Accuracy and reproducibility of CFD predicted wall shear stress using 3D ultrasound images

Abnormal flow pattern of low wall shear stress and high oscillatory shear index in spontaneous vertebral artery dissection with vertebral artery hypoplasia

Introduction

Spontaneous vertebral artery dissection (sVAD) might tend to develop in vertebral artery hypoplasia (VAH) with hemodynamic dysfunction and it is crucial to assess hemodynamics in sVAD with VAH to investigate this hypothesis. This retrospective study aimed to quantify hemodynamic parameters in patients with sVAD with VAH.

Methods

Patients who had suffered ischemic stroke due to an sVAD of VAH were enrolled in this retrospective study. The geometries of 14 patients (28 vessels) were reconstructed using Mimics and Geomagic Studio software from CT angiography (CTA). ANSYS ICEM and ANSYS FLUENT were utilized for mesh generation, set boundary conditions, solve governing equations, and perform numerical simulations. Slices were obtained at the upstream area, dissection or midstream area and downstream area of each VA. The blood flow patterns were visualized through instantaneous streamline and pressure at peak systole and late diastole. The hemodynamic parameters included pressure, velocity, time-averaged blood flow, time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), endothelial cell action potential (ECAP), relative residence time (RRT) and time-averaged nitric oxide production rate (TAR_NO).

Results

Significant focal increased velocity was present in the dissection area of steno-occlusive sVAD with VAH compared to other nondissected areas (0.910 m/s vs. 0.449 vs. 0.566, p < 0.001), while focal slow flow velocity was observed in the dissection area of aneurysmal dilatative sVAD with VAH according to velocity streamlines. Steno-occlusive sVAD with VAH arteries had a lower time-averaged blood flow (0.499 cm³/s vs. 2.268, p < 0.001), lower TAWSS (1.115 Pa vs. 2.437, p = 0.001), higher OSI (0.248 vs. 0.173, p = 0.006), higher ECAP (0.328 Pa^-1 vs. 0.094, p = 0.002), higher RRT (3.519 Pa^-1 vs. 1.044, p = 0.001) and deceased TAR_NO (104.014 nM/s vs. 158.195, p < 0.001) than the contralateral VAs.

Conclusion

Steno-occlusive sVAD with VAH patients had abnormal blood flow patterns of focal increased velocity, low time-averaged blood flow, low TAWSS, high OSI, high ECAP, high RRT and decreased TAR_NO. These results provide a good basis for further investigation of sVAD hemodynamics and support the applicability of the CFD method in testing the hemodynamic hypothesis of sVAD. More detailed hemodynamic conditions with different stages of sVAD are warranted in the future.

Computational Hemodynamic Modeling of Arterial Aneurysms: A Mini-Review

Arterial aneurysms are pathological dilations of blood vessels, which can be of clinical concern due to thrombosis, dissection, or rupture. Aneurysms can form throughout the arterial system, including intracranial, thoracic, abdominal, visceral, peripheral, or coronary arteries. Currently, aneurysm diameter and expansion rates are the most commonly used metrics to assess rupture risk. Surgical or endovascular interventions are clinical treatment options, but are invasive and associated with risk for the patient. For aneurysms in locations where thrombosis is the primary concern, diameter is also used to determine the level of therapeutic anticoagulation, a treatment that increases the possibility of internal bleeding. Since simple diameter is often insufficient to reliably determine rupture and thrombosis risk, computational hemodynamic simulations are being developed to help assess when an intervention is warranted. Created from subject-specific data, computational models have the potential to be used to predict growth, dissection, rupture, and thrombus-formation risk based on hemodynamic parameters, including wall shear stress, oscillatory shear index, residence time, and anomalous blood flow patterns. Generally, endothelial damage and flow stagnation within aneurysms can lead to coagulation, inflammation, and the release of proteases, which alter extracellular matrix composition, increasing risk of rupture. In this review, we highlight recent work that investigates aneurysm geometry, model parameter assumptions, and other specific considerations that influence computational aneurysm simulations. By highlighting modeling validation and verification approaches, we hope to inspire future computational efforts aimed at improving our understanding of aneurysm pathology and treatment risk stratification.

