Computation of hemodynamics in the left coronary artery with variable angulations

The purpose of this study was to investigate the hemodynamic effect of variations in the angulations of the left coronary artery, based on simulated and realistic coronary artery models. Twelve models consisting of four realistic and eight simulated coronary artery geometries were generated with the inclusion of left main stem, left anterior descending and left circumflex branches. The simulated models included various coronary artery angulations, namely, 15°, 30°, 45°, 60°, 75°, 90°, 105° and 120°. The realistic coronary angulations were based on selected patient's data with angles ranging from narrow angles of 58° and 73° to wide angles of 110° and 120°. Computational fluid dynamics analysis was performed to simulate realistic physiological conditions that reflect the in vivo cardiac hemodynamics. The wall shear stress, wall shear stress gradient, velocity flow patterns and wall pressure were measured in simulated and realistic models during the cardiac cycle. Our results showed that a disturbed flow pattern was observed in models with wider angulations, and wall pressure was found to reduce when the flow changed from the left main stem to the bifurcated regions, based on simulated and realistic models. A low wall shear stress gradient was demonstrated at left bifurcations with wide angles. There is a direct correlation between coronary angulations and subsequent hemodynamic changes, based on realistic and simulated models. Further studies based on patients with different severities of coronary artery disease are required to verify our results.     

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Healthy and diseased coronary bifurcation geometries influence near-wall and intravascular flow: A computational exploration of the hemodynamic risk

Local hemodynamics has been identified as one main determinant in the onset and progression of atherosclerotic lesions at coronary bifurcations. Starting from the observation that atherosensitive hemodynamic conditions in arterial bifurcation are majorly determined by the underlying anatomy, the aim of the present study is to investigate how peculiar coronary bifurcation anatomical features influence near-wall and intravascular flow patterns. Different bifurcation angles and cardiac curvatures were varied in population-based, idealized models of both stenosed and unstenosed bifurcations, representing the left anterior descending (LAD) coronary artery with its diagonal branch. Local hemodynamics was analyzed in terms of helical flow and exposure to low/oscillatory shear stress by performing computational fluid dynamics simulations.Results show that bifurcation angle impacts lowly hemodynamics in both stenosed and unstenosed cases. Instead, curvature radius influences the generation and transport of helical flow structures, with smaller cardiac curvature radius associated to higher helicity intensity. Stenosed bifurcation models exhibit helicity intensity values one order of magnitude higher than the corresponding unstenosed cases. Cardiac curvature radius moderately affects near-wall hemodynamics of the stenosed cases, with smaller curvature radius leading to higher exposure to low shear stress and lower exposure to oscillatory shear stress. In conclusion, the proposed controlled benchmark allows investigating the effect of various geometrical features on local hemodynamics at the LAD/diagonal bifurcation, highlighting that cardiac curvature influences near wall and intravascular hemodynamics, while bifurcation angle has a minor effect.     

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier–Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau–Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Hemodynamics analysis of a stenosed carotid bifurcation and its plaque-mitigating design

Considering transient two-dimensional laminar flow in a diseased carotid artery segment with realistic inlet and outflow conditions, detailed velocity profiles, pressure fields, wall shear stress distributions and coupled, localized plaque formations have been simulated. The type of outflow boundary condition influences to a certain degree the extent of plaque build-up, which in turn reduces "disturbed flow" phenomena such as flow separations, recirculation zones, and wavy flow patterns in the artery branches during portions of the pulse. Based on computer experiments varying key geometric factors, a plaque-mitigating design of a carotid artery bifurcation has been proposed. Elimination of the carotid bulb, a smaller bifurcation angle, lower area ratios, and smooth wall curvatures generated a design with favorable hemodynamics parameters, leading to reduced plaque build-up by factors of 10 and 2 in the internal carotid and in the external carotid, respectively.     

