Relationship between arterial diameter and perfused tissue volume in myocardial microcirculation: a micro-CT-based analysis

The volume of myocardial tissue that is perfused by an epicardial coronary artery has been shown to be predictably related to the diameter of the epicardial arterial lumen. However, to what extent the intramyocardial microvasculature follows the epicardial rules remains unclear. To explore the relationship between the diameter of coronary arterioles and their subsequent perfused myocardial volumes, we quantified the volume of nonperfused myocardium resulting from an embolized arteriole of a certain diameter. We injected a single dose of microspheres selected from one of nine possible microsphere combinations (10, 30, and 100 microm diameter, each at three possible doses) into the left anterior descending coronary and/or left circumflex arteries of seven anesthetized pigs. At postmortem, the coronary arteries were infused with a radiopaque silicon polymer. Embolized myocardium (1 cm(3)) was scanned with a microcomputerized tomography scanner and resulted in three-dimensional images that consisted of 20 microm/side cubic voxels and a subvolume of the specimen with 4 microm/side cubic voxels. Image analysis provided the number and volumes of myocardial perfusion defects for each size and dose of microspheres. The smallest individual myocardial perfusion defects, which correspond to the volume of myocardium perfused by a single embolized arteriole, were found to be 0.0004 +/- 0.0002, 0.02 +/- 0.004, and 0.62 +/- 0.099 mm(3) for the 10-, 30-, and 100-microm microspheres, respectively. The number of myocardial perfusion defects in the embolized myocardium was inversely related to the dose of the injected microspheres. This reflects a clustering behavior that is consistent with a random distribution process of the individual embolized perfusion defects.     

Effect of passive myocardium on the compliance of porcine coronary arteries

The objective of this study was to determine the effect of passive myocardium on the coronary arteries under distension and compression. To simulate distension and compression, we placed a diastolic-arrested heart in a Lucite box, where both the intravascular pressure and external (box) pressure were varied independently and expressed as a pressure difference (DeltaP = intravascular pressure - box pressure). The DeltaP-cross-sectional area relationship of the first several generations of porcine coronary arteries and the DeltaP-volume relationship of the coronary arterial tree (vessels >0.5 mm in diameter) were determined using a video densitometric technique in the range of +150 to -150 mmHg. The vasodilated left anterior descending (LAD) coronary artery of six KCl-arrested hearts were perfused with iodine and 3% Cab-O-Sil. The intravascular pressure was varied in a triangular pattern, whereas the absolute cross-sectional area of each vessel and the total arterial volume were calculated using video densitometry under different box pressures (0, 50, 100, and 150 mmHg). In the range of positive DeltaP, we found that the compliance of the proximal LAD artery in situ (4.85 +/- 3.8 x 10-3 mm2/mmHg) is smaller than that of the same artery in vitro (16.5 +/- 6 x 10-3 mm2/mmHg; P = 0.009). Hence, the myocardium restricts the compliance of the epicardial artery under distension. In the negative DeltaP range, the LAD artery does not collapse, whereas the same vessel readily collapses when tested in vitro. Hence, we conclude that myocardial tethering prevents collapse of large blood vessel under compression.     

Analysis of blood flow in the entire coronary arterial tree

A hemodynamic analysis of coronary blood flow must be based on the measured branching pattern and vascular geometry of the coronary vasculature. We recently developed a computer reconstruction of the entire coronary arterial tree of the porcine heart based on previously measured morphometric data. In the present study, we carried out an analysis of blood flow distribution through a network of millions of vessels that includes the entire coronary arterial tree down to the first capillary branch. The pressure and flow are computed throughout the coronary arterial tree based on conservation of mass and momentum and appropriate pressure boundary conditions. We found a power law relationship between the diameter and flow of each vessel branch. The exponent is approximately 2.2, which deviates from Murray's prediction of 3.0. Furthermore, we found the total arterial equivalent resistance to be 0.93, 0.77, and 1.28 mmHg.ml(-1).s(-1).g(-1) for the right coronary artery, left anterior descending coronary artery, and left circumflex artery, respectively. The significance of the present study is that it yields a predictive model that incorporates some of the factors controlling coronary blood flow. The model of normal hearts will serve as a physiological reference state. Pathological states can then be studied in relation to changes in model parameters that alter coronary perfusion.     

