MRI measurement of wall shear stress vectors in bifurcation models and comparison with CFD predictions

Assessment of Complex Flow Patterns in Patients With Carotid Webs, Patients With Carotid Atherosclerosis, and Healthy Subjects Using 4D Flow MRI

BACKGROUND

Carotid webs (CaWs) are fibromuscular projections in the internal carotid artery (ICA) that cause mild luminal narrowing (<50%), but may be causative in up to one-third of seemingly cryptogenic strokes. Understanding hemodynamic alterations caused by CaWs is imperative to assessing stroke risk. Time-Average Wall Shear Stress (TAWSS) and Oscillatory Shear Index (OSI) are hemodynamic parameters linked to vascular dysfunction and thrombosis.

PURPOSE

To test the hypothesis: "CaWs are associated with lower TAWSS and higher OSI than mild atherosclerosis or healthy carotid bifurcation."

STUDY TYPE

Prospective study.

POPULATION

A total of 35 subjects (N = 14 bifurcations with CaW, 11F, age: 49 ± 10, 10 mild atherosclerosis 6F, age: 72 ± 9, 11 healthy 9F, age: 42 ± 13).

FIELD STRENGTH/SEQUENCE

4D flow/STAR-MATCH/3D TOF/3T MRI, CTA.

ASSESSMENT

4D Flow velocity data were analyzed in two ways: 1) 3D ROI in the ICA bulbar segment (complex flow patterns are expected) was used to quantify the regions with low TAWSS and high OSI. 2) 2D planes were placed perpendicular to the centerline of the carotid bifurcation for detailed analysis of TAWSS and OSI.

STATISTICAL TESTS

Independent-samples Kruskal-Wallis-H test with 0.05 used for statistical significance.

RESULTS

The percent surface area where low TAWSS was present in the ICA bulb was 12.3 ± 8.0% (95% CI: 7.6-16.9) in CaW subjects, 1.6 ± 1.9% (95% CI: 0.2-2.9) in atherosclerosis, and 8.5 ± 7.7% (95% CI: 3.6-13.4) in healthy subjects, all differences were statistically significant (ƞ2 = 0.3 [95% CI: 0.05-0.5], P-value CaW vs. healthy = 0.2). OSI had similar values in the CCA between groups (ƞ2 = 0.07 [95% CI: 0.0-0.2], P-value = 0.5), but OSI was significantly higher downstream of the bifurcation in CaW subjects compared to atherosclerosis and normal subjects. OSI returned to similar values between groups 1.5 diameters distal to the bifurcation (ƞ2 = 0.03 [95% CI: 0.0-0.2], P-value = 0.7).

CONCLUSION

Lower TAWSS and higher OSI are present in the ICA bulb in patients with CaW when compared to patients with atherosclerotic or healthy subjects.

EVIDENCE LEVEL

2 TECHNICAL EFFICACY: Stage 2.

A New Method for Quantifying Abdominal Aortic Wall Shear Stress Using Phase Contrast Magnetic Resonance Imaging and the Womersley Solution

Wall shear stress (WSS) is an important mediator of cardiovascular pathologies and there is a need for its reliable evaluation as a potential prognostic indicator. The purpose of this work was to develop a method that quantifies WSS from two-dimensional (2D) phase contrast magnetic resonance (PCMR) imaging derived flow waveforms, apply this method to PCMR data acquired in the abdominal aorta of healthy volunteers, and to compare PCMR-derived WSS values to values predicted from a computational fluid dynamics (CFD) simulation. The method uses PCMR-derived flow versus time waveforms constrained by the Womersley solution for pulsatile flow in a cylindrical tube. The method was evaluated for sensitivity to input parameters, intrastudy repeatability and was compared with results from a patient-specific CFD simulation. 2D-PCMR data were acquired in the aortas of healthy men (n = 12) and women (n = 15) and time-averaged WSS (TAWSS) was compared. Agreement was observed when comparing TAWSS between CFD and the PCMR flow-based method with a correlation coefficient of 0.88 (CFD: 15.0 ± 1.9 versus MRI: 13.5 ± 2.4 dyn/cm2) though comparison of WSS values between the PCMR-based method and CFD predictions indicate that the PCMR method underestimated instantaneous WSS by 3.7 ± 7.6 dyn/cm2. We found no significant difference in TAWSS magnitude between the sexes; 8.19 ± 2.25 versus 8.07 ± 1.71 dyn/cm2, p = 0.16 for men and women, respectively.

Fast prediction of blood flow in stenosed arteries using machine learning and immersed boundary-lattice Boltzmann method

A fast prediction of blood flow in stenosed arteries with a hybrid framework of machine learning and immersed boundary-lattice Boltzmann method (IB–LBM) is presented. The integrated framework incorporates the immersed boundary method for its excellent capability in handling complex boundaries, the multi-relaxation-time LBM for its efficient modelling for unsteady flows and the deep neural network (DNN) for its high efficiency in artificial learning. Specifically, the stenosed artery is modelled by a channel for two-dimensional (2D) cases or a tube for three-dimensional (3D) cases with a stenosis approximated by a fifth-order polynomial. An IB–LBM is adopted to obtain the training data for the DNN which is constructed to generate an approximate model for the fast flow prediction. In the DNN, the inputs are the characteristic parameters of the stenosis and fluid node coordinates, and the outputs are the mean velocity and pressure at each node. To characterise complex stenosis, a convolutional neural network (CNN) is built to extract the stenosis properties by using the data generated by the aforementioned polynomial. Both 2D and 3D cases (including 3D asymmetrical case) are constructed and examined to demonstrate the effectiveness of the proposed method. Once the DNN model is trained, the prediction efficiency of blood flow in stenosed arteries is much higher compared with the direct computational fluid dynamics simulations. The proposed method has a potential for applications in clinical diagnosis and treatment where the real-time modelling results are desired.

