Wall Shear Stress Oscillations Research Articles

Hemodynamics in arterial bypass graft anastomoses with varying cuff sizes and proximal flow paths: a fluid–structure interaction study

This article investigates the effect of the cuff size of arterial bypass grafts and the flow conditions on the hemodynamics in the anastomosis (connection) to the artery, using numerical simulations. We consider a fluid-structure interaction problem which is solved based on a partitioned scheme. Additionally, we employ computational fluid dynamics to investigate the effect of a rigid wall assumption. The work focuses on clinically relevant hemodynamic quantities associated with the development of intimal hyperplasia. We also include a model for the prediction of hemolysis into the simulation. The results show that even minor changes of the cuff size can result into significant differences in the corresponding quantities of interest. The importance of the inflow path is shown to be lower than that of the cuff size. The usually employed rigid wall assumption is found to be adequate to address wall shear stress oscillations but falls short on predicting maximum and minimum wall shear stress-related quantities of interest.

Risk evaluation of type B aortic dissection based on WSS-based indicators distribution in different types of aortic arch

Background and ObjectiveThe underlying mechanism of aortic dissection (AD) remains unclear and the onset of AD is still unpredictable. Although clinical study with statistical analysis has reported that type III aortic arch may have strong correlation with type B AD (TBD), the effects of different arch types on the wall shear stress (WSS) have not been clarified. MethodsAs a complementary work, this study numerically investigated the distribution of five WSS-based indicators in thirty aortic arches without AD, which were classified into three groups based on the arch types. ResultsThe distribution of most WSS indicators, such as time averaged WSS (TAWSS), oscillatory shear index (OSI) and relative residence time (RRT) had no significant difference among different types of aortic arches (P>0.05). However, a multidirectional WSS index, namely CFI, was found its maximum value was positively correlated with type III aortic arch in proximal descending aorta (p<0.001, r = 0.65). ConclusionsIt can be concluded that the enhancement or oscillation of WSS may not be the main reason of TBD is prevalence in type III arches, while the multidirectional WSS distribution may be an important factor. It can be further referred that the CFI may have a potential to predict the onset of TBD.

Probing the possibility of lesion formation/progression in vicinity of a primary atherosclerotic plaque: A fluid-solid interaction study and angiographic evidences.

It is shown that certain locations in the arterial tree, such as coronary and cerebral arteries, are more prevalent to plaque formation. Endothelial activation and consequent plaque development are attributed to local hemodynamic parameters such as wall shear stress (WSS), oscillatory shear index (OSI), relative residence time (RRT), and stress phase angle. After a certain level of plaque progression, these hemodynamic parameters are disturbed before and after the plaque. In the current study, it is hypothesized that the vicinity of a primary lesion is susceptible for further degeneration and second plaque formation. A fluid-solid interaction (FSI) model of the coronary artery with different levels of asymmetric constriction, is simulated and the trend of hemodynamic parameters were studied in both of the plaque side (PS) and the opposite wall (facing the plaque [PF]). Also, a novel factor is introduced that can identify the high-risk regions associated with WSS oscillations to negative values. Our results indicate that when more than half of the artery is constricted, the downstream of the plaque is highly exposed to endothelial pathogenesis the PS, such that negative WSS, and as well, critical values of OSI and RRT, that is, -1.2 Pa, 0.42 and 6.5s, respectively arise in this region. PS endothelial cells in this region exposed to the highest risk of atherosclerosis based on the proposed index (3 out of 3). As well, three cases of angiographic images are provided that confirms existence of secondary lesion close to the primary one as predicted by our computational simulations.

Effect of Viscoelasticity on Arterial-Like Pulsatile Flow Dynamics and Energy.

