Computer simulation of arterial flow with applications to arterial and aortic stenoses

A computer model for simulating pressure and flow propagation in the human arterial system is developed. The model is based on the one-dimensional flow equations and includes nonlinearities arising from geometry and material properties. Fifty-five arterial segments, representing the various major arteries, are combined to form the model of the arterial system. Particular attention is paid to the development of peripheral pressure and flow pulses under normal flow conditions and under conditions of arterial and aortic stenoses. Results show that the presence of severe arterial stenoses significantly affects the nature of the distal pressure and flow pulses. Aortic stenoses also have a profound effect on central and peripheral pressure pulse formation. Comparison with the published experimental data suggests that the model is capable of simulating arterial flow under normal flow conditions as well as conditions of stenotic obstructions in a satisfactory manner.     

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.     

Coronary circulatory pressure gradients

The pressure gradients of the canine coronary circulation were measured in 37 dogs during control and following eight interventions: left stellate ganglion or left vagosympathetic trunk stimulation, as well as isoproterenol, acetylcholine, noradrenaline, adenosine, phenylephrine, or adrenaline infusions. During control, pressure gradients in the epicardial coronary arteries (measured from the aorta to coronary artery branch) were 15.2 +/- 1 mmHg (1 mmHg (1 mmHg = 133.32 Pa) during systole and 10.6 +/- 1.5 mmHg during diastole. Adrenaline increased this systolic gradient, while acetylcholine and phenylephrine decreased it. In contrast, the pressure gradients in the small coronary arteries (from the branch of an epicardial artery to the pressure in an obstructed coronary artery) were 56 +/- 1.3 mmHg during systole and 63.7 +/- 1.3 mmHg during diastole. These gradients were increased by phenylephrine during both systole and diastole, noradrenaline and adrenaline during diastole and decreased by isoproterenol (systolic), left vagosympathetic trunk stimulation (diastolic), acetylcholine (systolic and diastolic), and adenosine (diastolic). The microcirculation and small vein gradients during control were 16.4 +/- 1.2 mmHg during systole and 8.5 +/- 0.8 mmHg during diastole. Decreases in this gradient were produced by isoproterenol, acetylcholine, and adenosine during systole and adenosine during diastole. These observations are consistent with the concept that the coronary circulation has considerable regulatory capacity in all of its component parts. Specifically, epicardial arteries appear to function as both conduits and as resistance vessels, small arteries as major resistance vessels, and the microcirculation and small veins as both capacitors and resistors.     

Hemodynamic diagnostics of epicardial coronary stenoses: <Emphasis Type="Italic">in-vitro</Emphasis> experimental and computational study

Background  

The severity of epicardial coronary stenosis can be assessed by invasive measurements of trans-stenotic pressure drop and flow. A pressure or flow sensor-tipped guidewire inserted across the coronary stenosis causes an overestimation in true trans-stenotic pressure drop and reduction in coronary flow. This may mask the true severity of coronary stenosis. In order to unmask the true severity of epicardial stenosis, we evaluate a diagnostic parameter, which is obtained from fundamental fluid dynamics principles. This experimental and numerical study focuses on the characterization of the diagnostic parameter, pressure drop coefficient, and also evaluates the pressure recovery downstream of stenoses.     

Chronic exercise training preserves prostaglandin-induced dilation of epicardial coronary artery during development of heart failure in awake dogs

Although it has been shown that long-term exercise training preserves endothelium-mediated nitric oxide vasodilator function in chronic heart failure (CHF), whether exercise training exerts similar beneficial effects on endothelial/prostaglandin-mediated vasodilator capacity in coronary circulation during the development of CHF has not been determined. Fifteen mongrel dogs were surgically instrumented for measurement of left ventricular pressure, aortic pressure, coronary blood flow and left circumflex coronary artery diameter. Dogs (n = 5) who underwent 4 weeks of cardiac pacing (210 b/min for 3 weeks and 240 b/min for the 4th week) developed CHF as characterized by significant reduction in left ventricular systolic pressure, mean arterial pressure and left ventricular dP/dt, increases in left ventricular end-diastolic pressure and heart rate, as well as clinical signs of CHF. Endothelial prostaglandin-mediated vasodilation of the epicardial coronary artery was impaired, as manifested by an attenuated arachidonic acid (AA)-induced dilation of the artery (epicardial artery diameter increased by: 0.78 +/- 0. 84% in CHF versus 4.6 +/- 0.89% in normal, P < 0.05); however, prostacyclin (PGI(2))-induced and nitroglycerin-induced vasodilation of the coronary circulation were not altered. In contrast, dogs (n = 6) with cardiac pacing plus daily exercise training (4.4 +/- 0.3 km/h, 2 h/day) only developed mild cardiac dysfunction, and the response of the epicardial coronary artery diameter to AA was preserved (epicardial artery diameter increased by 4.2 +/- 0.98% from baseline, P 0.05 compared to its respective control). Thus, long-term exercise training preserves endothelial/prostaglandin-mediated dilation of epicardial coronary artery during development of CHF.     