Modelling of hemodynamics in bifurcation lesions of coronary arteries before and after myocardial revascularization

Modelling of patient-specific hemodynamics for a clinical case of severe coronary artery disease with the bifurcation stenosis was carried out with allowance for standard angiographic data obtained before and after successfully performed myocardial revascularization by stenting of two arteries. Based on a non-Newtonian fluid model and an original algorithm for fluid dynamics computation operated with a limited amount of initial data, key characteristics of blood flow were determined to analyse the features of coronary disease and the consequences of its treatment. The results of hemodynamic modelling near bifurcation sites are presented with an emphasis on physical, physiological and clinical phenomena to demonstrate the feasibility of the proposed approach. The main limitations and ways to minimize them are the subjects of discussion as well. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Geometrically induced wall shear stress variability in CFD-MRI coupled simulations of blood flow in the thoracic aortas

Aortic aneurysm is associated with aberrant blood flow and wall shear stress (WSS). This can be studied by coupling magnetic resonance imaging (MRI) with computational fluid dynamics (CFD). For patient-specific simulations, extra attention should be given to the variation in segmentation of the MRI data-set and its effect on WSS. We performed CFD simulations of blood flow in the aorta for ten different volunteers and provided corresponding WSS distributions. The aorta of each volunteer was segmented four times. The same inlet and outlet boundary conditions were applied for all segmentation variations of each volunteer. Steady-state CFD simulations were performed with inlet flow based on phase-contrast MRI during peak systole. We show that the commonly used comparison of mean and maximal values of WSS, based on CFD in the different segments of the thoracic aorta, yields good to excellent correlation (0.78-0.95) for rescan and moderate to excellent correlation (0.64-1.00) for intra- and interobserver reproducibility. However, the effect of geometrical variations is higher for the voxel-to-voxel comparison of WSS. With this analysis method, the correlation for different segments of the whole aorta is poor to moderate (0.43-0.66) for rescan and poor to good (0.48-0.73) for intra- and interobserver reproducibility. Therefore, we advise being critical about the CFD results based on the MRI segmentations to avoid possible misinterpretation. While the global values of WSS are similar for different modalities, the variation of results is high when considering the local distributions.

From 2D to 4D Phase-Contrast MRI in the Neurovascular System: Will It Be a Quantum Jump or a Fancy Decoration?

Considering the crosstalk between the flow and vessel wall, hemodynamic assessment of the neurovascular system may offer a well-integrated solution for both diagnosis and management by adding prognostic significance to the standard CT/MR angiography. 4D flow MRI or time-resolved 3D velocity-encoded phase-contrast MRI has long been promising for the hemodynamic evaluation of the great vessels, but challenged in clinical studies for assessing intracranial vessels with small diameter due to long scan times and low spatiotemporal resolution. Current accelerated MRI techniques, including parallel imaging with compressed sensing and radial k-space undersampling acquisitions, have decreased scan times dramatically while preserving spatial resolution. 4D flow MRI visualized and measured 3D complex flow of neurovascular diseases such as aneurysm, arteriovenous shunts, and atherosclerotic stenosis using parameters including flow volume, velocity vector, pressure gradients, and wall shear stress. In addition to the noninvasiveness of the phase contrast technique and retrospective flow measurement through the wanted windows of the analysis plane, 4D flow MRI has shown several advantages over Doppler ultrasound or computational fluid dynamics. The evaluation of the flow status and vessel wall can be performed simultaneously in the same imaging modality. This article is an overview of the recent advances in neurovascular 4D flow MRI techniques and their potential clinical applications in neurovascular disease. LEVEL OF EVIDENCE: 5 TECHNICAL EFFICACY STAGE: 3.

Towards quantitative evaluation of wall shear stress from 4D flow imaging

Wall shear stress (WSS) is a relevant hemodynamic indicator of the local stress applied on the endothelium surface. More specifically, its spatiotemporal distribution reveals crucial in the evolution of many pathologies such as aneurysm, stenosis, and atherosclerosis. This paper introduces a new solution, called PaLMA, to quantify the WSS from 4D Flow MRI data. It relies on a two-step local parametric model, to accurately describe the vessel wall and the velocity-vector field in the neighborhood of a given point of interest. Extensive validations have been performed on synthetic 4D Flow MRI data, including four datasets generated from patient specific computational fluid dynamics simulations on carotids. The validation tests are focused on the impact of the noise component, of the resolution level, and of the segmentation accuracy concerning the vessel position in the context of complex flow patterns. In simulated cases aimed to reproduce clinical acquisition conditions, the WSS quantification performance reached by PaLMA is significantly higher (with a gain in RMSE of 12 to 27%) than the reference one obtained using the smoothing B-spline method proposed by Potters et al. (2015) method, while the computation time is equivalent for both WSS quantification methods.

Blood flow simulations in patient-specific geometries of the carotid artery: A systematic review

Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) are currently widely applied in the study of blood flow parameters and their alterations under pathological conditions, which are important indicators for diagnosis of atherosclerosis. In this manuscript, a systematic review of the published literature was conducted, according to the guidelines of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses, on the simulation studies of blood flow in patient-specific geometries of the carotid artery bifurcation. Scopus, PubMed and ScienceDirect databases were used in the literature search, which was completed on the 3rd of August 2020. Forty-nine articles were included after the selection process and were organized in two distinct categories: the CFD studies (36/49 articles), which comprise only the fluid analysis and the FSI studies (13/49 articles), which includes both fluid and Fluid-Structure domain in the analysis. The data of the research works was structured in different categories (Geometry, Viscosity models, Type of Flow, Boundary Conditions, Flow Parameters, Type of Solver and Validation). The aim of this systematic review is to demonstrate the methodology in the modelling, simulation and analysis of carotid blood flow and also identify potential gaps and challenges in this research field.

