Accurate noninvasive quantitation of blood flow, cross-sectional lumen vessel area and wall shear stress by three-dimensional paraboloid modeling of magnetic resonance imaging velocity data

Validation of Signal Intensity Gradient from TOF-MRA for Wall Shear Stress by Phase-Contrast MR

To validate the correlation between the signal intensity gradient (SIG) from time-of-flight magnetic resonance angiography (TOF-MRA) and wall shear stress (WSS) determined by phase contrast magnetic resonance (PC-MR), we conducted both experimental and human studies. In the experimental study, we measured WSS in four tubes of different sizes with variable flow rates using PC-MR and TOF-MRA. The flow rates of water in the experimental study ranged from 0.06 to 12.75 mL/s, resulting in PC-WSS values between 0.1 and 1.6 dyne/cm2. The correlation between PC-WSS and SIG was statistically significant, showing a coefficient of 0.86 (P < 0.001, R2 = 0.75). The line fit provided the conversion equation as Y = 1.6287X - 1.1563 (Y = PC-WSS, X = SIG). For the human study, 28 subjects underwent TOF-MRA and PC-MR examinations of carotid and vertebral arteries. Arterial PC-WSS and SIG were determined in the same segment for each subject. The arterial PC-WSS ranged from 1.9 to 21.0 dyne/cm2. Both carotid and vertebral arteries showed significant correlations between PC-WSS and SIG, with coefficients of 0.85, 0.86, 0.91, and 0.81 in the right and left carotid and vertebral arteries, respectively. Our results show that SIG from TOF-MRA and SIG-WSS derived from the conversion equation provide concurrent in vivo hemodynamic information on arterial shear stress. This study was registered on ClinicalTrials.gov with the identifier NCT04585971 on October 14, 2020.

An in vivo investigation on the effects of stent implantation on hematological and hemorheological parameters

BACKGROUND

Even though cardiovascular stenting is widely used for the treatment of coronary artery disease, information on how it can affect the hematological and hemorheological profile is scarce in the literature. Most of the work on this issue is based on theoretical or computational fluid dynamics models, lacking in-depth in vitro and in vivo experimental verification.

OBJECTIVE

This work investigates, in an in vivo setting, the effects of stenting and the implantation time-course on hematological and hemorheological parameters that could potentially compromise the device's functionality and longevity.

METHODS

Custom-made self-expanding nitinol stents were implanted in the common carotid artery of male CD1 mice. Whole blood samples were collected from control (non-stented) and stented animals at 5 and 10 weeks post-implantation. Hematological measurements and blood viscosity, red blood cell aggregation, and deformability were performed using standard techniques.

RESULTS

Implant-induced changes were observed in some of the hematological and hemorheological indices. Blood viscosity seems to have been negatively affected by an increased hematocrit and reduced RBC deformability, at 10 weeks post-implantation, despite a slight decrease in RBC aggregation.

CONCLUSIONS

Although the alterations observed may be the result of the peri-implant inflammatory response, the physiological consequences due to hemorheological changes need to be further investigated.

Underlying mechanism of hemodynamics and intracranial aneurysm

In modern society, subarachnoid hemorrhage, mostly caused by intracranial aneurysm rupture, is accompanied by high disability and mortality rate, which has become a major threat to human health. Till now, the etiology of intracranial aneurysm has not been entirely clarified. In recent years, more and more studies focus on the relationship between hemodynamics and intracranial aneurysm. Under the physiological condition, the mechanical force produced by the stable blood flow in the blood vessels keeps balance with the structure of the blood vessels. When the blood vessels are stimulated by the continuous abnormal blood flow, the functional structure of the blood vessels changes, which becomes the pathophysiological basis of the inflammation and atherosclerosis of the blood vessels and further promotes the occurrence and development of the intracranial aneurysm. This review will focus on the relationship between hemodynamics and intracranial aneurysms, will discuss the mechanism of occurrence and development of intracranial aneurysms, and will provide a new perspective for the research and treatment of intracranial aneurysms.

