Numerical modelling of simulated blood flow in idealized composite arterial coronary grafts: transient flow

In composite arterial coronary grafts (CACGs), transport phenomena and geometry may considerably alter blood flow dynamics. CACGs aim at revascularizing pathological arteries according to the human anatomy. However, the exact mechanisms causing the failure of coronary bypass grafting are not yet well elucidated. In the present study, computational fluid dynamics (CFD) techniques are applied for the simulation of multi-branched CACGs under physiologically realistic inflow waveforms. The numerical solution is obtained by a finite-volume method formulated in non-orthogonal, curvilinear coordinates and a multi-grid approach. The geometrical models, consisting of idealized and rigid vessels, include the typical T- and a rather new pi-graft configuration. The stenotic effect is also investigated by comparing computational results for three different degrees of area constriction, namely 25%, 50% and 75%, as well as the case without stenosis. Different grafting distances and various inflow rate ratios are imposed, to give an insight into haemodynamical alterations of CACGs and to study the process of restenosis. The results focus on the interaction between the grafts and coronary flows in terms of spatial and temporal variations of velocity and wall shear stress (WSS) distribution. Prominent variations among the different geometries, concerning the velocity profiles and secondary flow motion, are shown. Moreover, the residual flow emerging from different degrees of area constriction shows that low and oscillating shear stresses may arise for even moderate stenotic fields.     

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.     

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.     

Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta

Three non-Newtonian blood viscosity models plus the Newtonian one are analysed for a patient-specific thoracic aorta anatomical model under steady-state flow conditions via wall shear stress (WSS) distribution, non-Newtonian importance factors, blood viscosity and shear rate. All blood viscosity models yield a consistent WSS distribution pattern. The WSS magnitude, however, is influenced by the model used. WSS is found to be the lowest in the vicinity of the three arch branches and along the distal walls of the branches themselves. In this region, the local non-Newtonian importance factor and the blood viscosity are elevated, and the shear rate is low. The present study revealed that the Newtonian assumption is a good approximation at mid-and-high flow velocities, as the greater the blood flow, the higher the shear rate near the arterial wall. Furthermore, the capabilities of the applied non-Newtonian models appeared at low-flow velocities. It is concluded that, while the non-Newtonian power-law model approximates the blood viscosity and WSS calculations in a more satisfactory way than the other non-Newtonian models at low shear rates, a cautious approach is given in the use of this blood viscosity model. Finally, some preliminary transient results are presented.     

Impact of plaques in the left coronary artery on wall shear stress and pressure gradient in coronary side branches

In this study, we investigate plaques located at the left coronary bifurcation. We focus on the effect that the resulting changes in wall shear stress (WSS) and wall pressure stress gradient (WPSG) have on atherosclerotic progress in coronary artery disease. Coronary plaques were simulated and placed at the left main stem and the left anterior descending to produce >50% narrowing of the coronary lumen. Computational fluid dynamics analysis was carried out, simulating realistic physiological conditions that show the in vivo cardiac haemodynamic. WSS and WPSG in the left coronary artery were calculated and compared in the left coronary models, with and without the presence of plaques during cardiac cycles. Our results showed that WSS decreased while WPSG was increased in coronary side branches due to the presence of plaques. There is a direct correlation between coronary plaques and subsequent WSS and WPSG variations based on the bifurcation plaques simulated in the realistic coronary models.     

Analysis of blood flow in an out-of-plane CABG model

Coronary artery bypass graft (CABG) is a routine surgical treatment for ischemic and infarcted myocardium. A large number of CABG fail postoperatively because of intimal hyperplasia within months or years. The cause of this failure is thought to be partly related to the flow patterns and shear stresses acting on the endothelial cells. An accurate representation of the flow field and associated wall shear stress (WSS) requires a detailed three-dimensional (3D) model of the CABG. The purpose of this study is to present a detailed analysis of blood flow in a 3D aorto/left CABG, bypassing the occluded left anterior descending coronary (LAD) artery. The analysis takes into account the influence of the out-of-plane geometry of the graft. The finite volume technique was employed to model the 3D blood flow pattern to determine the velocity and WSS distributions. This study presents the flow field distributions of the velocity and WSS at four instances of the cardiac cycle, two in systole and two in diastole. Our results reveal that the CABG geometry has a significant effect on the velocity distribution. The axial velocity profiles at different instances of the cardiac cycle exhibit strong skewing; significant secondary flow and vortex structures are seen in the in-plane velocity patterns. The maximum WSS on the bed of the occluded LAD artery opposite to the graft junction is 14 Pa in middiastole, whereas there is a significantly lower and more uniform distribution of WSS on the bed of the anastomosis. The present results indicate that nonplanarity of the blood vessel along with the inflow conditions has a substantial effect on the fluid mechanics of CABG that contribute to the patency of graft.     