3-D Flow Reconstruction Using Divergence-Free Interpolation of Multiple 2-D Contrast-Enhanced Ultrasound Particle Imaging Velocimetry Measurements

Quantification of 3-D intravascular flow is valuable for studying arterial wall diseases but currently there is a lack of effective clinical tools for this purpose. Divergence-free interpolation (DFI) using radial basis function (RBF) is an emerging approach for full-field flow reconstruction using experimental sparse flow field samples. Previous DFI reconstructs full-field flow from scattered 3-D velocity input obtained using phase-contrast magnetic resonance imaging with low temporal resolution. In this study, a new DFI algorithm is proposed to reconstruct full-field flow from scattered 2-D in-plane velocity vectors obtained using ultrafast contrast-enhanced ultrasound (>1000 fps) and particle imaging velocimetry. The full 3-D flow field is represented by a sum of weighted divergence-free RBFs in space. Because the acquired velocity vectors are only in 2-D and hence the problem is ill-conditioned, a regularized solution of the RBF weighting is achieved through singular value decomposition (SVD) and the L-curve method. The effectiveness of the algorithm is determined via numerical experiments for Poiseuille flow and helical flow with added noise, and it is found that an accuracy as high as 95.6% can be achieved for Poiseuille flow (with 5% input noise). Experimental feasibility is also determined by reconstructing full-field 3-D flow from experimental 2-D ultrasound image velocimetry measurements in a carotid bifurcation phantom. The method is typically faster for a range of problems compared with computational fluid dynamics, and has been found to be effective for the three flow cases.

Computational Fluid Dynamics Modeling of the Human Pulmonary Arteries with Experimental Validation

Pulmonary hypertension (PH) is a chronic progressive disease characterized by elevated pulmonary arterial pressure, caused by an increase in pulmonary arterial impedance. Computational fluid dynamics (CFD) can be used to identify metrics representative of the stage of PH disease. However, experimental validation of CFD models is often not pursued due to the geometric complexity of the model or uncertainties in the reproduction of the required flow conditions. The goal of this work is to validate experimentally a CFD model of a pulmonary artery phantom using a particle image velocimetry (PIV) technique. Rapid prototyping was used for the construction of the patient-specific pulmonary geometry, derived from chest computed tomography angiography images. CFD simulations were performed with the pulmonary model with a Reynolds number matching those of the experiments. Flow rates, the velocity field, and shear stress distributions obtained with the CFD simulations were compared to their counterparts from the PIV flow visualization experiments. Computationally predicted flow rates were within 1% of the experimental measurements for three of the four branches of the CFD model. The mean velocities in four transversal planes of study were within 5.9 to 13.1% of the experimental mean velocities. Shear stresses were qualitatively similar between the two methods with some discrepancies in the regions of high velocity gradients. The fluid flow differences between the CFD model and the PIV phantom are attributed to experimental inaccuracies and the relative compliance of the phantom. This comparative analysis yielded valuable information on the accuracy of CFD predicted hemodynamics in pulmonary circulation models.

Inter-operator Reliability of Magnetic Resonance Image-Based Computational Fluid Dynamics Prediction of Cerebrospinal Fluid Motion in the Cervical Spine

For the first time, inter-operator dependence of MRI based computational fluid dynamics (CFD) modeling of cerebrospinal fluid (CSF) in the cervical spinal subarachnoid space (SSS) is evaluated. In vivo MRI flow measurements and anatomy MRI images were obtained at the cervico-medullary junction of a healthy subject and a Chiari I malformation patient. 3D anatomies of the SSS were reconstructed by manual segmentation by four independent operators for both cases. CFD results were compared at nine axial locations along the SSS in terms of hydrodynamic and geometric parameters. Intraclass correlation (ICC) assessed the inter-operator agreement for each parameter over the axial locations and coefficient of variance (CV) compared the percentage of variance for each parameter between the operators. Greater operator dependence was found for the patient (0.19 < ICC < 0.99) near the craniovertebral junction compared to the healthy subject (ICC > 0.78). For the healthy subject, hydraulic diameter and Womersley number had the least variance (CV = ~2%). For the patient, peak diastolic velocity and Reynolds number had the smallest variance (CV = ~3%). These results show a high degree of inter-operator reliability for MRI-based CFD simulations of CSF flow in the cervical spine for healthy subjects and a lower degree of reliability for patients with Type I Chiari malformation.

Accuracy of computational cerebral aneurysm hemodynamics using patient-specific endovascular measurements

Computational hemodynamic simulations of cerebral aneurysms have traditionally relied on stereotypical boundary conditions (such as blood flow velocity and blood pressure) derived from published values as patient-specific measurements are unavailable or difficult to collect. However, controversy persists over the necessity of incorporating such patient-specific conditions into computational analyses. We perform simulations using both endovascularly-derived patient-specific and typical literature-derived inflow and outflow boundary conditions. Detailed three-dimensional anatomical models of the cerebral vasculature are developed from rotational angiography data, and blood flow velocity and pressure are measured in situ by a dual-sensor pressure and velocity endovascular guidewire at multiple peri-aneurysmal locations in 10 unruptured cerebral aneurysms. These measurements are used to define inflow and outflow boundary conditions for computational hemodynamic models of the aneurysms. The additional in situ measurements which are not prescribed in the simulation are then used to assess the accuracy of the simulated flow velocity and pressure drop. Simulated velocities using patient-specific boundary conditions show good agreement with the guidewire measurements at measurement locations inside the domain, with no bias in the agreement and a random scatter of ≈25%. Simulated velocities using the simplified, literature-derived values show a systematic bias and over-predicted velocity by ≈30% with a random scatter of ≈40%. Computational hemodynamics using endovascularly measured patient-specific boundary conditions have the potential to improve treatment predictions as they provide more accurate and precise results of the aneurysmal hemodynamics than those based on commonly accepted reference values for boundary conditions.