Optimization of 4D flow MRI velocity field in the aorta with divergence-free smoothing

Divergence-free smoothing with wall treatment (DFS_wt) method is proposed for processing with four-dimensional (4D) flow magnetic resonance imaging (MRI) data of blood flows to enhance the quality of flow field with physical constraints. The new method satisfies the no-slip wall boundary condition and applies wall function of velocity profile for better estimating the velocity gradient in the near-wall region, and consequently improved wall shear stress (WSS) calculation against the issue of coarse resolution of 4D flow MRI. In the first testing case, blood flow field obtained from 4D flow MRI is well smoothed by DFS_wt method. A great consistency is observed between the post-processed 4D flow MRI data and the computational fluid dynamics (CFD) data in the interested velocity field. WSS has an apparent improvement due to the proposed near-wall treatment with special wall function comparing to the result from original 4D flow MRI data or the DFS-processed data with no wall function. The other five cases also show the same performance that smoothed velocity field and improved WSS estimation are achieved on 4D flow MRI data optimized by DFS_wt. The improvements will benefit the study of hemodynamics regarding the determination of location or the potential possibility of lesions.

High shear stress enhances endothelial permeability in the presence of the risk haplotype at 9p21.3

Single nucleotide polymorphisms (SNPs) are exceedingly common in non-coding loci, and while they are significantly associated with a myriad of diseases, their specific impact on cellular dysfunction remains unclear. Here, we show that when exposed to external stressors, the presence of risk SNPs in the 9p21.3 coronary artery disease (CAD) risk locus increases endothelial monolayer and microvessel dysfunction. Endothelial cells (ECs) derived from induced pluripotent stem cells of patients carrying the risk haplotype (R/R WT) differentiated similarly to their non-risk and isogenic knockout (R/R KO) counterparts. Monolayers exhibited greater permeability and reactive oxygen species signaling when the risk haplotype was present. Addition of the inflammatory cytokine TNFα further enhanced EC monolayer permeability but independent of risk haplotype; TNFα also did not substantially alter haplotype transcriptomes. Conversely, when wall shear stress was applied to ECs in a microfluidic vessel, R/R WT vessels were more permeable at lower shear stresses than R/R KO vessels. Transcriptomes of sheared cells clustered more by risk haplotype than by patient or clone, resulting in significant differential regulation of EC adhesion and extracellular matrix genes vs static conditions. A subset of previously identified CAD risk genes invert expression patterns in the presence of high shear concomitant with altered cell adhesion genes, vessel permeability, and endothelial erosion in the presence of the risk haplotype, suggesting that shear stress could be a regulator of non-coding loci with a key impact on CAD.

An LDV based method to quantify the error of PC-MRI derived Wall Shear Stress measurement

Wall Shear Stress (WSS) has been demonstrated to be a biomarker of the development of atherosclerosis. In vivo assessment of WSS is still challenging, but 4D Flow MRI represents a promising tool to provide 3D velocity data from which WSS can be calculated. In this study, a system based on Laser Doppler Velocimetry (LDV) was developed to validate new improvements of 4D Flow MRI acquisitions and derived WSS computing. A hydraulic circuit was manufactured to allow both 4D Flow MRI and LDV velocity measurements. WSS profiles were calculated with one 2D and one 3D method. Results indicated an excellent agreement between MRI and LDV velocity data, and thus the set-up enabled the evaluation of the improved performances of 3D with respect to the 2D-WSS computation method. To provide a concrete example of the efficacy of this method, the influence of the spatial resolution of MRI data on derived 3D-WSS profiles was investigated. This investigation showed that, with acquisition times compatible with standard clinical conditions, a refined MRI resolution does not improve WSS assessment, if the impact of noise is unreduced. This study represents a reliable basis to validate with LDV WSS calculation methods based on 4D Flow MRI.

