Tissue-growth-based synthetic tree generation and perfusion simulation

Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.

     

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.     

Myocardial blood perfusion and transport modeling using inert-tracer techniques: a review and recent investigations

The inert-gas clearance method for measuring blood perfusion in the heart may be useful in detecting and assessing coronary disease and myocardial infarctions. Estimating perfusion from clearance data requires a model of tracer transport. The tracer transport models in use are the compartmental model, the kinetic model, and more complex models which yield estimates by optimal estimation techniques. The implementation of one such complex model in which tissue need not be assumed homogeneous, and the resulting myocardial perfusion and diffusibility estimates, are discussed. Methods are reviewed which may be used to detect and assess coronary disease by average and regional myocardial-perfusion measurements. Possible explanations for the observed multicompartment myocardial clearance curve are discussed.     

Use and limitations of magnetic resonance phase-contrast assessment of coronary flow reserve in a model of collateral dependence

Phase-contrast magnetic resonance imaging (PC-MRI) is useful for assessing coronary artery flow reserves (CFR) in man and acute animal models with intermediate coronary lesions. The present study examines the use of PC-MRI for assessing CFR in a model with critical stenosis and collateral dependence. PC-MRI quantitative flow measurements from the proximal left anterior descending (LAD) and left circumflex (LCX) coronary arteries were compared with myocardial tissue perfusion reserve measurements (microsphere techniques) after placement of a 2.25-mm ameroid constrictor on the proximal LCX in a porcine model; measurements were obtained at implantation (n = 4) and at 3 to 4 weeks (n = 4) and 6 weeks (n = 5) postimplantation. CFR is defined as the ratio of maximal hyperemic flow to baseline flow. Hyperemia was induced using intravenous adenosine (140 mg/kg/min). Collateral dependence in the LCX distri bution was evidenced by angiographic findings of critical stenosis with minimal myocardial histological changes and normal baseline myocardial perfusion (microsphere techniques). In this setting, PC-MRI CFR was correlated with microsphere measures of perfusion reserve. Collateral dependence was confirmed by Evan's blue dye injection. This study provides angiographic, myocardial perfusion, and histological correlates associated with PC-MRI epicardial CFR changes during chronic, progressive coronary artery constriction. It also demonstrates the disparity between epicardial and myocardial measures of coronary flow reserve with collateral dependence and the caveats for PC-MRI use in models of progressive coronary constriction.     

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.     

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.     

Altered coronary vascular control during cold stress in healthy older adults

Cardiovascular-related mortality increases in the cold winter months, particularly in older adults. Previously, we reported that determinants of myocardial O(2) demand, such as the rate-pressure product, increase more in older adults compared with young adults during cold stress. The aim of the present study was to determine if aging influences the coronary hemodynamic response to cold stress in humans. Transthoracic Doppler echocardiography was used to noninvasively measure peak coronary blood velocity in the left anterior descending artery before and during acute (20 min) whole body cold stress in 10 young adults (25 ± 1 yr) and 11 older healthy adults (65 ± 2 yr). Coronary vascular resistance (diastolic blood pressure/peak coronary blood velocity), coronary perfusion time fraction (coronary perfusion time/R-R interval), and left ventricular wall stress were calculated. We found that cooling (via a water-perfused suit) increased left ventricular wall stress, a primary determinant of myocardial O(2) consumption, in both young and older adults, although the magnitude of this increase was nearly twofold greater in older adults (change of 9.1 ± 3.5% vs. 17.6 ± 3.2%, P < 0.05, change from baseline in young and older adults and young vs. older adults). Despite the increased myocardial O(2) demand during cooling, coronary vasodilation (decreased coronary vascular resistance) occurred only in young adults (3.22 ± 0.23 to 2.85 ± 0.18 mmHg·cm(-1)·s(-1), P < 0.05) and not older adults (3.97 ± 0.24 to 3.79 ± 0.27 mmHg·cm(-1)·s(-1), P > 0.05). Consistent with a blunted coronary vascular response, absolute coronary perfusion time tended to decrease (P = 0.13) and coronary perfusion time fraction decreased (P < 0.05) during cooling in older adults but not young adults. Collectively, these data suggest that older adults demonstrate an altered coronary hemodynamic response to acute cold stress.     