Time-dependent arterial wall property is an important but difficult topic in vascular mechanics. Hysteresis, which appears during the measurement of arterial pressure-diameter relationship through a cardiac cycle, has been used to indicate time-dependent mechanics of arteries. However, the cause-effect relationship between viscoelastic (VE) properties of the arterial wall and hemodynamics, particularly the viscous contribution to hemodynamics, remains challenging. Herein, we show direct comparisons between elastic (E) (loss/storage < 0.1) and highly viscoelastic (loss/storage > 0.45) conduit structures with arterial-like compliance, in terms of their capability of altering pulsatile flow, wall shear, and energy level. Conduits were made from varying ratio of vinyl- and methyl-terminated poly(dimethylsiloxane) and were fit in a mimetic circulatory system measuring volumetric flow, pressure, and strain. Results indicated that when compared to elastic conduits, viscoelastic conduits attenuated lumen distension waveforms, producing an average of 11% greater cross-sectional area throughout a mimetic cardiac cycle. In response to such changes in lumen diameter strain, pressure and volumetric flow waves in viscoelastic conduits decreased by 3.9% and 6%, respectively, in the peak-to-peak amplitude. Importantly, the pulsatile waveforms for both diameter strain and volumetric flow demonstrated greater temporal alignment in viscoelastic conduits due to pulsation attenuation, resulting in 25% decrease in the oscillation of wall shear stress (WSS). We hope these findings may be used to further examine time-dependent arterial properties in disease prognosis and progression, as well as their use in vascular graft design.

The carotid sinus acts as a mechanotransducer of shear oscillation rather than a baroreceptor

The carotid sinus is a dilated area at the base of the internal carotid artery of humans and is located immediately superior to the bifurcation of the internal and external carotid arteries. It is widely accepted, in the fields of medicine and physiology, to function as a baroreceptor in its central control role. This paper presents a hypothesis challenging this paradigm - that the carotid sinus functions by detecting oscillations at the vessel wall which result from shear stress due to vortical flow. This is contrary to conventional thinking which presumes that the carotid sinus responds to blood pressure or wall pressure. Our hypothesis is based on anatomy, physiology and physical properties of fluid which make the sinus the area of highest vorticity. Utilizing magnetic resonance angiograms of undiseased carotid vessels, we computed the oscillatory shear index (OSI) via a computational fluid dynamics simulation of flow. This region of highest OSI coincides with the area where the nerve to the carotid sinus lies within the vessel wall. Accordingly, the hypothesis is that the carotid sinus acts as a mechanotransducer of wall shear stress oscillation and not as a baroreceptor.

Validation of numerical models for flow simulation and wave propagation along human aorta

Numerical computations on 2d model of blood flow along human aorta based on incompressible axisymmetric Navier-Stokes equations for blood and momentum equations for incompressible viscoelastic arterial wall are compared to the blood flow oscillation curves measured in vivo by Doppler ultrasound in the larger systemic arteries of healthy volunteers. The analysis of the wave propagation and reflection along the geometrical 91-tube model of aorta as a tube with side branches is based on Lighthill’s theory of waves in arteries. It is shown due to individual geometry positive wave reflections at some aortic branches and aortic bifurcation may lead to increase of the pressure amplitudes, high pressure and wall shear stress oscillations that may lead to wall damage and development of aortic aneurism and stenoses of branched arteries. The numerical results obtained on the linearized 2d and nonlinear 1d models are compared to the in vivo pressure and flow measurements along the aorta and in its branches. A good qualitative correspondence is obtained. The model can be used for determination of the individual parameters for patient-specific cardiovascular models.

Influence of aging-induced flow waveform variation on hemodynamics in aneurysms present at the internal carotid artery: A computational model-based study

The variation of blood flow waveform in the internal carotid artery (ICA) with age is a well-documented hemodynamic phenomenon, but little is known about how such variation affects the characteristics of blood flow in aneurysms present in the region. In the study, hemodynamic simulations were conducted for 26 ICA aneurysms, with flow waveforms measured in the ICAs of young and older adults being used respectively to set the inflow boundary conditions. Obtained results showed that replacing the young-adult flow waveform with the older-adult one led to little changes (<10%) in simulated time-averaged wall shear stress (WSS), transient maximum WSS, relative residence time and trans-aneurysm pressure loss coefficient, but resulted in a marked increase (32.36 ± 17.24%) in oscillatory shear index (OSI). Frequency-domain wave analysis revealed that the progressive enhancement of low-frequency harmonics dominated the observed flow waveform variation with age and was a major factor contributing to the increase in OSI. Cross-sectional comparisons among the aneurysms further revealed that the degree of increase in OSI correlated positively with some specific morphological features of aneurysm, such as aspect ratio and size ratio. In summary, the study demonstrates that the variation in flow waveform with age augments the oscillation of WSS in ICA aneurysms, which underlies the importance of setting patient-specific boundary conditions in hemodynamic studies on cerebral aneurysms, especially those involving long-term patient follow-up or cross-sectional comparison among patients of different ages.

