inc.