<Emphasis Type="Italic">In silico</Emphasis> coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.     

A 3D porous media liver lobule model: the importance of vascular septa and anisotropic permeability for homogeneous perfusion

The hepatic blood circulation is complex, particularly at the microcirculatory level. Previously, 2D liver lobule models using porous media and a 3D model using real sinusoidal geometries have been developed. We extended these models to investigate the role of vascular septa (VS) and anisotropic permeability. The lobule was modelled as a hexagonal prism (with or without VS) and the tissue was treated as a porous medium (isotropic or anisotropic permeability). Models were solved using computational fluid dynamics. VS inclusion resulted in more spatially homogeneous perfusion. Anisotropic permeability resulted in a larger axial velocity component than isotropic permeability. A parameter study revealed that results are most sensitive to the lobule size and radial pressure drop. Our model provides insight into hepatic microhaemodynamics, and suggests that inclusion of VS in the model leads to perfusion patterns that are likely to reflect physiological reality. The model has potential for applications to unphysiological and pathological conditions.     

血管内皮生长因子对猪心肌侧枝血管生成的作用

为检测血管内皮生长因子165（VEGF165)能否促进冠状动脉侧枝血管形成,实验在成功制作小型猪慢性心肌缺血模型后,将以复制缺陷复组腺病毒为载体的人VEGF165互补脱氧核糖核酸[(cDNA)Ad-VEGF165]直接注入左回旋支（LCX）分布的缺血心肌内,以心电图门控单光子发射计算机断层摄影和离体太动脉造影检测冠状动脉侧枝形成,心肌灌注和功能变化,结果显示,与对照组和自身给预Ad-VEGF165前比较,给予Ad-VEGF165四周后心肌缺血面积（P＜0．01）和最大缺血程度（P＜0．01）明显减小,左心室射血分数（P＜0．01）TCX区局部心室壁运动（P＜0．05）明显改善,治疗组侧枝血管生成明显多于对照组（P＜0．05）,表明Ad-VEGF165能诱导心肌侧肢血管形成并改善心肌灌注与运动功能。     

Flash双源CT冠脉成像联合心肌灌注显像对猪急性心肌梗死模型的诊断价值

目的:探讨Flash双源CT(DSCT)冠脉成像联合心肌灌注显像对猪急性心肌梗死模型的诊断价值。方法:使用明胶海绵栓塞法建立5只猪急性心肌梗死模型,使用DSCT冠脉成像联合心肌灌注显像进行"一站式"扫描得到冠脉图像和心肌灌注图像,并与冠脉造影和病理染色相比较。结果:DSCT得到的心肌灌注图像结果与病理染色相比较,敏感性为93%,特异性为91%,阴性预测值为96%,阳性预测值为84%,Kappa值为0.82;DSCT得到的冠脉图像与冠脉造影相比较,敏感性为93%,特异性为81%,阴性预测值为95%,阳性预测值为75%,Kappa值为0.71。结论:DSCT冠脉成像联合心肌灌注显像与组织病理学及冠脉造影一致性较好,可以用于对猪急性心肌梗死模型的诊断。     

Rodent Working Heart Model for the Study of Myocardial Performance and Oxygen Consumption

