Inter-individual variations in wall shear stress and mechanical stress distributions at the carotid artery bifurcation of healthy humans

Fluid shear stress and mechanical wall stress may play a role in the formation of early atherosclerotic lesions, but these quantities are difficult to measure in vivo. Our objective was to quantify these parameters in normal subjects in a clinical setting, and to define regions of low wall shear stress and high mechanical stress. The right carotid bifurcations of five healthy male volunteers were investigated using a novel non-invasive technique which integrates magnetic resonance angiography, ultrasonography, tonometry and state-of-the-art computational fluid dynamics and solid mechanics models. Significant inter-subject variations in patterns as well as magnitude of wall shear stress and mechanical stress were found. In spite of individual variabilities, this study revealed that some regions of the artery wall are exposed simultaneously to low wall shear stress and high mechanical stress and that these regions correspond to areas where atherosclerotic plaque develops. The coexistence of regions of low wall shear stress and high tensile stress may be an important determinant of the formation of atheroma in human arteries.     

Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.     

Influence of stenosis on hemodynamic parameters in the realistic left coronary artery under hyperemic conditions

The current study investigates the hyperemic flow effects on heamodynamics parameters such as velocity, wall shear stress in 3D coronary artery models with and without stenosis. The hyperemic flow is used to evaluate the functional significance of stenosis in the current era. Patients CT scan data of having healthy and coronary artery disease was chosen for the reconstruction of 3D coronary artery models. The diseased 3D models of coronary artery shows a narrowing of >50% lumen area. Computational fluid dynamics was performed to simulate the hyperemic flow condition. The results showed that the recirculation zone was observed immediate to the stenosis and highest wall shear stress was observed across the stenosis. The decrease in pressure was found downstream to the stenosis as compared to the coronary artery without stenosis. Our analysis provides an insight into the distribution of wall shear stress and pressure drop, thus improving our understanding of hyperemic flow effect under both conditions.     

On the relative importance of rheology for image-based CFD models of the carotid bifurcation

BACKGROUND: Patient-specific computational fluid dynamics (CFD) models derived from medical images often require simplifying assumptions to render the simulations conceptually or computationally tractable. In this study, we investigated the sensitivity of image-based CFD models of the carotid bifurcation to assumptions regarding the blood rheology. METHOD OF APPROACH: CFD simulations of three different patient-specific models were carried out assuming: a reference high-shear Newtonian viscosity, two different non-Newtonian (shear-thinning) rheology models, and Newtonian viscosities based on characteristic shear rates or, equivalently, assumed hematocrits. Sensitivity of wall shear stress (WSS) and oscillatory shear index (OSI) were contextualized with respect to the reproducibility of the reconstructed geometry, and to assumptions regarding the inlet boundary conditions. RESULTS: Sensitivity of WSS to the various rheological assumptions was roughly 1.0 dyn/cm(2) or 8%, nearly seven times less than that due to geometric uncertainty (6.7 dyn/cm(2) or 47%), and on the order of that due to inlet boundary condition assumptions. Similar trends were observed regarding OSI sensitivity. Rescaling the Newtonian viscosity based on time-averaged inlet shear rate served to approximate reasonably, if overestimate slightly, non-Newtonian behavior. CONCLUSIONS: For image-based CFD simulations of the normal carotid bifurcation, the assumption of constant viscosity at a nominal hematocrit is reasonable in light of currently available levels of geometric precision, thus serving to obviate the need to acquire patient-specific rheological data.     