Simulation of left ventricle flow dynamics with dilated cardiomyopathy during the filling phase

Dilated cardiomyopathy (DCM) is a common cardiac disease which leads to the deterioration in cardiac performance. A computational fluid dynamics (CFD) approach can be used to enhance our understanding of the disease, by providing us with a detailed map of the intraventricular flow and pressure distributions. In the present work, effect of ventricular size on the intraventricular flow dynamics and intraventricular pressure gradients (IVPGs) was studied using two different implementation methods, i.e. the geometry-prescribed and the fluid structure interaction (FSI) methods. Results showed that vortex strength and IVPGs are significantly reduced in a dilated heart, leading to an increased risk of thrombus formation and impaired ventricular filling. We suggest FSI method as the ultimate method in studying ventricular dysfunction as it provides additional cardiac disease prognostic factors and more realistic model implementation.

Review on CFD simulation in heart with dilated cardiomyopathy and myocardial infarction

The heart is a sophisticated functional organ that plays a crucial role in the blood circulatory system. Hemodynamics within the heart chamber can be indicative of exert cardiac health. Due to the limitations of current cardiac imaging modalities, computational fluid dynamics (CFD) have been widely used for the purposes of cardiac function assessment and heart disease diagnosis, as they provide detailed insights into the cardiac flow field. An understanding of ventricular hemodynamics and pathological severities can be gained through studies that employ the CFD method. In this research the hemodynamics of two common myocardial diseases, dilated cardiomyopathy (DCM) and myocardial infarction (MI) were investigated, during both the filling phase and the whole cardiac cycle, through a prescribed geometry and fluid structure interaction (FSI) approach. The results of the research indicated that early stage disease identification and the improvement of cardiac assisting devices and therapeutic procedures can be facilitated through the use of the CFD method.

Flow characteristics in a canine aneurysm model: a comparison of 4D accelerated phase-contrast MR measurements and computational fluid dynamics simulations

PURPOSE

Our purpose was to compare quantitatively velocity fields in and around experimental canine aneurysms as measured using an accelerated 4D PC-MR angiography (MRA) method and calculated based on animal-specific CFD simulations.

METHODS

Two animals with a surgically created bifurcation aneurysm were imaged using an accelerated 4D PC-MRA method. Meshes were created based on the geometries obtained from the PC-MRA and simulations using "subject-specific" pulsatile velocity waveforms and geometries were then solved using a commercial CFD solver. Qualitative visual assessments and quantitative comparisons of the time-resolved velocity fields obtained from the PC-MRA measurements and the CFD simulations were performed using a defined similarity metric combining both angular and magnitude differences of vector fields.

RESULTS

PC-MRA and image-based CFD not only yielded visually consistent representations of 3D streamlines in and around both aneurysms, but also showed good agreement with regard to the spatial velocity distributions. The estimated similarity between time-resolved velocity fields from both techniques was reasonably high (mean value >0.60; one being the highest and zero being the lowest). Relative differences in inflow and outflow zones among selected planes were also reasonable (on the order of 10%-20%). The correlation between CFD-calculated and PC-MRA-measured time-averaged wall shear stresses was low (0.22 and 0.31, p < 0.001).

CONCLUSIONS

In two experimental canine aneurysms, PC-MRA and image-based CFD showed favorable agreement in intra-aneurismal velocity fields. Combining these two complementary techniques likely will further improve the ability to characterize and interpret the complex flow that occurs in human intracranial aneurysms.

Introduction to the biomechanics of carotid plaque pathogenesis and rupture: review of the clinical evidence

The management of patients with asymptomatic carotid disease is currently under debate and new methods are warranted for better risk stratification. The role of the biomechanical properties of the atherosclerotic arterial wall together with the effect of different stress types in plaque destabilisation has only been recently investigated. PubMed and Scopus databases were reviewed. There is preliminary clinical evidence demonstrating that the analysis of the combined effect of the various types of biomechanical stress acting on the carotid plaque may help us to identify the vulnerable plaque. At present, MRI and two-dimensional ultrasound are combined with fluid-structure interaction techniques to produce maps of the stress variation within the carotid wall, with increased cost and complexity. Stress wall analysis can be a useful tool for carotid plaque evaluation; however, further research and a multidisciplinary approach are deemed as necessary for further development in this direction.