A Systematic Review for the Design of In Vitro Flow Studies of the Carotid Artery Bifurcation

PURPOSE

In vitro blood flow studies in carotid artery bifurcation models may contribute to understanding the influence of hemodynamics on carotid artery disease. However, the design of in vitro blood flow studies involves many steps and selection of imaging techniques, model materials, model design, and flow visualization parameters. Therefore, an overview of the possibilities and guidance for the design process is beneficial for researchers with less experience in flow studies.

METHODS

A systematic search to in vitro flow studies in carotid artery bifurcation models aiming at quantification and detailed flow visualization of blood flow dynamics results in inclusion of 42 articles.

RESULTS

Four categories of imaging techniques are distinguished: MRI, optical particle image velocimetry (PIV), ultrasound and miscellaneous techniques. Parameters for flow visualization are categorized into velocity, flow, shear-related, turbulent/disordered flow and other parameters. Model materials and design characteristics vary between study type.

CONCLUSIONS

A simplified three-step design process is proposed for better fitting and adequate match with the pertinent research question at hand and as guidance for less experienced flow study researchers. The three consecutive selection steps are: flow parameters, image modality, and model materials and designs. Model materials depend on the chosen imaging technique, whereas choice of flow parameters is independent from imaging technique and is therefore only determined by the goal of the study.

Optimized vascular network by stereolithography for tissue engineered skin

This paper demonstrates the essential and efficient methods to design, and fabricate optimal vascular network for tissue engineering structures based on their physiological conditions. Comprehensive physiological requirements in both micro and macro scales were considered in developing the optimisation design for complex vascular vessels. The optimised design was then manufactured by stereolithography process using materials that are biocompatible, elastic and surface bio-coatable. The materials are self-developed photocurable resin consist of BPA-ethoxylated-diacrylate, lauryl acrylate and isobornylacrylate with Irgacure® 184, the photoinitiator. The optimised vascular vessel offers many advantages: 1) it provides the maximum nutrient supply; 2) it minimises the recirculation areas and 3) it allows the wall shear stress on the vessel in a healthy range. The stereolithography manufactured vascular vessels were then embedded in the hydrogel seeded with cells. The results of in vitro studies show that the optimised vascular network has the lowest cell death rate compared with a pure hydrogel scaffold and a hydrogel scaffold embedded within a single tube in day seven. Consequently, these design and manufacture routes were shown to be viable for exploring and developing a high range complex and specialised artificial vascular networks.

A comparison of 4D flow MRI-derived wall shear stress with computational fluid dynamics methods for intracranial aneurysms and carotid bifurcations - A review

BACKGROUND

4D flow MRI is a relatively quick method for obtaining wall shear stress (WSS) in vivo, a hemodynamic parameter which has shown promise in risk stratification for rupture of cerebrovascular diseases such as intracranial aneurysms and atherosclerotic plaques. The accuracy of such measurements is still largely unknown.

OBJECTIVE

To quantify the accuracy of 4D flow MRI-derived wall shear stress values for intracranial aneurysms and carotid bifurcations.

METHOD

We performed a review of all original research articles which compared the magnitudes of WSS derived from 4D flow MRI with corresponding values derived from computational fluid dynamics (CFD) within both intracranial aneurysms and carotid bifurcations.

RESULT

For intracranial aneurysms and carotid bifurcations, 4D flow MRI-derived WSS estimations are generally lower in magnitude compared to WSS derived by CFD methods. These differences are more pronounced in regions of higher WSS. However, the relative distributions of WSS derived from both methods are reasonably similar.

CONCLUSION

Pooled analysis suggests that WSS magnitudes obtained by 4D flow MRI are underestimated, while the relative distribution is reasonably accurate, the latter being an important factor for determining the natural history of intracranial aneurysms and other cerebrovascular diseases. 4D flow MRI shows enormous potential in providing new risk stratification parameters which could have significant impact on individualized treatment decisions and improved patient outcomes.

Direct Assessment of Wall Shear Stress by Signal Intensity Gradient from Time-of-Flight Magnetic Resonance Angiography

The aim of the study was to calculate the arterial wall signal intensity gradient (SIG) from time-of-flight MR angiography (TOF-MRA) and represent arterial wall shear stress. We developed a new algorithm that uses signal intensity (SI) of a TOF-MRA to directly calculate the signal intensity gradient (SIG). The results from our phantom study showed that the TOF-MRA SIG could be used to distinguish the magnitude of blood flow rate as high (mean SIG ± SD, 2.2 ± 0.4 SI/mm for 12.5 ± 2.3 L/min) and low (0.9 ± 0.3 SI/mm for 8.5 ± 2.6 L/min) in vessels (p < 0.001). Additionally, we found that the TOF-MRA SIG values were highly correlated with various flow rates (β = 0.96, p < 0.001). Remarkably, the correlation coefficient between the WSS obtained from the computational fluid dynamics (CFD) analysis and the TOF-MRA SIG was greater than 0.8 in each section at the carotid artery (p < 0.001 for all β values). This new technique using TOF-MRA could enable the rapid calculation of the TOF-MRA SIG and thereby the WSS. Thus, the TOF-MRA SIG can provide clinicians with an accurate and efficient screening method for making rapid decisions on the risk of vascular disease for a patient in clinical practice.

Vessel wall characterization using quantitative MRI: what's in a number?