Vascular metabolic dissipation in Murray's law

The metabolic dissipation in Murray's minimum energy hypothesis includes only the blood metabolism. The metabolic dissipation of the vascular tree, however, should also include the metabolism of passive and active components of the vessel wall. In this study, we extend the metabolic dissipation to include blood metabolism, as well as passive and active components of the vessel wall. The analysis is extended to the entire vascular arterial tree rather than a single vessel as in Murray's formulation. The calculations are based on experimentally measured morphological data of coronary artery network and the longitudinal distribution of blood pressure along the tree. Whereas the model includes multiple dissipation sources, the total metabolic consumption of a complex vascular tree is found to remain approximately proportional to the cumulative arterial volume of the unit. This implies that the previously described scaling relations for the various morphological features (volume, length, diameter, and flow) remain unchanged under the generalized condition of metabolic requirements of blood and blood vessel wall.     

Bifurcation asymmetry of the porcine coronary vasculature and its implications on coronary flow heterogeneity

The branching pattern of the coronary arteries and veins is asymmetric, i.e., many small vessels branch off of a large trunk such that the two daughter vessels at a bifurcation are of unequal diameters and lengths. One important implication of the geometric vascular asymmetry is the dispersion of blood flow at a bifurcation, which leads to large spatial heterogeneity of myocardial blood flow. To document the asymmetric branching pattern of the coronary vessels, we computed an asymmetry ratio for the diameters and lengths of all vessels, defined as the ratio of the daughter diameters and lengths, respectively. Previous data from silicone elastomer cast of the entire coronary vasculature including arteries, arterioles, venules, and veins were analyzed. Data on smaller vessels were obtained from histological specimens by optical sectioning, whereas data on larger vessels were obtained from vascular casts. Asymmetry ratios for vascular areas, volumes, resistances, and flows of the various daughter vessels were computed from the asymmetry ratios of diameters and lengths for every order of mother vessel. The results show that the largest orders of arterial and venous vessels are most asymmetric and the degree of asymmetry decreases toward the smaller vessels. Furthermore, the diameter asymmetry at a bifurcation is significantly larger for the coronary veins (1.7-6.8 for sinus veins) than the corresponding arteries (1.5-5.8 for left anterior descending coronary artery) for orders 2-10, respectively. The reported diameter asymmetry at a bifurcation leads to significant heterogeneity of blood flow at a bifurcation. Hence, the present data quantify the dispersion of blood flow at a bifurcation and are essential for understanding flow heterogeneity in the coronary circulation.     

Dynamic capacitance of epicardial coronary arteries in vivo

The dynamic capacitance of epicardial coronary arteries (i.d. greater than or equal to 0.4 mm) in vivo was assessed from the volume stiffness and volume of these arteries. The volume stiffness was derived from the pressure wave front velocity as determined in dogs by measuring the delay time between the pressure pulses recorded proximal and distal to a segment of the anterior descending branch of the left coronary artery. The pressure pulse was generated elsewhere in the arterial system during diastole. The volume of the epicardial coronary arteries was calculated from the lengths and diameters as measured in araldite casts, making corrections for in-vitro/in-vivo differences in dimensions. The dynamic capacitance of the right coronary artery, and the anterior descending and circumflex branches of the left coronary artery at an arterial pressure of 13.3 kPa and a frequency between 7 and 30 Hz was found to be 0.0024 +/- 0.0013, 0.0062 +/- 0.0028 and 0.0079 +/- 0.0035 mL/kPa (mean +/- SD), respectively. The total capacitance of the epicardial coronary arteries was calculated to be (0.007 mL/kPa)/100 g, which is small as compared to the total capacitance of the coronary vasculature, including the intramyocardial compartment, which is in the order of (0.5 mL/kPa)/100 g [1].     

