Epicardial coronary blood flow including the presence of stenoses and aorto-coronary bypasses--I: Model and numerical method

A computer model and numerical method for calculating left epicardial coronary blood flow has been developed. This model employs a finite-branching geometry of the coronary vasculature and the one-dimensional, unsteady equations for flow with friction. The epicardial coronary geometry includes the left main and its bifurcation, the left anterior descending and left circumflex coronary arteries, and a selected number of small branches. Each of the latter terminate in an impedance, whose resistive component is related to intramyocardial compression through a linear dependence on left ventricular pressure. The elastic properties of the epicardial arteries are taken to be non-linear and are prescribed by specifying the local small-disturbance wave speed. The model allows for the incorporation of multiple stenoses as well as aorto-coronary bypasses. Calculations using this model predict pressure and flow waveform development and allow for the systematic investigation of the dependence of coronary flow on various parameters, e.g., peripheral resistance, wall properties, and branching pattern, as well as the presence of stenoses and bypass grafts. Reasonable comparison between calculations and earlier experiments in horses has been obtained.     

Effect of geometrical assumptions on numerical modeling of coronary blood flow under normal and disease conditions

Shear stress plays a pivotal role in pathogenesis of coronary heart disease. The spatial and temporal variation in hemodynamics of blood flow, especially shear stress, is dominated by the vessel geometry. The goal of the present study was to investigate the effect of 2D and 3D geometries on the numerical modeling of coronary blood flow and shear stress distribution. We developed physiologically realistic 2D and 3D models (with similar geometries) of the human left coronary artery under normal and stenosis conditions (30%, 60%, and 80%) using PROE (WF 3). Transient blood flows in these models were solved using laminar and turbulent (k-ω) models using a computational fluid dynamics solver, FLUENT (v6.3.26). As the stenosis severity increased, both models predicted a similar pattern of increased shear stress at the stenosis throat, and in recirculation zones formed downstream of the stenosis. The 2D model estimated a peak shear stress value of 0.91, 2.58, 5.21, and 10.09 Pa at the throat location under normal, 30%, 60%, and 80% stenosis severity. The peak shear stress values at the same location estimated by the 3D model were 1.41, 2.56, 3.15, and 13.31 Pa, respectively. The 2D model underestimated the shear stress distribution inside the recirculation zone compared with that of 3D model. The shear stress estimation between the models diverged as the stenosis severity increased. Hence, the 2D model could be sufficient for analyzing coronary blood flow under normal conditions, but under disease conditions (especially 80% stenosis) the 3D model was more suitable.     

Arterial steal phenomenon in femoro-tibial bypass with arterio-venous shunt

Arterio-venous shunts are sometimes constructed at the distal anastomosis of femoro-tibial bypass grafts in order to increase blood flow velocity within the graft. However, the use of such a shunt may "steal' blood from an already ischaemic distal arterial bed. The aim of this study was to determine the conditions under which this might happen. Experiments were carried out on an in vitro model of the femoro-tibial bypass under steady flow conditions. The simple resistance model of Hyman and Brewer (J. Biomechanics 13, 469-675, 1980), modified to take into account the nonlinear pressure flow relationship through a stenosis, was used to interpret experimental data. Good agreement was obtained between measured and calculated steal.     

Hemodynamic aspects of obliterative processes in peripheral blood vessel--rigid and soft narrowing.

Hemodynamic aspects of obliterative processes in peripheral blood vessels were studied on a mechanical model built of distensible tubing, with a fixed peripheral resistance, through which citrated blood was circulated by pulsatile flow. Hemodynamics of progressive focal stenosis, elongated soft stenosis, and elongated rigid stenosis were assessed. By the use of a hydrodynamic model and a series of in vitro experiments, we have measured the pressure and flow characteristics, and calculated the pressure and energy losses for the various stenotic sites. The critical stricture was found to be larger for a rigid stenosis than a soft stenosis. The length of the stenosis was also an important factor. Increasing the length of a rigid stenosis, for example, by 50 percent resulted in an increase of 25 percent in the flow through the stenosis. The energy dissipation was determined as a preferred indication for several parameters such as: pressure drop, pulsed flow, pulse rate, and the geometry and mechanical properties of the stenosis.     

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).     

A nonlinear axisymmetric model with fluid-wall interactions for steady viscous flow in stenotic elastic tubes.

Arteries with high-grade stenoses may compress under physiologic conditions due to negative transmural pressure caused by high-velocity flow passing through the stenoses. To quantify the compressive conditions near the stenosis, a nonlinear axisymmetric model with fluid-wall interactions is introduced to simulate the viscous flow in a compliant stenotic tube. The nonlinear elastic properties of the tube (tube law) are measured experimentally and used in the model. The model is solved using ADINA (Automatic Dynamic Incremental Nonlinear Analysis), which is a finite element package capable of solving problems with fluid-structure interactions. Our results indicate that severe stenoses cause critical flow conditions such as negative pressure and high and low shear stresses, which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The pressure filed near a stenosis has a complex pattern not seen in one-dimensional models. Negative transmural pressure as low as -24 mmHg for a 78 percent stenosis by diameter is observed at the throat of the stenosis for a downstream pressure of 30 mmHg. Maximum shear stress as a high as 1860 dyn/cm2 occurs at the throat of the stenoses, while low shear stress with reversed direction is observed right distal to the stenosis. Compressive stresses are observed inside the tube wall. The maximal principal stress and hoop stress in the 78 percent stenosis are 80 percent higher than that from the 50 percent stenosis used in our simulation. Flow rates under different pressure drop conditions are calculated and compared with experimental measurements and reasonable agreement is found for the prebuckling stage.     

Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid-wall interactions.

Severe stenosis may cause critical flow and wall mechanical conditions related to artery fatigue, artery compression, and plaque rupture, which leads directly to heart attack and stroke. The exact mechanism involved is not well understood. In this paper a nonlinear three-dimensional thick-wall model with fluid-wall interactions is introduced to simulate blood flow in carotid arteries with stenosis and to quantify physiological conditions under which wall compression or even collapse may occur. The mechanical properties of the tube wall were selected to match a thick-wall stenosis model made of PVA hydrogel. The experimentally measured nonlinear stress-strain relationship is implemented in the computational model using an incremental linear elasticity approach. The Navier-Stokes equations are used for the fluid model. An incremental boundary iteration method is used to handle the fluid-wall interactions. Our results indicate that severe stenosis causes considerable compressive stress in the tube wall and critical flow conditions such as negative pressure, high shear stress, and flow separation which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The stress distribution has a very localized pattern and both maximum tensile stress (five times higher than normal average stress) and maximum compressive stress occur inside the stenotic section. Wall deformation, flow rates, and true severities of the stenosis under different pressure conditions are calculated and compared with experimental measurements and reasonable agreement is found.     

Influence of stenosis on hemodynamic parameters in the realistic left coronary artery under hyperemic conditions

The current study investigates the hyperemic flow effects on heamodynamics parameters such as velocity, wall shear stress in 3D coronary artery models with and without stenosis. The hyperemic flow is used to evaluate the functional significance of stenosis in the current era. Patients CT scan data of having healthy and coronary artery disease was chosen for the reconstruction of 3D coronary artery models. The diseased 3D models of coronary artery shows a narrowing of >50% lumen area. Computational fluid dynamics was performed to simulate the hyperemic flow condition. The results showed that the recirculation zone was observed immediate to the stenosis and highest wall shear stress was observed across the stenosis. The decrease in pressure was found downstream to the stenosis as compared to the coronary artery without stenosis. Our analysis provides an insight into the distribution of wall shear stress and pressure drop, thus improving our understanding of hyperemic flow effect under both conditions.     

Influence of hemodynamic conditions on fractional flow reserve: parametric analysis of underlying model

Pressure-based fractional flow reserve (FFR) is used clinically to evaluate the functional severity of a coronary stenosis, by predicting relative maximal coronary flow (Q(s)/Q(n)). It is considered to be independent of hemodynamic conditions, which seems unlikely because stenosis resistance is flow dependent. Using a resistive model of an epicardial stenosis (0-80% diameter reduction) in series with the coronary microcirculation at maximal vasodilation, we evaluated FFR for changes in coronary microvascular resistance (R(cor) = 0.2-0.6 mmHg. ml(-1). min), aortic pressure (P(a) = 70-130 mmHg), and coronary outflow pressure (P(b) = 0-15 mmHg). For a given stenosis, FFR increased with decreasing P(a) or increasing R(cor). The sensitivity of FFR to these hemodynamic changes was highest for stenoses of intermediate severity. For P(b) > 0, FFR progressively exceeded Q(s)/Q(n) with increasing stenosis severity unless P(b) was included in the calculation of FFR. Although the P(b)-corrected FFR equaled Q(s)/Q(n) for a given stenosis, both parameters remained equally dependent on hemodynamic conditions, through their direct relationship to both stenosis and coronary resistance.     

NONCARDIAC SURGERY COMBINED WITH CORONARY ARTERY BYPASS

The coexistence of coronary artery disease with noncardiac disease often leads to a dilemma in planning therapeutic procedures. This problem is especially difficult in the presence of accelerated angina or left coronary artery stenosis. A series of 17 patients is presented in which coronary artery bypass grafts were combined with noncardiac operations without mortality or significant morbidity. An illustrative case report shows the interrelated nature of the coexisting disorders. The conclusion of this study is that, at times, various surgical procedures should be combined with coronary artery bypass grafting for a smoother, less complicated recovery. However, there are no hard and fast rules dictating combined procedures; each operation must be planned according to the existing conditions and needs of the individual patient.     

Simulation study of the fluid dynamics of aorto-coronary bypass

It is well known that local fluid dynamic phenomena are the main factors affecting the failure of aorto-coronary bypass procedures. With the aim of investigating the influence of bypass geometrical parameters on the fluid dynamics around the anastomosis, a two-dimensional finite element model of a stenosed coronary artery with an aorto-coronary bypass has been developed. The geometrical parameters on which the study focused were the degree of coronary stenosis, the bypass diameter and the bypass angle. The fluid dynamic equations have been solved using the finite element method. The results show the development of a recirculation area immediately downstream of the anastomosis and its relationship with the investigated parameters. In particular, the magnitude of the recirculation increases with the bypass angle, the bypass diameter and the degree of coronary stenosis.     

Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.     

Concomitant transapical transcatheter aortic valve implantation and minimally invasive direct coronary artery bypass

We represent a successful minimally invasive combined off-pump procedure consisting of a transapical aortic valve implantation and a direct coronary artery bypass grafting in a woman with a severe aortic stenosis and a critical coronary artery disease. Due to her comorbidities, she was classified as a high-risk patient qualifying for a transcatheter procedure. We performed this combined procedure in a hybrid operation room, starting with the coronary bypass to maintain a coronary blood flow during the transapical valve implantation. The operation processed without any complications and she was discharged at the seventh postoperative day into the allocating hospital.     

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.     

Scientific Section: Coronary Artery Surgery,Task Force Appointed by the Conference of Deputy Ministers of Health: 2. Results,indications and recommendations

The large majority of reported studies of patients treated by aortocoronary bypass have not been randomized clinical trials, and hence must be interpreted with great caution.Review of the seven randomized clinical trials in the literature leads to only one firm, positive conclusion: aortocoronary bypass results in a reduction in the morbidity of coronary artery disease, due to the alleviation of cardiac pain, for at least 3 years. In addition, there is some evidence that mortality for symptomatic patients with significant left main-stem coronary artery stenosis may be reduced by coronary artery bypass surgery. A significant effect on mortaliy form other forms of coronary artery disease has not yet been conclusively demonstrated but also has not been excluded. Most of the reports are preliminary and involve small numbers of patients followed for relatively short periods. The operation is still being improved. It is to be hoped that the randomized trials, involving large numbers of patients, now in progress will supply some of these answers.Aortocoronary bypass surgery is the treatment of choice for patients with stable cardiac pain that is disabling despite adequate treatment, or when adequate treatment is impractial; for patients with unstable cardiac pain, uncontrolled despite adequate treatment; and for symptomatic patients with critical stenosis of the left main-stem coronary artery.     

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.     

Steady flow of a viscous fluid through a network of tubes with applications to the human arterial system

The paper presents a finite-element model for the analysis of steady flow of a viscous fluid through a connected system of elastic tubes with the aim of simulating the conditions of blood flow through the human arterial system. The governing equations of the model are non-linear in character and are solved through an iterative computational procedure. This model is capable of incorporating the effects of stenosis on flow and pressure. Typical results are presented and discussed. Quantitative results have been obtained on blood flow through a model of the human arterial system corresponding to the sets of prescribed conditions at the terminations. Also computational results on the effect of stenosis in typical arteries of the system are presented.     

Stenosis severity effects for unbalanced simple-pulsatile bifurcation flow

A numerical finite-difference analysis is made of a plane simple-pulsatile flow past a symmetrical bifurcation which contains an asymmetrical smooth-contoured stenosis in the trunk. In essence, such a situation could represent a stenosed common carotid artery immediately upstream from the carotid junction. The flow is unbalanced; two-thirds of it exits or enters through the lower branch. The effect on various flow parameters of the stenosis itself and on changes in its severity is investigated by comparing the results for a severe stenosis, a mild stenosis, and no stenosis. The simple-pulsatile forcing function is specified in terms of an oscillatory and a steady Karman number. To obtain a significant amount of backflow, the oscillatory trunk Karman number is taken as 1000 compared to the steady value of 250. The frequency of oscillation is stipulated by a trunk Stokes number of 10 pi. The numerical procedures utilize the vorticity-transport version of the Navier-Stokes governing equations. A non-orthogonal coordinate transform allows the calculations to be made in a rectangular grid where the central difference expressions are easily applied. The results are presented in terms of both kinematic and kinetic parameters. The variation in the basic kinematic variables of stream function and vorticity is shown by temporal sequences of contour plots at times of peak flow and during the flow reversal stages as well as by several velocity vector plots. Kinetic results are given in terms of the temporal variation in shear stresses along boundaries. The peak shears are found to occur at the zenith of the stenosis at times of peak flow: the value for the severe stenosis is twice as large as that for the mild stenosis. The midline pressure distribution in the trunk and the centerline pressure distributions in the branches are also included.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

Localization of bypass-induced changes in flow in coronary artery models

Right coronary artery bypass restores blood flow through heart tissues. This also induces changes in flow leading to its failure. By this work the sites which are prone to such changes are localized. The bypass models are developed from transparent silicon rubber of elastic properties similar to arterial tissues. Flow visualization is carried out by photoelasticity technique by using dilute solution of vanadium pentoxide. This analysis carried out under pulsatile flow conditions shows that the proximal stenotic region continues to contribute to the alteration in flow in the hood region of the bypass. Thus making its proximal and distal regions prone to flow-induced changes, which may lead to its blockage over the long duration.