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.     

Method for modelling cerebral blood vessels and their bifurcations using circular,homogeneous, generalised cylinders

A method for automatic modelling of blood vessels and their bifurcations from 3D scans of the brain is presented. The method is three-step procedure. First, a skeleton of the cerebral blood vessels is developed, and then the surfaces of the blood vessels are located using an active contour approach. The active contour approach uses circular homogeneous generalised cylinders (CHGCs) to model the thin, elongated blood vessels. Finally, a novel method for modelling the surfaces of the bifurcations in a vessel tree is presented. The method was tested on simulated data: a computed tomography angiography (CTA) and four magnetic resonance angiography (MRA) volumes. Furthermore, the method was tested on ten magnetic resonance images (MRIs) to demonstrate its robustness. The test on the simulated data indicated that the approach for the surface modelling of vessels had a mean radius error of less than 0.1 mm and a mean localisation error of 0.1 mm. Surface models evaluated by an expert in vascular neurosurgery were found to have a smooth appearance and generally agreed with the image data. The test on the MRI scans indicated that the method performed well in noisy environments.     

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

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 μm were reconstructed from cast data while vessels < 40 μm 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.     

Semi-automated tabulation of the 3D topology and morphology of branching networks using CT: application to the airway tree.

Detailed information on biological branching networks (optical nerves, airways or blood vessels) is often required to improve the analysis of 3D medical imaging data. A semi-automated algorithm has been developed to obtain the full 3D topology and dimensions (direction cosine, length, diameter, branching and gravity angles) of branching networks using their CT images. It has been tested using CT images of a simple Perspex branching network and applied to the CT images of a human cast of the airway tree. The morphology and topology of the computer derived network were compared with the manually measured dimensions. Good agreement was found. The airways dimensions also compared well with previous values quoted in literature. This algorithm can provide complete data set analysis much more quickly than manual measurements. Its use is limited by the CT resolution which means that very small branches are not visible. New data are presented on the branching angles of the airway tree.     

Analyzing the human liver vascular architecture by combining vascular corrosion casting and micro‐CT scanning: a feasibility study

Although a full understanding of the hepatic circulation is one of the keys to successfully perform liver surgery and to elucidate liver pathology, relatively little is known about the functional organization of the liver vasculature. Therefore, we materialized and visualized the human hepatic vasculature at different scales, and performed a morphological analysis by combining vascular corrosion casting with novel micro‐computer tomography (CT) and image analysis techniques. A human liver vascular corrosion cast was obtained by simultaneous resin injection in the hepatic artery (HA) and portal vein (PV). A high resolution (110 μm) micro‐CT scan of the total cast allowed gathering detailed macrovascular data. Subsequently, a mesocirculation sample (starting at generation 5; 88 × 68 × 80 mm³) and a microcirculation sample (terminal vessels including sinusoids; 2.0 × 1.5 × 1.7 mm³) were dissected and imaged at a 71‐μm and 2.6‐μm resolution, respectively. Segmentations and 3D reconstructions allowed quantifying the macro‐ and mesoscale branching topology, and geometrical features of HA, PV and hepatic venous trees up to 13 generations (radii ranging from 13.2 mm to 80 μm; lengths from 74.4 mm to 0.74 mm), as well as microvascular characteristics (mean sinusoidal radius of 6.63 μm). Combining corrosion casting and micro‐CT imaging allows quantifying the branching topology and geometrical features of hepatic trees using a multiscale approach from the macro‐ down to the microcirculation. This may lead to novel insights into liver circulation, such as internal blood flow distributions and anatomical consequences of pathologies (e.g. cirrhosis).     

Multi-branched model of the human arterial system

A model of the human arterial system was constructed based on the anatomical branching structure of the arterial tree. Arteries were divided into segments represented by uniform thin-walled elastic tubes with realistic arterial dimensions and wall properties. The configuration contains 128 segments accounting for all the central vessels and major peripheral arteries supplying the extremities including vessels of the order of 2·0 mm diameter. Vascular impedance and pressure and flow waveforms were determined at various locations in the system and good agreement was found with experimental measurements. Use of the model is illustrated in investigating wave propagation in the arterial system and in simulation of arterial dynamics in such pathological conditions as arteriosclerosis and presence of a stenosis in the femoral artery.     

