Analysis of non-Newtonian effects within an aorta-iliac bifurcation region

The geometry of the arteries at or near arterial bifurcation influences the blood flow field, which is an important factor affecting arteriogenesis. The blood can act sometimes as a non-Newtonian fluid. However, many studies have argued that for large and medium arteries, the blood flow can be considered to be Newtonian. In this work a comprehensive investigation of non-Newtonian effects on the blood fluid dynamic behavior in an aorta-iliac bifurcation is presented. The aorta-iliac geometry is reconstructed with references to the values reported in Shah et al. (1978); the 3D geometrical model consists of three filleted cylinders of different diameters. Governing equations with the appropriate boundary conditions are solved with a finite-element code. Different rheological models are used for the blood flow through the lumen and detailed comparisons are presented for the aorta-iliac bifurcation. Results are presented in terms of the velocity profiles in the bifurcation zone and Wall Shear Stress (WSS) for different sides of the bifurcation both for male and female geometries, showing that the Newtonian fluid assumption can be made without any particular loss in terms of accuracy with respect to the other more complex rheological models.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part II--pulsatile flow hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50< or =Re(m) < or =300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG), time-average wall shear stress (tau(w)*), and time-average Wall Shear Stress Gradient WSSG*. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Flow-induced Wall Shear Stress in Abdominal Aortic Aneurysms: Part II - Pulsatile Flow Hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 h Re m h 300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure ( p w ), wall shear stress ( w ), Wall Shear Stress Gradient (WSSG), time-average wall shear stress ( w *), and time-average Wall Shear Stress Gradient WSSG *. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

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.     

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.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part I--steady flow hemodynamics

Numerical predictions of blood flow patterns and hemodynamic stresses in Abdominal Aortic Aneurysms (AAAs) are performed in a two-aneurysm, axisymmetric, rigid wall model using the spectral element method. Homogeneous, Newtonian blood flow is simulated under steady conditions for the range of Reynolds numbers 10 < or =Re < or =2265. Flow hemodynamics are quantified by calculating the distributions of wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG). A correlation between maximum values of hemodynamic stresses and Reynolds number is established, and the spatial distribution of WSSG is considered as a hemodynamic force that may cause damage to the arterial wall at an intermediate stage of AAA growth. The temporal distribution of hemodynamic stresses in pulsatile flow and their physical implications in AAA rupture are discussed in Part II of this paper.     

Experimental flow studies in exact-replica phantoms of atherosclerotic carotid bifurcations under steady input conditions

Extensive flow studies are conducted in two carotid bifurcation flow phantoms. These phantoms exactly replicate the lumen of the plaque excised intact from two patients with severe carotid atherosclerosis. The input flow into the phantom's common carotid artery is steady. Novel scanning techniques for flow visualization and particle image velocimetry are used. In addition, a novel boundary treatment technique is employed in velocimetry to extract first order accurate velocity gradients at walls. The data show that the flow fields are highly three-dimensional. Numerous separation and recirculation zones dominate the flow domain, except at the lowest Reynolds numbers. The separation regions are often so severe that highly directed internal jets form. At high Reynolds numbers, the flows become unsteady and chaotic, even though the input flow is steady. Flow fields have large regions of energetic flow and almost stagnant recirculation zones. These recirculation zones range in size from the full size of the arteries to zones within crevasses smaller than 1 mm. Velocity field and streamline patterns conform well to the lumen geometry. The streamlines are highly tortuous. Stagnation points correlate well with the topological features of the stenosis. Vorticity maps confirm the highly complex and three dimensional nature of the flow. Wall shear stresses at the stenoses are estimated to be on the order of 10 Pa. These studies conclusively show that the nature of the flow in the diseased bifurcation is primarily dictated by the lumen geometry.     

Bifurcation asymmetry of the porcine coronary vasculature and its implications on coronary flow heterogeneity

The branching pattern of the coronary arteries and veins is asymmetric, i.e., many small vessels branch off of a large trunk such that the two daughter vessels at a bifurcation are of unequal diameters and lengths. One important implication of the geometric vascular asymmetry is the dispersion of blood flow at a bifurcation, which leads to large spatial heterogeneity of myocardial blood flow. To document the asymmetric branching pattern of the coronary vessels, we computed an asymmetry ratio for the diameters and lengths of all vessels, defined as the ratio of the daughter diameters and lengths, respectively. Previous data from silicone elastomer cast of the entire coronary vasculature including arteries, arterioles, venules, and veins were analyzed. Data on smaller vessels were obtained from histological specimens by optical sectioning, whereas data on larger vessels were obtained from vascular casts. Asymmetry ratios for vascular areas, volumes, resistances, and flows of the various daughter vessels were computed from the asymmetry ratios of diameters and lengths for every order of mother vessel. The results show that the largest orders of arterial and venous vessels are most asymmetric and the degree of asymmetry decreases toward the smaller vessels. Furthermore, the diameter asymmetry at a bifurcation is significantly larger for the coronary veins (1.7-6.8 for sinus veins) than the corresponding arteries (1.5-5.8 for left anterior descending coronary artery) for orders 2-10, respectively. The reported diameter asymmetry at a bifurcation leads to significant heterogeneity of blood flow at a bifurcation. Hence, the present data quantify the dispersion of blood flow at a bifurcation and are essential for understanding flow heterogeneity in the coronary circulation.     

A Novel Attempt to Standardize Results of CFD Simulations Basing on Spatial Configuration of Aortic Stent-Grafts

Currently, studies connected with Computational Fluid Dynamic (CFD) techniques focus on assessing hemodynamic of blood flow in vessels in different conditions e.g. after stent-graft’s placement. The paper propose a novel method of standardization of results obtained from calculations of stent-grafts'' “pushing forces” (cumulative WSS—Wall Shear Stress), and describes its usefulness in diagnostic process. AngioCT data from 27 patients were used to reconstruct 3D geometries of stent-grafts which next were used to create respective reference cylinders. We made an assumption that both the side surface and the height of a stent-graft and a reference cylinder were equal. The proposed algorithm in conjunction with a stent-graft “pushing forces” on an implant wall, allowed us to determine which spatial configuration of a stent-graft predispose to the higher risk of its migration. For stent-grafts close to cylindrical shape (shape factor φ close to 1) WSS value was about 267Pa, while for stent-grafts different from cylindrical shape (φ close to 2) WSS value was about 635Pa. It was also noticed that deformation in the stent-graft’s bifurcation part impaired blood flow hemodynamic. Concluding the proposed algorithm of standardization proved its usefulness in estimating the WSS values that may be useful in diagnostic process. Angular bends or tortuosity in bifurcations of an aortic implant should be considered in further studies of estimation of the risk of implantation failure.     

A numerical study on hemodynamics in the left coronary bifurcation with normal and hypertension conditions

In this study, a three-dimensional analysis of the non-Newtonian blood flow was carried out in the left coronary bifurcation. The Casson model and hyperelastic and rigid models were used as the constitutive equation for blood flow and vessel wall model, respectively. Physiological conditions were considered first normal and then compliant with hypertension disease with the aim of evaluating hemodynamic parameters and a better understanding of the onset and progression of atherosclerosis plaques in the coronary artery bifurcation. Two-way fluid–structure interaction method applying a fully implicit second-order backward Euler differencing scheme has been used which is performed in the commercial code ANSYS and ANSYS CFX (version 15.0). When artery deformations and blood pressure are associated, arbitrary Lagrangian–Eulerian formulation is employed to calculate the artery domain response using the temporal blood response. As a result of bifurcation, noticeable velocity reduction and backflow formation decrease shear stress and made it oscillatory at the starting point of the LCx branch which caused the shear stress to be less than 1 and 2 Pa in the LCx and the LAD branches, respectively. Oscillatory shear index (OSI) as a hemodynamic parameter represents the increase in residence time and oscillatory wall shear stress. Because of using the ideal 3D geometry and realistic physiological conditions, the values obtained for shear stress are more accurate than the previous studies. Comparing the results of this study with previous clinical investigations shows that the regions with low wall shear stress less than 1.20 Pa and with high OSI value more than 0.3 are in more potential risk to the atherosclerosis plaque development, especially in the posterior after the bifurcation.     

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.     

Computational Study of Anastomosis Angle of Arteriovenous Fistula for Hemodialysis

Arteriovenous fistula (AVF) is the endorsed method of vascular access for hemodialysis in end-stage renal disease (ESRD). However, more than 60% of AVF fail to mature for hemodialysis. Intimal hyperplasia leads to stenosis is the primary cause of fistula failure. Wall shear stress (WSS) is one of the important parameters that enact a crucial role in building of intimal hyperplasia. The prime purpose of this research work is to investigate the effect of anastomosis angle on WSS, pressure drop, venous outflow rate and identify the optimal angle of anastomosis of AVF, so that it helps to standardize the surgical technique. In this research work, three-dimensional idealized geometries of end-to-side type AVF for the four different angles of anastomosis are created. Numerical simulation performed using incompressible, Newtonian blood to calculate the WSS, blood flow rate at the distal end of the vein and pressure drop across the anastomosis for the three arterial inflow 350, 500 and 900 ml/min. For all three arterial inflow, the WSS is high at 75° compared to other angles and it is less at 60°. The WSS at 45° and 90° are moderate. The venous outflow is increasing with the increase in arterial inflow condition for all anastomosis angles except for 45°. The outflow rate at distal venous end is highest, 344.85 ml/min at 45° for 500 ml/min arterial inflow. Pressure drop high at 45° and lowest at 90°. The intensity of disturbed flow and recirculation zone was observed at the area of anastomosis and it is high at 75°. From the results and observations, it can be concluded that 45° angle is the best choice for the anastomosis of AVF. This finding will standardize the surgical technique and subsequently, it will help to mature the AVF early and for a long time.     

Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation

Finite element simulations of fluid-solid interactions were used to investigate inter-individual variations in flow dynamics and wall mechanics at the carotid artery bifurcation, and its effects on atherogenesis, in three healthy humans (normal volunteers: NV1, NV2, NV4). Subject-specific calculations were based on MR images of structural anatomy and ultrasound measurements of flow at domain boundaries. For all subjects, the largest contiguous region of low wall shear stress (WSS) occurred at the carotid bulb, WSS was high (6-10 Pa) at the apex, and a small localized region of WSS > 10 Pa occurred close to the inner wall of the external carotid artery (ECA). NV2 and NV4 had a "spot" of low WSS distal to the bifurcation at the inner wall of the ECA. Low WSS patches in the common carotid artery (CCA) were contiguous with the carotid bulb low WSS region in NV1 and NV2, but not in NV4. In all three subjects, areas of high oscillatory shear index (OSI) were confined to regions of low WSS. Only NV4 exhibited high levels of OSI on the external adjoining wall of the ECA and CCA. For all subjects, the maximum wall shear stress temporal gradient (WSSTG) was highest at the flow divider (reaching 1,000 Pa/s), exceeding 300 Pa/s at the walls connecting the ECA and CCA, but remaining below 250 Pa/s outside of the ECA. In all subjects, (maximum principle) cyclic strain (CS) was greatest at the apex (NV1: 14%; NV2: 11%; NV4: 6%), and a second high CS region occurred at the ECA-CCA adjoining wall (NV1: 11%, NV2: 9%, NV4: 5%). Wall deformability was included in one simulation (NV2) to verify that it had little influence on the parameters studied. Location and magnitude of low WSS were similar, except for the apex (differences of up to 25%). Wall distensibility also influenced OSI, doubling it in most of the CCA, separating the single high OSI region of the carotid bulb into two smaller regions, and shrinking the ECA internal and external walls' high OSI regions. These observations provide further evidence that significant intra-subject variability exists in those factors thought to impact atherosclerosis.     

Branch angle and flow into a symmetric bifurcation

Arterial branches are found to be a major site for formation of arterial plaque. In this study, we investigate the role of the bifurcation angle on the flow into a symmetric bifurcation. Specially, how the changes in the bifurcation angle influences the distribution of axial wall shear in the bifurcation model. The flow in a range of branch opening half-angle of pi/25< or =theta< or =pi/4 are numerically simulated. The flow in the above models is calculated for the inlet flow Reynolds numbers of 250, 500, 1000, and 2000. It is found that at higher values of the opening angle of the bifurcation, the possibility and severity of flow separation at the appropriate wall location increases.     

A new imaging technique to study 3-D plaque and shear stress distribution in human coronary artery bifurcations in vivo

OBJECTIVE: Bifurcations of coronary arteries are predilection sites for atherosclerosis and expansive remodeling, the latter being associated with plaque vulnerability. Both are related to blood flow-induced shear stress (SS). We present a new approach to generate 3-D reconstructions of coronary artery bifurcations in vivo and investigate the relationship between SS, wall thickness (WT) and remodeling. METHODS: The patient specific 3-D reconstruction of the main branch of the bifurcation was obtained by combining intravascular ultrasound and biplane angiography, and the 3-D lumen of the side branch was based on biplane angiography only. The two data sets were fused and computational methods were applied to determine the SS distribution, using patient derived flow and viscosity data. The intravascular ultrasound data allowed us to measure local WT and remodeling in the main branch. RESULTS: The lumen reconstruction procedure was successful and it was shown that the impact of the side branch on SS distribution in the main branch diminished within 3mm. Distal to the bifurcation, two continuous regions in the main branch were identified. In the proximal region, we observed lumen preservation, and expansive remodeling. Although a plaque was observed in the low SS region at the non-divider wall, no relationship between SS and WT was found. In the distal region, we observed lumen narrowing and a significant positive relationship between SS and WT. CONCLUSIONS: A new imaging technique was applied to generate a 3-D reconstruction of a human coronary artery bifurcation in vivo. The observed relationship between SS, WT and remodeling in this specific patient illustrates the spatial heterogeneity of the atherosclerosis in the vicinity of arterial bifurcations.     

Arterial bifurcation flows--effects of flow rate and area ratio.

Velocity profiles and surface shear rates, for three model symmetrical bifurcations made of glass from dimensions based on the arterial system, were investigated. The models studied had area ratios of 0.75, 1.02, and 1.29, with a common included angle of 75 degrees. Area ratio and parent tube flow rate were the two independent variables evaluated. Measurements were made with a tracer particle technique using cinephotography. Velocity profiles had their highest values on the inside, and lowest values on the outside, of the branch. Flow symmetry existed in the plane perpendicular to the plane of the bifurcation. Surface shear rates remained well above the daughter-tube developed values, between two and six diameters downstream from the carina. Shear rates below the daughter-tube developed value were found on the outside wall between the carina and two daughter-tube diameters downstream. Vortex-like flow was absent in this region for the 0.75 area ratio branch and was found above 900 Reynolds number in the 1.29 area ratio branch. The disturbed flow described by others in this region may not contain vortex-like streamlines for the physiologically important 0.75 area ratio.     

Inflow/Outflow Boundary Conditions for Particle-Based Blood Flow Simulations: Application to Arterial Bifurcations and Trees

When blood flows through a bifurcation, red blood cells (RBCs) travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and RBCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon validation of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the “all-or-nothing” phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Finally, we demonstrated the effectiveness of the new methodology in simulations of blood flow in vessels with multiple inlets and outlets, constructed using an angiogenesis model.     

Pulsatile non-newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles

Flow and stress patterns in human carotid artery bifurcation models, which differ in the bifurcation angle, are analysed numerically under physiologically relevant flow conditions. The governing Navier-Stokes equations describing pulsatile, three-dimensional flow of an incompressible non-Newtonian fluid are approximated using a pressure correction finite element method, which has been developed recently. The non-Newtonian behaviour of blood is modelled using Casson's relation, based on measured dynamic viscosity. The study concentrates on flow and stress characteristics in the carotid sinus. The results show that the complex flow in the sinus is affected by the angle variation. The magnitude of reversed flow, the extension of the recirculation zone in the outer sinus region and the duration of flow separation during the pulse cycle as well as the resulting wall shear stress are clearly different in the small angle and in the large angle bifurcation. The haemodynamic phenomena, which are important in atherogenesis, are more pronounced in the large angle bifurcation.     

Optimality principle in vascular bifurcation

The optimal geometry of the vascular bifurcation is interpreted on the basis of the principle of minimum work. We consider the energy expenditure due to the viscosity of blood, and that for maintaining the metabolic states of the blood cells and of the vessel wall. It is shown that the optimal radii of the stem and branch vessels and the optimal branching angle are related to two parameters which represent the morphologic and metabolic states of the blood and the vessel wall. In the special case of symmetrical bifurcation, it was found that as the metabolic demand of the vessel wall becomes more apparent when compared with that of the blood, the branch radius relative to that of the stem takes values of from 0.794 down to 0.758 minimally, and the angle from 37.5 degrees up to 48.7 degrees maximally with respect to the direction of the stem.     

Definition of the margin of major coronary artery bifurcations during radiotherapy with electrocardiograph-gated 4D-CT

PurposeThe aim was to measure the cardiac motion-induced displacements of major coronary artery bifurcations utilizing electrocardiography (ECG)-gated four-dimensional computed tomography (4D-CT) and to determine the margin of coronary artery bifurcations.MethodsThirty-seven female patients who underwent retrospective ECG-gated 4D-CT in inspiratory breath hold (IBH) were enrolled. The left main coronary artery bifurcation (LM), the obtuse marginal branch bifurcation (OM), the first diagonal branch bifurcation (D₁), the second diagonal branch bifurcation (D₂), the caudal portion of the left anterior descending branch (APX), the first right ventricular artery bifurcation (V) and the acute marginal branch bifurcation (AM) were contoured. The center of the contour of the coronary arterial bifurcations at end systole was defined as the standard, and the margin were then calculated.ResultsThe margin in the left–right (LR), cranio-caudal (CC), and anterior-posterior (AP) coordinates were as follows: LM 3, 3, and 3 mm; D₁ 6, 3, and 3 mm; D₂ 3, 3, and 3 mm; APX 4, 4, and 4 mm; OM 4, 6, and 5 mm; V 6, 8, and 7 mm; and AM 6, 8, and 7 mm, respectively.ConclusionCoronary artery bifurcations should be considered a separate organ at risk (OAR), and different margin should be provided due to the differences resulting from motion displacement. The maximum margin in the LR, CC, and AP coordinates of left coronary artery bifurcations were 6, 6, and 5 mm, and those of the right coronary artery bifurcations were 6, 8, and 7 mm, respectively.