The past decade has witnessed the rapid development of new MRI technology for vessel wall imaging. Today, with advances in MRI hardware and pulse sequences, quantitative MRI of the vessel wall represents a real alternative to conventional qualitative imaging, which is hindered by significant intra- and inter-observer variability. Quantitative MRI can measure several important morphological and functional characteristics of the vessel wall. This review provides a detailed introduction to novel quantitative MRI methods for measuring vessel wall dimensions, plaque composition and permeability, endothelial shear stress and wall stiffness. Together, these methods show the versatility of non-invasive quantitative MRI for probing vascular disease at several stages. These quantitative MRI biomarkers can play an important role in the context of both treatment response monitoring and risk prediction. Given the rapid developments in scan acceleration techniques and novel image reconstruction, we foresee the possibility of integrating the acquisition of multiple quantitative vessel wall parameters within a single scan session.

Four-dimensional MRI flow examinations in cerebral and extracerebral vessels - ready for clinical routine?

PURPOSE OF REVIEW

To evaluate the feasibility of 4-dimensional (4D) flow MRI for the clinical assessment of cerebral and extracerebral vascular hemodynamics in patients with neurovascular disease.

RECENT FINDINGS

4D flow MRI has been applied in multiple studies to qualitatively and quantitatively study intracranial aneurysm blood flow for potential risk stratification and to assess treatment efficacy of various neurovascular lesions, including intraaneurysmal and parent artery blood flow after flow diverter stent placement and staged embolizations of arteriovenous malformations and vein of Galen aneurysmal malformations. Recently, the technique has been utilized to characterize age-related changes of normal cerebral hemodynamics in healthy individuals over a broad age range.

SUMMARY

4D flow MRI is a useful tool for the noninvasive, volumetric and quantitative hemodynamic assessment of neurovascular disease without the need for gadolinium contrast agents. Further improvements are warranted to overcome technical limitations before broader clinical implementation. Current developments, such as advanced acceleration techniques (parallel imaging and compressed sensing) for faster data acquisition, dual or multiple velocity encoding strategies for more accurate arterial and venous flow quantification, ultrahigh-field strengths to achieve higher spatial resolution and streamlined postprocessing workflow for more efficient and standardized flow analysis, are promising advancements in 4D flow MRI.

Engineering design of artificial vascular junctions for 3D printing

Vascular vessels, including arteries, veins and capillaries, are being printed using additive manufacturing technologies, also known as 3D printing. This paper demonstrates that it is important to follow the vascular design by nature as close as possible when 3D printing artificial vascular branches. In previous work, the authors developed an algorithm of computational geometry for constructing smooth junctions for 3D printing. In this work, computational fluid dynamics (CFDs) is used to compare the wall shear stress and blood velocity field for the junctions of different designs. The CFD model can reproduce the expected wall shear stress at locations remote from the junction. For large vessels such as veins, it is shown that ensuring the smoothness of the junction and using smaller joining angles as observed in nature is very important to avoid high wall shear stress and recirculation. The issue is however less significant for capillaries. Large joining angles make no difference to the hemodynamic behavior, which is also consistent with the fact that most capillary junctions have large joining angles. The combination of the CFD analysis and the junction construction method form a complete design method for artificial vascular vessels that can be 3D printed using additive manufacturing technologies.

Relation between wall shear stress and carotid artery wall thickening MRI versus CFD

Wall shear stress (WSS), a parameter associated with endothelial function, is calculated by computational fluid dynamics (CFD) or phase-contrast (PC) MRI measurements. Although CFD is common in WSS (WSSCFD) calculations, PC-MRI-based WSS (WSSMRI) is more favorable in population studies; since it is straightforward and less time consuming. However, it is not clear if WSSMRI and WSSCFD show similar associations with vascular pathology. Our aim was to test the associations between wall thickness (WT) of the carotid arteries and WSSMRI and WSSCFD. The subjects (n=14) with an asymptomatic carotid plaque who underwent MRI scans two times within 4 years of time were selected from the Rotterdam Study. We compared WSSCFD and WSSMRI at baseline and follow-up. Baseline WSSMRI and WSSCFD values were divided into 3 categories representing low, medium and high WSS tertiles. WT of each tertile was compared by a one-way ANOVA test. The WSSMRI and WSSCFD were 0.50±0.13Pa and 0.73±0.25Pa at baseline. Although WSSMRI was underestimated, a significant regression was found between WSSMRI and WSSCFD (r(2)=0.71). No significant difference was found between baseline and follow-up WSS by CFD and MRI-based calculations. The WT at baseline was 1.36±0.16mm and did not change over time. The WT was 1.55±0.21mm in low, 1.33±0.20mm in medium and 1.21±0.21mm in the high WSSMRI tertiles. Similarly, the WT was 1.49±0.21mm in low, 1.33±0.20mm in medium and 1.26±0.21mm in high WSSCFD tertiles. We found that WSSMRI and WSSCFD were inversely related with WT. WSSMRI and WSSCFD patterns were similar although MRI-based calculations underestimated WSS.

Phase-contrast magnetic resonance imaging for the evaluation of wall shear stress in the common carotid artery of a spontaneously hypertensive rat model at 7T: Location-specific change, regional distribution along the vascular circumference, and reproducibility analysis

PURPOSE

To measure wall shear stress (WSS) in the common carotid arteries (CCA) of a spontaneously hypertensive rat (SHR) model and a normotensive Wistar Kyoto rat (WKY) model by 2D phase-contrast magnetic resonance imaging (PC-MRI).

MATERIALS AND METHODS

PC-MRI was performed on 7 SHR and 7 WKY at ages of 4 and 7months at a 7T scanner. Images in the middle CCA (CCAmid) and in the bifurcation of CCA (CCAbifur) were acquired. The WSS values for differentiating characteristics between two models were calculated. Further, its location-specific change, regional distribution along the CCA circumference, and the reproducibility were evaluated.

