Numerical modeling of simulated blood flow in idealized composite arterial coronary grafts: steady state simulations

This paper presents a comparative study of simulated blood flow in different configurations of simplified composite arterial coronary grafts (CACGs). Even though the composite arterial grafting is increasingly used in cardiac surgery, it is still questionable whether or not the blood flow in such grafts can adequately meet the demands of the native myocardial circulation. A computational fluid dynamics (CFD) model was developed to conduct computer-based studies of simulated blood flow in four different geometric configurations of CACGs, corresponding to routinely used networks in cardiac surgery coronary grafts (T, Y, Pi and sequential). The flow was assumed three-dimensional, laminar and steady and the fluid as Newtonian, while the vessel walls were considered as inelastic and impermeable. It was concluded that local haemodynamics, practically described by velocity, pressure drop, wall shear stress (WSS) and flow rates, may be strongly influenced by the local geometry, especially at the anastomotic sites. The computations were made at mean flow rates of 37.5, 75 and 150ml/min. The side-branch outflow rates, computed for each bypass graft, showed noticeable differences. The results, which were found both qualitatively and quantitatively consistent with other studies, indicate that the Pi-graft exhibits significantly less uniform distribution of outflow rates than the other geometric configurations. Moreover, prominent variations in WSS and velocity distribution among the assessed CACGs were predicted, showing remarkable flow interactions among the arterial branches. The lowest shear stress regions were found on the lateral walls of bifurcations, which are predominantly susceptible to the occurrence of coronary artery disease (CAD). In contrast, the highest WSS were observed at the turn of the arterial branches.     

Numerical simulations of the blood flow through vertebral arteries

Vertebral arteries are two arteries whose structure and location in human body result in development of special flow conditions. For some of the arteries, one can observe a significant difference between flow rates in the left and the right arteries during ultrasonography diagnosis. Usually the reason of such a difference was connected with pathology of the artery in which a smaller flow rate was detected. Simulations of the flow through the selected type of the vertebral artery geometry for twenty five cases of artery diameters have been carried out. The main aim of the presented experiment was to visualize the flow in the region of vertebral arteries junction in the origin of the basilar artery. It is extremely difficult to examine this part of human circulation system, thus numerical experiments may be helpful in understanding the phenomena occurring when two relatively large arteries join together to form one vessel. The obtained results have shown that an individual configuration and diameters of particular arteries can exert an influence on the flow in them and affect a significant difference between flow rates for vertebral arteries. It has been assumed in the investigations that modelled arteries were absolutely normal, without any pathology. In the numerical experiment, the non-Newtonian model of blood was employed.     

Nonquasi-steady character of pulsatile flow in human coronary arteries

This experiment was conducted to determine if the pulsatile flow through the proximal portion of the left coronary artery system in man exhibits quasi-steady characteristics. Steady and pulsatile flows were passed through an idealized model whose dimensions were based on a vascular cast. The mean Reynolds number was 180 and the unsteadiness number was 2.7. Velocity profiles were measured by laser Doppler anemometry at several locations along diameters in the parent and both daughter channels in the neighborhood of the "left main" bifurcation. Analysis of the results along one diameter in the "left main" channel shows that unsteady flow in the larger coronary arteries may not be simulated by a series of steady flow experiments.     

Influence of non-Newtonian properties of blood on the wall shear stress in human atherosclerotic right coronary arteries

The objective of this work is to investigate the effect of non-Newtonian properties of blood on the wall shear stress (WSS) in atherosclerotic coronary arteries using both Newtonian and non-Newtonian models. Numerical simulations were performed to examine how the spatial and temporal WSS distributions are influenced by the stenosis size, blood viscosity, and flow rate. The computational results demonstrated that blood viscosity properties had considerable effect on the magnitude of the WSS, especially where disturbed flow was observed. The WSS distribution is highly non-uniform both temporally and spatially, especially in the stenotic region. The maximum WSS occurred at the proximal side of the stenosis, near the outer wall in the curved artery with no stenosis. The lumen area near the inner wall distal to the stenosis region experienced a lower WSS during the entire cardiac cycle. Among the factors of stenosis size, blood viscosity, and flow rate, the size of the stenosis has the most significant effect on the spatial and temporal WSS distributions qualitatively and quantitatively.     