Exploring the Relationships Between Hemodynamic Stresses in the Carotid Arteries

Background: Atherosclerosis manifests as a focal disease, often affecting areas with complex hemodynamics such as the carotid bifurcation. The magnitude and regularity of the hemodynamic shear stresses acting on the vessel wall are thought to generate risk patterns unique to each patient and play a role in the pathogenesis of atherosclerosis. The involvement of different expressions of shear stress in the pathogenesis of carotid atherosclerosis highlights the need to characterize and compare the differential impact of the various expressions of shear stress in the atherosclerotic carotid bifurcation. Therefore, the aim of this study is to characterize and compare hemodynamic wall shear stresses (WSS) in the carotid arteries of subjects with asymptomatic atherosclerotic plaques. Shear stresses were also compared against vessel diameter and bifurcation angle to examine the relationships with the geometry of the carotid bifurcation. Methods: 4D Flow MRI and contrast-enhanced MRA data were acquired for 245 subjects with atherosclerotic plaques of at least 2.7 mm in conjunction with the Swedish CArdioPulmonary bioImage Study (SCAPIS). Following automatic segmentation and geometric analysis, time-resolved WSS and near-wall turbulent kinetic energy (nwTKE) were derived from the 4D Flow data. Whole-cycle parameters including time-averaged WSS and nwTKE, and the oscillatory shear index (OSI) were calculated. Pairwise Spearman rank-correlation analyses were used to investigate relationships among the hemodynamic as well as geometric parameters. Results: One hundred and seventy nine subjects were successfully segmented using automated tools and subsequently geometric and hemodynamic analyses were performed. Temporally resolved WSS and nwTKE were strongly correlated, ρ = 0.64. Cycle-averaged WSS and nwTKE were moderately correlated, ρ = 0.57. Cycle-average nwTKE was weakly correlated to OSI (ρ = -0.273), revealing that nwTKE provides information about disturbed flow on the vessel wall that OSI does not. In this cohort, there was large inter-individual variation for both WSS and nwTKE. Both WSS and nwTKE varied most within the external carotid artery. WSS, nwTKE, and OSI were weakly correlated to vessel diameter and bifurcation angle. Conclusion: The turbulent and mean component of WSS were examined together in vivo for the first time, and a strong correlation was found between them. nwTKE presents the opportunity to quantify turbulent wall stresses in vivo and gain insight into the effects of disturbed flow on the vessel wall. Neither vessel diameter nor bifurcation angle were found to be strongly correlated to the turbulent or mean component of WSS in this cohort.

Influence of near-wall PIV data on recirculation hemodynamics in a patient-specific moderate stenosis: Experimental-numerical comparison

BACKGROUND

Recirculation zones within the blood vessels are known to influence the initiation and progression of atherosclerotic lesions. Quantification of recirculation parameters with accuracy remains subjective due to uncertainties in measurement of velocity and derived wall shear stress (WSS).

OBJECTIVE

The primary aim is to determine recirculation height and length from PIV experiments while validating with two different numerical methods: finite-element (FE) and -volume (FV). Secondary aim is to analyze how FE and FV compare within themselves.

METHODS

PIV measurements were performed to obtain velocity profiles at eight cross sections downstream of stenosis at flow rate of 200 ml/min. WSS was obtained by linear/quadratic interpolation of experimental velocity measurements close to wall.

RESULTS

Recirculation length obtained from PIV technique was 1.47 cm and was within 2.2% of previously reported in-vitro measurements. Derived recirculation length from PIV agreed within 6.8% and 8.2% of the FE and FV calculations, respectively. For lower shear rate, linear interpolation with five data points results in least error. For higher shear rate either higher order (quadratic) interpolation with five data points or lower order (linear) with lesser (three) data points leads to better results.

CONCLUSION

Accuracy of the recirculation parameters is dependent on number of near wall PIV data points and the type of interpolation algorithm used.

Four-Dimensional Magnetic Resonance Imaging Assessment of Intracranial Aneurysms: A State-of-the-Art Review

