Numerical analysis of flow through a severely stenotic carotid artery bifurcation

Turbulence intensity measurements using particle image velocimetry in diseased carotid artery models: effect of stenosis severity, plaque eccentricity, and ulceration

Clinical decision-making for the treatment of patients with diseased carotid artery is mainly based on the severity of the stenosis. However, stenosis severity alone is not a sensitive indicator, and other local factors for the assessment of stroke risk are required. Flow disturbance is of particular interest due to its proven association with increased thromboembolic activities. The objective of this study was to investigate the level of turbulence intensity (TI) with regards to certain geometrical features of the plaque - namely stenosis severity, eccentricity, and ulceration. A family of eight carotid-artery bifurcation models was examined using particle image velocimetry. Results showed a marked difference in turbulence intensity among these models; increasing degree of stenosis severity resulted in increased turbulence intensity, going from 0.12 m/s for mild stenosis to 0.37 m/s for severe stenosis (with concentric geometry). Moreover, independent of stenosis severity, eccentricity led to further elevations in turbulence intensity, increasing TI by 0.05-0.10 m/s over the counterpart concentric plaque. The presence of ulceration (in a 50% eccentric plaque) produced a larger portion of moderate turbulence intensity (~0.10 m/s) compared to the non-ulcerated model, more proximal to the bifurcation apex in the post-stenotic recirculation zone. The effect of plaque eccentricity and ulceration in enhancing the downstream turbulence has potential clinical implications for a more sensitive assessment of stroke risk beyond stenosis severity alone.

Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis

Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.

Impact of stent mis-sizing and mis-positioning on coronary fluid wall shear and intramural stress

Stent deployments with geographical miss (GM) are associated with increased risk of target-vessel revascularization and periprocedural myocardial infarction. The aim of the current study was to investigate the underlying biomechanical mechanisms for adverse events with GM. The hypothesis is that stent deployment with GM [longitudinal GM, or LGM (i.e., stent not centered on the lesion); or radial GM, RGM (i.e., stent oversizing)] results in unfavorable fluid wall shear stress (WSS), WSS gradient (WSSG), oscillatory shear index (OSI), and intramural circumferential wall stress (CWS). Three-dimensional computational models of stents and plaque were created using a computer-assisted design package. The models were then solved with validated finite element and computational fluid dynamic packages. The dynamic process of large deformation stent deployment was modeled to expand the stent to the desired vessel size. Stent deployed with GM resulted in a 45% increase in vessel CWS compared with stents that were centered and fully covered the lesion. A 20% oversized stent resulted in 72% higher CWS than a correct sized stent. The linkages between the struts had much higher stress than the main struts (i.e., 180 MPa vs. 80 MPa). Additionally, LGM and RGM reduced endothelial WSS and increased WSSG and OSI. The simulations suggest that both LGM and RGM adversely reduce WSS but increase WSSG, OSI, and CWS. These findings highlight the potential mechanical mechanism of the higher adverse events and underscore the importance of stent positioning and sizing for improved clinical outcome.

Hemodynamics analysis of patient-specific carotid bifurcation: a CFD model of downstream peripheral vascular impedance

The study of cardiovascular models was presented in this paper based on medical image reconstruction and computational fluid dynamics. Our aim is to provide a reality platform for the purpose of flow analysis and virtual intervention outcome predication for vascular diseases. By connecting two porous mediums with transient permeability at the downstream of the carotid bifurcation branches, a downstream peripheral impedance model was developed, and the effect of the downstream vascular bed impedance can be taken into consideration. After verifying its accuracy with a healthy carotid bifurcation, this model was implemented in a diseased carotid bifurcation analysis. On the basis of time-averaged wall shear stress, oscillatory shear index, and the relative residence time, fractions of abnormal luminal surface were highlighted, and the atherosclerosis was assessed from a hemodynamic point of view. The effect of the atherosclerosis on the transient flow division between the two branches because of the existence of plaque was also analysed. This work demonstrated that the proposed downstream peripheral vascular impedance model can be used for computational modelling when the outlets boundary conditions are not available, and successfully presented the potential of using medical imaging and numerical simulation to provide existing clinical prerequisites for diagnosis and therapeutic treatment.

A simplified murine intimal hyperplasia model founded on a focal carotid stenosis

Murine models offer a powerful tool for unraveling the mechanisms of intimal hyperplasia and vascular remodeling, although their technical complexity increases experimental variability and limits widespread application. We describe a simple and clinically relevant mouse model of arterial intimal hyperplasia and remodeling. Focal left carotid artery (LCA) stenosis was created by placing 9-0 nylon suture around the artery using an external 35-gauge mandrel needle (middle or distal location), which was then removed. The effect of adjunctive diet-induced obesity was defined. Flowmetry, wall strain analyses, biomicroscopy, and histology were completed. LCA blood flow sharply decreased by ∼85%, followed by a responsive right carotid artery increase of ∼71%. Circumferential strain decreased by ∼2.1% proximal to the stenosis in both dietary groups. At 28 days, morphologic adaptations included proximal LCA intimal hyperplasia, which was exacerbated by diet-induced obesity. The proximal and distal LCA underwent outward and negative inward remodeling, respectively, in the mid-focal stenosis (remodeling indexes, 1.10 and 0.53). A simple, defined common carotid focal stenosis yields reproducible murine intimal hyperplasia and substantial differentials in arterial wall adaptations. This model offers a tool for investigating mechanisms of hemodynamically driven intimal hyperplasia and arterial wall remodeling.

Direct observation of von Willebrand factor elongation and fiber formation on collagen during acute whole blood exposure to pathological flow

OBJECTIVE

In severe stenosis, von Willebrand factor (vWF) experiences millisecond exposures to pathological wall shear rates (γ(w)). We sought to evaluate the deposition of vWF onto collagen surfaces under flow in these environments.