Acquisition of 3-D arterial geometries and integration with computational fluid dynamics

A system for acquisition of 3-D arterial ultrasound geometries and integration with computational fluid dynamics (CFD) is described. The 3-D ultrasound is based on freehand B-mode imaging with positional information obtained using an optical tracking system. A processing chain was established, allowing acquisition of cardiac-gated 3-D data and segmentation of arterial geometries using a manual method and a semi-automated method, 3D meshing and CFD. The use of CFD allowed visualization of flow streamlines, 2-D velocity contours and 3-D wall shear stress. Three-dimensional positional accuracy was 0.17-1.8mm, precision was 0.06-0.47mm and volume accuracy was 4.4-15%. Patients with disease and volunteers were scanned, with data collection from one or more of the carotid bifurcation, femoral bifurcation and abdominal aorta. An initial comparison between a manual segmentation method and a semi-automated method suggested some advantages to the semi-automated method, including reduced operator time and the production of smooth surfaces suitable for CFD, but at the expense of over-smoothing in the diseased region. There were considerable difficulties with artefacts and poor image quality, resulting in 3-D geometry data that was unsuitable for CFD. These artefacts were exacerbated in disease, which may mean that future effort, in the integration of 3-D arterial geometry and CFD for clinical use, may best be served using alternative 3-D imaging modalities such as magnetic resonance imaging and computed tomography.

Haemodynamics and blood flow measured using ultrasound imaging

Visualization of, and measurements related to, haemodynamic phenomena in arteries may be made using ultrasound systems. Most ultrasound technology relies on simple measurements of blood velocity taken from a single site, such as the peak systolic velocity for assessment of the degree of lumen reduction caused by an arterial stenosis. Real-time two-dimensional (2D) flow field visualization is possible using several methods, such as colour flow, blood flow imaging, and echo particle image velocimetry; these have applications in the examination of the flow field in diseased arteries and in heart chambers. Three-dimensional (3D) and four-dimensional ultrasound systems have been described. These have been used to provide 2D velocity profile data for the estimation of volumetric flow. However, they are limited for haemodynamic evaluation in that they provide only one component of the velocity. The provision of all seven components (three space, three velocity, and one time) is possible using image-guided modelling, in which 3D ultrasound is combined with computational fluid dynamics. This method also allows estimation of turbulence data and of relevant quantities such as the wall shear stress.

3D blood flow characteristics in the carotid artery bifurcation assessed by flow-sensitive 4D MRI at 3T

To determine three-dimensional (3D) blood flow patterns in the carotid bifurcation, 10 healthy volunteers and nine patients with internal carotid artery (ICA) stenosis > or =50% were examined by flow-sensitive 4D MRI at 3T. Absolute and mean blood velocities, pulsatility index (PI), and resistance index (RI) were measured in the common carotid arteries (CCAs) by duplex sonography (DS) and compared with flow-sensitive 4D MRI. Furthermore, 3D MRI blood flow patterns in the carotid bifurcation of volunteers and patients before and after recanalization were graded by two independent readers. Blood flow velocities measured by MRI were 31-39% lower than in DS. However, PI and RI differed by only 13-16%. Rating of 3D flow characteristics in the ICA revealed consistent patterns for filling and helical flow in volunteers. In patients with ICA stenosis, 3D blood flow visualization was successfully employed to detect markedly altered filling and helical flow patterns (forward-moving spiral flow) in the ICA bulb and to evaluate the effect of revascularization, which restored filling and helical flow. Our results demonstrate the feasibility of flow-sensitive 4D MRI for the quantification and 3D visualization of physiological and pathological flow patterns in the carotid artery bifurcation.

Low wall shear stress predicts subsequent development of wall hypertrophy in lower limb bypass grafts

Background

Venous grafts commonly develop myointimal hyperplasia, which can lead to stenoses and, ultimately, with expression of adhesion molecules, lumenal occlusion. The aim of the present study was to investigate whether wall shear stress measured post-operatively would predict subsequent myointimal hypertrophy in lower limb venous bypass grafts.

Methods

Magnetic resonance imaging and ultrasound were performed in a cohort of patients following lower limb venous bypass graft surgery for peripheral arterial disease at baseline (1-2 weeks) and at follow-up (9-12 months). Wall shear stress was determined at baseline using computational fluid dynamics techniques and intima-media thickness along the length of the graft was measured by ultrasound at baseline and follow up.