Diameter-dependent axial prestretch of porcine coronary arteries and veins

The pressure-diameter relation (PDR) and the wall strain of coronary blood vessels have important implications for coronary blood flow and arthrosclerosis, respectively. Previous studies have shown that these mechanical quantities are significantly affected by the axial stretch of the vessels. The objective of this study was to measure the physiological axial stretch in the coronary vasculature; i.e., from left anterior descending (LAD) artery tree to coronary sinus vein and to determine its effect on the PDR and hence wall stiffness. Silicone elastomer was perfused through the LAD artery and coronary sinus trees to cast the vessels at the physiologic pressure. The results show that the physiological axial stretch exists for orders 4 to 11 (> 24 μm in diameter) arteries and orders -4 to -12 (>38 μm in diameter) veins but vanishes for the smaller vessels. Statistically, the axial stretch is higher for larger vessels and is higher for arteries than veins. The axial stretch λ(z) shows a linear variation with the order number (n) as: λ(z) = 0.062n + 0.75 (R(2) = 0.99) for artery and λ(z) = -0.029n + 0.89 (R(2) = 0.99) for vein. The mechanical analysis shows that the axial stretch significantly affects the PDR of the larger vessels. The circumferential stretch/strain was found to be significantly higher for the epicardial arteries (orders 9-11), which are free of myocardium constraint, than the intramyocardial arteries (orders 4-8). These findings have fundamental implications for coronary blood vessel mechanics.     

犬冠状动脉阻力的胆碱能调节

本实验在麻醉开胸犬,采用冠状动脉左旋支恒流灌注,于搏动的和心室纤颤(VF)的心脏,研究了电刺激迷走神经(VNS)及冠状动脉内注入乙酰胆碱(ACh)对冠状动脉阻力的影响。当 VNS 和冠脉内给 ACh 时,(1)心肌内小冠状动脉阻力显著减低,而心外膜大冠状动脉阻力并无明显变化;(2)冠状动脉左旋支总阻力的减低幅度在 VF 的心脏比在搏动的心脏显著减小。以上结果表明,迷走-ACh 扩张冠脉的作用主要是舒张心肌内小冠状动脉,并可通过减低心肌收缩力而间接降低冠状动脉阻力。     

Vessel tortuousity and reduced vascularization in the fetoplacental arterial tree after maternal exposure to polycyclic aromatic hydrocarbons

Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous environmental pollutants and the main toxicants found in cigarettes. Women are often exposed to PAHs before pregnancy, typically via prepregnancy smoking. To determine how prepregnancy exposure affects the fetoplacental vasculature of the placenta, we exposed female mice to PAHs before conception, perfused the fetoplacental arterial trees with X-ray contrast agent, and imaged the vasculature ex vivo by microcomputed tomography (micro-CT) at embryonic day 15.5. Automated vascular segmentation and flow calculations revealed that in control trees, <40 chorionic plate vessels (diameter>180 μm) gave rise to ～1,300 intraplacental arteries (50-180 μm), predicting an arterial vascular resistance of 0.37±0.04 mmHg·s·μl(-1). PAH exposure increased vessel curvature of chorionic plate vessels and significantly increased the tortuousity ratio of the tree. Intraplacental arteries were reduced by 17%, primarily due to a 27% decrease in the number of arteriole-sized (50-100 μm) vessels. There were no changes in the number of chorionic vessels, the depth or span of the tree, the diameter scaling coefficient, or the segment length-to-diameter ratio. PAH exposure resulted in a tree with a similar size and dichotomous branching structure, but one that was comparatively sparse so that arterial vascular resistance was increased by 30%. Assuming the same pressure gradient, blood flow would be 19% lower. Low flow may contribute to the 23% reduction observed in fetal weight. New insights into the specific effects of PAH exposure on a developing arterial tree were achieved using micro-CT imaging and automated vascular segmentation analysis.     