METHODS AND RESULTS

Distinct from viscometry experiments that last many seconds, we deployed microfluidic devices for single-pass perfusion of whole blood or platelet-free plasma over fibrillar type 1 collagen (<50 ms transit time) at pathological γ(w) or spatial wall shear rate gradients (grad γ(w)). Using fluorescent anti-vWF, long thick vWF fibers (>20 μm) bound to collagen were visualized at constant γ(w)>30000 s(-1) during perfusion of platelet-free plasma, a process enhanced by EDTA. Rapid acceleration or deceleration of EDTA platelet-free plasma at grad γ(w)=±1.1×10(5) to ±4.3×10(7) s(-1)/cm did not promote vWF deposition. At 19400 s(-1), EDTA blood perfusion resulted in rolling vWF-platelet nets, although blood perfusion (normal Ca(2+)) generated large vWF/platelet deposits that repeatedly embolized and were blocked by anti-glycoprotein Ib or the α(IIb)β(3) inhibitor GR144053 and did not require grad γ(w). Blood perfusion at venous shear rate (200 s(-1)) produced a stable platelet deposit that was a substrate for massive but unstable vWF-platelet aggregates when flow was increased to 7800 s(-1).

CONCLUSIONS

Triggered by collagen and enhanced by platelet glycoprotein Ib and α(IIb)β(3), vWF fiber formation occurred during acute exposures to pathological γ(w) and did not require gradients in wall shear rate.

Transitional flow analysis in the carotid artery bifurcation by proper orthogonal decomposition and particle image velocimetry

Blood flow instabilities in the carotid artery bifurcation have been highly correlated to clot formation and mobilization resulting in ischemic stroke. In this work, PIV-measured flow velocities in normal and stenosed carotid artery bifurcation models were analyzed by means of proper orthogonal decomposition (POD). Through POD analysis, transition to more complex flow was visualized and quantified for increasing stenosis severity. While no evidence of transitional flow was seen in the normal model, the 50%-stenosed model started to show characteristics of transitional flow, which became highly evident in the 70% model, with greatest manifestation during the systolic phase of the cardiac cycle. By means of a model comparison, we demonstrate two quantitative measures of the flow complexity through the power-law decay slope of the energy spectrum and the global entropy. The more complex flow in the 70%-stenosed model showed a flatter slope of energy decay (-0.91 compared to -1.34 for 50% stenosis) and higher entropy values (0.26 compared to 0.17). Finally, the minimum temporal resolution required for POD analysis of carotid artery flow was found to be 100 Hz when determined through a more typical energy-mode convergence test, as compared to 400 Hz based on global entropy values.

Transitional Flow in a Cylindrical Flow Chamber for Studies at the Cellular Level

Fluid shear stress is an important regulator of vascular and endothelial cell (EC) functions. Its effect is dependent not only on magnitude but also on flow type. Although laminar flow predominates in the vasculature, transitional flow can occur and is thought to play a role in vascular diseases. While a great deal is known about the mechanisms and signaling cascades through which laminar shear stress regulates cells, little is known on how transitional shear stress regulates cells. To better understand the response of endothelial cells to transitional shear stress, a novel cylindrical flow chamber was designed to expose endothelial cells to a transitional flow environment similar to that found in vivo. The velocity profiles within the transitional flow chamber at Reynolds numbers 2200 and 3000 were measured using laser Doppler anemometry (LDA). At both Reynolds numbers, the velocity profiles are blunt (non-parabolic) with fluctuations larger than 5% of the velocity at the center of the pipe indicating the flows are transitional. Based on near wall velocity measurements and well established data for flow at these Reynolds numbers, the wall shear stress was estimated to be 3–4 and 5–6 dynes/cm² for Reynolds number 2200 and 3000, respectively. In contrast to laminar shear stress, no cell alignment was observed under transitional shear stress at both Reynolds numbers. However, transitional shear stress at the higher Reynolds number caused cell elongation similar to that of laminar shear stress at 3 dynes/cm². The fluctuating component of the wall shear stress may be responsible for these differences. The transitional flow chamber will facilitate cellular studies to identify the mechanisms through which transitional shear stress alters EC biology, which will assist in the development of vascular therapeutic treatments.

A novel formulation for Neumann inflow boundary conditions in biomechanics

Neumann boundary conditions prescribing the total momentum flux at inflow boundaries of biomechanical problems are proposed in this study. This approach enables the simultaneous application of velocity/flow rate and pressure curves at inflow boundaries. As the basic numerical method, a residual-based variational multiscale (or stabilized) finite element method is presented. The focus of the numerical examples in this work is on respiratory flows with complete flow reversals. However, the proposed formulation is just as well suited for cardiovascular flow problems with partial retrograde flow. Instabilities, which were reported for such problems in the literature, are resolved by the present approach without requiring the additional consideration of a Lagrange multiplier technique. The suitability of the approach is demonstrated for two respiratory flow examples, a rather simple tube and complex tracheobronchial airways (up to the fourth generation, segmented from end-expiratory CT images). For the latter example, the boundary conditions are generated from mechanical ventilation data obtained from an intensive care unit patient suffering from acute lung injury. For the tube, analytical pressure profiles can be replicated, and for the tracheobronchial airways, a correct distribution of the prescribed total momentum flux at the inflow boundary into velocity and pressure part is observed.