Treatment of unruptured intracranial aneurysms can reduce the risk of subarachnoid hemorrhage and its associated morbidity and mortality. However, current methods to predict the risk of rupture and optimize treatment strategies for intracranial aneurysms are limited. Assessment of intra-aneurysmal flow using 4-dimensional magnetic resonance imaging (4D MRI) is a novel tool that could be used to guide therapy. A systematic search of the literature was performed to provide a state-of-the-art review on 4D MRI assessment of unruptured intracranial aneurysms. A total of 18 studies were available for review. Eccentric flow on 4D MRI is associated with a greater aspect ratio and peak wall shear stress (WSS). WSS, vorticity, and peak velocity are greater in saccular than fusiform aneurysms. Unstable aneurysms are associated with greater WSS, peak wall stress, and flow jet angle and may exhibit wall enhancement. In comparison to computational fluid dynamics (CFD), 4D MRI has a lower spatial resolution and reports lower WSS and velocity magnitudes, but these parameters equalize when spatial resolution is matched. 4D MRI demonstrates the intra-aneurysmal hemodynamic changes associated with flow diversion, including significantly decreased flow velocity. Thus, 4D MRI is a novel, noninvasive imaging tool used for the evaluation of hemodynamics within intracranial aneurysms. Hemodynamic indices derived from 4D MRI appear to correlate well with the simulated (CFD) values and may be used to measure the success of endovascular therapies and risk factors for aneurysm growth and rupture.

Carotid artery displacement and cardiovascular disease risk in the Multi-Ethnic Study of Atherosclerosis

Novel technology permits quantification of common carotid artery (CCA) displacement, which is traditionally ignored. We evaluated associations with CCA displacement and cardiovascular disease (CVD) risk and events in a large, multi-ethnic cohort. Right CCA longitudinal displacement (LD), transverse displacement (TD), and grayscale median (GSM) were evaluated using ultrasound speckle-tracking and texture analysis software in 2050 participants. Regression analyses were used to define relationships between CCA LD, TD, GSM, and CVD risk factors. Cox proportional hazards models were used to assess relationships between LD, TD, and incident CVD events. Participants were mean (SD) 64 (10) years old. There were 791 cases with a CVD event over a 12-year median follow-up. The mean LD was 0.29 (0.20) mm. In multivariable models including age, sex, race/ethnicity, heart rate, and CVD risk factors, LD was associated positively with active smoking (β = 0.08, p < 0.001) and inversely with black (β = −0.08, p < 0.001), Chinese (β = −0.05, p < 0.001), and Hispanic (β = −0.04, p < 0.05) race/ethnicities relative to white individuals, heart rate (β = −0.03/10 beats/min, p < 0.001), and diastolic blood pressure (β = −0.01/5 mmHg, p < 0.05). In fully adjusted models, LD and TD were associated with GSM ( p < 0.01), but neither predicted incident CVD events (LD: hazard ratio (HR) 0.77 [0.48 to 1.24], p = 0.3; TD: HR 1.12 [0.8 to 1.57], p = 0.5). CCA LD and TD are associated with race/ethnicity and CVD risk factors but not incident CVD events. LD and TD are not measures of arterial stiffness but their association with GSM suggests that lower LD and TD may be related to structural changes within the carotid arterial wall.

Volumetric segmentation-free method for rapid visualization of vascular wall shear stress using 4D flow MRI

PURPOSE

To develop a rapid segmentation-free method to visualize and compute wall shear stress (WSS) throughout the aorta using 4D Flow MRI data. WSS is the drag force-per-area the vessel endothelium exerts on luminal blood; abnormal levels of WSS are associated with cardiovascular pathologies. Previous methods for computing WSS are bottlenecked by labor-intensive manual segmentation of vessel boundaries. A rapid automated segmentation-free method for computing WSS is presented.

THEORY AND METHODS

Shear stress is the dot-product of the viscous stress tensor and the inward normal vector. The inward normal vectors are approximated as the gradient of fluid speed at every voxel. Subsequently, a 4D map of shear stress is computed as the partial derivatives of velocity with respect to the inward normal vectors. We highlight the shear stress near the wall by fusing visualization with edge-emphasized anatomical data.

RESULTS

As a proof-of-concept, four cases with aortic pathologies are presented. Visualization allows for rapid localization of pathologic WSS. Subsequent analysis of these pathological regions enables quantification of WSS. Average WSS during peak systole measures approximately 50-60 cPa in nonpathological regions of the aorta and is elevated in regions of stenosis, coarctation, and dissection. WSS is reduced in regions of aneurysm.

CONCLUSION

A volumetric technique for calculation and visualization of WSS from 4D Flow MRI data is presented. Traditional labor-intensive methods for WSS rely on explicit manual segmentation of vessel boundaries before visualization. This automated volumetric strategy for visualization and quantification of WSS may facilitate its clinical translation.