The influence of boundary conditions on wall shear stress distribution in patients specific coronary trees

Patient specific geometrical data on human coronary arteries can be reliably obtained multislice computer tomography (MSCT) imaging. MSCT cannot provide hemodynamic variables, and the outflow through the side branches must be estimated. The impact of two different models to determine flow through the side branches on the wall shear stress (WSS) distribution in patient specific geometries is evaluated. Murray's law predicts that the flow ratio through the side branches scales with the ratio of the diameter of the side branches to the third power. The empirical model is based on flow measurements performed by Doriot et al. (2000) in angiographically normal coronary arteries. The fit based on these measurements showed that the flow ratio through the side branches can best be described with a power of 2.27. The experimental data imply that Murray's law underestimates the flow through the side branches. We applied the two models to study the WSS distribution in 6 coronary artery trees. Under steady flow conditions, the average WSS between the side branches differed significantly for the two models: the average WSS was 8% higher for Murray's law and the relative difference ranged from -5% to +27%. These differences scale with the difference in flow rate. Near the bifurcations, the differences in WSS were more pronounced: the size of the low WSS regions was significantly larger when applying the empirical model (13%), ranging from -12% to +68%. Predicting outflow based on Murray's law underestimates the flow through the side branches. Especially near side branches, the regions where atherosclerotic plaques preferentially develop, the differences are significant and application of Murray's law underestimates the size of the low WSS region.     

Large eddy simulation of LDL surface concentration in a subject specific human aorta

The development of atherosclerosis is correlated to the accumulation of lipids in the arterial wall, which, in turn, may be caused by the build-up of low-density lipoproteins (LDL) on the arterial surface. The goal of this study was to model blood flow within a subject specific human aorta, and to study how the LDL surface concentration changed during a cardiac cycle. With measured velocity profiles as boundary conditions, a scale-resolving technique (large eddy simulation, LES) was used to compute the pulsatile blood flow that was in the transitional regime. The relationship between wall shear stress (WSS) and LDL surface concentration was investigated, and it was found that the accumulation of LDL correlated well with WSS. In general, regions of low WSS corresponded to regions of increased LDL concentration and vice versa. The instantaneous LDL values changed significantly during a cardiac cycle; during systole the surface concentration was low due to increased convective fluid transport, while in diastole there was an increased accumulation of LDL on the surface. Therefore, the near-wall velocity was investigated at four representative locations, and it was concluded that in regions with disturbed flow the LDL concentration had significant temporal changes, indicating that LDL accumulation is sensitive to not only the WSS but also near-wall flow.     

A study on the compliance of a right coronary artery and its impact on wall shear stress

A computational model incorporating physiological motion and uniform transient wall deformation of a branchless right coronary artery (RCA) was developed to assess the influence of artery compliance on wall shear stress (WSS). Arterial geometry and deformation were derived from modern medical imaging techniques, whereas the blood flow was solved numerically employing a moving-grid approach using a well-validated in-house finite element code. The simulation results indicate that artery compliance affects the WSS in the RCA heterogeneously, with the distal region mostly experiencing these effects. Under physiological inflow conditions, coronary compliance contributed to phase changes in the WSS time history, without affecting the temporal gradient of the local WSS nor the bounds of the WSS magnitude. Compliance does not cause considerable changes to the topology of WSS vector patterns nor to the localization of WSS minima along the RCA. We conclude that compliance is not an important factor affecting local hemodynamics in the proximal region of the RCA while the influence of compliance in the distal region needs to be evaluated in conjunction with the outflow to the myocardium through the major branches of the RCA.     

Flow patterns in three-dimensional porcine epicardial coronary arterial tree

The branching pattern of epicardial coronary arteries is clearly three-dimensional, with correspondingly complex flow patterns. The objective of the present study was to perform a detailed hemodynamic analysis using a three-dimensional finite element method in a left anterior descending (LAD) epicardial arterial tree, including main trunk and primary branches, based on computed tomography scans. The inlet LAD flow velocity was measured in an anesthetized pig, and the outlet pressure boundary condition was estimated based on scaling laws. The spatial and temporal wall shear stress (WSS), gradient of WSS (WSSG), and oscillatory shear index (OSI) were calculated and used to identify regions of flow disturbances in the vicinity of primary bifurcations. We found that low WSS and high OSI coincide with disturbed flows (stagnated, secondary, and reversed flows) opposite to the flow divider and lateral to the junction orifice of the main trunk and primary branches. High time-averaged WSSG occurs in regions of bifurcations, with the flow divider having maximum values. Low WSS and high OSI were found to be related through a power law relationship. Furthermore, zones of low time-averaged WSS and high OSI amplified for larger diameter ratio and high inlet flow rate. Hence, different focal atherosclerotic-prone regions may be explained by different physical mechanism associated with certain critical levels of low WSS, high OSI, and high WSSG, which are strongly affected by the diameter ratio. The implications of the flow patterns for atherogenesis are enumerated.     