Large deforming buoyant embolus passing through a stenotic common carotid artery: a computational simulation

Arterial embolism is responsible for the death of lots of people who suffers from heart diseases. The major risk of embolism in upper limbs is that the ruptured particles are brought into the brain, thus stimulating neurological symptoms or causing the stroke. We presented a computational model using fluid-structure interactions (FSI) to investigate the physical motion of a blood clot inside the human common carotid artery. We simulated transportation of a buoyant embolus in an unsteady flow within a finite length tube having stenosis. Effects of stenosis severity and embolus size on arterial hemodynamics were investigated. To fulfill realistic nonlinear property of a blood clot, a rubber/foam model was used. The arbitrary Lagrangian-Eulerian formulation (ALE) and adaptive mesh method were used inside fluid domain to capture the large structural interfacial movements. The problem was solved by simultaneous solution of the fluid and the structure equations. Stress distribution and deformation of the clot were analyzed and hence, the regions of the embolus prone to lysis were localized. The maximum magnitude of arterial wall shear stress during embolism occurred at a short distance proximal to the throat of the stenosis. Through embolism, arterial maximum wall shear stress is more sensitive to stenosis severity than the embolus size whereas role of embolus size is more significant than the effect of stenosis severity on spatial and temporal gradients of wall shear stress downstream of the stenosis and on probability of clot lysis due to clot stresses while passing through the stenosis.

Assessment of the accuracy of MRI wall shear stress estimation using numerical simulations

PURPOSE

To investigate the accuracy of wall shear stress (WSS) estimation using MRI. Specifically, to investigate the impact of different parameters and if MRI WSS estimates are monotonically related to actual WSS.

MATERIALS AND METHODS

The accuracy of WSS estimation using methods based on phase-contrast (PC) MRI velocity mapping, Fourier velocity encoding (FVE) and intravoxel velocity standard deviation mapping were studied using numerical simulations. The influence of spatial resolution, velocity encoding, wall segmentation, and voxel location were investigated over a range of WSS values.

RESULTS

WSS estimates were found to be sensitive to parameter settings in general and spatial resolution in particular. All methods underestimated WSS, except for the FVE-based method, which instead was extremely sensitive to voxel position relative to the wall. Methods using PC-based WSS estimation with wall segmentation showed to be accurate for low WSS, but were sensitive to segmentation errors.

CONCLUSION

Even in the absence of noise and for relatively simple velocity profiles, MRI WSS estimates cannot always be assumed to be linearly or even monotonically related to actual WSS. High WSS values cannot be resolved and the estimates depend on parameter setting. Nevertheless, distinguishing areas of low and moderate WSS may be feasible.

Computational fluid dynamic characterization of carotid bifurcation stenosis in patient-based geometries

Hemodynamic forces play a role in determining endothelial cell (EC) phenotype and influence vascular remodeling. We present a lesion-based computational fluid dynamic (CFD) pilot analysis to understand the complex spatial and temporal hemodynamic changes that prevail in patients with high-grade carotid artery stenosis (CS). High-resolution three-dimensional (3D) rotational angiography datasets were acquired in eight patients, and used to generate computational meshes. CFD analysis was carried out implementing realistic shear-dependent viscosity for blood. The mean wall shear stress (WSS) within the stenosis region was 107 ± 73 dyn/cm(2) rapidly followed by direction reversal and lower oscillating values in the recirculation zone at a mean of 19 ± 14 dyn/cm(2). WSS vectors exhibited complex dynamic directional and amplitude oscillations not seen in healthy segments, along with time-dependent convergence and divergence strips during the cardiac cycle. The spatial gradient of WSS revealed an elevated average magnitude at the throat of the stenosis of 1425 ± 1012 dyn/cm(3). In conclusion, patient-based CFD analysis of CS predicts a complex hemodynamic environment with large spatial WSS variations that occur very rapidly over short distances. Our results improve estimates of the flow changes and forces at the vessel wall in CS and the link between hemodynamic changes and stenosis pathophysiology.

Impact of main branch stenting on endothelial shear stress: role of side branch diameter, angle and lesion

In-stent restenosis and stent thrombosis remain clinically significant problems for bifurcation lesions. The objective of this study is to determine the haemodynamic effect of the side branch (SB) on main branch (MB) stenting. We hypothesize that the presence of a SB has a negative effect on MB wall shear stress (WSS), wall shear stress gradient (WSSG) and oscillatory shear index (OSI); and that the bifurcation diameter ratio (SB diameter/MB diameter) and angle are important contributors. We further hypothesized that stent undersizing exaggerates the negative effects on WSS, WSSG and OSI. To test these hypotheses, we developed computational models of stents and non-Newtonian blood. The models were then interfaced, meshed and solved in a validated finite-element package. Stents at bifurcation models were created with 30° and 70° bifurcation angles and bifurcations with diameter ratios of SB/MB = 1/2 and 3/4. It was found that stents placed in the MB at a bifurcation lowered WSS dramatically, while elevating WSSG and OSI. Undersizing the stent exaggerated the decrease in WSS, increase in WSSG and OSI, and disturbed the flow between the struts and the vessel wall. Stenting the MB at bifurcations with larger SB/MB ratios or smaller SB angles (30°) resulted in lower WSS, higher WSSG and OSI. Stenosis at the SB lowered WSS and elevated WSSG and OSI. These findings highlight the effects of major biomechanical factors in MB stenting on endothelial WSS, WSSG, OSI and suggests potential mechanisms for the potentially higher adverse clinical events associated with bifurcation stenting.

ROLE OF SLIP VELOCITY IN BLOOD FLOW THROUGH STENOSED ARTERIES: A NON-NEWTONIAN MODEL

A mathematical model is developed in this paper for studying blood flow through a stenosed arterial segment by taking into account the slip velocity at the wall of the artery. Consideration of the non-Newtonian character of blood is made, where a constitutive relation of blood is described by the Herschel–Bulkley equation. The effect of slip at the arterial wall in the presence of mild, moderate, and severe stenosis growth at the lumen of an artery is investigated. Analytical expressions for skin friction, flow resistance, and the flow rate are derived by using the model. The derived expressions are computed numerically by considering an illustrative example. The study provides an insight into the effects of slip velocity on the volumetric flow rate of blood, flow resistance, and skin friction.