RESULTS

In the 4-month-old rats, SHR showed lower temporal averaged WSS (WSSavg) and peak systolic WSS (WSSs) in the CCAbifur in comparison with WKY (WSSavg: 0.95±0.18 vs. 1.30±0.36N/m(2) (P<0.01); WSSs: 1.68±0.70 vs. 3.22±2.49N/m(2) (P<0.05)). We observed the same trends in the 7-month-old rats. In the SHR model, the WSSavg was lower in the CCAbifur than in the CCAmid. The regional distribution of WSSavg along the circumference of CCA showed lower values in WKY, particularly in posterior segments of CCAbifur. The intra-observer, intra-scan and inter-scan reproducibility was acceptable and the disagreements were ranged from -0.05 to 0.06N/m(2).

CONCLUSION

This study evaluated WSS in SHR and WKY models by 2D PC-MRI. High reproducibility analyses further indicated the reliability of measurements of WSS in the CCA of SHR and WKY models using PC-MRI at 7T.

Numerical Simulation of Nonlinear Pulsatile Newtonian Blood Flow through a Multiple Stenosed Artery

An appropriate nonlinear blood flow model under the influence of periodic body acceleration through a multiple stenosed artery is investigated with the help of finite difference method. The arterial segment is simulated by a cylindrical tube filled with a viscous incompressible Newtonian fluid described by the Navier-Stokes equation. The nonlinear equation is solved numerically with the proper boundary conditions and pressure gradient that arise from the normal functioning of the heart. Results are discussed in comparison with the existing models.

Measurement with microscopic MRI and simulation of flow in different aneurysm models

PURPOSE

The impact and the development of aneurysms depend to a significant degree on the exchange of liquid between the regular vessel and the pathological extension. A better understanding of this process will lead to improved prediction capabilities. The aim of the current study was to investigate fluid-exchange in aneurysm models of different complexities by combining microscopic magnetic resonance measurements with numerical simulations. In order to evaluate the accuracy and applicability of these methods, the fluid-exchange process between the unaltered vessel lumen and the aneurysm phantoms was analyzed quantitatively using high spatial resolution.

METHODS

Magnetic resonance flow imaging was used to visualize fluid-exchange in two different models produced with a 3D printer. One model of an aneurysm was based on histological findings. The flow distribution in the different models was measured on a microscopic scale using time of flight magnetic resonance imaging. The whole experiment was simulated using fast graphics processing unit-based numerical simulations. The obtained simulation results were compared qualitatively and quantitatively with the magnetic resonance imaging measurements, taking into account flow and spin-lattice relaxation.

RESULTS

The results of both presented methods compared well for the used aneurysm models and the chosen flow distributions. The results from the fluid-exchange analysis showed comparable characteristics concerning measurement and simulation. Similar symmetry behavior was observed. Based on these results, the amount of fluid-exchange was calculated. Depending on the geometry of the models, 7% to 45% of the liquid was exchanged per second.

CONCLUSIONS

The result of the numerical simulations coincides well with the experimentally determined velocity field. The rate of fluid-exchange between vessel and aneurysm was well-predicted. Hence, the results obtained by simulation could be validated by the experiment. The observed deviations can be caused by the noise in the measurement and by the limited resolution of the simulation. The resulting differences are small enough to allow reliable predictions of the flow distribution in vessels with stents and for pulsed blood flow.

Wall shear stress calculations based on 3D cine phase contrast MRI and computational fluid dynamics: a comparison study in healthy carotid arteries

Wall shear stress (WSS) is involved in many pathophysiological processes related to cardiovascular diseases, and knowledge of WSS may provide vital information on disease progression. WSS is generally quantified with computational fluid dynamics (CFD), but can also be calculated using phase contrast MRI (PC-MRI) measurements. In this study, our objectives were to calculate WSS on the entire luminal surface of human carotid arteries using PC-MRI velocities (WSSMRI ) and to compare it with WSS based on CFD (WSSCFD ). Six healthy volunteers were scanned with a 3 T MRI scanner. WSSCFD was calculated using a generalized flow waveform with a mean flow equal to the mean measured flow. WSSMRI was calculated by estimating the velocity gradient along the inward normal of each mesh node on the luminal surface. Furthermore, WSS was calculated for a down-sampled CFD velocity field mimicking the MRI resolution (WSSCFDlowres ). To ensure minimum temporal variation, WSS was analyzed only at diastole. The patterns of WSSCFD and WSSMRI were compared by quantifying the overlap between low, medium and high WSS tertiles. Finally, WSS directions were compared by calculating the angles between the WSSCFD and WSSMRI vectors. WSSMRI magnitude was found to be lower than WSSCFD (0.62 ± 0.18 Pa versus 0.88 ± 0.30 Pa, p < 0.01) but closer to WSSCFDlowres (0.56 ± 0.18 Pa, p < 0.01). WSSMRI patterns matched well with those of WSSCFD. The overlap area was 68.7 ± 4.4% in low and 69.0 ± 8.9% in high WSS tertiles. The angles between WSSMRI and WSSCFD vectors were small in the high WSS tertiles (20.3 ± 8.2°), but larger in the low WSS tertiles (65.6 ± 17.4°). In conclusion, although WSSMRI magnitude was lower than WSSCFD , the spatial WSS patterns at diastole, which are more relevant to the vascular biology, were similar. PC-MRI-based WSS has potential to be used in the clinic to indicate regions of low and high WSS and the direction of WSS, especially in regions of high WSS.