4-D blood flow in the human right ventricle

Right ventricular (RV) function is a powerful prognostic indicator in many forms of heart disease, but its assessment remains challenging and inexact. RV dysfunction may alter the normal patterns of RV blood flow, but those patterns have been incompletely characterized. We hypothesized that, based on anatomic differences, the proportions and energetics of RV flow components would differ from those identified in the left ventricle (LV) and that the portion of the RV inflow passing directly to outflow (Direct Flow) would be prepared for effective systolic ejection as a result of preserved kinetic energy (KE) compared with other RV flow components. Three-dimensional, time-resolved phase-contrast velocity, and balanced steady-state free-precession morphological data were acquired in 10 healthy subjects using MRI. A previously validated method was used to separate the RV and LV end-diastolic volumes into four flow components and measure their volume and KE over the cardiac cycle. The RV Direct Flow: 1) followed a smoothly curving route that did not extend into the apical region of the ventricle; 2) had a larger volume and possessed a larger presystolic KE (0.4 ± 0.3 mJ) than the other flow components (P < 0.001 and P < 0.01, respectively); and 3) represented a larger part of the end-diastolic blood volume compared with the LV Direct Flow (P < 0.01). These findings suggest that diastolic flow patterns distinct to the normal RV create favorable conditions for ensuing systolic ejection of the Direct Flow component. These flow-specific aspects of RV diastolic-systolic coupling provide novel perspectives on RV physiology and may add to the understanding of RV pathophysiology.     

Alpha-adrenergic vasoconstrictor tone limits right coronary blood flow in exercising dogs

In exercising dogs, increased myocardial O2 consumption (MVO2) of the left ventricle is met primarily by hyperemia, whereas increased O2 extraction makes a greater contribution to right ventricular (RV) O2 supply. We hypothesized that alpha-adrenergic vasoconstrictor tone limits right coronary (RC) blood flow during exercise, forcing increased O2 extraction. This tone might also contribute to lesser RC vascular conductance at rest. Accordingly, RV O2 balance was examined at rest and during graded treadmill exercise before and during alpha-adrenergic blockade with phentolamine (1 mg/kg, i.v., n=6). The transmural distribution of RC flow was measured with radiolabeled microspheres in 4 additional dogs. At rest, alpha-adrenergic receptor blockade did not significantly increase RC flow or conductance. During exercise, alpha-adrenergic blockade increased RC flow and conductance responses to increased RV MVO2 by 25% and 60%, respectively. The transmural distribution of RC flow was not altered by exercise or by alpha-adrenergic blockade. Before alpha-adrenergic blockade, hyperemia provided 39%-66% of the additional O2 consumed by the right ventricle during graded exercise; after alpha-adrenergic blockade, hyperemia contributed 74%-85%. After alpha-adrenergic blockade, the slope of the relationship between RC venous PO2 and RV MVO2 became less steep, reflecting less O2 extraction due to enhanced hyperemia. Additional experiments were conducted on 5 anesthetized, open-chest dogs with constant RC perfusion pressure and beta-adrenergic blockade. The RC flow response to intracoronary norepinephrine was shifted to the left compared with that measured in the left coronary circulation, consistent with observations in the conscious exercising dogs. In conclusion, alpha-adrenergic vasoconstrictor tone does not restrict resting RC blood flow, but during exercise, this tone transmurally blunts RC hyperemia and forces the right ventricle to mobilize its O2 extraction reserve. This effect is more pronounced than has been reported for the left ventricle.     

Computer simulations of atherosclerotic plaque growth in coronary arteries

A three dimensional mathematical model with a linear plaque growth function was developed to investigate the geometrical adaptation of atherosclerotic plaques in coronary arteries and study the influences of flow wall shear stress (WSS), blood viscosity and the inlet flow rate on the growth of atherosclerotic plaques using computational plaque growth simulations. The simulation results indicated that the plaque wall thickness at the neck of the stenosis increased at a decreasing rate in the atherosclerosis progression. The simulation results also showed a strong dependence of the plaque wall thickness increase on the blood viscosity and the inlet flow rate. The progression rate in a coronary artery was lower with a higher inlet velocity flow rate and higher with a smaller value of the blood viscosity.     