Roots and calibers of the human coronary arteries

The anatomical structure of the coronary-aortic junctions in humans is studied by using corrosion casts of the coronary network. A model is proposed for the specification of these junctions in terms of vessel diameters and branching angles, and the model is used to produce morphological data on these junctions which hitherto have not been available. This anatomical model correlates poorly with the accepted theoretical model of arterial bifurcations in the cardiovascular system. The results suggest that the structure of the coronary-aortic junctions is very different from the structure of typical arterial bifurcations and, by implication, that the flow conditions under which they function are very different. A good understanding of these junctions is important in coronary bypass surgery, where the coronary-aortic junctions are emulated by creating a new anastomosis for the graft at the base of the ascending aorta, and in coronary artery disease, where atherosclerotic lesions occur not far from the coronaiy-aortic junctions.     

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.     

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.     

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.     

Comparative morphometry of the upper bronchial tree in six mammalian species

The length, diameter, and angle of branching of all airways through the sixth level of branching below the trachea were measured on corrosion casts prepared from the lungs of two animals whose bronchial geometry has not previously been studied, namely the donkey and the rabbit. These measurements and morphometric data for the rat, hamster, dog, and human obtained from other sources were analyzed and compared. The cast prepared from human lungs exhibited an airway geometry that was clearly distinct from that shown by the nonhuman species. The human upper bronchial tree was the most symmetrical with respect to airway diameter and angle of branching. In all species studied, airway length was the most irregular parameter. The reasons for differences in branching geometry are not clearly understood. However, when attempting to determine whether a particular species may be used as a model for man in inhalation toxicology, and in the subsequent interpretation of animal data, an appreciation of differences in airway morphometry is essential.     

Multi-generational analysis and visualization of the vascular tree in 3D micro-CT images

Micro-CT scanners can generate large high-resolution three-dimensional (3D) digital images of small-animal organs, such as rat hearts. Such images enable studies of basic physiologic questions on coronary branching geometry and fluid transport. Performing such an analysis requires three steps: (1) extract the arterial tree from the image; (2) compute quantitative geometric data from the extracted tree; and (3) perform a numerical analysis of the computed data. Because a typical coronary arterial tree consists of hundreds of branches and many generations, it is impractical to perform such an integrated study manually. An automatic method exists for performing step (1), extracting the tree, but little effort has been made on the other two steps. We propose an environment for performing a complete study. Quantitative measures for arterial-lumen cross-sectional area, inter-branch segment length, branch surface area and others at the generation, inter-branch, and intra-branch levels are computed. A human user can then work with the quantitative data in an interactive visualization system. The system provides various forms of viewing and permits interactive tree editing for "on the fly" correction of the quantitative data. We illustrate the methodology for 3D micro-CT rat heart images.     

Staged Growth of Optimized Arterial Model Trees

There is a marked difference in the structure of the arterial tree between epi- and endocardial layers of the human heart. To model these structural variations, we developed an extension to the computational method of constrained constructive optimization (CCO). Within the framework of CCO, a model tree is represented as a dichotomously branching network of straight cylindrical tubes, with flow conditions governed by Poiseuille's law. The tree is grown by successively adding new terminal segments from randomly selected points within the perfusion volume while optimizing the geometric location and topological site of each new connection with respect to minimum intravascular volume. The proposed method of staged growth guides the generation of new terminal sites by means of an additional time-dependent boundary condition, thereby inducing a sequence of domains of vascular growth within the given perfusion volume. Model trees generated in this way are very similar to reality in their visual appearance and predict diameter ratios of parent and daughter segments, the distribution of symmetry, the transmural distribution of flow, the volume of large arteries, as well as the ratio of small arterial volume in subendocardial and subepicardial layers in good agreement with experimental data. From this study we conclude that the method of CCO combined with staged growth reproduces many characteristics of the different arterial branching patterns in the subendocardium and the subepicardium, which could not be obtained by applying the principle of minimum volume alone. © 2000 Biomedical Engineering Society. PAC00: 8719Uv, 8719Hh, 4760+i     