Steady flow through a double converging-diverging tube model for mild coronary stenoses

Velocity profiles and the pressure drop across two mild (62 percent) coronary stenoses in series have been investigated numerically and experimentally in a perspex-tube model. The mean flow rate was varied to correspond to a Reynolds number range of 50-400. The pressure drop across two identical (62 percent) stenoses show that for low Reynolds numbers the total effect of two stenoses equals that of two single stenoses. A reduction of 10 percent is found for the higher Reynolds numbers investigated. Numerical and experimental results obtained for the velocity profiles agree very well. The effect of varying the converging angle of a single mild (62 percent) coronary stenosis on the fluid flow has been determined numerically using a finite element method. Pressure-flow relation, especially with respect to relative short stenoses, is discussed.     

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].     

Biomechanical signals in the coronary artery triggering the metabolic processes during cardiac overload

Peculiarities in structure and deformability of epicardial conduit coronary arteries are described. The thin wall of animal coronary artery contrasts the human coronary artery in which the remarkable wall thickness is due namely by the intima thickness. Deformation in length and diameter of conduit coronary arteries, due to the left and right ventricle volume increase, has been defined in non-beating canine heart. Ramus interventricularis anterior being firmly tethered to the myocardium undergoes about 3 times larger deformation than ramus circumflexus In anaesthetized dogs a 30% increase in blood pressure, elicited by aortic constriction, induces an increase in diameter of coronary artery, in segment lenght, in blood flow and consequently in shear stress which represents a load for circumferentially running smooth muscle bundles, longitudinally running smooth muscle bundles, as well as for the endothelium. The above load lasting 4 h is already reflected by an increase in total RNA content and [¹⁴C] leucin incorporation in the left ventricle myocardium in the wall of ramus interventricularis anterior, not in ramus circumflexus. The finding fit completely with the different range of deformation of both the above coronary branches and indicates an increase in proteosynthesis not only in myocardium, but in ramus interventricularis anterior as well. An increase in ornithindecarboxylase activity in coronary wall leading to an increase in biogenic polyamines, is present in the case only, when blood pressure increase is induced by infusion of noradrenaline.     

Epicardial coronary blood flow including the presence of stenoses and aorto-coronary bypasses--II: Experimental comparison and parametric investigations

This article is the second in a series which presents a computer model of the left coronary arteries. The first article discussed the geometry, the governing equations, and the numerical method employed. This paper details an acute canine experiment used to validate the approach as well as the systematic investigation of several important parameters governing the left coronary circulation. These parameters include peripheral resistance, wall properties, and altered geometric properties through various stenosis/bypass configurations. With appropriate selection of parameters, the model reproduces an in vivo waveform very closely. The model also predicts many clinical phenomena, such as the "critical" value of stenosis, the dramatic reduction in flow through a stenosis when bypassed, and the restorative effect of the bypass upon flow to the distal bed. The model also is used to show that the autonomic state of the animal profoundly affects the influence of various factors, e.g., the critical value of a stenosis is much higher under resting conditions than under hyperemic conditions.     

Coronary three-vessel disease with occlusion of the right coronary artery: What are the most important factors that determine the right territory perfusion?