Modified heart-lung preparation for the evaluation of systolic and diastolic coronary flow in rats

A modified heart-lung preparation of the rat, which permits measuring systolic and diastolic coronary flow separately and enables coronary compliance to be evaluated, is described. The systemic circulation was substituted by a shunt circuit, and the elastic properties of the arterial tree were mimicked by a rubber balloon. Systolic and diastolic coronary flow was evaluated from the pulmonary and aortic flow signal. Integrated phasic pulmonary flow represented right ventricular stroke volume. Integrated phasic systolic aortic flow represented left ventricular stroke volume minus that volume flowing into the coronary arteries during systole, because the aortic flow probe had to be inserted distal to the origin of the coronary vessels. Because right and left ventricular stroke volume was identical under steady-state conditions, the difference between systolic pulmonary and systolic aortic flow resulted in systolic coronary flow. Diastolic coronary flow was measured by means of the retrograde flow through the aortic flow probe. Coronary compliance was calculated according to Frank's windkessel model from coronary resistance and from central diastolic aortic pressure, which decayed exponentially after switching out the rubber balloon and the shunt circuit. It could be shown that the proportion of systolic to diastolic coronary flow depends on coronary compliance.     

Flow patterns in three-dimensional porcine epicardial coronary arterial tree

The branching pattern of epicardial coronary arteries is clearly three-dimensional, with correspondingly complex flow patterns. The objective of the present study was to perform a detailed hemodynamic analysis using a three-dimensional finite element method in a left anterior descending (LAD) epicardial arterial tree, including main trunk and primary branches, based on computed tomography scans. The inlet LAD flow velocity was measured in an anesthetized pig, and the outlet pressure boundary condition was estimated based on scaling laws. The spatial and temporal wall shear stress (WSS), gradient of WSS (WSSG), and oscillatory shear index (OSI) were calculated and used to identify regions of flow disturbances in the vicinity of primary bifurcations. We found that low WSS and high OSI coincide with disturbed flows (stagnated, secondary, and reversed flows) opposite to the flow divider and lateral to the junction orifice of the main trunk and primary branches. High time-averaged WSSG occurs in regions of bifurcations, with the flow divider having maximum values. Low WSS and high OSI were found to be related through a power law relationship. Furthermore, zones of low time-averaged WSS and high OSI amplified for larger diameter ratio and high inlet flow rate. Hence, different focal atherosclerotic-prone regions may be explained by different physical mechanism associated with certain critical levels of low WSS, high OSI, and high WSSG, which are strongly affected by the diameter ratio. The implications of the flow patterns for atherogenesis are enumerated.     

The branching angles in computer-generated optimized models of arterial trees

The structure of a complex arterial tree model is generated on the computer using the newly developed method of "constrained constructive optimization." The model tree is grown step by step, at each stage of development fulfilling invariant boundary conditions for pressures and flows. The development of structure is governed by adopting minimum volume inside the vessels as target function. The resulting model tree is analyzed regarding the relations between branching angles and segment radii. Results show good agreement with morphometric measurements on corrosion casts of human coronary arteries reported in the literature.     

Distribution of stress and strain along the porcine aorta and coronary arterial tree

The existence of a homeostatic state of stresses and strains has been axiomatic in the cardiovascular system. The objective of this study was to determine the distribution of circumferential stress and strain along the aorta and throughout the coronary arterial tree to test this hypothesis. Silicone elastomer was perfused through the porcine aorta and coronary arterial tree to cast the arteries at physiological pressure. The loaded and zero-stress dimensions of the vessels were measured. The aorta (1.8 cm) and its secondary branches were considered down to 1.5 mm diameter. The left anterior descending artery (4.5 mm) and its branches down to 10 microm were also measured. The Cauchy mean circumferential stress and midwall stretch ratio were calculated. Our results show that the stretch ratio and Cauchy stress were lower in the thoracic than in the abdominal aorta and its secondary branches. The opening angle (theta) and midwall stretch ratio (lambda) showed a linear variation with order number (n) as follows: theta = 10.2n + 63.4 (R(2) = 0.989) and lambda = 4.47 x 10(-2)n + 1.1 (R(2) = 0.995). Finally, the stretch ratio and stress varied between 1.2 and 1.6 and between 10 and 150 kPa, respectively, along the aorta and left anterior descending arterial tree. The relative uniformity of strain (50% variation) from the proximal aorta to a 10-microm arteriole implies that the vascular system closely regulates the degree of deformation. This suggests a homeostasis of strain in the cardiovascular system, which has important implications for mechanotransduction and for vascular growth and remodeling.     