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.     

Computational study of pulsatile blood flow in prototype vessel geometries of coronary segments

The spatial and temporal distributions of wall shear stress (WSS) in prototype vessel geometries of coronary segments are investigated via numerical simulation, and the potential association with vascular disease and specifically atherosclerosis and plaque rupture is discussed. In particular, simulation results of WSS spatio-temporal distributions are presented for pulsatile, non-Newtonian blood flow conditions for: (a) curved pipes with different curvatures, and (b) bifurcating pipes with different branching angles and flow division. The effects of non-Newtonian flow on WSS (compared to Newtonian flow) are found to be small at Reynolds numbers representative of blood flow in coronary arteries. Specific preferential sites of average low WSS (and likely atherogenesis) were found at the outer regions of the bifurcating branches just after the bifurcation, and at the outer-entry and inner-exit flow regions of the curved vessel segment. The drop in WSS was more dramatic at the bifurcating vessel sites (less than 5% of the pre-bifurcation value). These sites were also near rapid gradients of WSS changes in space and time – a fact that increases the risk of rupture of plaque likely to develop at these sites. The time variation of the WSS spatial distributions was very rapid around the start and end of the systolic phase of the cardiac cycle, when strong fluctuations of intravascular pressure were also observed. These rapid and strong changes of WSS and pressure coincide temporally with the greatest flexion and mechanical stresses induced in the vessel wall by myocardial motion (ventricular contraction). The combination of these factors may increase the risk of plaque rupture and thrombus formation at these sites.     

Requirements for mesh resolution in 3D computational hemodynamics

Computational techniques are widely used for studying large artery hemodynamics. Current trends favor analyzing flow in more anatomically realistic arteries. A significant obstacle to such analyses is generation of computational meshes that accurately resolve both the complex geometry and the physiologically relevant flow features. Here we examine, for a single arterial geometry, how velocity and wall shear stress patterns depend on mesh characteristics. A well-validated Navier-Stokes solver was used to simulate flow in an anatomically realistic human right coronary artery (RCA) using unstructured high-order tetrahedral finite element meshes. Velocities, wall shear stresses (WSS), and wall shear stress gradients were computed on a conventional "high-resolution" mesh series (60,000 to 160,000 velocity nodes) generated with a commercial meshing package. Similar calculations were then performed in a series of meshes generated through an adaptive mesh refinement (AMR) methodology. Mesh-independent velocity fields were not very difficult to obtain for both the conventional and adaptive mesh series. However, wall shear stress fields, and, in particular, wall shear stress gradient fields, were much more difficult to accurately resolve. The conventional (nonadaptive) mesh series did not show a consistent trend towards mesh-independence of WSS results. For the adaptive series, it required approximately 190,000 velocity nodes to reach an r.m.s. error in normalized WSS of less than 10 percent. Achieving mesh-independence in computed WSS fields requires a surprisingly large number of nodes, and is best approached through a systematic solution-adaptive mesh refinement technique. Calculations of WSS, and particularly WSS gradients, show appreciable errors even on meshes that appear to produce mesh-independent velocity fields.     

Sequential venous anastomosis design to enhance patency of arterio-venous grafts for hemodialysis

Arterio-venous grafts (AVGs), the second best option as long-term vascular access for hemodialysis, face major issues of stenosis mainly due to development of intimal hyperplasia at the venous anastomosis which is linked to unfavorable hemodynamic conditions. We have investigated computationally the utility of a coupled sequential venous anastomotic design to replace conventional end-to-side (ETS) venous anastomosis, in order to improve the hemodynamic environment and consequently enhance the patency of AVGs. Two complete vascular access models with the conventional and the proposed venous anastomosis configurations were constructed. Three-dimensional, pulsatile blood flow through the models was simulated, and wall shear stress (WSS)-based hemodynamic parameters were calculated and compared between the two models. Simulation results demonstrated that the proposed anastomotic design provides: (i) a more uniform and smooth flow at the ETS anastomosis, without flow impingement and stagnation point on the artery bed and vortex formation in the heel region of the ETS anastomosis; (ii) more uniform distribution of WSS and substantially lower WSS gradients on the venous wall; and (iii) a spare route for the blood flow to the vein, to avoid re-operation in case of stenosis. The distinctive hemodynamic advantages observed in the proposed anastomotic design can enhance the patency of AVGs.     

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.     