With progressive occlusion of a coronary main artery, some anastomotic vessels are recruited in order to supply blood to the ischemic region. This collateral circulation is an important factor in the preservation of the myocardium until reperfusion of the area at risk. An accurate estimation of collateral flow is crucial in surgical bypass planning as it alters the blood flow distribution in the coronary network and can influence the outcome of a given treatment for a given patient. The evaluation of collateral flow is frequently achieved using an index based on pressure measurements. It is named collateral flow index (CFI) and defined as: (P_w − P_v)/(P_ao − P_v), where P_w is the pressure distal to the thrombosis, P_ao the aortic pressure and P_v the central venous pressure. In the present work, we study patients with severe coronary disease (stenoses on the left branches and total occlusion of the right coronary artery). Using a mathematical model that describes the coronary hemodynamics in that situation, we demonstrate that the dependence of the collateral circulation to the pressure values is not as simple as it is commonly believed: using pressures alone as an index of collateral flow is likely to result in misinterpretation of the collateral flow contribution, because collateral flow depends on many other factors related to the status of the native stenosed arteries and to the microvascular resistances (capillary and collateral resistances, and the proportion between them).     

A model of the coronary vascular bed and its verification by a physiological experiment

We analysed the relationship between artery pressure (AP) and coronary flow (F) in the canine coronary bed, using an electrical analog model of the coronary circulation. The model contained a capacitance of epicardial vessels, input and terminal resistances, diode, and the number of e.m.f., simulated the intramyocardial pressure and zero-flow pressure. These e.m.f. are assumed to be a linear functions of left ventricular and aortic pressure. The value of coronary blood flow was calculated from experimental curves of AP and LVP and setting parameters. Good agreement was obtained between theoretical and experimental curves of coronary blood flow.     

Wall shear stress in normal left coronary artery tree

Despite the fact that the role of wall shear stress (WSS) as a local mechanical factor in atherogenesis is well established, its distribution over the entire normal human left coronary artery (LCA) tree has not yet been studied. A three-dimensional computer generated model of the epicardial LCA tree, based on averaged human data set extracted from angiographies, was adopted for finite-element analysis of the Navier-Stokes flow equations treating blood as non-Newtonian fluid. The LCA tree includes the left main coronary artery (LMCA), the left anterior descending (LAD), the left circumflex artery (LCxA) and their major branches. In proximal LCA tree regions where atherosclerosis frequently occurs, low WSS appears. Low WSS regions occur at bifurcations in regions opposite the flow dividers, which are anatomic sites predisposed for atherosclerotic development. On the LMCA bifurcation, at regions opposite to the flow divider, dominant low WSS values occur ranging from 0.75 to 2.25 N/m2. High WSS values are encountered at all flow dividers. This work determines, probably for the first time, the topography of the WSS in the entire normal human LCA epicardial tree. It is also the first work determining the spatial WSS differentiation between proximal and distal normal human LCA parts. The haemodynamic analysis of the entire epicardial LCA tree further verifies the implications of the WSS in atherosclerosis mechanisms.     

Characterizing momentum change and viscous loss of a hemodynamic endpoint in assessment of coronary lesions

Myocardial fractional flow reserve (FFR(myo)) and coronary flow reserve (CFR), measured with guidewire, and quantitative angiography (QA) are widely used in combination to distinguish ischemic from non-ischemic coronary stenoses. Recent studies have shown that simultaneous measurements of FFR(myo) and CFR are recommended to dissociate conduit epicardial coronary stenoses from distal resistance microvascular disease. In this study, a more comprehensive diagnostic parameter, named as lesion flow coefficient, c, is proposed. The coefficient, c, which accounts for mean pressure drop, Delta p, mean coronary flow, Q, and percentage area stenosis, can be used to assess the hemodynamic severity of a coronary artery stenoses. Importantly, the contribution of viscous loss and loss due to momentum change for several lesion sizes can be distinguished using c. FFR(myo), CFR and c were calculated for pre-angioplasty, intermediate and post-angioplasty epicardial lesions, without microvascular disease. While hyperemic c decreased from 0.65 for pre-angioplasty to 0.48 for post-angioplasty lesion with guidewire of size 0.35 mm, FFR(myo) increased from 0.52 to 0.87, and CFR increased from 1.72 to 3.45, respectively. Thus, reduced loss produced by momentum change due to lower percentage area stenosis decreased c. For post-angioplasty lesion, c decreased from 0.55 to 0.48 with the insertion of guidewire. Hence, increased viscous loss due to the presence of guidewire decreased c compared with a lesion without guidewire. Further, c showed a linear relationship with FFR(myo), CFR and percentage area stenosis for pre-angioplasty, intermediate and post-angioplasty lesion. These baseline values of c were developed from fluid dynamics fundamentals for focal lesions, and provided a single hemodynamic endpoint to evaluate coronary stenosis severity.     