Multiphase hemodynamic simulation of pulsatile flow in a coronary artery

A multiphase transient non-Newtonian three-dimensional (3-D) computational fluid dynamics (CFD) simulation has been performed for pulsatile hemodynamics in an idealized curved section of a human coronary artery. We present the first prediction, to the authors' knowledge, of particulate buildup on the inside curvature using the multiphase theory of dense suspension hemodynamics. In this study, the particulates are red blood cells (RBCs). The location of RBC buildup on the inside curvature correlates with lower wall shear stress (WSS) relative to the outside curvature. These predictions provide insight into how blood-borne particulates interact with artery walls and hence, have relevance for understanding atherogenesis since clinical observations show that atherosclerotic plaques generally form on the inside curvatures of arteries. The buildup of RBCs on the inside curvature is driven by the secondary flow and higher residence times. The higher viscosity in the central portion of the curved vessel tends to block their flow, causing them to migrate preferentially through the boundary layer. The reason for this is the nearly neutrally buoyant nature of the dense two-phase hemodynamic flow. The two-phase non-Newtonian viscosity model predicts greater shear thinning than the single-phase non-Newtonian model. Consequently, the secondary flow induced in the curvature is weaker. The waveforms for computed hemodynamic parameters, such as hematocrit, WSS, and viscosity, follow the prescribed inlet velocity waveforms. The lower oscillatory WSS produced on the inside curvature has implications for understanding thickening of the intimal layer.     

Experimental determination of wall shear rate in canine carotid arteries perfused in vitro

The mathematical model of Hung (Tsai and Hung, 1984) is employed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to 'normotensive' hemodynamics, 'hypertension' simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the 'hypertension' simulations. The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to 'hypertensive' (vs 'normotensive') hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.     

Mechanical and hydrodynamic effects of stent expansion in tapered coronary vessels

Percutaneous coronary intervention (PCI) has become the primary treatment for patients with coronary heart disease because of its minimally invasive nature and high efficiency. Anatomical studies have shown that most coronary vessels gradually shrink, and the vessels gradually become thinner from the proximal to the distal end. In this paper, the effects of different stent expansion methods on the mechanical and hemodynamic behaviors of coronary vessels and stents were studied. To perform a structural-mechanical analysis of stent implantation, the coronary vessels with branching vessels and the coronary vessels with large bending curvature are selected. The two characteristic structures are implanted in equal diameter expansion mode and conical expansion mode, and the stress and mechanical behaviors of the coronary vessels and stents are analyzed. The results of the structural-mechanical analysis showed that the mechanical behaviors and fatigue performance of the cobalt-chromium alloy stent were good, and the different expansion modes of the stent had little effect on the fatigue performance of the stent. However, the equal diameter expansion mode increased distal coronary artery stress and the risk of vascular injury. The computational fluid dynamics analysis results showed that different stent expansion methods had varied effects on coronary vessel hemodynamics and that the wall shear stress distribution of conical stent expansion is more uniform compared with equal diameter expansion. Additionally, the vortex phenomenon is not apparent, the blood flow velocity is slightly increased, the hydrodynamic environment is more reasonable, and the risk of coronary artery injury is reduced.

     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

Blood velocity patterns in poststenotic regions and velocity waveforms for myocardial inflow associated with coronary artery stenosis in dogs.

Velocity profiles across a vessel were investigated in poststenotic regions of the canine left coronary artery by our 80-channel 20 MHz ultrasound velocimeter. The velocity waveform in a small artery just before its penetration into myocardium was measured by our laser Doppler method. The poststenotic velocity configuration was characterized by a narrow region of high velocity with diastolic reverse flow near the wall which may dissipate energy. The velocity waveform in the distal small arteries exhibited increased systolic reverse flow with decreased diastolic forward flow, resulting in a remarkable reduction of coronary inflow into the myocardium.     

Combined Effects of Flow Diverting Strategies and Parent Artery Curvature on Aneurysmal Hemodynamics: A CFD Study

Purpose

Flow diverters (FD) are increasingly being considered for treating large or giant wide-neck aneurysms. Clinical outcome is highly variable and depends on the type of aneurysm, the flow diverting device and treatment strategies. The objective of this study was to analyze the effect of different flow diverting strategies together with parent artery curvature variations on altering intra-aneurysmal hemodynamics.

Methods

Four ideal intracranial aneurysm models with different parent artery curvature were constructed. Computational fluid dynamics (CFD) simulations of the hemodynamics before and after applying five types of flow diverting strategies (single FD, single FD with 5% and 10% packing density of coils, two FDs with 25% and 50% overlapping rate) were performed. Changes in pressure, wall shear stress (WSS), relative residence time (RRT), inflow velocity and inflow volume rate were calculated and compared.

Results

Each flow diverting strategy resulted in enhancement of RRT and reduction of normalized mean WSS, inflow volume rate and inflow velocity in various levels. Among them, 50% overlapped FD induced most effective hemodynamic changes in RRT and inflow volume rate. The mean pressure only slightly decreased after treatment. Regardless of the kind of implantation of FD, the mean pressure, inflow volume rate and inflow velocity increased and the RRT decreased as the curvature of the parent artery increased.