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.

Echo Particle Image Velocimetry for Estimation of Carotid Artery Wall Shear Stress: Repeatability, Reproducibility and Comparison with Phase-Contrast Magnetic Resonance Imaging

Measurement of hemodynamic wall shear stress (WSS) is important in investigating the role of WSS in the initiation and progression of atherosclerosis. Echo particle image velocimetry (echo PIV) is a novel ultrasound-based technique for measuring WSS in vivo that has previously been validated in vitro using the standard optical PIV technique. We evaluated the repeatability and reproducibility of echo PIV for measuring WSS in the human common carotid artery. We measured WSS in 28 healthy participants (18 males and 10 females, mean age: 56 ± 12 y). Echo PIV was highly repeatable, with an intra-observer variability of 1.0 ± 0.1 dyn/cm² for peak systolic (maximum), 0.9 dyn/cm² for mean and 0.5 dyn/cm² for end-diastolic (minimum) WSS measurements. Likewise, echo PIV was reproducible, with a low inter-observer variability (max: 2.0 ± 0.2 dyn/cm², mean: 1.3 ± 0.1 dyn/cm², end-diastolic: 0.7 dyn/cm²) and more variable inter-scan (test-retest) variability (max: 7.1 ± 2.3 dyn/cm², mean: 2.9 ± 0.4 dyn/cm², min: 1.5 ± 0.1 dyn/cm²). We compared echo PIV with the reference method, phase-contrast magnetic resonance imaging (PC-MRI); echo PIV-based WSS measurements agreed qualitatively with PC-MRI measurements (r = 0.89, p < 0.05). Significant differences were observed in some WSS measurements (echo PIV vs. PC-MRI): WSS at peak systole: 21 ± 7.0 dyn/cm² vs. 15 ± 5.0 dyn/cm²; time-averaged WSS: 8.9 ± 3.0 dyn/cm² vs. 7.1 ± 3.0 dyn/cm² (p < 0.05); WSS at end diastole: 3.8 ± 2.8 dyn/cm² vs. 3.9 ± 2 dyn/cm² (p > 0.05). For the first time, we report that echo PIV can measure WSS with good repeatability and reproducibility in adult humans with a broad age range. Echo PIV is feasible in humans and offers an easy-to-use, ultrasound-based, quantitative technique for measuring WSS in vivo in humans with good repeatability and reproducibility.

Omics-based approaches to understand mechanosensitive endothelial biology and atherosclerosis

Atherosclerosis is a multifactorial disease that preferentially occurs in arterial regions exposed to d-flow can be used to indicate disturbed flow or disturbed blood flow. The mechanisms by which d-flow induces atherosclerosis involve changes in the transcriptome, methylome, proteome, and metabolome of multiple vascular cells, especially endothelial cells. Initially, we begin with the pathogenesis of atherosclerosis and the changes that occur at multiple levels owing to d-flow, especially in the endothelium. Also, there are a variety of strategies used for the global profiling of the genome, transcriptome, miRNA-ome, DNA methylome, and metabolome that are important to define the biological and pathophysiological mechanisms of endothelial dysfunction and atherosclerosis. Finally, systems biology can be used to integrate these 'omics' datasets, especially those that derive data based on a single animal model, in order to better understand the pathophysiology of atherosclerosis development in a holistic manner and how this integrative approach could be used to identify novel molecular diagnostics and therapeutic targets to prevent or treat atherosclerosis. WIREs Syst Biol Med 2016, 8:378-401. doi: 10.1002/wsbm.1344 For further resources related to this article, please visit the WIREs website.