Approaches for treatment of aortic arch aneurysm,a numerical study

Aortic arch aneurysm is a complex pathology which requires coverage of one or more aortic arch vessels. In this study we explore the hemodynamic behavior of the aortic arch in aneurysmatic and treated cases with three currently available treatment approaches: Surgery Graft, hybrid Stent-Graft and chimney Stent Graft. The analysis included four models of the time-dependent fluid domains of aneurysmatic arch and of the surgery, hybrid and chimney endovascular techniques. Dimensions of the models are based on typical anatomy, and boundary conditions are based on typical physiological flow.The simulations used computational fluid dynamics (CFD) methods to delineate the time-dependent flow dynamics in the four geometric models.Results of velocity vectors, flow patterns, blood pressure and wall shear stress distributions are presented.The results delineate disturbed and recirculating flow in the aortic arch aneurysm accompanied with low wall shear stress and velocities, compared to a uniformly directed flow and nominal wall shear stress (WSS) in the model of Surgery graft. Out of the two endograft procedures, the hybrid procedure clearly exhibits better hemodynamic performances over the chimney model, with lower WSS, lower pressure drop and less disturbed and vortical flow regions. Although the chimney procedure requires less manufacturing time and cost, it is associated with higher risk rates, and therefore, it is recommended only for emergency cases. This study may shed light on the hemodynamic factors for these complications and provide insight into ways to improve the procedure.     

Fluid dynamics of a textured blood-contacting surface

This study examined the fluid dynamics of a textured blood-contacting surface using a computational fluid-dynamic modeling technique. The texture consisted of a regular array of microfibers of length 50 or 100 microm, spaced 100 microm apart, projecting perpendicularly to the surface. The results showed that the surface texture served as a flow-retarding solid boundary for a laminar viscous flow, resulting in a lowered wall shear stress on the hase-plane surface. However, the maximum wall shear stress on the fibers was much higher than the shear stress on the nontextured phase plane. At all fractions of fiber height down past 10 microm, the permeability of the textured region greatly exceeded the analytically predictable permeability of an equivalent array of infinite-height fihers. The lowered suiface shear stress appears to explain in part the enhanced deposition of formed blood elements on the textured surface.     

Experimental and numerical study of pulsatile flows through stenosis: wall shear stress analysis.

Different shapes of pulsatile flows through a model of stenosis are experimentally and numerically modeled to validate both methods and to determine the wall shear stress temporal evolution downstream from the stenosis. Two-dimensional velocity measurements are performed in a 75% severity stenosis using a pulsed Doppler ultrasonic velocimeter. Finite element package is employed for the transient numerical simulations. Polynomial method, based on the experimental velocity values, is proposed to determine the wall shear stress temporal evolution. There is a good agreement between the numerical and experimental results. The wall shear stress temporal analysis shows oscillating wall shear stress values during the cycle with high wall shear stress values at the throat of about 120 dyn/cm2, and low values downstream from the stenosis of about - 2.5 dyn/cm2. The key result of the study is that the presence of the stenosis leads the artery to work in a direction which is opposite to the direction of a healthy artery.     

Non-Newtonian blood flow in human right coronary arteries: steady state simulations

This study looks at blood flow through four different right coronary arteries, which have been reconstructed from bi-plane angiograms. Five non-Newtonian blood models, as well as the usual Newtonian model of blood viscosity, are used to study the wall shear stress in each of these arteries at a particular point in the cardiac cycle. It was found that in the case of steady flow in a given artery, the pattern of wall shear stress is consistent across all models. The magnitude of wall shear stress, however, is influenced by the model used and correlates with graphs of shear stress versus strain for each model. For mid-range velocities of around 0.2 m s(-1) the models are virtually indistinguishable. Local and global non-Newtonian importance factors are introduced, in an attempt to quantify the types of flows where non-Newtonian behaviour is significant. It is concluded that, while the Newtonian model of blood viscosity is a good approximation in regions of mid-range to high shear, it is advisable to use the Generalised Power Law model (which tends to the Newtonian model in those shear ranges in any case) in order to achieve better approximation of wall shear stress at low shear.     