The effects of stenosis severity on the hemodynamic parameters-assessment of the correlation between stress phase angle and wall shear stress

To study the effects of increase in the degree of stenosis severity and subsequent complexity of hemodynamic patterns on hemodynamic parameters, experimental investigations and numerical simulations were performed. The correlations between the large negative Stress Phase Angle (SPA), the low mean Wall Shear Stress (WSS) and high Oscillatory Shear Index (OSI) were investigated at the distal shoulder and post-stenotic regions as the outcomes of elevated stenosis severity. Models included non-Newtonian fluid flow in stenotic arteries with 30-80% symmetrical stenoses. To study the interactions between pulsatile WSS and pulsatile wall circumferential stress (WCS) acting on endothelial cells, SPA as the phase difference between WSS and WCS waves was used. Moreover, the distribution of SPA on the lumen axis was compared to the distributions of the mean WSS and OSI that have been regarded until now as the determinants of atherosclerosis-prone regions. Results indicate that an increase in stenosis severity, not only affects the mean WSS, mean WCS and pulse amplitudes, but also influences the phase difference between them. The SPA is large negative on the distal shoulder and post-stenotic areas where atherosclerotic plaque develops. The increasing stenosis severity and the subsequent increasing complexity of hemodynamic patterns affect the correlation between any of the low mean WSS and high OSI with large negative SPA, such that it not only leads to create and develop some regions where the correlation between any of the low mean WSS and high OSI with large negative SPA is well but also leads to create and develop other regions where such correlations fail.

Numerical modeling of stress in stenotic arteries with microcalcifications: a micromechanical approximation

Most finite element models of atherosclerotic arteries do not account for the heterogeneity of the plaque constituents at the microscale. Failure of plaque lesions has been shown to be a local event, linked to stress concentrations caused by cap thinning, inflammation, macroscopic heterogeneity, and recently, the presence of microcalcifications. There is growing evidence that microcalcifications exist in the fibrous cap of plaque lesions. However, their role is not yet fully understood. The goal of the present work is to investigate the effects of localized regions of microcalcifications on the stress field of atherosclerotic plaque caps in a section of carotid artery. This is achieved by performing finite element simulations of three-dimensional fluid-structure interaction models. The material response in the region of microcalcification is modeled using a combination of finite elements, homogenization theory, and a stress concentration function that approximates the average local stresses in the fibrous tissue and microcalcification phases. The results indicate that the circumferential stress in the fibrous tissue phase increases as the volume fraction of microcalcifications is increased, and that the stress exceeds a critical threshold when the fibrous cap thickness is decreased. Furthermore, the presence of the microcalcifications significantly influences the distribution of stress by shifting the maximum circumferential stress away from the cap shoulders, where failure is most common when the effective region of microcalcification is located at the center of the cap. This is a possible explanation of why 40% of plaque ruptures occur away from the shoulder region of the cap.

Possibility of atherosclerosis in an arterial bifurcation model

INTRODUCTION

Arterial bifurcations are susceptible locations for formation of atherosclerotic plaques. In the present study, steady blood flow is investigated in a bifurcation model with a non-planar branch.

METHODS

The influence of different bifurcation angles and non-planar branch is demonstrated on wall shear stress (WSS) distribution using three-dimensional Navier-Stokes equations.

RESULTS

The WSS values are low in two locations at the top and bottom walls of the mother vessels just before the bifurcation, especially for higher bifurcation angles. These regions approach the apex of bifurcation with decreasing the bifurcation angle. The WSS magnitudes approach near to zero at the outer side of bifurcation plane and these locations are separation-prone. By increasing the bifurcation angle, the minimum WSS decreases at the outer side of bifurcation plane but low WSS region squeezes. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these initial peaks drop as bifurcation angle is increased.

CONCLUSION

It is concluded that the non-planarity of the daughter vessel lowers the minimum WSS at the outer side of bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky.

Hemodynamics of ulcerated plaques: before and after

The hemodynamics and fluid mechanical forces in blood vessels have long been implicated in the deposition and growth of atherosclerotic plaque. Detailed information about the hemodynamics in vessels affected by significant plaque deposits can also provide insight into the mechanisms and likelihood of plaque weakening and rupture. In the current study, the governing equations are solved in their finite volume formulation in several patient-specific stenotic geometries. Of specific interest are the flow patterns and forces near ulcerations in the plaque. The flow patterns and forces in vessels with ulcerated plaques are compared with those in stenotic vessels without evidence of ulceration and to the hemodynamics in the same vessels as they likely appeared prior to ulceration. Hemodynamics "before" and "after" hemorrhage may suggest fluid mechanical and morphological factors of diagnostic and predictive value. Recirculation zones, vortex shedding, and secondary flows are captured by both laminar and turbulent solutions. The forces on vessel walls are shown to correlate with unstable plaque deposits. Performing before and after studies of vessels in long-term radiology studies may illuminate mechanisms of hemorrhage and other vessel remodeling.

Feasibility of in vivo measurement of carotid wall shear rate using spiral Fourier velocity encoded MRI

Arterial wall shear stress is widely believed to influence the formation and growth of atherosclerotic plaque; however, there is currently no gold standard for its in vivo measurement. The use of phase contrast MRI has proved to be challenging due to partial-volume effects and inadequate signal-to-noise ratio at the high spatial resolutions that are required. This work evaluates the use of spiral Fourier velocity encoded MRI as a rapid method for assessing wall shear rate in the carotid arteries. Wall shear rate is calculated from velocity histograms in voxels spanning the blood/vessel wall interface, using a method developed by Frayne and Rutt (Magn Reson Med 1995;34:378-387). This study (i) demonstrates the accuracy of the velocity histograms measured by spiral Fourier velocity encoding in a pulsatile carotid flow phantom compared with high-resolution two-dimensional Fourier transform phase contrast, (ii) demonstrates the accuracy of Fourier velocity encoding-based shear rate measurements in a numerical phantom designed using a computational fluid dynamics simulation of carotid flow, and (iii) demonstrates in vivo measurement of regional wall shear rate and oscillatory shear index in the carotid arteries of healthy volunteers at 3 T.