Microvascularization of thalamus and metathalamus in common tree shrew (Tupaia glis)

The microangioarchitecture of the thalamus and metathalamus in common tree shrew (Tupaia glis) was studied using vascular corrosion cast/stereomicroscope and SEM technique. The arterial supply of the thalamus and metathalamus was found to originate from perforating branches of the posterior communicating artery, the posterior cerebral artery, the middle cerebral artery, and the anterior choroidal artery. These perforating arteries gave rise to numerous bipinnate arterioles which in turn, with decreasing vessel diameters, branched into a non-fenestrated capillary bed. Venous blood from the superficial parts of the thalamus and metathalamus was collected into the thalamocollicular vein, whereas venous blood from internal aspects of the thalamus was conveyed to the internal cerebral vein. Some venous blood from the most rostral part of the thalamus flowed into tributaries of the middle cerebral vein before draining into the cavernous sinus. Further, the thalamic and metathalamic vascular arrangement was found to be of centripetal type. In addition, thalamic arterial anastomosis was rarely observed. Thus, obstruction of thalamic blood supply could easily lead to thalamic infraction.     

Femoropopliteal artery centerline interpolation using contralateral shape

Curved planar reformation allows comprehensive visualization of arterial flow channels, providing information about calcified and noncalcified plaques and degrees of stenoses. Existing semiautomated centerline-extraction algorithms for curved planar reformation generation fail in severely diseased and occluded arteries. We explored whether contralateral shape information could be used to reconstruct centerlines through femoropopliteal occlusions. We obtained CT angiography data sets of 29 subjects (16m/13f, 19-86yo) without peripheral arterial occlusive disease and five consecutive subjects (1m/4f, 54-85yo) with unilateral femoropopliteal arterial occlusions. A gradient-based method was used to extract the femoropopliteal centerlines in nondiseased segments. Centerlines of the five occluded segments were manually determined by four experts, two times each. We interpolated missing centerlines in 2475 simulated occlusions of various occlusion lengths in nondiseased subjects. We used different curve registration methods (reflection, similarity, affine, and global polynomial) to align the nonoccluded segments, matched the end points of the occluded segments to the corresponding patent end points, and recorded maximum Euclidean distances to the known centerlines. We also compared our algorithm to an existing knowledge-based PCA interpolation algorithm using the nondiseased subjects. In the five subjects with real femoropopliteal occlusions, we measured the maximum Euclidean distance and the percentage of the interpolation that remained within a typical 3 mm radius vessel. In the nondiseased subjects, we found that the rigid registration methods were not significantly (p<0.750) different among themselves but were more accurate than the nonrigid methods (p<0.001). In simulations using nondiseased subjects, our method produced centerlines that stayed within 3 mm of a semiautomatically tracked centerline in occlusions up to 100 mm in length; however, the PCA method was significantly more accurate for all occlusions lengths. In the actual clinical cases, we found the following [occlusion length (mm):error (mm)]: 16.5:0.775, 42.0:1.54, 79.9:1.82, 145:3.23, and 292:6.13, which were almost always more accurate than the PCA algorithm. We conclude that the use of contralateral shape information, when available, is a promising method for the interpolation of centerlines through arterial occlusions.     

Angioarchitecture of the coeliac sympathetic ganglion complex in the common tree shrew (Tupaia glis)

The angioarchitecture of the coeliac sympathetic ganglion complex (CGC) of the common tree shrew ( Tupaia glis ) was studied by the vascular corrosion cast technique in conjunction with scanning electron microscopy. The CGC of the tree shrew was found to be a highly vascularised organ. It normally received arterial blood supply from branches of the inferior phrenic, superior suprarenal and inferior suprarenal arteries and of the abdominal aorta. In some animals, its blood supply was also derived from branches of the middle suprarenal arteries, coeliac artery, superior mesenteric artery and lumbar arteries. These arteries penetrated the ganglion at variable points and in slightly different patterns. They gave off peripheral branches to form a subcapsular capillary plexus while their main trunks traversed deeply into the inner part before branching into the densely packed intraganglionic capillary networks. The capillaries merged to form venules before draining into collecting veins at the peripheral region of the ganglion complex. Finally, the veins coursed to the dorsal aspect of the ganglion to drain into the renal and inferior phrenic veins and the inferior vena cava. The capillaries on the coeliac ganglion complex do not possess fenestrations.     