Right Internal Mammary Artery Implantation into Right Ventricular Myocardium for Revascularization of the Entire Heart: Experimental Data and Preliminary Report

The left internal mammary artery implant combined with epicardiectomy and free omental graft provides three extra-coronary sources of blood. This operation tested in dogs with 92% main-stem occlusion of three coronary arteries protected 75% of the animals. Applied clinically in over 100 patients, the operation resulted in 90% improvement. To obtain complete myocardial revascularization, the right internal mammary artery has been used as a fourth source of extra-coronary blood. In 57 animals, the right internal mammary arteries were implanted into the anterior walls of the right ventricle; in 80% this vessel formed anastomoses with the right coronary tree, and in 65% with the right and left coronary arteriolar systems. Six patients are described who underwent right internal mammary artery implantation; five of these in addition had the combined operation of left internal mammary artery implant, epicardiectomy and free omental graft. All patients had completely blocked right coronary arteries; in addition, five had advanced disease of the left coronary arterial tree.     

Quantification of Blood Supply to the Left Ventricular Myocardium in Normal Subjects and Patients with Coronary Heart Disease

The subjects who underwent diagnostic coronarography and detailed examination included 274 patients with lesions in the left coronary artery and its branches and 50 subjects without pathological changes in the coronary arteries or left ventricle. The authors also examined 149 patients with unchanged coronary arteries (67 with small vessel disease 42 with cardiomyopathy of various etiology; and 40 with other pathologies, such as the WPW syndrome, arterial hypertension, aortic stenosis, etc.). In addition to routine retrograde left heart catheterization and recording of the hemodynamic parameters demonstrated by ventriculography, the coronary blood flow was measured in all patients. Its normalized (specific) values are a basis for the coronary blood flow quantification in normal subjects, patients with the coronary heart disease (with insufficient oxygen supply to the myocardium), and those with cardiomyopathy of various genesis (when the myocardial oxygen demand increases together with the left ventricular myocardium mass).     

Assessment of coronary flow reserve in nuclear cardiology

The coronary flow reserve is a quantitative parameter defined by the ratio maximal myocardial blood flow to rest myocardial blood flow, which allows to give functional information on the whole coronary arterial tree, integrating both epicardial arteries and microcirculatory. The coronary flow reserve is a powerful tool to guide therapy and to assess prognosis. Exploratory tools, initially limited to experimental invasive techniques, have evolved over the last 10 years, allowing to envisage its use in daily clinical practice. This article reviews the pathophysiology of the coronary flow reserve and the various invasive and non-invasive exploration tools available to practitioners, integrating them into clinical practice.     

Homogenization modeling for the mechanics of perfused myocardium

Altered coronary perfusion can change the apparent diastolic stiffness of ventricular myocardium--the ‘garden hose’ effect. Our recent findings showed that myocardial strains are reduced during ventricular filling, primarily along the directions transverse to the coronary microvessels. In this article, we review hypotheses and theoretical models regarding the role that regional wall stress plays in the mechanical interaction between myocardium and coronary circulation. Various mechanisms have been used to explain the effects of the tissue stress on coronary flow, as well as the effect of coronary dynamics on myocardial mechanics. Many models of coronary pressure-flow relations using lumped parameter circuit analogs. Poroelasticity and swelling theories have been used to model the mechanics of perfused muscle. Here, we describe a new mathematical model of the mechanics of perfused myocardium derived using homogenization theory. In this model, perfused myocardium is treated as a nonlinear anisotropic elastic solid embedded with cylindrical vessels of known distensibility. The solid compartment is incompressible but the vascular compartment may change volume according to a simple relation between vessel diameter and perfusion pressure. The work done by the perfusion pressure in changing vascular volume contributes to the macroscopic strain energy and hence affects the stress and stiffness of the composite. Conversely, the stress in the tissue affects microvessel diameter and volume, since tractions transverse to the vessel axis oppose the internal blood pressure. Finite element simulations of passive filling show good agreement of model with experimental results.     