Partial renal coverage in endovascular aneurysm repair causes unfavorable renal flow patterns in an infrarenal aneurysm model

ObjectiveTo achieve an optimal sealing zone during endovascular aneurysm repair, the intended positioning of the proximal end of the endograft fabric should be as close as possible to the most caudal edge of the renal arteries. Some endografts exhibit a small offset between the radiopaque markers and the proximal fabric edge. Unintended partial renal artery coverage may thus occur. This study investigated the consequences of partial coverage on renal flow patterns and wall shear stress (WSS). MethodsIn vitro models of an abdominal aortic aneurysm were used to visualize pulsatile flow using two-dimensional particle image velocimetry under physiologic resting conditions. One model served as control and two models were stented with an Endurant endograft (Medtronic Inc, Minneapolis, Minn), one without and one with partial renal artery coverage with 1.3 mm of stent fabric extending beyond the marker (16% area coverage). The magnitude and oscillation of WSS, relative residence time, and backflow in the renal artery were analyzed. ResultsIn both stented models, a region along the caudal renal artery wall presented with low and oscillating WSS, not present in the control model. A region with very low WSS (<0.1 Pa) was present in the model with partial coverage over a length of 7 mm compared with a length of 2 mm in the model without renal coverage. Average renal backflow area percentage in the renal artery incrementally increased from control (0.9%) to the stented model without (6.4%) and with renal coverage (18.8%). ConclusionsIn this flow model, partial renal coverage after endovascular aneurysm repair causes low and marked oscillations in WSS, potentially promoting atherosclerosis and subsequent renal artery stenosis. Awareness of the device-dependent offset between the fabric edge and the radiopaque markers is therefore important in endovascular practice.

Hemodynamic Characteristics of Ruptured and Unruptured Multiple Aneurysms at Mirror and Ipsilateral Locations.

Different hemodynamic patterns have been associated with aneurysm rupture. The objective was to test whether hemodynamic characteristics of the ruptured aneurysm in patients with multiple aneurysms were different from those in unruptured aneurysms in the same patient. Twenty-four mirror and 58 ipsilateral multiple aneurysms with 1 ruptured and the others unruptured were studied. Computational fluid dynamics models were created from 3D angiographies. Case-control studies of mirror and ipsilateral aneurysms were performed with paired Wilcoxon tests. In mirror pairs, the ruptured aneurysm had more oscillatory wall shear stress (P = .007) than the unruptured one and tended to be more elongated (higher aspect ratio), though this trend achieved only marginal significance (P = .03, 1-sided test). In ipsilateral aneurysms, ruptured aneurysms had larger maximum wall shear (P = .05), more concentrated (P < .001) and oscillatory wall shear stress (P < .001), stronger (P < .001) and more concentrated inflow jets (P < .001), larger maximum velocity (P < .001), and more complex flow patterns (P < .001) compared with unruptured aneurysms. Additionally, ruptured aneurysms were larger (P < .001) and more elongated (P < .001) and had wider necks (P < .001) and lower minimum wall shear stress (P < .001) than unruptured aneurysms. High wall shear stress oscillations and larger aspect ratios are associated with rupture in mirror aneurysms. Adverse flow conditions characterized by high and concentrated inflow jets; high, concentrated, and oscillatory wall shear stress; and strong, complex and unstable flow patterns are associated with rupture in ipsilateral multiple aneurysms. In multiple ipsilateral aneurysms, these unfavorable flow conditions are more likely to develop in larger, more elongated, more wide-necked, and more distal aneurysms.

Insights into the co-localization of magnitude-based versus direction-based indicators of disturbed shear at the carotid bifurcation

The observed co-localization of disturbed flow and lesion prevalence at predisposed districts such as the carotid bifurcation has led to the identification of the wall shear stress (WSS) as biomechanical localizing factor of vascular dysfunction. In particular, a proatherogenic role is attributed to low and oscillatory WSS. However, the endothelial cells (ECs) are exposed to a complex hemodynamic milieu that can be only partially described by low/oscillatory WSS. Recently, in the attempt to close this gap, descriptors of the complex multidirectional nature of WSS have been proposed, i.e., the axial component of WSS (aligned with the vessel׳s centerline, to quantify flow reversal), and the transverse WSS (transWSS, quantifying the WSS component orthogonal to the cycle averaged WSS direction).Here we explore the relationship between recently-proposed indicators quantifying WSS multidirectionality and "established" WSS-based hemodynamic descriptors of low/oscillatory WSS, in a representative sample (N=46) of subject-specific computational hemodynamics models of ostensibly normal carotid bifurcations. To do it, we quantitatively assess the co-localization of those descriptors at the luminal surface, aiming at providing connections among the peculiar hemodynamic features captured by the different descriptors.According to our findings: (1) regions of flow reversal are moderately co-localized with low WSS; (2) high WSS oscillations (quantified by the oscillatory shear index, OSI) at the carotid bulb are prevalently aligned with the main flow, where flow reversal is predominant; (3) regions where transWSS is high do not co-localize with the other descriptors. We suggest that the investigated WSS-based descriptors might represent different hemodynamic disturbances with different impact on ECs homeostasis, potentially being part of WSS phenotypes more effective in localizing the map of vascular atherosclerotic lesions.