Conclusions

Of all flow diverting strategies, overlapping FDs induced most favorable hemodynamic changes. Hemodynamics alterations post treatment were substantially influenced by parent artery curvature. Our results indicate the need of an individualized flow diverting strategy that is tailored for a specific aneurysm.     

Experimental determination of wall shear rate in canine carotid arteries perfused in vitro

The mathematical model of Hung (Tsai and Hung, 1984) is empolyed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to ‘normotensive’ hemodynamics, ‘hypertension’ simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the ‘hypertension’ simulations.The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to ‘hypertensive’ (vs ‘normotensive’) hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.     

Measurement and prediction of flow through a replica segment of a mildly atherosclerotic coronary artery of man

Pressure distributions were measured along a hollow vascular axisymmetric replica of a segment of the left circumflex coronary artery of man with mildly atherosclerotic diffuse disease. A large range of physiological Reynolds numbers from about 60 to 500, including hyperemic response, was spanned in the flow investigation using a fluid simulating blood kinematic viscosity. Predicted pressure distributions from the numerical solution of the Navier-Stokes equations were similar in trend and magnitude to the measurements. Large variations in the predicted velocity profiles occurred along the lumen. The influence of the smaller scale multiple flow obstacles along the wall (lesion variations) led to sharp spikes in the predicted wall shear stresses. Reynolds number similarity was discussed, and estimates of what time averaged in vivo pressure drop and shear stress might be were given for a vessel segment.     

Hemodynamic Characteristics of the Vertebrobasilar System Analyzed Using MRI-Based Models

The vertebrobasilar system (VBS) is unique in human anatomy in that two arteries merge into a single vessel, and it is especially important because it supplies the posterior circulation of the brain. Atherosclerosis develops in this region, and atherosclerotic plaques in the vertebrobasilar confluence can progress with catastrophic consequences, including artery occlusion. Quantitative assessments of the flow characteristics in the VBS could elucidate the factors that influence flow patterns in this confluence, and deviations from normal patterns might then be used to predict locations to monitor for potential pathological changes, to detect early signs of disease, and to evaluate treatment options and efficacy. In this study, high-field MRI was used in conjunction with computational fluid dynamics (CFD) modeling to investigate the hemodynamics of subject-specific confluence models (n = 5) and to identify different geometrical classes of vertebrobasilar systems (n = 12) of healthy adult subjects. The curvature of the vessels and their mutual orientation significantly affected flow parameters in the VBS. The basilar artery geometry strongly influenced both skewing of the velocity profiles and the wall shear stress distributions in the VBS. All five subjects modeled possessed varying degrees of vertebral asymmetry, and helical flow was observed in four cases, suggesting that factors other than vertebral asymmetry influence mixing of the vertebral artery flow contributions. These preliminary studies verify that quantitative, MR imaging techniques in conjunction with subject-specific CFD models of healthy adult subjects may be used to characterize VBS hemodynamics and to predict flow features that have been related to the initiation and development of atherosclerosis in large arteries. This work represents an important first step towards applying this approach to study disease initiation and progression in the VBS.     

Hydrodynamic effects of compliance mismatch in stented arteries

Cardiovascular diseases are the number one cause of death in the world, making the understanding of hemodynamics and development of treatment options imperative. The most common modality for treatment of occlusive coronary artery diseases is the use of stents. Stent design profoundly influences the postprocedural hemodynamic and solid mechanical environment of the stented artery. However, despite their wide acceptance, the incidence of stent late restenosis is still high (Zwart et al., 2010, "Coronary Stent Thrombosis in the Current Era: Challenges and Opportunities for Treatment," Current Treatment Options in Cardiovascular Medicine, 12(1), pp. 46-57), and it is most prevailing at the proximal and distal ends of the stent. In this work, we focus our investigation on the localized hemodynamic effects of compliance mismatch due to the presence of a stent in an artery. The compliance mismatch in a stented artery is maximized at the proximal and distal ends of the stent. Hence, it is our objective to understand and reveal the mechanism by which changes in compliance contribute to the generation of nonphysiological wall shear stress (WSS). Such adverse hemodynamic conditions could have an effect on the onset of restenosis. Three-dimensional, spatiotemporally resolved computational fluid dynamics simulations of pulsatile flow with fluid-structure interaction were carried out for a simplified coronary artery with physiologically relevant flow parameters. A model with uniform elastic modulus is used as the baseline control case. In order to study the effect of compliance variation on local hemodynamics, this baseline model is compared with models where the elastic modulus was increased by two-, five-, and tenfold in the middle of the vessel. The simulations provided detailed information regarding the recirculation zone dynamics formed during flow reversals. The results suggest that discontinuities in compliance cause critical changes in local hemodynamics, namely, altering the local pressure and velocity gradients. The change in pressure gradient at the discontinuity was as high as 90%. The corresponding changes in WSS and oscillatory shear index calculated were 9% and 15%, respectively. We demonstrate that these changes are attributed to the physical mechanism associating the pressure gradient discontinuities to the production of vorticity (vorticity flux) due to the presence of the stent. The pressure gradient discontinuities and augmented vorticity flux are affecting the wall shear stresses. As a result, this work reveals how compliance variations act to modify the near wall hemodynamics of stented arteries.     

Frequency dependence of dynamic curvature effects on flow through coronary arteries

The flow through a curved tube model of a coronary artery was investigated computationally to determine the importance of time-varying curvature on flow patterns that have been associated with the development of atherosclerosis. The entry to the tube was fixed while the radius of curvature varied sinusoidally in time at a frequency of 1 or 5 Hz. Angiographic data from other studies suggest that the radius of curvature waveform contains significant spectral content up to 6 Hz. The overall flow patterns were similar to those observed in stationary curved tubes; velocity profile skewed toward the outer wall, secondary flow patterns, etc. The effects of time-varying curvature on the changes in wall shear rate were expressed by normalizing the wall shear rate amplitude with the shear rate calculated at the static mean radius of curvature. It was found that the wall shear rate varied as much as 94 percent of the mean wall shear rate at the mid wall of curvature for a mean curvature ratio of 0.08 and a 50 percent change in radius of curvature. The effects of 5 Hz deformation were not well predicted by a quasi-static approach. The maximum values of the normalized inner wall shear rate amplitude were found to scale well with a dimensionless parameter equivalent to the product of the mean curvature ratio (delta), normalized change in radius of curvature (epsilon), and a Womersley parameter (alpha). This parameter was less successful at predicting the amplitudes elsewhere in the tube, thus additional studies are necessary. The mean wall shear rate was well predicted with a static geometry. These results indicate that dynamic curvature plays an important role in determining the inner wall shear rates in coronary arteries that are subjected to deformation levels of epsilon delta alpha > 0.05. The effects were not always predictable with a quasi-static approach. These results provide guidelines for constructing more realistic models of coronary artery flow for atherogenesis research.     

Curvature effect on hemodynamic conditions at the inner bend of the carotid siphon and its relation to aneurysm formation

Although high-impact hemodynamic forces are thought to lead to cerebral aneurysmal change, little is known about the aneurysm formation on the inner aspect of vascular bends such as the internal carotid artery (ICA) siphon where wall shear stress (WSS) is expected to be low. This study evaluates the effect of vessel curvature and hemodynamics on aneurysm formation along the inner carotid siphon. Catheter 3D-rotational angiographic volumes of 35 ICA (10 aneurysms, 25 controls) were evaluated in 3D for radius of curvature and peak curvature of the siphon bend, followed by univariate statistical analysis. Computational fluid dynamic (CFD) simulations were performed on patient-derived models after aneurysm removal and on synthetic variants of increasing curvature. Peak focal siphon curvature was significantly higher in aneurysm bearing ICAs (0.36±0.045 vs. 0.30±0.048 mm⁻¹, p=0.003), with no difference in global radius of curvature (p=0.36). In CFD simulations, increasing parametric curvature tightness (from 5 to 3 mm radius) resulted in dramatic increase of WSS and WSS gradient magnitude (WSSG) on the inner wall of the bend. In patient-derived data, the location of aneurysms coincided with regions of low WSS (<4 Pa) flanked by high WSS and WSSG peaks. WSS peaks correlated with the aneurysm neck. In contrast, control siphon bends displayed low, almost constant, WSS and WSSG profiles with little spatial variation. High bend curvature induces dynamically fluctuating high proximal WSS and WSSG followed by regions of flow stasis and recirculation, leading to local conditions known to induce destructive vessel wall remodeling and aneurysmal initiation.     

Prevention of postischemic lesions of the myocardium using liposomes]

The experiments on dogs showed that 60-min blood flow restriction in the left coronary artery branch resulted in pumping and contractile heart dysfunctions. The removal of the blood flow barrier caused reinforcement of the above dysfunctions. The administration of 50 mg/kg liposome prior to reperfusion improved pumping and contractile heart functions and allowed maintenance of stable hemodynamics during the reperfusion.