Is arterial wall-strain stiffening an additional process responsible for atherosclerosis in coronary bifurcations?: an in vivo study based on dynamic CT and MRI

Coronary bifurcations represent specific regions of the arterial tree that are susceptible to atherosclerotic lesions. While the effects of vessel compliance, curvature, pulsatile blood flow, and cardiac motion on coronary endothelial shear stress have been widely explored, the effects of myocardial contraction on arterial wall stress/strain (WS/S) and vessel stiffness distributions remain unclear. Local increase of vessel stiffness resulting from wall-strain stiffening phenomenon (a local process due to the nonlinear mechanical properties of the arterial wall) may be critical in the development of atherosclerotic lesions. Therefore, the aim of this study was to quantify WS/S and stiffness in coronary bifurcations and to investigate correlations with plaque sites. Anatomic coronary geometry and cardiac motion were generated based on both computed tomography and MRI examinations of eight patients with minimal coronary disease. Computational structural analyses using the finite element method were subsequently performed, and spatial luminal arterial wall stretch (LW(Stretch)) and stiffness (LW(Stiff)) distributions in the left main coronary bifurcations were calculated. Our results show that all plaque sites were concomitantly subject to high LW(Stretch) and high LW(Stiff), with mean amplitudes of 34.7 ± 1.6% and 442.4 ± 113.0 kPa, respectively. The mean LW(Stiff) amplitude was found slightly greater at the plaque sites on the left main coronary artery (mean value: 482.2 ± 88.1 kPa) compared with those computed on the left anterior descending and left circumflex coronary arteries (416.3 ± 61.5 and 428.7 ± 181.8 kPa, respectively). These findings suggest that local wall stiffness plays a role in the initiation of atherosclerotic lesions.     

Modeling the large-scale geometry of human coronary arteries

Two principles suffice to model the large-scale geometry of normal human coronary arterial networks. The first principle states that artery diameters are set to minimize the power required to distribute blood through the network. The second principle states that arterial tree geometries are set to globally minimize the lumen volume. Given only the coordinates of an arterial tree's source and "leaves", the model predicts the nature of the network connecting the source to the leaves. Measurements were made of the actual geometries of arterial trees from postmortem healthy human coronary arteriograms. The tree geometries predicted by the model look qualitatively similar to the actual tree geometries and have volumes that are within a few percent of those of the actual tree geometries. Human coronary arteries are therefore within a few percent of perfect global volume optimality. A possible mechanism for this near-perfect global volume optimality is suggested. Also, the model performs best under the assumption that the flow is not entirely steady and laminar.     

Simulation of coronary circulation with special regard to the venous bed and coronary sinus occlusion

The vascular beds of the left circumflex and the left anterior descending coronary arteries are modelled by means of coupled differential equations that consider an arterial, a capillary and a venous section. In a stepwise procedure, experimental data from normal coronary perfusion and coronary sinus occlusion are used to assess the model parameters. For venous distensibility, a non-linear form of pressure-volume relationship proved vital to reproduce the characteristics of the rise in venous pressure after the onset of coronary sinus occlusion. Numerical integration was carried out for normal perfusion and for coronary sinus occlusion, yielding time courses of flows, volumes and pressures within large coronary arteries, capillaries and coronary veins. Coronary sinus occlusion reduces total mean flow by 18% and divides intramyocardial flow between the capillaries and the veins into a forward component of 3.03 mls⁻¹ and a backward component of − 1.54 mls⁻¹. This result represents a prediction for a haemodynamic quantity which is therapeutically important but inacessible to measurement. Varying degrees of systolic myocardial squeezing are studied to display the impact of myocardial contractility and vessel collapse on the mean values and phasic components of intra-myocardial flows.