Fluid–structure interaction in aortic cross-clamping: Implications for vessel injury

Vascular cross-clamping is applied in many cardiovascular surgeries such as coronary bypass, aorta repair and valve procedures. Experimental studies have found that clamping of various degrees caused damage to arteries. This study examines the effects of popular clamps on vessel wall. Models of the aorta and clamp were created in Computer Assisted Design and Finite Element Analysis packages. The vessel wall was considered as a non-linear anisotropic material while the fluid was simulated as Newtonian with pulsatile flow. The clamp was applied through displacement time function. Fully coupled two-way solid–fluid interaction models were developed. It was found that the clamp design significantly affected the stresses in vessel wall. The clamp with a protrusion feature increased the overall Von Mises stress by about 60% and the compressive stress by more than 200%. Interestingly, when the protrusion clamp was applied, the Von Mises stress at the lumen (endothelium) side of artery wall was about twice that of the outer wall. This ratio was much higher than that of the plate-like clamp which was about 1.3. The flow reversal process was demonstrated during clamping. Vibrations, flow and wall shear stress oscillations were detected immediately before total vessel occlusion. The commonly used protrusion clamp increased stresses in vessel wall, especially the compressive stress. This design also significantly increased the stresses on endothelium, detrimental to vessel health. The present findings are relevant to surgical clamp design as well as the transient mechanical loading on the endothelium and potential injury. The deformation and stress analysis may provide valuable insights into the mode of tissue injury during cross-clamping.

A Simulation of Vessel–Clamp Interaction: Transient Closure Dynamics

Cross-clamping of aorta is routinely performed in cardiac surgery. The objective of this study was to simulate cross-clamping of the aorta to elucidate the perturbation of stresses in the wall (solid mechanics) and lumen of the vessel (fluid mechanics). Models of the aorta and clamp were created in Computer Assisted Design and Finite Element Analysis packages. The vessel wall was considered as a non-linear anisotropic material while the fluid was simulated as Newtonian with pulsatile flow. The clamp was applied to produce total occlusion in approximately 1 s. A cylindrical and rectangular geometry for the clamp were considered. High jet speed and flow reversal were demonstrated during clamping. It was found that the clamp design and vessel wall anisotropy affected both the fluid wall shear stress (WSS) and solid stresses in vessel wall. The maximum wall stresses increased by about 170 and 220% during closure in the cases of plate and cylindrical clamps, respectively. The plate clamp design was superior for reduction of both solid stresses as well as fluid shear stresses. The cylindrical clamp causes much larger stresses than the plate clamp in each of the stress components; e.g., radial compression of -180 vs. -50 kPa. Vibrations, flow and WSS oscillations were detected immediately before total vessel occlusion. The present findings provide valuable insights into the mode of tissue injury during clamping and may also be useful for improving surgical clamp designs.

ESTIMATION OF WALL SHEAR STRESS DYNAMIC FLUCTUATIONS IN INTRACRANIAL ATHEROSCLEROTIC LESIONS USING COMPUTATIONAL FLUID DYNAMICS