Volumetric arterial wall shear stress calculation based on cine phase contrast MRI

PURPOSE

To assess the accuracy and precision of a volumetric wall shear stress (WSS) calculation method applied to cine phase contrast magnetic resonance imaging (PC-MRI) data.

MATERIALS AND METHODS

Volumetric WSS vectors were calculated in software phantoms. WSS algorithm parameters were optimized and the influence of spatial resolution and segmentation was evaluated. Subsequently, 2D cine PC-MRI data in the carotid and the aorta at varying spatial resolutions were obtained (n = 2) and compared with the simulations. Finally, volumetric WSS was calculated in 3D cine PC-MRI data of the carotid bifurcation and the aorta (n = 6).

RESULTS

We found that at least 8 voxels across the diameter are required to obtain a WSS accuracy of 5% and a precision of 20% in software phantoms. Systematic WSS quantification errors up to 40% were found in the case of segmentation errors. The in vivo measurements using 2D cine PC-MRI exhibited WSS increase at increasing spatial resolutions, similar to the results in software phantoms. Volumetric WSS vectors were successfully calculated in three healthy carotid bifurcations and aortas.

CONCLUSION

The effects of resolution and segmentation on the accuracy and precision of the WSS algorithm were quantified. We were able to calculate volumetric WSS in the carotid bifurcation and the aorta.

Three-dimensional hemodynamics in intracranial aneurysms: influence of size and morphology

PURPOSE

To use four-dimensional (4D)-flow MRI for the comprehensive in vivo analysis of hemodynamics and its relationship to size and morphology of different intracranial aneurysms (IA). We hypothesize that different IA groups, defined by size and morphology, exhibit different velocity fields, wall shear stress, and vorticity.

MATERIALS AND METHODS

The 4D-flow MRI (spatial resolution = 0.99-1.8 × 0.78-1.46 × 1.2-1.4 mm(3) , temporal resolution = 44-48 ms) was performed in 19 IAs (18 patients, age = 55.4 ± 13.8 years) with saccular (n = 16) and fusiform (n = 3) morphology and different sizes ranging from small (n = 8; largest dimension = 6.2 ± 0.4 mm) to large and giant (n = 11; 25 ± 7 mm). Analysis included quantification of volumetric spatial-temporal velocity distribution, vorticity, and wall shear stress (WSS) along the aneurysm's 3D surface.

RESULTS

The 4D-flow MRI revealed distinct hemodynamic patterns for large/giant saccular aneurysms (Group 1), small saccular aneurysms (Group 2), and large/giant fusiform aneurysms (Group 3). Saccular IA (Groups 1, 2) demonstrated significantly higher peak velocities (P < 0.002) and WSS (P < 0.001) compared with fusiform aneurysms. Although intra-aneurysmal 3D velocity distributions were similar for Group 1 and 2, vorticity and WSS was significantly (P < 0.001) different (increased in Group 1 by 54%) indicating a relationship between IA size and hemodynamics. Group 3 showed reduced velocities (P < 0.001) and WSS (P < 0.001).

CONCLUSION

The 4D-flow MRI demonstrated the influence of lesion size and morphology on aneurysm hemodynamics suggesting the potential of 4D-flow MRI to assist in the classification of individual aneurysms.

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.

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.

Complex flow patterns in a real-size intracranial aneurysm phantom: phase contrast MRI compared with particle image velocimetry and computational fluid dynamics

The aim of this study was to validate the flow patterns measured by high-resolution, time-resolved, three-dimensional phase contrast MRI in a real-size intracranial aneurysm phantom. Retrospectively gated three-dimensional phase contrast MRI was performed in an intracranial aneurysm phantom at a resolution of 0.2 × 0.2 × 0.3 mm(3) in a solenoid rat coil. Both steady and pulsatile flows were applied. The phase contrast MRI measurements were compared with particle image velocimetry measurements and computational fluid dynamics simulations. A quantitative comparison was performed by calculating the differences between the magnitude of the velocity vectors and angles between the velocity vectors in corresponding voxels. Qualitative analysis of the results was executed by visual inspection and comparison of the flow patterns. The root-mean-square errors of the velocity magnitude in the comparison between phase contrast MRI and computational fluid dynamics were 5% and 4% of the maximum phase contrast MRI velocity, and the medians of the angle distribution between corresponding velocity vectors were 16° and 14° for the steady and pulsatile measurements, respectively. In the phase contrast MRI and particle image velocimetry comparison, the root-mean-square errors were 12% and 10% of the maximum phase contrast MRI velocity, and the medians of the angle distribution between corresponding velocity vectors were 19° and 15° for the steady and pulsatile measurements, respectively. Good agreement was found in the qualitative comparison of flow patterns between the phase contrast MRI measurements and both particle image velocimetry measurements and computational fluid dynamics simulations. High-resolution, time-resolved, three-dimensional phase contrast MRI can accurately measure complex flow patterns in an intracranial aneurysm phantom.

Estimation of blood velocity, volumetric flow and wall shear rate using Doppler ultrasound

Commercial ultrasound systems can make a number of measurements related to haemodynamics which are relevant to clinical practice and to clinical research. These include maximum velocity, volumetric flow and wall shear rate. Using appropriate protocols, measurements can be made averaged over the cardiac cycle, or as a function of time through the cardiac cycle. Maximum velocity underpins most of these measurements. Maximum velocity is overestimated as a result of geometric spectral broadening, by typically up to 30%, but by much larger amounts as the angle approaches 90°. Though not used in clinical practice, a simple correction technique using a string phantom can substantially reduce these errors. For volumetric flow and wall shear rate, methods such as specialist multi-gate ultrasound systems, magnetic resonance imaging and image guided modelling are available. Before resorting to these more complex methods users might consider that, with care and attention to procedure, high quality information may be obtained using commercial ultrasound systems. Manufacturers could make more use of the colour flow image for quantification of velocity, and adopt vector Doppler techniques.