Outflow Conditions for Image-Based Hemodynamic Models of the Carotid Bifurcation: Implications for Indicators of Abnormal Flow

Computational fluid dynamics (CFD) models have become very effective tools for predicting the flow field within the carotid bifurcation, and for understanding the relationship between local hemodynamics, and the initiation and progression of vascular wall pathologies. As prescribing proper boundary conditions can affect the solutions of the equations governing blood flow, in this study, we investigated the influence to assumptions regarding the outflow boundary conditions in an image-based CFD model of human carotid bifurcation. Four simulations were conducted with identical geometry, inlet flow rate, and fluid parameters. In the first case, a physiological time-varying flow rate partition at branches along the cardiac cycle was obtained by coupling the 3D model of the carotid bifurcation at outlets with a lumped-parameter model of the downstream vascular network. Results from the coupled model were compared with those obtained by imposing three fixed flow rate divisions (50/50, 60/40, and 70/30) between the two branches of the isolated 3D model of the carotid bifurcation. Three hemodynamic wall parameters were considered as indicators of vascular wall dysfunction. Our findings underscore that the overall effect of the assumptions done in order to simulate blood flow within the carotid bifurcation is mainly in the hot-spot modulation of the hemodynamic descriptors of atherosusceptible areas, rather than in their distribution. In particular, the more physiological, time-varying flow rate division deriving from the coupled simulation has the effect of damping wall shear stress (WSS) oscillations (differences among the coupled and the three fixed flow partition models are up to 37.3% for the oscillating shear index). In conclusion, we recommend to adopt more realistic constraints, for example, by coupling models at different scales, as in this study, when the objective is the outcome prediction of alternate therapeutic interventions for individual patients, or to test hypotheses related to the role of local fluid dynamics and other biomechanical factors in vascular diseases.

Flow patterns in carotid bifurcation models using pulsed Doppler ultrasound: effect of concentric vs. eccentric stenosis on turbulence and recirculation

Hemodynamics play a significant role in stroke risk, where thrombus formation may be accelerated in regions of slow or recirculating flow, high shear and increased turbulence. An in vitro investigation was performed with pulsed Doppler ultrasound (DUS) using the complete spectral data to investigate the three-dimensional (3-D) distribution of advanced parameters that may have potential for making a more specific in vivo diagnosis of carotid disease and stroke risk. The effect of stenosis symmetry and the potential of DUS spectral parameters for visualizing regions of recirculation or turbulence were explored. DUS was used to map pulsatile flow in four model geometries representing two different plaque symmetries (eccentricity) and two stenosis severities (mild, severe). Qualitative comparisons were made with flow patterns visualized using digital particle imaging. Color-encoded maps of DUS spectral parameters (mean velocity, spectral-broadening index and turbulence intensity) clearly distinguished regions of slow or recirculating flow and disturbed or turbulent flow. Distinctly different flow patterns resulted from stenoses of equal severity but different eccentricity. Noticeable differences were seen in both the size and location of recirculation zones and in the paths of high-velocity jets. Highly elevated levels of turbulence intensity were seen distal to severe stenosis. Results demonstrated the importance of plaque shape, which is typically not considered in standard diagnosis, in addition to stenosis severity.

Computer simulation of vertebral artery occlusion in endovascular procedures

OBJECTIVE

The aim of this work is to establish a computational pipeline for the simulation of blood flow in vasculatures and apply this pipeline to endovascular interventional scenarios, e.g. angioplasty in vertebral arteries.

METHODS

A patient-specific supra-aortal vasculature is digitized from a 3D CT angiography image. By coupling a reduced formulation of the governing Navier-Stokes equations with a wall constitutive equation we are able to solve the transient flow in elastic vessels. By further incorporating a bifurcation model the blood flow across vascular branches can be evaluated, thus flow in a large vasculature can be modeled. Vascular diseases are simulated by modifying the arterial tree configurations, e.g. the effective diameters, schematic connectivity, etc. Occlusion in an artery is simulated by removing that artery from the arterial tree.

RESULTS

It takes about 2 min per cardiac cycle to compute blood flow in an arterial tree consisting of 38 vessels and 18 bifurcations on a laptop PC. The simulation results show that blood supply in the posterior region is compensated from the contralateral vertebral artery and the anterior cerebral arteries if one of the vertebral arteries is occluded.

CONCLUSION

The computational pipeline is computationally efficient and can capture main flow patterns at any point in the arterial tree. With further improvement it can serve as a powerful tool for the haemodynamic analysis in patient-specific vascular structures.

Analyzing transient turbulence in a stenosed carotid artery by proper orthogonal decomposition

High-resolution three-dimensional simulations (involving 100 million degrees of freedom) were employed to study transient turbulent flow in a carotid arterial bifurcation with a stenosed internal carotid artery (ICA). The geometrical model was reconstructed from MRI images, and in vivo velocity measurements were incorporated in the simulations to provide inlet and outlet boundary conditions. Due to the high degree of the ICA occlusion and the variable flow rate, a transitional and intermittent flow between laminar and turbulent states was established. Time- and space-window proper orthogonal decomposition (POD) was applied to quantify the different flow regimes in the occluded artery. A simplified version of the POD analysis that utilizes 2D slices only--more appropriate in the clinical setting--was also investigated.

Effects of vessel compliance on flow pattern in porcine epicardial right coronary arterial tree

The compliance of the vessel wall affects hemodynamic parameters which may alter the permeability of the vessel wall. Based on experimental measurements, the present study established a finite element (FE) model in the proximal elastic vessel segments of epicardial right coronary arterial (RCA) tree obtained from computed tomography. The motion of elastic vessel wall was measured by an impedance catheter and the inlet boundary condition was measured by an ultrasound flow probe. The Galerkin FE method was used to solve the Navier-Stokes and Continuity equations, where the convective term in the Navier-Stokes equation was changed in the arbitrary Lagrangian-Eulerian (ALE) framework to incorporate the motion due to vessel compliance. Various hemodynamic parameters (e.g., wall shear stress-WSS, WSS spatial gradient-WSSG, oscillatory shear index-OSI) were analyzed in the model. The motion due to vessel compliance affects the time-averaged WSSG more strongly than WSS at bifurcations. The decrease of WSSG at flow divider in elastic bifurcations, as compared to rigid bifurcations, implies that the vessel compliance decreases the permeability of vessel wall and may be atheroprotective. The model can be used to predict coronary flow pattern in subject-specific anatomy as determined by noninvasive imaging.