Intracranial stenosis (IS) is associated with significant morbidity and mortality from hypoperfusion and thromboembolism. We used computational fluid dynamic methods to analyze luminal patterns of wall shear stress (WSS), a known critical modulator of endothelial function, within patient-based IS lesions undergoing percutaneous angioplasty and stenting. High-resolution three-dimensional rotational angiographic data sets were reconstructed to yield a fine-resolution computational mesh allowing application of pulsatile computational fluid dynamic analysis with a non-Newtonian realistic model of blood. WSS and its gradient were analyzed spatiotemporally in five IS lesions before and after percutaneous angioplasty and stenting. WSS within the stenosis reached average shear magnitudes of 1870 +/- 783 dyn/cm with rapidly reversing direction to oscillating low values in the recirculation zone. WSS vectors revealed complex dynamic directional and amplitude oscillations not seen in healthy segments with time-dependent convergence and divergence strips sweeping back and forth across the lesion during the cardiac cycle. These areas also underwent extreme temporal WSS oscillation of 2052 +/- 909 dyn/cm over a short time interval. The endothelial mechanotransductive response to such extreme WSS magnitudes and gradients, which were normalized by percutaneous angioplasty and stenting in the current study, remains undefined. Computational fluid dynamic analysis of IS has uncovered a complex and hostile microhemodynamic environment characterized by wide and rapid shear variations in time and space. Characterization of the mechanical forces acting on the wall can help in determining the molecular transduction response of the luminal endothelium to these extreme stresses and may lead to better understanding of the hemodynamic contribution to stenosis pathophysiology.

Intra-aneurysmal hemodynamics in a large middle cerebral artery aneurysm with wall atherosclerosis

Background The remodeling of arterial extra-cellular matrix induced by hemodynamic stimuli is involved in the process of atherosclerosis in the carotid and cerebral arteries. Scarce information is available on the relationship between atherosclerotic changes in brain aneurysms itself and its intra-aneurysmal hemodynamics. Methods Surgical exploration of a large MCA aneurysm depicted extensive atherosclerotic changes in the aneurysm wall. Computational tomographic angiography of this aneurysm was used to create an in vitro aneurysm model. This model was used to perform intra-aneurysmal flow measurement using particle imaging velocimetry and LDV. Intra-aneurysmal hemodynamic pattern with wall shear stress distribution was compared between areas with and without atherosclerotic changes. Results No high oscillation of wall shear stress was observed on the atherosclerotic plaque area. However, the magnitude of wall shear stress tended to be higher in the area without atherosclerotic changes than the area with those changes ( P < .001). There was no atherosclerotic change at the aneurysm inflow zone, where relatively fast flow velocity and higher magnitude of wall shear stress was noted. Conclusions This single case of atherosclerosis in an aneurysm shows some similarity in hemodynamic values observed in cases of carotid atherosclerotic plaques.

Spatial and phasic oscillation of non-Newtonian wall shear stress in human left coronary artery bifurcation: an insight to atherogenesis

To investigate the wall shear stress oscillation in a normal human left coronary artery bifurcation computational model by applying non-Newtonian blood properties and phasic flow. The three-dimensional geometry of the investigated model included the left main coronary artery along with its two main branches, namely the left anterior descending and the left circumflex artery. For the computational analyses a pulsatile non-Newtonian flow was applied. To evaluate the cyclic variations in wall shear stress, six characteristic time-points of the cardiac cycle were selected. The non-Newtonian wall shear stress variation was compared with the Newtonian one. The wall shear stress varied remarkably in time and space. The flow divider region encountered higher wall shear stress values than the lateral walls throughout the entire cardiac cycle. The wall shear stress exhibited remarkably lower and oscillatory values in systole as compared with that in diastole in the entire bifurcation region, especially in the lateral walls. Although the Newtonian wall shear stress experienced consistently lower values throughout the entire cardiac cycle than the non-Newtonian wall shear stress, the general pattern of lower wall shear stress values at the lateral walls, particularly during systole, was evident regardless of the blood properties. The lateral walls of the bifurcation, where low and oscillating wall shear stress is observed, are more susceptible to atherosclerosis. The systolic period, rather than the diastolic one, favors the development and progression of atherosclerosis. The blood viscosity properties do not seem to qualitatively affect the spatial and temporal distribution of the wall shear stress.

The Influence of Flow, Vessel Diameter, and Non-Newtonian Blood Viscosity on the Wall Shear Stress in a Carotid Bifurcation Model for Unsteady Flow