Haemodynamic assessment of human coronary arteries is affected by degree of freedom of artery movement

Abnormal haemodynamic parameters are associated with atheroma plaque progression and instability in coronary arteries. Flow recirculation, shear stress and pressure gradient are understood to be important pathogenic mediators in coronary disease. The effect of freedom of coronary artery movement on these parameters is still unknown. Fluid–structure interaction (FSI) simulations were carried out in 25 coronary artery models derived from authentic human coronaries in order to investigate the effect of degree of freedom of movement of the coronary arteries on flow recirculation, wall shear stress (WSS) and wall pressure gradient (WPG). Each FSI model had distinctive supports placed upon it. The quantitative and qualitative differences in flow recirculation, maximum wall shear stress (MWSS), areas of low wall shear stress (ALWSS) and maximum wall pressure gradient (MWPG) for each model were determined. The results showed that greater freedom of movement was associated with lower MWSS, smaller ALWSS, smaller flow recirculation zones and lower MWPG. With increasing percentage diameter stenosis (%DS), the effect of degree of freedom on flow recirculation and WSS diminished. Freedom of movement is an important variable to be considered for computational modelling of human coronary arteries, especially in the setting of mild to moderate stenosis.

Abbreviations: 3D: Three-dimensional; 3DR: Three-dimensional Reconstruction; 3D-QCA: Three-dimensional quantitative coronary angiography; ALWSS: Areas of low wall shear stress; CAD: Coronary artery disease; CFD: Computational fluid dynamics; %DS: Diameter stenosis percentage; EPCS: End point of counter-rotating streamlines; FSI: Fluid–structure interaction; IVUS: Intravascular ultrasound; LAD: Left anterior descending; MWSS: Maximum wall shear stress; SST: Shear stress transport; TAWSS: Time-averaged wall shear stress; WSS: wall shear stress; WPG: Wall pressure gradient; MWPG: Maximum wall pressure gradient; FFR: Fractional flow reserve; iFR: Instantaneous wave-free ratio     

Including surrounding tissue improves ultrasound-based 3D mechanical characterization of abdominal aortic aneurysms

ObjectivesIn this study the influence of surrounding tissues including the presence of the spine on wall stress analysis and mechanical characterization of abdominal aortic aneurysms using ultrasound imaging has been investigated.MethodsGeometries of 7 AAA patients and 11 healthy volunteers were acquired using 3-D ultrasound and converted to finite element based models. Model complexity of externally unsupported (aorta-only) models was complemented with inclusion of both soft tissue around the aorta and a spine support dorsal to the aorta. Computed 3-D motion of the aortic wall was verified by means of ultrasound speckle tracking. Resulting stress, strain, and estimated shear moduli were analyzed to quantify the effect of adding surrounding material supports.ResultsAn improved agreement was shown between the ultrasound measurements and the finite element tissue and spine models compared to the aorta-only models. Peak and 99-percentile Von Mises stress showed an overall decrease of 23–30%, while estimated shear modulus decreased with 12–20% after addition of the soft tissue. Shear strains in the aortic wall were higher in areas close to the spine compared to the anterior region.ConclusionsImproving model complexity with surrounding tissue and spine showed a homogenization of wall stresses, reduction in homogeneity of shear strain at the posterior side of the AAA, and a decrease in estimated aortic wall shear modulus. Future research will focus on the importance of a patient-specific spine geometry and location.     

Numerical simulations of pulsatile flow in an end-to-side anastomosis model

A potential interaction between the local hemodynamics and the artery wall response has been suggested for vascular graft failure by intimal hyperplasia (IH). Among the various hemodynamic factors, wall shear stress has been implicated as the primary factor responsible for the development of IH. In order to explore the role of hemodynamics in the formation of IH in end-to-side anastomosis, computational fluid dynamics is employed. To validate the numerical simulations, comparisons with existing experimental data are performed for both steady and pulsatile flows. Generally, good agreement is observed with the velocity profiles whereas some discrepancies are found in wall shear stress (WSS) distributions. Using the same end-to-side anastomosis geometry, numerical simulations are extended using a femoral artery waveform to identify the possible role of unsteady hemodynamics. In the current simulations, Carreau-Yasuda model is used to account for the non-Newtonian nature of blood. Computations indicated a disturbed flow field at the artery-graft junction leading to locally elevated shear stresses on the vascular wall. Furthermore, the shear stress distribution followed the same behavior with oscillating magnitude over the entire flow cycle. Thus, distal IH observed in end-to-side artery-graft models may be caused by the fluctuations in WSS's along the wall.     