Isolated working heart models have been used to understand the effects of loading conditions, heart rate and medications on myocardial performance in ways that cannot be accomplished in vivo. For example, inotropic medications commonly also affect preload and afterload, precluding load-independent assessments of their myocardial effects in vivo. Additionally, this model allows for sampling of coronary sinus effluent without contamination from systemic venous return, permitting assessment of myocardial oxygen consumption. Further, the advent of miniaturized pressure-volume catheters has allowed for the precise quantification of markers of both systolic and diastolic performance. We describe a model in which the left ventricle can be studied while performing both volume and pressure work under controlled conditions. In this technique, the heart and lungs of a Sprague-Dawley rat (weight 300-500 g) are removed en bloc under general anesthesia. The aorta is dissected free and cannulated for retrograde perfusion with oxygenated Krebs buffer. The pulmonary arteries and veins are ligated and the lungs removed from the preparation. The left atrium is then incised and cannulated using a separate venous cannula, attached to a preload block. Once this is determined to be leak-free, the left heart is loaded and retrograde perfusion stopped, creating the working heart model. The pulmonary artery is incised and cannulated for collection of coronary effluent and determination of myocardial oxygen consumption. A pressure-volume catheter is placed into the left ventricle either retrograde or through apical puncture. If desired, atrial pacing wires can be placed for more precise control of heart rate. This model allows for precise control of preload (using a left atrial pressure block), afterload (using an afterload block), heart rate (using pacing wires) and oxygen tension (using oxygen mixtures within the perfusate).     

Modeling tree water flow as an unsaturated flow through a porous medium

The electric circuit analogy has had a profound influence on how tree physiologists measure, model and think about tree water flow. For example, previous models that attempt to account for changes in saturation use the electric circuit analogy to define capacitance as the change in saturation per change in pressure. Given that capacitance is constant, this relationship implies that subjecting a block of wood to a pressure of -2.5 MPa for 2 min results in the same change in saturation as subjecting the same block to the same pressure for 2 days. Given the definition of capacitance, it is unclear how the electric circuit analogy could be used to predict changes in saturation separately from changes in pressure. The inadequacies in the electric circuit analogy discussed in this paper necessitate a new theory of tree water flow that recognizes the sapwood as being a porous medium and explicitly deals with the full implications of the unsaturated flow occurring in the sapwood. The theory proposed in this paper combines the Cohesion theory with a mathematical theory of multiphase flow through porous media. Based on this theory, both saturated and unsaturated tree water flow models are presented. Previous partial differential equation models of tree water flow based on the electric circuit analogy are shown to be mathematically equivalent to the model of saturated porous flow. The unsaturated model of tree water flow explicitly models the pressure profile and the rates of change in saturation and specific interfacial area (a measure of how the water in the unsaturated sapwood is partitioned between mobile and immobile components). The unsaturated model highlights the differences between saturated and unsaturated flow and the need to measure the variables governing tree water flow at higher spatial and temporal resolutions.     

Scaling of myocardial mass to flow and morphometry of coronary arteries.

There is no doubt that scaling relations exist between myocardial mass and morphometry of coronary vasculature. The purpose of this study is to quantify several morphological (diameter, length, and volume) and functional (flow) parameters of the coronary arterial tree in relation to myocardial mass. Eight normal porcine hearts of 117-244 g (mean of 177.5 +/- 32.7) were used in this study. Various coronary subtrees of the left anterior descending, right coronary, and left circumflex arteries were perfused at pressure of 100 mmHg with different colors of a polymer (Microfil) to obtain rubber casts of arterial trees corresponding to different regions of myocardial mass. Volume, diameter, and cumulative length of coronary arteries were reconstructed from casts to analyze their relationship to the perfused myocardial mass. Volumetric flow was measured in relationship with perfused myocardial mass. Our results show that arterial volume is linearly related to regional myocardial mass, whereas the sum of coronary arterial branch lengths, vessel diameters, and volumetric flow show an approximately 3/4, 3/8, and 3/4 power-law relationship, respectively, in relation to myocardial mass. These scaling laws suggest fundamental design principles underlying the structure-function relationship of the coronary arterial tree that may facilitate diagnosis and management of diffuse coronary artery disease.     