Results

Complete follow-up was possible in eight patients, in whom low wall shear stress at baseline predicted high intima-media thickness. The relationship between wall shear stress (WSS) and intima-media thickness (IMT) was curvilinear with IMT increasing sharply at lower levels of WSS (IMT >1.0 mm at <0.3 Pa).

Conclusions

Low wall shear stress is associated with subsequent increase in myointimal thickness in lower limb venous bypass grafts. This is believed to be the first prospective study in humans to demonstrate the relationship between low wall shear stress and myointimal thickening and indicates a likely causative role for low wall shear stress in the development of myointimal hyperplasia.

Computational patient-specific models based on 3-D ultrasound data to quantify uterine arterial flow during pregnancy

Information on uterine blood flow rate during pregnancy would widely improve our knowledge on feto-placental patho-physiology. Ultrasonographic flow rate evaluation requires the knowledge of the spatial velocity profiles throughout the investigated vessel; these data may be obtained from hemodynamic simulations with accurate computational models. Recently, computational models of superficial vessels have been created using 3-D ultrasound data; unfortunately, common reconstruction methods are unsuitable for the uterine arteries due to the low quality achievable of imaged deep vessels. In this paper a simplified spline-based technique was applied to create computational models for patient-specific simulations of uterine arterial heamodynamics. Moreover, a novel method to quantify the uterine flow rates was developed based on echo-Doppler measurements and computational data. Preliminary results obtained for four patients indicated a quite narrow range for the blood flow rate through the main uterine artery with large variability in the flow split between corporal and cervical branches. Furthermore, parabolic-like velocity profiles were obtained in the branching region of the different patients, suggesting a clinical use of averaged, not patient-specific, spatial velocity distribution coefficients for the blood flow rate calculation. The developed reconstruction method based on 3-D ultrasound imaging is efficient for creating realistic custom models of the uterine arteries. The results of the fluid dynamic simulations allowed us to quantify the uterine arterial flow and its repartition in normal pregnancies.

Simulation and validation of arterial ultrasound imaging and blood flow

We reviewed the simulation and validation of arterial ultrasound imaging and blood flow assessment. The physical process of ultrasound imaging and measurement is complex, especially in disease. Simulation of physiological flow in a phantom with tissue equivalence of soft tissue, vessel wall and blood is now achievable. Outstanding issues are concerned with production of anatomical models, simulation of arterial disease, refinement of blood mimics to account for non-Newtonian behavior and validation of velocity measurements against an independent technique such as particle image velocimetry. String and belt phantoms offer simplicity of design, especially for evaluation of velocity estimators, and have a role as portable test objects. Electronic injection and vibrating test objects produce nonphysiologic Doppler signals, and their role is limited. Computational models of the ultrasound imaging and measurement process offer considerable flexibility in their ability to alter multiple parameters of both the propagation medium and ultrasound instrument. For these models, outstanding issues are concerned with the inclusion of different tissue types, multilayer arteries, inhomogeneous tissues and diseased tissues.

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.

Analysis of complex flow and the relationship between blood pressure, wall shear stress, and intima-media thickness in the human carotid artery

BACKGROUND

Previous clinical studies have observed relationships between increased intima-media thickness (IMT) in the carotid artery, elevated blood pressure, and low wall shear stress (WSS) calculated from the Poiseuille equation. This study used numerical methods to more accurately determine WSS in the carotid artery and to investigate possible determinants of increased IMT.

METHODS

IMT [common carotid artery (CCA) and bulb], CCA flow velocity, brachial systolic (SBP) and diastolic blood pressure (DBP), and carotid systolic pressure (cSBP) were measured in 14 healthy subjects (aged 44 +/- 16 yr). Flow patterns in the carotid bifurcation were determined by computational fluid dynamics (CFD) based on three-dimensional ultrasound geometry. Instantaneous and time-averaged wall shear stress (WSS(av)), oscillatory shear index (OSI), and wall shear stress angle gradients (WSSAG) were calculated.

RESULTS

IMT was positively related to SBP, DBP, cSBP, and WSSAG and inversely related to WSS(av) in the CCA. In the bulb, IMT was positively related to SBP and cSBP but was not significantly related to WSS(av) or WSSAG. IMT was unrelated to OSI in both the CCA and the bulb.

CONCLUSION

Increased carotid artery IMT in healthy subjects with no evidence of focal plaques is primarily a response to elevated pressure.