Approximating hemodynamics of cerebral aneurysms with steady flow simulations

Computational fluid dynamics (CFD) simulations can be employed to gain a better understanding of hemodynamics in cerebral aneurysms and improve diagnosis and treatment. However, introduction of CFD techniques into clinical practice would require faster simulation times. The aim of this study was to evaluate the use of computationally inexpensive steady flow simulations to approximate the aneurysm's wall shear stress (WSS) field. Two experiments were conducted. Experiment 1 compared for two cases the time-averaged (TA), peak systole (PS) and end diastole (ED) WSS field between steady and pulsatile flow simulations. The flow rate waveform imposed at the inlet was varied to account for variations in heart rate, pulsatility index, and TA flow rate. Consistently across all flow rate waveforms, steady flow simulations accurately approximated the TA, but not the PS and ED, WSS field. Following up on experiment 1, experiment 2 tested the result for the TA WSS field in a larger population of 20 cases covering a wide range of aneurysm volumes and shapes. Steady flow simulations approximated the space-averaged WSS with a mean error of 4.3%. WSS fields were locally compared by calculating the absolute error per node of the surface mesh. The coefficient of variation of the root-mean-square error over these nodes was on average 7.1%. In conclusion, steady flow simulations can accurately approximate the TA WSS field of an aneurysm. The fast computation time of 6 min per simulation (on 64 processors) could help facilitate the introduction of CFD into clinical practice.     

PIV measurements of flow in a centrifugal blood pump: steady flow

Magnetically suspended left ventricular assist devices have only one moving part, the impeller. The impeller has absolutely no contact with any of the fixed parts, thus greatly reducing the regions of stagnant or high shear stress that surround a mechanical or fluid bearing. Measurements of the mean flow patterns as well as viscous and turbulent stresses were made in a shaft-driven prototype of a magnetically suspended centrifugal blood pump at several constant flow rates (3-9 L/min) using particle image velocimetry (PIV). The chosen range of flow rates is representative of the range over which the pump may operate while implanted. Measurements on a three-dimensional measurement grid within several regions of the pump, including the inlet, blade passage, exit volute, and diffuser are reported. The measurements are used to identify regions of potential blood damage due to high shear stress and/or stagnation of the blood, both of which have been associated with blood damage within artificial heart valves and diaphragm-type pumps. Levels of turbulence intensity and Reynolds stresses that are comparable to those in artificial heart valves are reported. At the design flow rate (6 L/min), the flow is generally well behaved (no recirculation or stagnant flow) and stress levels are below levels that would be expected to contribute to hemolysis or thrombosis. The flow at both high (9 L/min) and low (3 L/min) flow rates introduces anomalies into the flow, such as recirculation, stagnation, and high stress regions. Levels of viscous and Reynolds shear stresses everywhere within the pump are below reported threshold values for damage to red cells over the entire range of flow rates investigated; however, at both high and low flow rate conditions, the flow field may promote activation of the clotting cascade due to regions of elevated shear stress adjacent to separated or stagnant flow.     

Blood flow patterns in the proximal human coronary arteries: relationship to atherosclerotic plaque occurrence

Atherosclerotic plaques in human coronary arteries are focal manifestations of systemic disease, and biomechanical factors have been hypothesized to contribute to plaque genesis and localization. We developed a computational fluid dynamics (CFD) model of the ascending aorta and proximal sections of the right and left coronary arteries of a normal human subject using computed tomography (CT) and magnetic resonance imaging (MRI) and determined the pulsatile flow field. Results demonstrate that flow patterns in the ascending aorta contribute to a pro-atherosclerotic flow environment, specifically through localization of low and oscillatory wall shear stress in the neighborhood of coronary orifices. Furthermore, these patterns differ in their spatial distribution between right and left coronary arteries. Entrance effects of aortic flow diminish within two vessel diameters. We examined relationships between spatial distributions of wall shear stress and reports of plaque occurrence in the literature. Results indicate low wall shear stress is co-located with increased incidence of lesions, and higher wall shear stresses are associated with lesion-resistant areas. This investigation does not consider plaque progression or advanced lesions, inasmuch as the CFD model was developed from a normal individual and the clinical data used for comparisons were obtained from autopsy specimens of subjects who died from non-cardiovascular causes. The data reported are consistent with the hypothesis that low wall shear stress is associated with the localization of atherosclerotic lesions, and the results demonstrate the importance of aortic flow on flow patterns in the proximal segments of the coronary arteries.     