Coronary vasodilator reserve, capillarity, and mitochondria in trained hypertensive rats

To test the hypothesis that exercise training can reverse the decrements in coronary reserve, capillary density, and mitochondrial volume density evident during established hypertension, we trained spontaneously hypertensive (SHR) and normotensive (WKY) rats on a treadmill over a 3-mo period. At 7 mo of age we used microspheres to evaluate myocardial perfusion in conscious rats. Exercise training did not alter hypertension or left ventricular hypertrophy but did increase maximal O2 consumption in both SHR and WKY. A decrement in left and right ventricular coronary reserve in SHR, compared with WKY, was indicated by 1) a smaller increment in myocardial perfusion during maximal vasodilation with dipyridamole and 2) a higher minimal coronary vascular resistance per unit mass. Exercise training had no significant effect on any index of myocardial perfusion in SHR or WKY. A 12% decrement in capillary numerical density in the endomyocardium of SHR was not reversed by exercise training. We estimated the volume densities of mitochondria, myofibrils, and sarcoplasm using electron microscopy and point-counting stereology on perfusion-fixed hearts. None of the parameters in either SHR or WKY was changed by exercise training. It is concluded that exercise training does not reverse the decrements in coronary reserve and capillary numerical density associated with hypertension in adult rats. Moreover the previously observed enhancement of mitochondrial volume density due to exercise in young hypertensive rats was not observed in adult SHR.     

Should patients with an incidental finding of focal myocardial 18FDG uptake be screened by myocardial perfusion scintigraphy?

PurposeFocal F-18-fluoro-deoxy-glucose uptake in the myocardium can be a sign of resting myocardial ischemia. The purpose of our study was to assess the relevance of performing myocardial perfusion scintigraphy to screen for myocardial ischemia in patients with an incidental finding of focal myocardial F-18-fluoro-deoxy-glucose uptake on a routine F-18-fluoro-deoxy-glucose positron-emission-tomography-computed-tomography.MethodsIn our retrospective multicentric study, patients were included if they had had an incidental finding of myocardial focal F-18-fluoro-deoxy-glucose uptake on a routine F-18-fluoro-deoxy-glucose positron-emission-tomography-computed-tomography and had also undergone myocardial perfusion scintigraphy within 3 months before or after the F-18-fluoro-deoxy-glucose positron-emission-tomography-computed-tomography. Patients with a pattern of ischemia or scar on the myocardial perfusion scintigraphy in the same territory as the focal F-18-fluoro-deoxy-glucose uptake were considered positive.ResultsSeven of the 34 included patients were positive, with an abnormality on the MPS data in the same territory as the focal myocardial F-18-fluoro-deoxy-glucose uptake. 2 of the 6 patients with focal F-18-fluoro-deoxy-glucose uptake in the left anterior descending vascular supply territory and 2 of the 4 patients with focal F-18-fluoro-deoxy-glucose uptake in the standard right coronary artery territory had an abnormal myocardial perfusion scintigraphy. All 12 patients with focal F-18-fluoro-deoxy-glucose uptake restricted to the basal anterolateral and basal inferolateral segments were negative.ConclusionPatients with an incidental finding of focal F-18-fluoro-deoxy-glucose uptake on a routine F-18-fluoro-deoxy-glucose positron-emission-tomography-computed-tomography may be considered as being at risk for coronary artery disease, when this uptake is multisegmentary in the same typical coronary territory and not restricted to the basal anterolateral and basal inferolateral segments.     

Adiposity Is Associated with Gender-Specific Reductions in Left Ventricular Myocardial Perfusion during Dobutamine Stress

Background

Obesity and visceral adiposity are increasingly recognized risk factors for cardiovascular disease. Visceral fat may reduce myocardial perfusion by impairing vascular endothelial function. Women experience more anginal symptoms compared to men despite less severe coronary artery stenosis, as assessed by angiography. Women and men have different fat storage patterns which may account for the observed differences in cardiovascular disease. Therefore, our objective was to evaluate the relationship between visceral adipose tissue distributions and myocardial perfusion in men and women.