Numerical simulations of flow in cerebral aneurysms: comparison of CFD results and in vivo MRI measurements

Computational fluid dynamics (CFD) methods can be used to compute the velocity field in patient-specific vascular geometries for pulsatile physiological flow. Those simulations require geometric and hemodynamic boundary values. The purpose of this study is to demonstrate that CFD models constructed from patient-specific magnetic resonance (MR) angiography and velocimetry data predict flow fields that are in good agreement with in vivo measurements and therefore can provide valuable information for clinicians. The effect of the inlet flow rate conditions on calculated velocity fields was investigated. We assessed the internal consistency of our approach by comparing CFD predictions of the in-plane velocity field to the corresponding in vivo MR velocimetry measurements. Patient-specific surface models of four basilar artery aneurysms were constructed from contrast-enhanced MR angiography data. CFD simulations were carried out in those models using patient-specific flow conditions extracted from MR velocity measurements of flow in the inlet vessels. The simulation results computed for slices through the vasculature of interest were compared with in-plane velocity measurements acquired with phase-contrast MR imaging in vivo. The sensitivity of the flow fields to inlet flow ratio variations was assessed by simulating five different inlet flow scenarios for each of the basilar aneurysm models. In the majority of cases, altering the inlet flow ratio caused major changes in the flow fields predicted in the aneurysm. A good agreement was found between the flow fields measured in vivo using the in-plane MR velocimetry technique and those predicted with CFD simulations. The study serves to demonstrate the consistency and reliability of both MR imaging and numerical modeling methods. The results demonstrate the clinical relevance of computational models and suggest that realistic patient-specific flow conditions are required for numerical simulations of the flow in aneurysmal blood vessels.

Analysis of Flow Disturbance in a Stenosed Carotid Artery Bifurcation Using Two-Equation Transitional and Turbulence Models

In this study, newly developed two-equation turbulence models and transitional variants are employed for the prediction of blood flow patterns in a diseased carotid artery where the growth, progression, and structure of the plaque at rupture are closely linked to low and oscillating wall shear stresses. Moreover, the laminar-turbulent transition in the poststenotic zone can alter the separation zone length, wall shear stress, and pressure distribution over the plaque, with potential implications for stresses within the plaque. Following the validation with well established experimental measurements and numerical studies, a magnetic-resonance (MR) image-based model of the carotid bifurcation with 70% stenosis was reconstructed and simulated using realistic patient-specific conditions. Laminar flow, a correlation-based transitional version of Menter’s hybrid k‐ϵ∕k‐ω shear stress transport (SST) model and its “scale adaptive simulation” (SAS) variant were implemented in pulsatile simulations from which analyses of velocity profiles, wall shear stress, and turbulence intensity were conducted. In general, the transitional version of SST and its SAS variant are shown to give a better overall agreement than their standard counterparts with experimental data for pulsatile flow in an axisymmetric stenosed tube. For the patient-specific case reported, the wall shear stress analysis showed discernable differences between the laminar flow and SST transitional models but virtually no difference between the SST transitional model and its SAS variant.

Numerical modeling of the flow in intracranial aneurysms: prediction of regions prone to thrombus formation

The deposition of intralumenal thrombus in intracranial aneurysms adds a risk of thrombo-embolism over and above that posed by mass effect and rupture. In addition to biochemical factors, hemodynamic factors that are governed by lumenal geometry and blood flow rates likely play an important role in the thrombus formation and deposition process. In this study, patient-specific computational fluid dynamics (CFD) models of blood flow were constructed from MRA data for three patients who had fusiform basilar aneurysms that were thrombus free and then proceeded to develop intralumenal thrombus. In order to determine whether features of the flow fields could suggest which regions had an elevated potential for thrombus deposition, the flow was modeled in the baseline, thrombus-free geometries. Pulsatile flow simulations were carried out using patient-specific inlet flow conditions measured with MR velocimetry. Newtonian and non-Newtonian blood behavior was considered. A strong similarity was found between the intra-aneurysmal regions with CFD-predicted slow, recirculating flows and the regions of thrombus deposition observed in vivo in the follow-up MR studies. In two cases with larger aneurysms, the agreement between the low velocity zones and clotted-off regions improved when non-Newtonian blood behavior was taken into account. A similarity was also found between the calculated low shear stress regions and the regions that were later observed to clot.

Direct numerical simulation of transitional flow in a stenosed carotid bifurcation

The blood flow dynamics of a stenosed, subject-specific, carotid bifurcation were numerically simulated using the spectral element method. Pulsatile inlet conditions were based on in vivo color Doppler ultrasound measurements of blood velocity. The results demonstrated the transitional or weakly turbulent state of the blood flow, which featured rapid velocity and pressure fluctuations in the post-stenotic region of the internal carotid artery (ICA) during systole and laminar flow during diastole. High-frequency vortex shedding was greatest downstream of the stenosis during the deceleration phase of systole. Velocity fluctuations had a frequency within the audible range of 100-300Hz. Instantaneous wall shear stress (WSS) within the stenosis was relatively high during systole ( approximately 25-45Pa) compared to that in a healthy carotid. In addition, high spatial gradients of WSS were present due to flow separation on the inner wall. Oscillatory flow reversal and low pressure were observed distal to the stenosis in the ICA. This study predicts the complex flow field, the turbulence levels and the distribution of the biomechanical stresses present in vivo within a stenosed carotid artery.