Branching characteristics of human coronary arteries

Branching angles and branch diameters were measured in a total of 850 arterial junctions in the coronary networks of two human hearts. Comparison is made with similar data obtained previously from the coronary networks of rats, and with what is considered to be optimum on theoretical grounds. It is concluded that the branching characteristics of the human coronary arteries are closer to the theoretical optimum than those of the coronary networks of rats. While the human data exhibit some departure from optimality and a good amount of scatter, these are well within levels observed elsewhere in the cardiovascular systems of man and animals, and considerably better than those found in the coronary networks of rats. The departure from optimality, in terms of physiological cost to the system, is within 5% for most data points.     

Shape optimization in steady blood flow: a numerical study of non-Newtonian effects

We investigate the influence of the fluid constitutive model on the outcome of shape optimization tasks, motivated by optimal design problems in biomedical engineering. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. The generalized Newtonian treatment exhibits striking differences in the velocity field for smaller shear rates. We apply sensitivity-based optimization procedure to a flow through an idealized arterial graft. For this problem we study the influence of the inflow velocity, and thus the shear rate. Furthermore, we introduce an additional factor in the form of a geometric parameter, and study its effect on the optimal shape obtained.     

Effects of periodic accelerations on blood flow in arteries

This paper discusses the flow of blood in large artries under the influence of linear periodic acceleration. The governing equations and boundary conditions are established and analytical solutions for the velocity, fluid acceleration, bulk flow and shear stress are obtained. The results for these physical quantitites are computed for the case of an artery the size of a normal human aorta. It is found that the flow field variables are directly proportional to the external accelerating force. The behaviour of the velocity profile along the radial distance at different stages of times at fixed applied acceleration is also shown.     

Transient blood flow in elastic coronary arteries with varying degrees of stenosis and dilatations: CFD modelling and parametric study

In this paper, we have analysed pulsatile flow through partially occluded elastic arteries, to determine the haemodynamic parameters of wall shear stress (WSS), wall pressure gradient and pressure drops (ΔP), contributing to enhanced flow resistance and myocardial ischaemic regions which impair cardiac contractility and cause increased work load on the heart. In summary, it can be observed that stenoses in an artery significantly influence the haemodynamic parameters of wall shear stress and pressure drop in contrast to dilatations case. This deduces that stenosis plays a more critical role in plaque growth and vulnerability in contrast to dilatation, and should be the key element in cardiovascular pathology and diagnosis. Through quantitative analysis of WSS and ΔP, we have provided a clearer insight into the haemodynamics of atherosclerotic arteries. Determination of these parameters can be helpful to cardiologists, because it is directly implicated in the genesis and development of atherosclerosis.     

Analysis of oxygen transport from pulsatile, viscous blood flow to diseased coronary arteries of man

Oxygen transport to multiple “non-obstructive” plaque regions in main coronary arteries of man was examined by numerically solving the oxygen transport equation for convective and diffusive processes in the lumen for actual variations of blood flow rate and the velocity field during the cardiac cycle. Oxygen transport to the wall varied significantly along the arterial section, was strongly dependent upon the various flow regions that occurred, and varied considerably during the cardiac cycle. A drastic reduction in oxygen transport to the arterial wall occurred at the incipient separation location on the back side of a plaque where it is believed that the lumen side resistance to oxygen transport is at least an order of magnitude greater than the inner avascular wall resistance, and therefore the availability of oxygen for cellular respiration is essentially boundary layer controlled. In vivo measurements with oxygen microelectrodes in animals are needed to learn more about variations of oxygen transport in plaque regions, in particular on the back side of plaques where hypoxia may occur.