Methods

Visceral and subcutaneous fat distributions and myocardial perfusion were measured in 69 men and women without coronary artery disease using magnetic resonance imaging techniques. Myocardial perfusion index was quantified after first-pass perfusion with gadolinium contrast at peak dose dobutamine stress.

Results

We observed inverse relationships between female gender (r = -0.35, p = 0.003), pericardial fat (r = -0.36, p = 0.03), intraperitoneal fat (r = -0.37, p = 0.001), and retroperitoneal fat (r = -0.36, p = 0.002) and myocardial perfusion index. Visceral fat depots were not associated with reduced myocardial perfusion at peak dose dobutamine in men. However, in women, BMI (r = -0.33, p = 0.04), pericardial fat (r = -0.53, p = 0.02), subcutaneous fat (r = -0.39, p = 0.01) and intraperitoneal fat (r = -0.30, p = 0.05) were associated with reduced myocardial perfusion during dobutamine stress.

Conclusions

Higher visceral fat volumes are associated with reduced left ventricular myocardial perfusion at peak dose dobutamine stress in women but not in men. These findings suggest that visceral fat may contribute to abnormal microcirculatory coronary artery perfusion syndromes, explaining why some women exhibit more anginal symptoms despite typically lower grade epicardial coronary artery stenoses than men.     

Human mesenchymal stem cell-conditioned medium improves cardiac function following myocardial infarction

Recent studies suggest that the therapeutic effects of stem cell transplantation following myocardial infarction (MI) are mediated by paracrine factors. One of the main goals in the treatment of ischemic heart disease is to stimulate vascular repair mechanisms. Here, we sought to explore the therapeutic angiogenic potential of mesenchymal stem cell (MSC) secretions. Human MSC secretions were collected as conditioned medium (MSC-CM) using a clinically compliant protocol. Based on proteomic and pathway analysis of MSC-CM, an in vitro assay of HUVEC spheroids was performed identifying the angiogenic properties of MSC-CM. Subsequently, pigs were subjected to surgical left circumflex coronary artery ligation and randomized to intravenous MSC-CM treatment or non-CM (NCM) treatment for 7 days. Three weeks after MI, myocardial capillary density was higher in pigs treated with MSC-CM (645 ± 114 vs 981 ± 55 capillaries/mm(2); P = 0.021), which was accompanied by reduced myocardial infarct size and preserved systolic and diastolic performance. Intravenous MSC-CM treatment after myocardial infarction increases capillary density and preserves cardiac function, probably by increasing myocardial perfusion.     

Morphometry of the coronary microvasculature of the canine left ventricle

The objective of this study was to test for the presence of transmural gradients of various components of the coronary microvasculature of the canine left ventricle. In order to achieve study objectives, the heart and coronary circulation were fixed in a reproducible state of myocardial and vascular tone (diastolic cardiac arrest and maximal coronary vasodilation). Morphometric methods which treat the coronary microvasculature as anisotropically arranged structures were applied for quantitative structural analysis. Eight dog hearts were fixed with a glutaraldehyde-cacodylate-buffered fixative by retrograde perfusion of the aorta with the heart in diastolic arrest and with maximal coronary vasodilation. Tissue samples were taken from areas near to the anterior and posterior papillary muscles from the subendocardium, subepicardium, and intermediate transmural locations. Morphometric results showed a homogeneously arranged array of microvascular and myocardial components with no significant differences in any of the primary morphometric measurements, down to the ultrastructural level, in myocytes relative to transmural location. The results suggest that transmural differences in coronary blood flow are not due to transmural structural differences but rather are due to physiological regulatory mechanisms of coronary blood flow. Further, the results indicate that failure to correct for anisotropy of myocardial structures can lead to erroneous conclusions concerning the structural basis of function in the heart.