False-negative myocardial scintigraphy in balanced three-vessel disease,revealed by coronary pressure measurement

In nuclear perfusion imaging of the myocardium, a false-negative test result in patients with balanced three-vessel disease is a well-known pitfall. This paper describes a patient with typical chest pain and a negative myocardial perfusion scintigram. At coronary angiography, intermediate stenoses in the left anterior descending (LAD), left circumflex (LCX), and right coronary (RCA) arteries were present. Fractional flow reserve, measured by coronary pressure measurement, was 0.54, 0.56, and 0.66 respectively for the LAD, LCX, and RCA, unequivocally demonstrating the presence of balanced three-vessel disease. The patient underwent successful bypass surgery and remained event-free thereafter.     

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

Using a frequency-domain Womersley-type model, we previously simulated pulsatile blood flow throughout the coronary arterial tree. Although this model represents a good approximation for the smaller vessels, it does not take into account the nonlinear convective energy losses in larger vessels. Here, using Womersley's theory, we present a hybrid model that considers the nonlinear effects for the larger epicardial arteries while simulating the distal vessels (down to the 1st capillary segments) with the use of Womersley's Theory. The main trunk and primary branches were discretized and modeled with one-dimensional Navier-Stokes equations, while the smaller-diameter vessels were treated as Womersley-type vessels. Energy losses associated with vessel bifurcations were incorporated in the present analysis. The formulation enables prediction of impedance and pressure and pulsatile flow distribution throughout the entire coronary arterial tree down to the first capillary segments in the arrested, vasodilated state. We found that the nonlinear convective term is negligible and the loss of energy at a bifurcation is small in the larger epicardial vessels of an arrested heart. Furthermore, we found that the flow waves along the trunk or at the primary branches tend to scale (normalized with respect to their mean values) to a single curve, except for a small phase angle difference. Finally, the model predictions for the inlet pressure and flow waves are in excellent agreement with previously published experimental results. This hybrid one-dimensional/Womersley model is an efficient approach that captures the essence of the hemodynamics of a complex large-scale vascular network. The present model has numerous applications to understanding the dynamics of coronary circulation.     

Transcardiac adiponectin gradient is independently related to endothelial vasomotor function in large and resistance coronary arteries in humans

Adiponectin, an adipocyte-derived protein, has been shown to have vasculoprotective effects. This study examined the possible relationship between coronary vasomotor function and the transcardiac gradient of adiponectin, reflecting adiponectin utilization and/or accumulation in the coronary vascular bed. The epicardial diameter and blood flow response of the left anterior descending coronary artery to intracoronary infusions of ACh was analyzed in 108 consecutive subjects who had a normal coronary angiogram and left ventriculogram. Adiponectin levels were measured by ELISA in plasma obtained from the aortic root (Ao) and the anterior interventricular vein (AIV). Adiponectin levels in the AIV were lower than levels in the Ao. In multivariate linear regression analysis, the transcardiac gradient of adiponectin (Ao - AIV levels) showed a positive correlation with increases in epicardial coronary diameter and coronary blood flow in response to ACh that was independent of traditional coronary risk factors. The transcardiac gradient of adiponectin was not significantly associated with the coronary dilator response to isosorbide dinitrate and the coronary flow response to sodium nitroprusside. In other groups of patients with coronary spastic angina (n = 41) or microvascular angina (n = 32) who had impaired coronary vasomotor responses, there was no significant gradient of adiponectin between the Ao and AIV. The transcardiac gradient of adiponectin may modulate endothelial vasomotor function in large and resistance coronary arteries and may play a role in the pathogenesis of diseases presenting with coronary vasomotor dysfunction.     

Coronary artery diameter can be assessed reliably with transthoracic echocardiography

We studied whether diameters of coronary arteries can be measured accurately with the use of transthoracic echocardiography (TTE). By knowing the anatomic diameter of the coronary artery together with coronary flow velocity it is possible to measure coronary flow volume more precisely by TTE. However, the suitability of TTE for measurement of diameters of all main epicardial coronary arteries has not been systematically validated. We measured the diameters of the left main (LM), left anterior descending (LAD), left circumflex (LCX), and right coronary arteries (RCA) with the use of TTE [manual two-dimensional (2D), color-Doppler, and automated 2D analysis] in 30 patients who had normal coronary anatomy. We compared these diameters to those measured with quantitative coronary angiography (QCA). We could measure diameters of LM, LAD, LCX, and RCA by TTE in up to 37%, 63%, 7%, and 60% of patients, respectively. The overall correlation coefficients between TTE and QCA measurements were 0.83 (P < 0.01) with manual 2D analysis, 0.82 (P < 0.01) with automated 2D analysis, and 0.94 (P < 0.01) with a color-Doppler-based analysis. Interobserver variability of TTE measurements was low (coefficient of variation 5.4 +/- 4.6-7.5 +/- 8.8%). TTE is an accurate method to evaluate coronary artery diameter in patients with healthy coronary arteries.     