The atherosclerotic process in arteries is correlated with the local wall shear stress (WSS). Plaque development particularly occurs in regions with recirculation (ie, where the WSS oscillates). We investigated the effects of non-Newtonian blood viscosity, variations in flow rate, and vessel diameter on wall phenomena in a carotid bifurcation model. The flow through a model of a carotid artery bifurcation was simulated by means of the finite element method. The whole-blood viscosity is a function of shear rate, and was modeled by the Carreau-Yasuda (CY) model. Flow rate and vessel morphology were assessed with magnetic resonance imaging. Flow rate, blood viscosity, and hematocrit levels (Hct) were measured in 49 healthy volunteers. We propose an adaptation of the CY model so that differences in Hct can be incorporated; furthermore, plasma viscosity was varied in the CY model. The data from our model indicate that flow increases have a larger effect on the WSS than predicted with a simple paraboloid model. Hct had more influence on the WSS when the plasma viscosity was low. Low plasma viscosity was associated with a low WSS, which implies a contradiction, because both high WSS and low plasma viscosity are thought to be indicators for a healthy system. Maximum WSS oscillations were found at the edges of the recirculation region. Flow and diameter changes have significant influence on wall shear stress values; the same is true for the viscosity, but to a lesser extent.

Abdominal aortic hemodynamic conditions in healthy subjects aged 50–70 at rest and during lower limb exercise: in vivo quantification using MRI

The prevalence of atherosclerosis in the abdominal aorta increases with age and is hypothesized to be related to adverse hemodynamic conditions including flow recirculation and low wall shear stress. Exercise has been shown to modulate these adverse conditions observed in the infrarenal aorta of healthy young subjects at rest. A custom magnetic resonance (MR)-compatible stationary cycle, an open MRI, and custom image processing software were used to quantify hemodynamic conditions in the abdominal aorta at rest and during cycling exercise in healthy subjects aged 50–70 years. The subjects increased their heart rate from 63±8 bpm at rest to 95±12 bpm during cycling exercise. Supraceliac blood flow increased from 2.3±0.4 to 6.0±1.4 l/min ( P<0.001) and infrarenal flow increased from 0.9±0.3 to 4.9±1.7 l/min ( P<0.001) from rest to exercise. Wall shear stress increased from 2.0±0.7 to 7.3±2.4 dynes/cm 2 at the supraceliac level ( P<0.001) and 1.4±0.8 to 16.5±5.1 dynes/cm 2 at the infrarenal level ( P<0.001) from rest to exercise. Flow and shear oscillations present at rest were eliminated during exercise. At rest, these older subjects experienced lower mean wall shear stress at the supraceliac level of the aorta and greater oscillations in wall shear stress as compared to a group of younger subjects (23.6±2.2 years). Compared to the younger subjects, the older subjects also experienced greater increases in mean wall shear stress and greater decreases in wall shear stress oscillations from rest to exercise.

Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis

Numerical simulations of pulsatile blood flow in straight tube stenosis models were performed to investigate the poststenotic flow phenomena. In this study, three axisymmetrical and three asymmetrical stenosis models with area reduction of 25%, 50% and 75% were constructed. A measured human common carotid artery blood flow waveform was used as the upstream flow condition which has a mean Reynold's number of 300. All calculations were performed with high spatial and temporal resolutions. Flow features such as velocity profiles, flow separation zone (FSZ), and wall shear stress (WSS) distributions in the poststenotic region for all models are presented. The results have demonstrated that the formation and development of FSZs in the poststenotic region are very complex, especially in the flow deceleration phase. In axisymmetric stenoses the poststenotic flow is more sensitive to changes in the degree of stenosis than in asymmetric models. For severe stenoses, the stenosis influence length is shorter in asymmetrical models than in axisymmetrical cases. WSS oscillations (between positive and negative values) have been observed at various downstream locations in some models. The amplitude of the oscillation depends strongly on the axial location and the degree of stenosis.

Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery.

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.

Large curvature effect on pulsatile entrance flow in a curved tube: model experiment simulating blood flow in an aortic arch.

We measured the velocity profiles of pulsatile entrance flow in a strongly curved tube using a laser-Doppler anemometer in order to simulate blood flow in the aortic arch under various conditions, i.e., a ratio of tube to curvature radius of 1/3, Womersley parameters of 12 and 18, and peak Dean number up to 1200. Axial isovelocity contours of the cross-section showed the potential vortex to be near the entrance, and with the maximum velocity there being skewed towards the inner wall; thereafter shifting towards the outer wall. During the deceleration phase, reverse axial flow occurred near the inner wall, and a region of this flow extended downstream. The large curvature contributes to the enhancement of the secondary flow and flow reversal, which elevates the wall-shear stress oscillations. The location of elevated wall-shear oscillations corresponds to the vessel wall region where atherosclerotic formation frequently occurs; thereby indicating that both the large curvature and pulsatility play key roles in formation of localized atherosclerotic lesions.