On the sensitivity of wall stresses in diseased arteries to variable material properties

Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.     

Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.     

Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation

The pulsatile flow in an anatomically realistic compliant human carotid bifurcation was simulated numerically. Pressure and mass flow waveforms in the carotid arteries were obtained from an individual subject using non-invasive techniques. The geometry of the computational model was reconstructed from magnetic resonance angiograms. Maps of time-average wall shear stress, contours of velocity in the flow field as well as wall movement and tensile stress on the arterial wall are all presented. Inconsistent with previous findings from idealised geometry models, flow in the carotid sinus is dominated by a strong helical flow accompanied by a single secondary vortex motion. This type of flow is induced primarily by the asymmetry and curvature of the in vivo geometry. Flow simulations have been carried out under the rigid wall assumption and for the compliant wall, respectively. Comparison of the results demonstrates the quantitative influence of the vessel wall motion. Generally there is a reduction in the magnitude of wall shear stress, with its degree depending on location and phase of the cardiac cycle. The region of slow or reversed flow was greater, in both spatial and temporal terms in the compliant model, but the global characteristics of the flow and stress patterns remain unchanged. The analysis of mechanical stresses on the vessel surface shows a complicated stress field. Stress concentration occurs at both the anterior and posterior aspects of the proximal internal bulb. These are also regions of low wall shear stress. The comparison of computed and measured wall movement generally shows good agreement.     

Computational haemodynamics in two idealised cerebral wide-necked aneurysms after stent placement

Endovascular stents are being commonly used to treat cerebral wide-necked aneurysms recently. The effect of a stent placed in the parent artery is not only to protect the parent artery from occlusion, due to extension of coils and thrombosis, but also to act as flow diverter to vary the haemodynamics in the aneurysm. In this article, two idealised cerebral wide-necked aneurysms were created, one was sidewall aneurysm with curved parent vessel and the other was terminal aneurysm with the bifurcated parent vessel. The plexiglass models of the two aneurysms were ‘treated’ with commercial porous intravascular stents. The stented physical models were scanned by Micro-CT and the numerical models of the two idealised cerebral wide-necked aneurysms after stent placement were constructed from the scanned image files. The pulsatile flow of non-Newtonian fluid inside the models was simulated by using computational fluid dynamics package. From the simulated flow dynamics, various haemodynamic characteristics such as velocity contours, wall shear stress and oscillatory shear index (OSI) were computed. The velocity of the jet entering the sacs reduced after stent was deployed across the necks of both sidewall and terminal aneurysms; the wall shear stress on the distal neck of sidewall aneurysm reduced, the wall shear stress on the dome of the terminal aneurysm increased and the OSI on the dome of the terminal aneurysm reduced. Therefore, stent placement not only promotes thrombus formation in both aneurysm models but also reduces the regrowth risk of the sidewall aneurysm and the rupture risk of the terminal aneurysm.     

Computational haemodynamics in two idealised cerebral wide-necked aneurysms after stent placement