Use of an ultrasound blood-mimicking fluid for Doppler investigations of turbulence in vitro

Turbulence is an important factor in the assessment of stenotic disease and a possible causative mechanism for thromboembolism. Previous Doppler studies of turbulence have typically used whole-blood preparations or suspensions of erythrocytes. Recently, a water-glycerol based blood-mimicking fluid (BMF) has been developed for use in Doppler ultrasound studies. This fluid has desirable ultrasound properties but it has not previously been described during in vitro investigations of turbulence intensity. We report on investigations of grid-generated and constrained-jet turbulence in an in vitro test system. The BMF was found to generate significant levels of turbulence during steady flow at physiological flow rates, producing turbulent patterns in the distal region that were consistent with previous studies. Turbulence intensity increased significantly with flow rate (p < 0.005) for both the constrained jet and the constrained grid. Based on our observations, we conclude that a water-glycerol based BMF provides a suitable working fluid during in vitro investigations of turbulence using Doppler ultrasound.

Wall shear stress gradient analysis within an idealized stenosis using non-Newtonian flow

OBJECTIVE

The endothelium is functionally regulated by the magnitude and spatiotemporal gradients of wall shear stress (WSS). Although flow separation and reversal occur beyond high-grade stenoses, little is known of the WSS pattern within clinically relevant mild to moderate stenoses.

METHODS

An axisymmetric geometry with 25, 50, and 75% stenosis criteria (quantified in accordance with the North American Symptomatic Carotid Endarterectomy Trial) was used to generate a high-resolution, hybrid, tetrahedral-hexahedral computational mesh with boundary-layer enrichment to improve near-wall shear stress gradient (WSSG) computation. Time-dependent computational fluid dynamic analysis was performed using a non-Newtonian Carreau-Yasuda model of blood to yield the shear-dependent viscosity.

RESULTS

Transition to secondary flow patterns was demonstrated in stenoses of 25, 50, and 75%. A focal region with near-wall flow reversal and retrograde WSS was identified within the stenosis itself and was found to migrate cyclically during the cardiac pulse. A zone of zero WSS and divergent WSSG that shifts in toward the throat with increasing stenotic severity was identified. Focal zones of high WSSG with converging and/or diverging direction were uncovered within the stenosis itself, as were expected changes in the distal poststenotic region. These zones of divergent WSSG shift over a substantial length of the stenosis during the course of the cardiac cycle.

CONCLUSION

Luminal WSS demonstrates dynamic direction reversal and high spatial gradients within the distal stenosis throat of even clinically moderate lesions. These findings shed light on the complex vessel wall hemodynamics within clinical stenoses and reveal a mechanical microenvironment that is conducive to perpetual endothelial functional dysregulation and stenosis progression.

Mining data from hemodynamic simulations via Bayesian emulation

Background:

Arterial geometry variability is inevitable both within and across individuals. To ensure realistic prediction of cardiovascular flows, there is a need for efficient numerical methods that can systematically account for geometric uncertainty.

Methods and results:

A statistical framework based on Bayesian Gaussian process modeling was proposed for mining data generated from computer simulations. The proposed approach was applied to analyze the influence of geometric parameters on hemodynamics in the human carotid artery bifurcation. A parametric model in conjunction with a design of computer experiments strategy was used for generating a set of observational data that contains the maximum wall shear stress values for a range of probable arterial geometries. The dataset was mined via a Bayesian Gaussian process emulator to estimate: (a) the influence of key parameters on the output via sensitivity analysis, (b) uncertainty in output as a function of uncertainty in input, and (c) which settings of the input parameters result in maximum and minimum values of the output. Finally, potential diagnostic indicators were proposed that can be used to aid the assessment of stroke risk for a given patient's geometry.

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.

The influences of stenosis on the downstream flow pattern in curved arteries

The influence of stenosis on the pulsatile blood flow pattern in curved arteries with stenosis at inner wall was investigated by computer simulations. Numerical calculations were performed with various values of physiological parameters to examine the effect of a stenosis on the hemodynamic characteristics such as secondary flow, flow separation, wall shear stress (WSS) and pressure drop. The results demonstrated that when the severity of a stenosis at the inner wall of a curved artery reaches a certain level, the flow pattern in the downstream of the artery shows a dramatic change compared to that of a curved artery with no stenosis. According to previous studies, a flow separation occurs at the inner wall of the bend in a curved artery. The present work reports an analysis of such a flow separation area at the inner wall of the post stenosis region in curved arteries with a stenosis. In addition, another area of flow separation with low and oscillating WSS and blood pressure at the outer wall in a downstream tube was also found and investigated. The observed characteristic change of the flow downstream may suggest a formation of a new plaque at the outer wall downstream.

Flow and myocardial interaction: an imaging perspective

Heart failure due to coronary artery disease has considerable morbidity and poor prognosis. An understanding of the underlying mechanics governing myocardial contraction is a prerequisite for interpreting and predicting changes induced by heart disease. Gross changes in contractile behaviour of the myocardium are readily detected with existing techniques. For more subtle changes during early stages of cardiac dysfunction, however, a sensitive method for measuring, as well as a precise criterion for quantifying, normal and impaired myocardial function is required. The purpose of this paper is to outline the role of imaging, particularly cardiovascular magnetic resonance (CMR), for investigating the fundamental relationships between cardiac morphology, function and flow. CMR is emerging as an important clinical tool owing to its safety, versatility and the high-quality images it produces that allow accurate and reproducible quantification of cardiac structure and function. We demonstrate how morphological and functional assessment of the heart can be achieved by CMR and illustrate how blood flow imaging can be used to study flow and structure interaction, particularly for elucidating the underlying haemodynamic significance of directional changes and asymmetries of the cardiac looping. Future outlook on combining imaging with engineering approaches in subject-specific biomechanical simulation is also provided.