Anatomical flow phantoms of the nonplanar carotid bifurcation, part I: computer-aided design and fabrication

Doppler ultrasound is widely used in the diagnosis and monitoring of arterial disease. Current clinical measurement systems make use of continuous and pulsed ultrasound to measure blood flow velocity; however, the uncertainty associated with these measurements is great, which has serious implications for the screening of patients for treatment. Because local blood flow dynamics depend to a great extent on the geometry of the affected vessels, there is a need to develop anatomically accurate arterial flow phantoms with which to assess the accuracy of Doppler blood flow measurements made in diseased vessels. In this paper, we describe the computer-aided design and manufacturing (CAD-CAM) techniques that we used to fabricate anatomical flow phantoms based on images acquired by time-of-flight magnetic resonance imaging (TOF-MRI). Three-dimensional CAD models of the carotid bifurcation were generated from data acquired from sequential MRI slice scans, from which solid master patterns were made by means of stereolithography. Thereafter, an investment casting procedure was used to fabricate identical flow phantoms for use in parallel experiments involving both laser and Doppler ultrasound measurement techniques.

Validation of CFD simulations of cerebral aneurysms with implication of geometric variations

BACKGROUND

Computational fluid dynamics (CFD) simulations using medical-image-based anatomical vascular geometry are now gaining clinical relevance. This study aimed at validating the CFD methodology for studying cerebral aneurysms by using particle image velocimetry (PIV) measurements, with a focus on the effects of small geometric variations in aneurysm models on the flow dynamics obtained with CFD.

METHOD OF APPROACH

An experimental phantom was fabricated out of silicone elastomer to best mimic a spherical aneurysm model. PIV measurements were obtained from the phantom and compared with the CFD results from an ideal spherical aneurysm model (S1). These measurements were also compared with CFD results, based on the geometry reconstructed from three-dimensional images of the experimental phantom. We further performed CFD analysis on two geometric variations, S2 and S3, of the phantom to investigate the effects of small geometric variations on the aneurysmal flow field. Results. We found poor agreement between the CFD results from the ideal spherical aneurysm model and the PIV measurements from the phantom, including inconsistent secondary flow patterns. The CFD results based on the actual phantom geometry, however, matched well with the PIV measurements. CFD of models S2 and S3 produced qualitatively similar flow fields to that of the phantom but quantitatively significant changes in key hemodynamic parameters such as vorticity, positive circulation, and wall shear stress.

CONCLUSION

CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. Small geometric variations on the aneurysm model can significantly alter the flow-field and key hemodynamic parameters. Since medical images are subjected to geometric uncertainties, image-based patient-specific CFD results must be carefully scrutinized before providing clinical feedback.

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 modelling of Newtonian and non-Newtonian representation of blood in a distal end-to-side vascular bypass graft anastomosis

The proliferation of disease at the bed of the distal junction of an end-to-side anastomosis is attributed to abnormal wall shear stress (WSS) distribution. WSS is proportional to the viscosity and shear rate of the flowing fluid. Blood is characterised by a shear rate dependent viscosity. Various constitutive equations have been developed to represent the shear rate dependence of blood viscosity: Newtonian, Carreau, Power law, Carreau-Yasuda, Bi-exponential, Cross, Modified Cross, Herschel-Bulkley, etc. In the femoral artery, the instantaneous shear rate varies from 1-1200 s(-1) over a cardiac cycle. An idealised, 45 degrees rigid, 6mm diameter, end-to-side femoral anastomosis was modelled on a Computational Fluid Dynamic software package Fluent 6.0. A steady flow of 0.15 and 0.01 m/s was applied to the inlet to model high and low wall shear rate environments respectively. Blood was modelled using the various constitutive equations. The resulting WSS distribution on the bed of the artery was then obtained. At high shear rates there was no significant difference between WSS distribution. At low shear rates there were qualitative differences of up to 300%. In conclusion, the choice of blood constitutive equation has to be based on the particular situation under study e.g. flow rate, steady/unsteady flow, and geometry.

Various issues relating to computational fluid dynamics simulations of carotid bifurcation flow based on models reconstructed from three-dimensional ultrasound images

Computational fluid dynamics (CFD) flow simulation techniques have the potential to enhance understanding of how haemodynamic factors are involved in atherosclerosis. Recently, three-dimensional ultrasound has emerged as an alternative to other three-dimensional imaging techniques, such as magnetic resonance angiography (MRA). The method can be used to generate accurate vascular geometry suitable for CFD simulations and can be coupled with Doppler ultrasound to provide physiologically realistic flow boundary conditions. However, there are various ways to utilize the flow data acquired, possibly leading to different results regarding both flow and wall shear stress patterns. A disadvantage of three-dimensional ultrasound for imaging the carotid bifurcation has been established as being the scanning limitation of the jawbone position. This may make artificial extensions of the internal and/or external carotid arteries necessary, which in turn may influence the predicted flow patterns. Flow simulations were carried out for three outflow calculation schemes as well as four geometries with different extensions to the carotid daughter vessels. It was found that variation of flow patterns was more strongly influenced by the outflow conditions than by the extensions of the daughter vessels. Consequently, it is recommended that for future CFD simulations of carotid flow using three-dimensional ultrasound data, the outflow boundary conditions should rely on the most accurate measurement available, and flow data recorded in the common and internal carotid are considered more reliable than data from the external carotid. Even though the extended lengths of the daughter vessels have insignificant effects on the predicted haemodynamic parameters, it would be a safer option to extend the internal carotid by approximately three times the diameter of the common carotid artery.