Comparison of blood velocity measurements between ultrasound Doppler and accelerated phase-contrast MR angiography in small arteries with disturbed flow

Ultrasound Doppler (UD) velocity measurements are commonly used to quantify blood flow velocities in vivo. The aim of our work was to investigate the accuracy of in vivo spectral Doppler measurements of velocity waveforms. Waveforms were derived from spectral Doppler signals and corrected for intrinsic spectral broadening errors by applying a previously published algorithm. The method was tested in a canine aneurysm model by determining velocities in small arteries (3-4 mm diameter) near the aneurysm where there was moderately disturbed flow. Doppler results were compared to velocity measurements in the same arteries acquired with a rapid volumetric phase contrast MR angiography technique named phase contrast vastly undersampled isotropic projection reconstruction magnetic resonance angiography (PC-VIPR MRA). After correcting for intrinsic spectral broadening, there was a high degree of correlation between velocities obtained by the real-time UD and the accelerated PC-MRA technique. The peak systolic velocity yielded a linear correlation coefficient of r = 0.83, end diastolic velocity resulted in r = 0.81, and temporally averaged mean velocity resulted in r = 0.76. The overall velocity waveforms obtained by the two techniques were also highly correlated (r = 0.89 ± 0.06). There were, however, only weak correlations for the pulsatility index (PI: 0.25) and resistive index (RI: 0.14) derived from the two techniques. Results demonstrate that to avoid overestimations of peak systolic velocities, the results for UD must be carefully corrected to compensate for errors caused by intrinsic spectral broadening.

Ultrasonic particle image velocimetry for improved flow gradient imaging: algorithms, methodology and validation

This paper presents a new algorithm for ultrasonic particle image velocimetry (Echo PIV) for improving the flow velocity measurement accuracy and efficiency in regions with high velocity gradients. The conventional Echo PIV algorithm has been modified by incorporating a multiple iterative algorithm, sub-pixel method, filter and interpolation method, and spurious vector elimination algorithm. The new algorithms' performance is assessed by analyzing simulated images with known displacements, and ultrasonic B-mode images of in vitro laminar pipe flow, rotational flow and in vivo rat carotid arterial flow. Results of the simulated images show that the new algorithm produces much smaller bias from the known displacements. For laminar flow, the new algorithm results in 1.1% deviation from the analytically derived value, and 8.8% for the conventional algorithm. The vector quality evaluation for the rotational flow imaging shows that the new algorithm produces better velocity vectors. For in vivo rat carotid arterial flow imaging, the results from the new algorithm deviate 6.6% from the Doppler-measured peak velocities averagely compared to 15% of that from the conventional algorithm. The new Echo PIV algorithm is able to effectively improve the measurement accuracy in imaging flow fields with high velocity gradients.

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.

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.

Advanced techniques for MRI of atherosclerotic plaque

This review examines the state of the art in vessel wall imaging by magnetic resonance imaging (MRI) with an emphasis on the biomechanical assessment of atherosclerotic plaque. Three areas of advanced techniques are discussed. First, alternative contrast mechanisms, including susceptibility, magnetization transfer, diffusion, and perfusion, are presented as to how they facilitate accurate determination of plaque constituents underlying biomechanics. Second, imaging technologies including hardware and sequences, are reviewed as to how they provide the resolution and signal-to-noise ratio necessary for determining plaque structure. Finally, techniques for combining MRI data into an overall assessment of plaque biomechanical properties, including wall shear stress and internal plaque strain, are presented. The paper closes with a discussion of the extent to which these techniques have been applied to different arteries commonly targeted by vessel wall MRI.

Wall shear stress measurement using phase contrast magnetic resonance imaging with phase contrast magnetic resonance angiography in arteriovenous polytetrafluoroethylene grafts

PURPOSE

The purpose of the present article was to determine the changes in luminal vessel area, blood flow, and wall shear stress in both the inflow artery and the venous stenosis of arteriovenous polytetrafluoroethylene (PTFE) grafts.

METHODS AND MATERIALS

Polytetrafluoroethylene grafts were placed from the carotid artery to the ipsilateral jugular vein in 8 castrated juvenile male pigs. Contrast-enhanced magnetic resonance angiography (MRA) with cine phase-contrast magnetic resonance imaging (MRI) was performed 2 weeks after graft placement.

RESULTS

The mean wall shear stress at the venous stenosis was 4 times higher than the control vein, while the inflow artery was only 2-fold higher. By day 14, venous stenosis had formed, which was characterized by narrowed area and elevated blood flow.

CONCLUSION

By day 14, there is venous stenosis formation in porcine arteriovenous PTFE grafts with increased shear stress with decreased area when compared to control vein.

Phase-contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: comparison with computational fluid dynamics

Evolution of intracranial aneurysms is known to be related to hemodynamic forces such as wall shear stress (WSS) and maximum shear stress (MSS). Estimation of these parameters can be performed using numerical simulations with computational fluid dynamics (CFD), but can also be directly measured with magnetic resonance imaging (MRI) using a time-dependent 3D phase-contrast sequence with encoding of each of the three components of the velocity vectors (7D-MRV). To study the accuracy of 7D-MRV in estimating these parameters in vivo, in comparison with CFD, 7D-MRV and patient-specific CFD modeling was performed for 3 patients who had intracranial aneurysms. Visual and quantitative analyses of the flow pattern and distribution of velocities, MSS, and WSS were performed using the two techniques. Spearman's coefficients of correlation between the two techniques were 0.56 for the velocity field, 0.48 for MSS, and 0.59 for WSS. Visual analysis and Bland-Altman plots showed good agreement for flow pattern and velocities but large discrepancies for MSS and WSS. These results indicate that 7D-MRV can be used in vivo to measure velocity flow fields and for estimating MSS and WSS. Currently, however, this method cannot accurately quantify the latter two parameters.