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.     

Towards a patient-specific hepatic arterial modeling for microspheres distribution optimization in SIRT protocol

Selective internal radiation therapy (SIRT) using Yttrium-90 loaded glass microspheres injected in the hepatic artery is an emerging, minimally invasive therapy of liver cancer. A personalized intervention can lead to high concentration dose in the tumor, while sparing the surrounding parenchyma. We propose a computational model for patient-specific simulation of entire hepatic arterial tree, based on liver, tumors, and arteries segmentation on patient’s tomography. Segmentation of hepatic arteries down to a diameter of 0.5 mm is semi-automatically performed on 3D cone-beam CT angiography. The liver and tumors are extracted from CT-scan at portal phase by an active surface method. Once the images are registered through an automatic multimodal registration, extracted data are used to initialize a numerical model simulating liver vascular network. The model creates successive bifurcations from given principal vessels, observing Poiseuille’s and matter conservation laws. Simulations provide a coherent reconstruction of global hepatic arterial tree until vessel diameter of 0.05 mm. Microspheres distribution under simple hypotheses is also quantified, depending on injection site. The patient-specific character of this model may allow a personalized numerical approximation of microspheres final distribution, opening the way to clinical optimization of catheter placement for tumor targeting.     

A physical model of the human systemic arterial tree

A physical model of the human arterial tree has been developed to be used in a computer controlled mock circulatory system (MCS). Its aim is to represent systemic arterial tree properties and extend the capacity of the MCS to intraortic balloon pump (IABP) testing. The main problem was to model the aorta simply and to accurately reproduce aortic impedance and related flow and pressure waveforms at different sections. The model is composed of eight segments; lumped parameter models are used for its peripheral loads. After the numerical simulation, the physical model was reproduced as a silicon rubber tapered tube. This rubber was chosen for its stability over time and the acceptable behaviour of its Young's modulus (Ey = 22.23 gf x mm(-2)) with different loads and in comparison with data from the literature (Ey approximately 20.4 gf x mm(-2)). The properties of each segment of the aorta were defined in terms of compliance, resistance and inertance as a function of length, radius and thickness. The variable thickness was obtained using positive and negative molds. Total static compliance of the aorta model is about 1.125 x 10(-3) g(-1) x cm4 x sec2 (1.5 cm3 x mmHg(-1)). Measurements were performed both on numerical and physical models (in open and closed loop configuration). Data reported show pressure and flow waveforms along with input impedance modulus and phase. The results are in good agreement with data from the literature.     

脊髓内部动脉构筑的优化分析

4例新鲜足月胎儿尸体脊髓,经墨汁灌注,厚片透明后,选择Y型的动脉分支314个(颈段91个,胸段125个,腰段98个),同步测量动脉分支管径和夹角,对其进行了优化分析。从实测值和理论值的定性比较图中可以看出,动脉分支的管径和夹角的实测值和理论值是近乎一致的,同时又具有合理的生物学离散特点,从定量角度出发,如果规定实测值与理论值的相对误差低于10％时为优化状态,据此标准较大分支的管径处于优化状态的动脉分支有51％,较小分支的管径处于优化状态的动脉分支有50％,较大分支与母管夹角处于优化状态的有47％,较小分支与母管夹角处于优化状态的有28％,分支总角度处于优化状态的有49％,面积比处于优化状态的有49％。以上结果显示人脊髓内部动脉分支的几何形态也支持有关动脉分支的理论假设,即心血管系统动脉分支的管径和夹角被某些与心血管系统生理机能有关的优化原则所制约。