Turbulence modeling in three-dimensional stenosed arterial bifurcations

Under normal healthy conditions, blood flow in the carotid artery bifurcation is laminar. However, in the presence of a stenosis, the flow can become turbulent at the higher Reynolds numbers during systole. There is growing consensus that the transitional k-omega model is the best suited Reynolds averaged turbulence model for such flows. Further confirmation of this opinion is presented here by a comparison with the RNG k-epsilon model for the flow through a straight, nonbifurcating tube. Unlike similar validation studies elsewhere, no assumptions are made about the inlet profile since the full length of the experimental tube is simulated. Additionally, variations in the inflow turbulence quantities are shown to have no noticeable affect on downstream turbulence intensity, turbulent viscosity, or velocity in the k-epsilon model, whereas the velocity profiles in the transitional k-omega model show some differences due to large variations in the downstream turbulence quantities. Following this validation study, the transitional k-omega model is applied in a three-dimensional parametrically defined computer model of the carotid artery bifurcation in which the sinus bulb is manipulated to produce mild, moderate, and severe stenosis. The parametric geometry definition facilitates a powerful means for investigating the effect of local shape variation while keeping the global shape fixed. While turbulence levels are generally low in all cases considered, the mild stenosis model produces higher levels of turbulent viscosity and this is linked to relatively high values of turbulent kinetic energy and low values of the specific dissipation rate. The severe stenosis model displays stronger recirculation in the flow field with higher values of vorticity, helicity, and negative wall shear stress. The mild and moderate stenosis configurations produce similar lower levels of vorticity and helicity.

Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses

Hemodynamics factors and biomechanical forces play key roles in atherogenesis, plaque development and final rupture. In this paper, we investigated the flow field and stress field for different degrees of stenoses under physiological conditions. Disease is modelled as axisymmetric cosine shape stenoses with varying diameter reductions of 30%, 50% and 70%, respectively. A simulation model which incorporates fluid-structure interaction, a turbulence model and realistic boundary conditions has been developed. The results show that wall motion is constrained at the throat by 60% for the 30% stenosis and 85% for the 50% stenosis; while for the 70% stenosis, wall motion at the throat is negligible through the whole cycle. Peak velocity at the throat varies from 1.47 m/s in the 30% stenosis to 3.2m/s in the 70% stenosis against a value of 0.78 m/s in healthy arteries. Peak wall shear stress values greater than 100 Pa were found for > or =50% stenoses, which in vivo could lead to endothelial stripping. Maximum circumferential stress was found at the shoulders of plaques. The results from this investigation suggest that severe stenoses inhibit wall motion, resulting in higher blood velocities and higher peak wall shear stress, and localization of hoop stress. These factors may contribute to further development and rupture of plaques.

Quantifying effects of plaque structure and material properties on stress distributions in human atherosclerotic plaques using 3D FSI models

BACKGROUND

Atherosclerotic plaques may rupture without warning and cause acute cardiovascular syndromes such as heart attack and stroke. Methods to assess plaque vulnerability noninvasively and predict possible plaque rupture are urgently needed.

METHOD

MRI-based three-dimensional unsteady models for human atherosclerotic plaques with multi-component plaque structure and fluid-structure interactions are introduced to perform mechanical analysis for human atherosclerotic plaques.

RESULTS

Stress variations on critical sites such as a thin cap in the plaque can be 300% higher than that at other normal sites. Large calcification block considerably changes stress/strain distributions. Stiffness variations of plaque components (50% reduction or 100% increase) may affect maximal stress values by 20-50%. Plaque cap erosion causes almost no change on maximal stress level at the cap, but leads to 50% increase in maximal strain value.

CONCLUSIONS

Effects caused by atherosclerotic plaque structure, cap thickness and erosion, material properties, and pulsating pressure conditions on stress/strain distributions in the plaque are quantified by extensive computational case studies and parameter evaluations. Computational mechanical analysis has good potential to improve accuracy of plaque vulnerability assessment.

Flow imaging and computing: large artery hemodynamics

The objective of our session at the International Bio-Fluid Mechanics Symposium and Workshop was at the International Bio-Fluid Mechanics Symposium and Workshop to review the state-of-the-art in, and identify future directions for, imaging and computational modeling of blood flow in the large arteries and the microcirculation. Naturally, talks in other sessions of the workshop overlapped this broad topic, and so here we summarize progress within the last decade in terms of the technical development and application of flow imaging and computing, rather than the knowledge derived from specific studies. We then briefly discuss ways in these tools may be extended, and their application broadened, in the next decade. Furthermore, owing to the conceptual division between the hemodynamics of large arteries, and those within the microcirculation, we review these regimes separately: The former here by Steinman and Taylor; and the latter in a separate paper by Cristini.

Numerical simulation of magnetic resonance angiographies of an anatomically realistic stenotic carotid bifurcation

Magnetic Resonance Angiography (MRA) has become a routine imaging modality for the clinical evaluation of obstructive vascular disease. However, complex circulatory flow patterns, which redistribute the Magnetic Resonance (MR) signal in a complicated way, may generate flow artifacts and impair image quality. Numerical simulation of MRAs is a useful tool to study the mechanisms of artifactual signal production. The present study proposes a new approach to perform such simulations, applicable to complex anatomically realistic vascular geometries. Both the Navier-Stokes and the Bloch equations are solved on the same mesh to obtain the distribution of modulus and phase of the magnetization. The simulated angiography is subsequently constructed by a simple geometric procedure mapping the physical plane into the MRA image plane. Steady bidimensional numerical simulations of MRAs of an anatomically realistic severely stenotic carotid artery bifurcation are presented, for both time-of-flight and contrast-enhanced imaging modalities. These simulations are validated by qualitative comparison with flow phantom experiments performed under comparable conditions.

Two-equation turbulence modeling of pulsatile flow in a stenosed tube

The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.