Computational modeling of coupled blood-wall mass transport of LDL: effects of local wall shear stress

The work herein represents a novel approach for the modeling of low-density lipoprotein (LDL) transport from the artery lumen into the arterial wall, taking into account the effects of local wall shear stress (WSS) on the endothelial cell layer and its pathways of volume and solute flux. We have simulated LDL transport in an axisymmetric representation of a stenosed coronary artery, where the endothelium is represented by a three-pore model that takes into account the contributions of the vesicular pathway, normal junctions, and leaky junctions also employing the local WSS to yield the overall volume and solute flux. The fraction of leaky junctions is calculated as a function of the local WSS based on published experimental data and is used in conjunction with the pore theory to determine the transport properties of this pathway. We have found elevated levels of solute flux at low shear stress regions because of the presence of a larger number of leaky junctions compared with high shear stress regions. Accordingly, we were able to observe high LDL concentrations in the arterial wall in these low shear stress regions despite increased filtration velocity, indicating that the increase in filtration velocity is not sufficient for the convective removal of LDL.     

Hemodynamic impacts of various types of stenosis in the left coronary artery bifurcation: A patient-specific analysis

This study investigates the hemodynamic changes to various types of coronary stenosis in the left coronary artery bifurcation, based on a patient-specific analysis. Twenty two patients with left coronary artery disease were included in this study. All stenoses involving the left coronary artery bifurcation were classified into four types, according to their locations: A) left circumflex (LCx) and left anterior descending (LAD), B) LCx only, C) left main stem only, and D) LAD only. Computational fluid dynamics (CFD) was performed to analyze the flow and wall shear stress (WSS) changes in all reconstructed left coronary geometries. Our results showed that the flow velocity and WSS were significantly increased at stenotic locations. High WSS was found at >70% lumen stenosis, which ranged from 2.5 Pa to 3.5 Pa. This study demonstrates that in patients with more than 50% stenosis in the left coronary artery bifurcation, WSS plays an important role in providing information about the extent of coronary atherosclerosis in the left coronary artery branch.     

Numerical simulation of wall shear stress conditions and platelet localization in realistic end-to-side arterial anastomoses

Research studies over the last three decades have established that hemodynamic interactions with the vascular surface as well as surgical injury are inciting mechanisms capable of eliciting distal anastomotic intimal hyperplasia (IH) and ultimate bypass graft failure. While abnormal wall shear stress (WSS) conditions have been widely shown to affect vascular biology and arterial wall self-regulation, the near-wall localization of critical blood particles by convection and diffusion may also play a significant role in IH development. It is hypothesized that locations of elevated platelet interactions with reactive or activated vascular surfaces, due to injury or endothelial dysfunction, are highly susceptible to IH initialization and progression. In an effort to assess the potential role of platelet-wall interactions, experimentally validated particle-hemodynamic simulations have been conducted for two commonly implemented end-to-side anastomotic configurations, with and without proximal outflow. Specifically, sites of significant particle interactions with the vascular surface have been identified by a novel near-wall residence time (NWRT) model for platelets, which includes shear stress-based factors for platelet activation as well as endothelial cell expression of thrombogenic and anti-thrombogenic compounds. Results indicate that the composite NWRT model for platelet-wall interactions effectively captures a reported shift in significant IH formation from the arterial floor of a relatively high-angle (30 deg) graft with no proximal outflow to the graft hood of a low-angle graft (10 deg) with 20% proximal outflow. In contrast, other WSS-based hemodynamic parameters did not identify the observed system-dependent shift in IH formation. However, large variations in WSS-vector magnitude and direction, as encapsulated by the WSS-gradient and WSS-angle-gradient parameters, were consistently observed along the IH-prone suture-line region. Of the multiple hemodynamic factors capable of eliciting a hyperplastic response at the cellular level, results of this study indicate the potential significance of platelet-wall interactions coinciding with regions of low WSS in the development of IH.     

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.     

Impedance-based outflow boundary conditions for human carotid haemodynamics

In this study, we develop structured tree outflow boundary conditions for modelling the human carotid haemodynamics. The model geometry was reconstructed through computerised tomography scan. Unsteady-state computational fluid dynamic analyses were performed under different conditions using a commercial software package ADINA R&D, Inc., (Watertown, MA, USA) in order to assess the impact of the boundary conditions on the flow variables. In particular, the results showed that the peripheral vessels massively impact the pressure while the flow is relatively unaffected. As an example of application of these outflow conditions, an unsteady fluid-structure interaction (FSI) simulation was carried out and the dependence of the wall shear stress (WSS) on the arterial wall compliance in the carotid bifurcation was studied. In particular, a comparison between FSI and rigid-wall models was conducted. Results showed that the WSS distributions were substantially affected by the diameter variation of the arterial wall. In particular, even similar WSS distributions were found for both cases, and differences in the computed WSS values were also found.