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

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

Operator dependence of 3-D ultrasound-based computational fluid dynamics for the carotid bifurcation

The association between vascular wall shear stress (WSS) and the local development of atherosclerotic plaque makes estimation of in vivo WSS of considerable interest. Three-dimensional ultrasound (3DUS) combined with computational fluid dynamics (CFD) provides a potentially valuable tool for acquiring subject-specific WSS, but the interoperator and intraoperator variability associated with WSS calculations using this method is not known. Here, the accuracy, reproducibility and operator dependence of 3DUS-based computational fluid dynamics were examined through a phantom and in vivo studies. A carotid phantom was scanned and reconstructed by two operators. In the in vivo study, four operators scanned a healthy subject a total of 11 times, and their scan data were processed by three individuals. The study showed that with some basic training, operators could acquire accurate carotid geometry for flow reconstructions. The variability of measured cross-sectional area and predicted shear stress was 8.17% and 0.193 N/m2 respectively for the in vivo study. It was shown that the variability of the examined parameters was more dependent on the scan operators than the image processing operator. The range of variability of geometrical and flow parameters reported here can be used as a reference for future in vivo studies using the 3DUS-based CFD approach.

Physics-Driven CFD Modeling of Complex Anatomical Cardiovascular Flows?A TCPC Case Study

Recent developments in medical image acquisition combined with the latest advancements in numerical methods for solving the Navier-Stokes equations have created unprecedented opportunities for developing simple and reliable computational fluid dynamics (CFD) tools for meeting patient-specific surgical planning objectives. However, for CFD to reach its full potential and gain the trust and confidence of medical practitioners, physics-driven numerical modeling is required. This study reports on the experience gained from an ongoing integrated CFD modeling effort aimed at developing an advanced numerical simulation tool capable of accurately predicting flow characteristics in an anatomically correct total cavopulmonary connection (TCPC). An anatomical intra-atrial TCPC model is reconstructed from a stack of magnetic resonance (MR) images acquired in vivo. An exact replica of the computational geometry was built using transparent rapid prototyping. Following the same approach as in earlier studies on idealized models, flow structures, pressure drops, and energy losses were assessed both numerically and experimentally, then compared. Numerical studies were performed with both a first-order accurate commercial software and a recently developed, second-order accurate, in-house flow solver. The commercial CFD model could, with reasonable accuracy, capture global flow quantities of interest such as control volume power losses and pressure drops and time-averaged flow patterns. However, for steady inflow conditions, both flow visualization experiments and particle image velocimetry (PIV) measurements revealed unsteady, complex, and highly 3D flow structures, which could not be captured by this numerical model with the available computational resources and additional modeling efforts that are described. Preliminary time-accurate computations with the in-house flow solver were shown to capture for the first time these complex flow features and yielded solutions in good agreement with the experimental observations. Flow fields obtained were similar for the studied total cardiac output range (1-3 1/min); however hydrodynamic power loss increased dramatically with increasing cardiac output, suggesting significant energy demand at exercise conditions. The simulation of cardiovascular flows poses a formidable challenge to even the most advanced CFD tools currently available. A successful prediction requires a two-pronged, physics-based approach, which integrates high-resolution CFD tools and high-resolution laboratory measurements.

Ultrasound image-based computer model of a common carotid artery with a plaque

Ultrasound scans were acquired from a common carotid artery in a patient with an early atherosclerotic plaque forming a mild asymmetrical stenosis. The 3D vascular geometry of the diseased arterial segment was reconstructed from a series of 2D cross-sectional images, and computational meshes for the flow and wall domains were developed. Numerical flow simulations incorporating coupled fluid-solid interaction were implemented using flow and pressure waveforms measured in vivo. The effects of wall distensibility were investigated by comparing the predictions obtained with different wall compliance, one with 'natural' compliance and another with a stiffer wall. Limited flow separation was predicted in the post-stenotic zone. The non-uniform thickness of the diseased wall restricted the wall motion locally and re-distributed the stress, giving raised concentrations at the plaque shoulders.