Endovascular stents are being commonly used to treat cerebral wide-necked aneurysms recently. The effect of a stent placed in the parent artery is not only to protect the parent artery from occlusion, due to extension of coils and thrombosis, but also to act as flow diverter to vary the haemodynamics in the aneurysm. In this article, two idealised cerebral wide-necked aneurysms were created, one was sidewall aneurysm with curved parent vessel and the other was terminal aneurysm with the bifurcated parent vessel. The plexiglass models of the two aneurysms were 'treated' with commercial porous intravascular stents. The stented physical models were scanned by Micro-CT and the numerical models of the two idealised cerebral wide-necked aneurysms after stent placement were constructed from the scanned image files. The pulsatile flow of non-Newtonian fluid inside the models was simulated by using computational fluid dynamics package. From the simulated flow dynamics, various haemodynamic characteristics such as velocity contours, wall shear stress and oscillatory shear index (OSI) were computed. The velocity of the jet entering the sacs reduced after stent was deployed across the necks of both sidewall and terminal aneurysms; the wall shear stress on the distal neck of sidewall aneurysm reduced, the wall shear stress on the dome of the terminal aneurysm increased and the OSI on the dome of the terminal aneurysm reduced. Therefore, stent placement not only promotes thrombus formation in both aneurysm models but also reduces the regrowth risk of the sidewall aneurysm and the rupture risk of the terminal aneurysm.     

Comparison of blood rheological models for physiological flow simulation

The present study investigates the flow effects that different blood constitutive equations induce when employed in numerical simulations in the framework of computational hemodynamics. In accord with experimental studies on the rheological behavior of blood, three blood constitutive equations namely the Casson, Power-Law and Quemada models were used for simulating the shear flow behavior of blood. The case studied is the flow in a channel with a moving part of the boundary and was selected because it reproduces the flow phenomena occurring in realistic arterial conditions. Flow simulation for every model is carried out assuming the same flow rate at the inlet of the channel and different Strouhal numbers reflecting different intensities of the boundary movement. Results show that the modeling of blood as non-Newtonian fluid has marked qualitative and quantitative effects on both the flow field and the wall shear stress whereas comparison of the different models shows good agreement between the flow effects by the Casson and Quemada models.     

FLUID SHEAR-STIMULATED DINOFLAGELLATE BIOLUMINESCENCE

Bioluminescence studies provide insight into the properties of water motion that are stimulatory to flow-sensitive organisms such as dinoflagellates, the most common sources of near-surface oceanic bioluminescence. Previous laboratory studies employing steady flows have characterized the luminescent response of dinoflagellates in terms of shear stress. In the present study, computational and experimental approaches were used to investigate the contributions of shear and acceleration to cells responding in a laminar converging flow field, where regions of high acceleration and shear are spatially separated. Flow-stimulated flashes by the dinoflagellates Lingulodinium polyedrum and Ceratocorys horrida were used as a near-instantaneous monitor of cell response. By combining video analysis of flash trajectories with computational methods, the location of each stimulated cell was determined and flow parameters at that location were calculated. Based on several criteria, shear stress was considered the flow parameter most stimulatory to cells. For both dinoflagellates species and for all flow rates, essentially all cells responded downstream near the wall where shear stress levels were maximal, and levels of acceleration and extensional stress were as much as two orders of magnitude less than locations away from the wall. Minimum shear stress levels at the cell positions were consistent with response thresholds based on previous studies. Bioluminescence is an excellent tool for examining how organisms respond to flow at the small temporal and spatial scales relevant to planktonic organisms.     

The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anastomosis

We present an experimental and computational investigation of time-varying flow in an idealized fully occluded 45 degrees distal end-to-side anastomosis. Two geometric configurations are assessed, one where the centerlines of host and bypass vessels lie within a plane, and one where the bypass vessel is deformed out of the plane of symmetry, respectively, termed planar and non-planar. Flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral/hp algorithm. Results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time-averaged peak wall shear stress magnitude by 10% in the non-planar model as compared to the planar configuration. In the planar geometry the stagnation point follows a straight-line path along the host artery bed with a path length of 0.8 diameters. By contrast in the non-planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall, and follows a parabolic path with a 0.7 diameter longitudinal and 0.5 diameter transverse excursion. A definition of the oscillatory shear index (OSI) is introduced that varies between 0 and 0.5 and that accounts for a continuous range of wall shear stress vector angles. In both models, regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow. The mean oscillatory shear magnitude (considering sites where OSI>0.1) in the non-planar geometry was reduced by 22% as compared to the planar configuration. These changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out-of-plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions.