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.     

Wall shear stress distribution in a model human aortic arch: assessment by an electrochemical technique

Wall shear stress (WSS) distribution in a human aortic arch model is studied using 130 cathode electrodes flush-mounted on the model walls. Flow visualizations are made in a transparent geometry model to identify the regions of fluid mechanical interests, e.g. regions of flow separation, eddy formation and flow stagnancy. The 130 electrodes are strategically positioned in the arch based on information obtained from the flow visualizations. The measured data indicate that the aortic arch may be categorized into eight regions: three along the inner wall of the arch (A,B,C); and five near the outer wall (D,E,F,G,H). (1) The regions of low WSS are distributed along the inner wall of the ascending aorta A; the inner wall of the descending aorta C; and the upstream inner wall of the innominate and the common carotid branchings F. (2) The high WSS regions are distributed along the outer wall of the arch E; and the inner wall in the arch opposite to the left subclavian branching B. (3) In certain regions, high and low WSS may be found next to each other (e.g. G and H) without a definable boundary in between; and (4) as the Reynolds number increases, the areas of low WSS decrease, while the high WSS areas increase with no obvious change in magnitude of the stress along the inner wall of the arch. At the branchings, the WSS distribution is not affected by the Reynolds number within the range of observations. The measured WSS distribution is compared with Rodkiewicz's map of early atherosclerotic lesions in the aortic arch of cholesterol fed rabbits.     

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 analysis of hemodynamics in spastic middle cerebral arteries

Cerebral vasospasm (CVS) is the most common serious complication of subarachnoid hemorrhage. Among the many factors that are associated with the pathogenesis of CVS, hemodynamics plays an important role in the initiation and development of CVS. Numerical simulation was carried out to obtain the flow patterns and wall shear stress (WSS) distribution in spastic middle cerebral arteries. The blood was assumed to be incompressible, laminar, homogenous, Newtonian, and steady. Our simulations reveal that flow velocity and WSS level increase at the stenosis segment of the spastic vessels, but further downstream of stenosis, the WSS significantly decreases along the inner wall, and flow circulation and stagnation are observed. The hydrodynamic resistance increases with the increase of vessel spasm. Moreover, the change of flow field and hydrodynamic forces are not linearly proportional to the spasm level, and the rapid change of hemodynamic parameters is observed as the spasm is more than 50%. Accordingly, in the view of hemodynamic physiology, vessels with less than 30% stenosis are capable of self-restoration towards normal conditions. However, vessels with more than 50% stenosis may eventually lose their capacity to adapt to differing physiologic conditions due to the extreme non-physilogic hemodynamic environment, and the immediate expansion of the vessel lumen might be needed to minimize serious and non-reversible effects.     

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.     

Abdominal aortic hemodynamics in young healthy adults at rest and during lower limb exercise: quantification using image-based computer modeling

Localization of atherosclerotic lesions in the abdominal aorta has been previously correlated to areas of adverse hemodynamic conditions, such as flow recirculation, low mean wall shear stress, and high temporal oscillations in shear. Along with its many systemic benefits, exercise is also proposed to have local benefits in the vasculature via the alteration of these regional flow patterns. In this work, subject-specific models of the human abdominal aorta were constructed from magnetic resonance angiograms of five young, healthy subjects, and computer simulations were performed under resting and exercise (50% increase in resting heart rate) pulsatile flow conditions. Velocity fields and spatial variations in mean wall shear stress (WSS) and oscillatory shear index (OSI) are presented. When averaged over all subjects, WSS increased from 4.8 +/- 0.6 to 31.6 +/- 5.7 dyn/cm2 and OSI decreased from 0.22 +/- 0.03 to 0.03 +/- 0.02 in the infrarenal aorta between rest and exercise. WSS significantly increased, whereas OSI decreased between rest and exercise at the supraceliac, infrarenal, and suprabifurcation levels, and significant differences in WSS were found between anterior and posterior sections. These results support the hypothesis that exercise provides localized benefits to the cardiovascular system through acute mechanical stimuli that trigger longer-term biological processes leading to protection against the development or progression of atherosclerosis.     

Does Lower Limb Exercise Worsen Renal Artery Hemodynamics in Patients with Abdominal Aortic Aneurysm?

Renal artery stenosis (RAS) and renal complications emerge in some patients after endovascular aneurysm repair (EVAR) to treat abdominal aorta aneurysm (AAA). The mechanisms for the causes of these problems are not clear. We hypothesized that for EVAR patients, lower limb exercise could negatively influence the physiology of the renal artery and the renal function, by decreasing the blood flow velocity and changing the hemodynamics in the renal arteries. To evaluate this hypothesis, pre- and post-operative models of the abdominal aorta were reconstructed based on CT images. The hemodynamic environment was numerically simulated under rest and lower limb exercise conditions. The results revealed that in the renal arteries, lower limb exercise decreased the wall shear stress (WSS), increased the oscillatory shear index (OSI) and increased the relative residence time (RRT). EVAR further enhanced these effects. Because these parameters are related to artery stenosis and atherosclerosis, this preliminary study concluded that lower limb exercise may increase the potential risk of inducing renal artery stenosis and renal complications for AAA patients. This finding could help elucidate the mechanism of renal artery stenosis and renal complications after EVAR and warn us to reconsider the management and nursing care of AAA patients.     

Numerical simulation of aortic bifurcation flows: The effect of flow divider curvature

Two dimensional steady flow calculations in computational regions obtained from radiographs of human aortic bifurcations correlate well with unsteady measurements of wall shear in flow-through casts of the same vessels. The results suggest that wall slope may be an important factor affecting the variability of shear along the medial walls of this arterial segment. If extremes of shear stress promote atherogenesis, then variations in the curvature of the proximal iliac arteries may affect the susceptibility of these vessels to vascular disease on their medial aspect.     

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.     

Influence of the renal artery ostium flow diverter on hemodynamics and atherogenesis

The structure and function of the renal artery ostium flow diverter on the caudal side of the renal branch point were previously reported; in this study, we further evaluate the diverter?s possible functions. The protrusion of this structure into the abdominal aorta suggests that the diverter may preferentially direct blood flow to the renal arteries, and that it may also influence flow patterns and recirculation known to be involved in atherogenesis. Three-dimensional computational fluid dynamics (CFD) simulations of steady and pulsatile blood flow are performed to investigate the influence of diverter size and position, and vascular geometry, on the flow patterns and fluid mechanical forces in the neighborhood of the diverter. CFD results show that the flow diverter does affect the blood distribution; depending on the diverter?s position, the flow to the renal arteries may be increased or reduced. Calculated results also demonstrate the diverter?s effect on the wall shear stress (WSS) distribution, and suggest that the diverter contributes to an atherogenic environment in the abdominal aorta, while being atheroprotective in the renal arteries themselves. These results support previous clinical findings, and suggest directions for further clinical study. The results of this work have direct implications in understanding the physiological significance of the diverter, and its potential role in the pathophysiological development of atherosclerosis.     

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.     

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.     

Pulsatile flow visualization in the abdominal aorta under differing physiologic conditions: implications for increased susceptibility to atherosclerosis.

The infrarenal abdominal aorta is a common site for clinically significant atherosclerosis. As has been shown in other susceptible locations, vessel geometry, flow division rates, and pulsatility may result in hemodynamic conditions which influence the preferential localization of disease in the abdominal aorta segment. Pulsatile flow visualization was performed in a glass model of the aorta constructed from measurements of angiograms and cadaver aortas. Flow rates and pulsatile waveforms were varied to reflect typical physiological conditions. Under normal resting conditions, the flow patterns in the infrarenal aorta were more complex than those in the suprarenal location. Time varying vortex patterns appeared at the level of the renal arteries and propagated through the infrarenal aorta into the common iliac arteries. A region of oscillating velocity direction extended from the renal arteries to the aortic bifurcation along the posterior wall. Dye became trapped along the posterior wall, requiring several cardiac cycles for clearance. In contrast, there was rapid clearance of the dye in the anterior aorta. Under postprandial conditions, the flow patterns in the aorta were basically unchanged. Simulated exercise conditions created laminar hemodynamic features very different from the resting conditions, including a decrease in dye residence time. This study reveals significant time-dependent variations in the hemodynamics of the abdominal aorta under differing physiologic conditions. Hemodynamic factors such as low wall shear stress, oscillating shear direction, and high particle residence time may be related to the clinically seen preferential plaque localization in the infrarenal aorta.     

Computational fluid dynamics study of common stent models inside idealised curved coronary arteries

The haemodynamic behaviour of blood inside a coronary artery after stenting is greatly affected by individual stent features as well as complex geometrical properties of the artery including tortuosity and curvature. Regions at higher risk of restenosis, as measured by low wall shear stress (WSS < 0.5 Pa), have not yet been studied in detail in curved stented arteries. In this study, three-dimensional computational modelling and computational fluid dynamics methodologies were used to analyse the haemodynamic characteristics in curved stented arteries using several common stent models. Results in this study showed that stent strut thickness was one major factor influencing the distribution of WSS in curved arteries. Regions of low WSS were found behind struts, particularly those oriented at a large angle relative to the streamwise flow direction. These findings were similar to those obtained in studies of straight arteries. An uneven distribution of WSS at the inner and outer bends of curved arteries was observed where the WSS was lower at the inner bend. In this study, it was also shown that stents with a helical configuration generated an extra swirling component of the flow based on the helical direction; however, this extra swirl in the flow field did not cause significant changes on the distribution of WSS under the current setup.     

Computational study of the effect of geometric and flow parameters on the steady flow field at the rabbit aorto-celiac bifurcation

Arterial hemodynamic forces may play a role in the localization of early atherosclerotic lesions. We have been developing numerical techniques based on overset or "Chimera" type formulations to solve the Navier-Stokes equations in complex geometries simulating arterial bifurcations. This paper presents three-dimensional steady flow computations in a model of the rabbit aorto-celiac bifurcation. The computational methods were validated by comparing the numerical results to previously-obtained flow visualization data. Once validated, the numerical algorithms were used to investigate the sensitivity of the computed flow field and resulting wall shear stress distribution to various geometric and hemodynamic parameters. The results demonstrated that a decrease in the extent of aortic taper downstream of the celiac artery induced looping fluid motion along the lateral walls of the aorta and shifted the peak wall shear stress from downstream of the celiac artery to upstream. Increasing the flow Reynolds number led to a sharp increase in spatial gradients of wall shear stress. The flow field was highly sensitive to the flow division ratio, i.e., the fraction of total flow rate that enters the celiac artery, with larger values of this ratio leading to the occurrence of flow separation along the dorsal wall of the aorta. Finally, skewness of the inlet velocity profile had a profound impact on the wall shear stress distribution near the celiac artery. While not physiological due to the assumption of steady flow, these results provide valuable insight into the fluid physics at geometries simulating arterial bifurcations.     

Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model

Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.     

Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model

Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.     

Toward translating near-infrared spectroscopy oxygen saturation data for the non-invasive prediction of spatial and temporal hemodynamics during exercise

Image-based computational fluid dynamics (CFD) studies conducted at rest have shown that atherosclerotic plaque in the thoracic aorta (TA) correlates with adverse wall shear stress (WSS), but there is a paucity of such data under elevated flow conditions. We developed a pedaling exercise protocol to obtain phase contrast magnetic resonance imaging (PC-MRI) blood flow measurements in the TA and brachiocephalic arteries during three-tiered supine pedaling at 130, 150, and 170 % of resting heart rate (HR), and relate these measurements to non-invasive tissue oxygen saturation \((\hbox {StO}_{2})\) acquired by near-infrared spectroscopy (NIRS) while conducting the same protocol. Local quantification of WSS indices by CFD revealed low time-averaged WSS on the outer curvature of the ascending aorta and the inner curvature of the descending aorta (dAo) that progressively increased with exercise, but that remained low on the anterior surface of brachiocephalic arteries. High oscillatory WSS observed on the inner curvature of the aorta persisted during exercise as well. Results suggest locally continuous exposure to potentially deleterious indices of WSS despite benefits of exercise. Linear relationships between flow distributions and tissue oxygen extraction calculated from \(\hbox {StO}_{2}\) were found between the left common carotid versus cerebral tissue \((r^{2}=0.96)\) and the dAo versus leg tissue \((r^{2}=0.87)\). A resulting six-step procedure is presented to use NIRS data as a surrogate for exercise PC-MRI when setting boundary conditions for future CFD studies of the TA under simulated exercise conditions. Relationships and ensemble-averaged PC-MRI inflow waveforms are provided in an online repository for this purpose.     

Hemodynamics in coronary arteries with overlapping stents

Coronary artery stenosis is commonly treated by stent placement via percutaneous intervention, at times requiring multiple stents that may overlap. Stent overlap is associated with increased risk of adverse clinical outcome. While changes in local blood flow are suspected to play a role therein, hemodynamics in arteries with overlapping stents remain poorly understood. In this study we analyzed six cases of partially overlapping stents, placed ex vivo in porcine left coronary arteries and compared them to five cases with two non-overlapping stents. The stented vessel geometries were obtained by micro-computed tomography of corrosion casts. Flow and shear stress distribution were calculated using computational fluid dynamics. We observed a significant increase in the relative area exposed to low wall shear stress (WSS<0.5 Pa) in the overlapping stent segments compared both to areas without overlap in the same samples, as well as to non-overlapping stents. We further observed that the configuration of the overlapping stent struts relative to each other influenced the size of the low WSS area: positioning of the struts in the same axial location led to larger areas of low WSS compared to alternating struts. Our results indicate that the overlap geometry is by itself sufficient to cause unfavorable flow conditions that may worsen clinical outcome. While stent overlap cannot always be avoided, improved deployment strategies or stent designs could reduce the low WSS burden.     

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.