Heat transfer mediated by coronary circulation in Langendorff-perfused isolated whole hearts

Although coronary flow is essential for oxygen supply, which is a prerequisite for cardiac electrical activity, energy metabolism and mechanical performance, the roles of coronary circulation on heat transfer to the heart have received less attention. This study investigated the effects of coronary circulation on epicardial temperature, the effects of temperature on coronary resistance, and the effects of ischemia on temperature fall, using isolated perfused rat or guinea pig hearts. Monophasic action potential (MAP) and epicardial temperature were recorded by a pair of suction electrodes and thermisters, while whole heart conductance (WHC) was estimated by a two-electrode instrument arranged in a diagonal array, under the alteration of the coronary flow rate of perfusate with different temperatures. MAP duration was sensitive to the local temperature, and lowering the temperature caused reduced WHC and increased coronary resistance calculated by dividing perfusion pressure by flow rate. After the onset of ischemia, WHC fell immediately in a single exponential manner, and MAP duration was abbreviated after transient behaviors explained well by the exquisite temperature gradient governed by coronary artery geometry. Epicardial temperature is maintained by coronary circulation in isolated perfused heart. Temperature-sensitive coronary tonus and MAP duration indicate that an exquisite temperature gradient underlies inhomogeneous distributions of coronary flow and electrical property. No-flow ischemia disturbs heat transfer and augments the temperature gradient transiently. Therefore, an isolated perfused heart can be considered as a heat transfer model where thermoregulation is maintained by warm coronary perfusion.     

Glutathione attenuates coronary constriction to acetylcholine in patients with coronary spastic angina

This study examined the effect of reduced glutathione (GSH), an important antioxidant that restores intracellular redox imbalance and prevents inactivation of endothelial-derived nitric oxide, on the abnormal vasomotor reactivity in spastic coronary arteries. The responses of epicardial diameter of the left coronary arteries to intracoronary infusion of acetylcholine (ACh; 50 microg/min) were measured by quantitative coronary angiography before and during combined intracoronary infusion of GSH (50 mg/min for 6 min) or saline as a placebo in 24 patients with coronary spastic angina and in 28 control patients. All of the spastic coronary arteries showed constrictor response to ACh, whereas the control coronary arteries as a whole showed only minimal diameter changes to ACh. GSH infusion suppressed constrictor response of epicardial diameter to ACh in patients with coronary spastic angina, whereas it had no significant effect in control subjects. Saline infusion did not have any effects. The results indicate that GSH attenuated the constrictor response to ACh in epicardial coronary arteries of patients with coronary spastic angina. GSH may have an important role in the regulation of coronary vasomotor function in patients with coronary spastic angina.     

Effects of myocardial constraint on the passive mechanical behaviors of the coronary vessel wall

The large epicardial coronary arteries and veins span the surface of the heart and gradually penetrate into the myocardium. It has recently been shown that remodeling of the epicardial veins in response to pressure overload strongly depends on the degree of myocardial support. The nontethered regions of the vessel wall show significant intimal hyperplasia compared with the tethered regions. Our hypothesis is that such circumferentially nonuniform structural adaptation in the vessel wall is due to nonuniform wall stress and strain. Transmural stress and strain are significantly influenced by the support of the surrounding myocardial tissue, which significantly limits distension of the vessel. In this finite-element study, we modeled the nonuniform support by embedding the left anterior descending artery into the myocardium to different depths and analyzed deformation and strain in the vessel wall. Circumferential wall strain was much higher in the untethered than tethered region at physiological pressure. On the basis of the hypothesis that elevated wall strain is the stimulus for remodeling, the simulation results suggest that large epicardial coronary vessels have a greater tendency to become thicker in the absence of myocardial constraint. This study provides a mechanical basis for understanding the local growth and remodeling of vessels subjected to various degrees of surrounding tissue.