Quantitative 2D and 3D phase contrast MRI: optimized analysis of blood flow and vessel wall parameters

Quantification of CINE phase contrast (PC)-MRI data is a challenging task because of the limited spatiotemporal resolution and signal-to-noise ratio (SNR). The method presented in this work combines B-spline interpolation and Green's theorem to provide optimized quantification of blood flow and vessel wall parameters. The B-spline model provided optimal derivatives of the measured three-directional blood velocities onto the vessel contour, as required for vectorial wall shear stress (WSS) computation. Eight planes distributed along the entire thoracic aorta were evaluated in a 19-volunteer study using both high-spatiotemporal-resolution planar two-dimensional (2D)-CINE-PC ( approximately 1.4 x 1.4 mm(2)/24.4 ms) and lower-resolution 3D-CINE-PC ( approximately 2.8 x 1.6 x 3 mm(3)/48.6 ms) with three-directional velocity encoding. Synthetic data, error propagation, and interindividual, intermodality, and interobserver variability were used to evaluate the reliability and reproducibility of the method. While the impact of MR measurement noise was only minor, the limited resolution of PC-MRI introduced systematic WSS underestimations. In vivo data demonstrated close agreement for flow and WSS between 2D- and 3D-CINE-PC as well as observers, and confirmed the reliability of the method. WSS analysis along the aorta revealed the presence of a circumferential WSS component accounting for 10-20%. Initial results in a patient with atherosclerosis suggest the potential of the method for understanding the formation and progression of cardiovascular diseases.

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.

A method to estimate wall shear rate with a clinical ultrasound scanner

A simple technique to estimate the wall shear rate in healthy arteries using a clinical ultrasound scanner has been developed. This method uses the theory of fully developed oscillatory flow together with a spectral Doppler trace and an estimate of mean arterial diameter. A method using color flow imaging was compared with the spectral Doppler method in vascular phantoms and found to have errors that were on average 35% greater. Differences from the theoretic value for the time averaged wall shear rate using the spectral Doppler method varied by artery: brachial -9 (1) %; carotid -7 (1) %; femoral -22 (4) %; and fetal aorta -17 (10) %. Test measurements obtained from one healthy volunteer demonstrated the feasibility of the technique in vivo.

Laser Doppler velocimetry (LDV) and 3D phase-contrast magnetic resonance angiography (PC-MRA) velocity measurements: validation in an anatomically accurate cerebral artery aneurysm model with steady flow

PURPOSE

To verify the accuracy of velocity mapping with three-dimensional (3D) phase-contrast magnetic resonance angiography (PC-MRA) for steady flow in a realistic model of a cerebral artery aneurysm at a 3T scanner.

MATERIALS AND METHODS

Steady flow through an original geometry model of a cerebral aneurysm was mapped at characteristic positions by state-of-the-art laser Doppler velocimetry (LDV) as well as 3D PC-MRA at 3T. The spatial distributions and local values of two velocity components obtained with these two measurement methods were compared.

RESULTS

The 3D PC-MRA velocity field distribution and mean velocity values exhibited only minor differences to compare to the LDV measurements in straight artery regions for both main and secondary velocities. The differences increased in regions with disturbed flow and in cases where the measurement plane was not perpendicular to the main flow direction.

CONCLUSION

3D PC-MRA can provide reliable measurements of velocity components of steady flow in small arteries. The accuracy of such measurements depends on the artery size and the measurement plane positioning.

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.

A reconstruction method for gappy and noisy arterial flow data

Proper orthogonal decomposition (POD), Kriging interpolation, and smoothing are applied to reconstruct gappy and noisy data of blood flow in a carotid artery. While we have applied these techniques to clinical data, in this paper in order to rigorously evaluate their effectiveness we rely on data obtained by computational fluid dynamics (CFD). Specifically, gappy data sets are generated by removing nodal values from high-resolution 3-D CFD data (at random or in a fixed area) while noisy data sets are formed by superimposing speckle noise on the CFD results. A combined POD-Kriging procedure is applied to planar data sets mimicking coarse resolution "ultrasound-like" blood flow images. A method for locating the vessel wall boundary and for calculating the wall shear stress (WSS) is also proposed. The results show good agreement with the original CFD data. The combined POD-Kriging method, enhanced by proper smoothing if needed, holds great potential in dealing effectively with gappy and noisy data reconstruction of in vivo velocity measurements based on color Doppler ultrasound (CDUS) imaging or magnetic resonance angiography (MRA).

The integration of medical imaging and computational fluid dynamics for measuring wall shear stress in carotid arteries

The link between atherosclerosis and wall shear stress (WSS) has lead to considerable interest in the in vivo estimation of WSS. Both magnetic resonance imaging (MRI) and three-dimensional ultrasound (3DUS) are capable of providing the anatomical and flow data required for subject-specific computational fluid dynamics (CFD) simulations. This study compares, for the first time, 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 computed and compared. There was a good qualitative agreement between results derived from MRI and 3DUS, embodied by a strong linear correlation between the patched representations of the haemodynamic wall parameters. 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; OSI: 0.048; temporal WSSG: 2.29 N/(s.m/sup 2/); spatial WSSG: 150 N/m/sup 3/; WSSAG: 87.6 rad/m). In conclusion, MRI and 3DUS are comparable techniques for combining with CFD in the carotid artery. The relatively high cost of MRI favour 3DUS to MRI for future haemodynamic studies of superficial arteries.

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.

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.