Image-based carotid flow reconstruction: a comparison between MRI and ultrasound

Atherosclerosis is a major cause of morbidity and mortality. Its apparent link with wall shear stress (WSS) has led to considerable interest in the in vivo estimation of WSS. Determining WSS by combining medical images with computational fluid dynamics (CFD) simulations can be performed both with magnetic resonance imaging (MRI) and three-dimensional ultrasound (3DUS). This study compares predicted 3D flow patterns based on black blood MRI and 3DUS. Velocity fields in the carotid arteries of nine subjects have been reconstructed, and the haemodynamic wall parameters WSS, oscillatory shear index (OSI), WSS gradients (WSSG) and angle gradients (WSSAG) were compared between the two imaging techniques. There was a good qualitative agreement between results derived from MRI and 3DUS (average correlation strength above 0.60). The root mean square error between haemodynamic wall parameters was comparable to the range of the expected variability of each imaging technique (WSS: 0.411 N m(-2); OSI: 0.048; temporal WSSG: 150 N s(-1) m(-2); spatial WSSG: 2.29 N m(-3); WSSAG: 87.6 rad m(-1)). In conclusion, MRI and 3DUS are capable of providing haemodynamic parameters when combined with CFD, and the predictions are in most cases qualitatively and quantitatively similar. The relatively high cost of MRI and continuing improvement in ultrasound favour US to MRI for future haemodynamic studies of superficial arteries.

Influence of head position on carotid hemodynamics in young adults

Studies in adults have shown marked changes in geometry and relative positions of the carotid arteries when rotating the head. The aim of this study was to quantify the change in geometry and analyze its effect on carotid hemodynamics as a result of head rotation. The right carotid arteries of nine young adult subjects were investigated in supine position with straight and left turned head positions, respectively. The three-dimensional (3D) carotid geometry was reconstructed by using 3D ultrasound (3D US), and the carotid hemodynamics were calculated by combining 3D US with computational fluid dynamics. It was observed that cross-sectional areas and shapes did not change markedly with head rotation, but carotid vessel center lines altered with planarification of the common carotid artery as a main feature ( P < 0.05). Measured common carotid flow rates changed significantly at the individual level when the head was turned, but on the average, the change in mean common carotid flow rate was relatively small (0.37 ± 1.11 ml/s). The effect of the altered center lines and flow rates on the atherogenic nature of the carotid bifurcation was evaluated by using calculated hemodynamic wall parameters, such as wall shear stress (WSS) and oscillatory shear index (OSI). It was found that WSS and OSI patterns changed significantly with head rotation, but the variations were very subject dependent and could not have been predicted without assessing the altered geometry and flow of the carotid bifurcation for individual cases. This study suggests that there is a need for standardization of the choice of head position in the 3D US scan protocol, and that carotid stents and emboli diverters should be studied in different head positions.

Reconstruction and quantification of the carotid artery bifurcation from 3-D ultrasound images

Three-dimensional (3-D) ultrasound is a relatively new technique, which is well suited to imaging superficial blood vessels, and potentially provides a useful, noninvasive method for generating anatomically realistic 3-D models of the peripheral vasculature. Such models are essential for accurate simulation of blood flow using computational fluid dynamics (CFD), but may also be used to quantify atherosclerotic plaque more comprehensively than routine clinical methods. In this paper, we present a spline-based method for reconstructing the normal and diseased carotid artery bifurcation from images acquired using a freehand 3-D ultrasound system. The vessel wall (intima-media interface) and lumen surfaces are represented by a geometric model defined using smoothing splines. Using this coupled wall-lumen model, we demonstrate how plaque may be analyzed automatically to provide a comprehensive set of quantitative measures of size and shape, including established clinical measures, such as degree of (diameter) stenosis. The geometric accuracy of 3-D ultrasound reconstruction is assessed using pulsatile phantoms of the carotid bifurcation, and we conclude by demonstrating the in vivo application of the algorithms outlined to 3-D ultrasound scans from a series of patient carotid arteries.

Carotid geometry reconstruction: a comparison between MRI and ultrasound

Image-based Computational Fluid Dynamics (CFD) has become a popular tool for the prediction of in vivo flow profiles and hemodynamic wall parameters. Currently, Magnetic Resonance Imaging (MRI) is most widely used for in vivo geometry acquisition. For superficial arteries such as the carotids and the femoral artery, three-dimensional (3-D) extravascular ultrasound (3-DUS) could be a cost-effective alternative to MRI. In this study, nine healthy subjects were scanned both with MRI and 3-DUS. The reconstructed carotid artery geometries for each subject were compared by evaluating cross-sectional areas, centerlines, and carotid nonplanarity. Lumen areas agreed very well between the two different acquisition techniques, whereas centerlines and nonplanarity parameters showed measurable disagreement, possibly due to the different neck and head positions adopted for 3-DUS versus MRI. With the current level of agreement achieved, 3-DUS has the potential to become an inexpensive and fast alternative to MRI for image-based CFD modeling of superficial arteries.