MRI-based biomechanical parameters for carotid artery plaque vulnerability assessment

Carotid atherosclerotic plaques are a major cause of ischaemic stroke. The biomechanical environment to which the arterial wall and plaque is subjected to plays an important role in the initiation, progression and rupture of carotid plaques. MRI is frequently used to characterize the morphology of a carotid plaque, but new developments in MRI enable more functional assessment of carotid plaques. In this review, MRI based biomechanical parameters are evaluated on their current status, clinical applicability, and future developments. Blood flow related biomechanical parameters, including endothelial wall shear stress and oscillatory shear index, have been shown to be related to plaque formation. Deriving these parameters directly from MRI flow measurements is feasible and has great potential for future carotid plaque development prediction. Blood pressure induced stresses in a plaque may exceed the tissue strength, potentially leading to plaque rupture. Multi-contrast MRI based stress calculations in combination with tissue strength assessment based on MRI inflammation imaging may provide a plaque stress-strength balance that can be used to assess the plaque rupture risk potential. Direct plaque strain analysis based on dynamic MRI is already able to identify local plaque displacement during the cardiac cycle. However, clinical evidence linking MRI strain to plaque vulnerability is still lacking. MRI based biomechanical parameters may lead to improved assessment of carotid plaque development and rupture risk. However, better MRI systems and faster sequences are required to improve the spatial and temporal resolution, as well as increase the image contrast and signal-to-noise ratio.

The role of endothelial mechanosensitive genes in atherosclerosis and omics approaches

Atherosclerosis is the leading cause of morbidity and mortality in the U.S., and is a multifactorial disease that preferentially occurs in regions of the arterial tree exposed to disturbed blood flow. The detailed mechanisms by which d-flow induces atherosclerosis involve changes in the expression of genes, epigenetic patterns, and metabolites of multiple vascular cells, especially endothelial cells. This review presents an overview of endothelial mechanobiology and its relation to the pathogenesis of atherosclerosis with special reference to the anatomy of the artery and the underlying fluid mechanics, followed by a discussion of a variety of experimental models to study the role of fluid mechanics and atherosclerosis. Various in vitro and in vivo models to study the role of flow in endothelial biology and pathobiology are discussed in this review. Furthermore, strategies used for the global profiling of the genome, transcriptome, miR-nome, DNA methylome, and metabolome, as they are important to define the biological and pathophysiological mechanisms of atherosclerosis. These "omics" approaches, especially those which derive data based on a single animal model, provide unprecedented opportunities to not only better understand the pathophysiology of atherosclerosis development in a holistic and integrative manner, but also to identify novel molecular and diagnostic targets.

Carotid Artery Longitudinal Displacement, Cardiovascular Disease and Risk Factors: The Multi-Ethnic Study of Atherosclerosis

BACKGROUND

Associations between carotid artery longitudinal displacement, cardiovascular disease risk factors, and events were evaluated in a large, multi-ethnic cohort.

MATERIALS AND METHODS

A novel, reproducible protocol was developed for measuring right common carotid artery longitudinal displacement using ultrasound speckle-tracking. Total longitudinal displacement was measured in 389 randomly selected participants from the Multi-Ethnic Study of Atherosclerosis that were free of cardiovascular disease at baseline. Univariate analyses and Pearson Correlations were used to define relationships between longitudinal displacement with traditional cardiovascular risk factors and traditional measures of arterial stiffness. Hazard ratios of longitudinal displacement for cardiovascular disease and coronary heart disease events were compared using Cox proportional hazards models.

RESULTS

Participants were a mean (standard deviation) 59.0 (8.7) years old, 48% female, 39% White, 26% Black, 22% Hispanic, and 14% Chinese. They had 19 (4.9%) cardiovascular disease and 14 (3.6%) coronary heart disease events over a mean 9.5 years of follow-up. Less longitudinal displacement was associated with Chinese (β = -0.11, p = 0.02) compared to White race/ethnicity and greater longitudinal displacement was associated with higher carotid intima-media thickness (β = 0.26, p = 0.004). Longitudinal displacement was not associated with other cardiovascular disease risk factors or markers of arterial stiffness. After adjustment for age and sex, and heart rate, Chinese race/ethnicity (β = -0.10, p = 0.04) and carotid intima-media thickness (β = 0.30 p = 0.003) were associated independently with longitudinal displacement. Longitudinal displacement predicted coronary heart disease (Hazard ratio [HR] 3.3, 95% Confidence intervals [CI] 0.96-11.14, p = 0.06) and cardiovascular disease (HR 2.1, 95% CI 0.6-7.3, p = 0.23) events.

CONCLUSIONS

Less longitudinal displacement is associated with Chinese ethnicity and greater carotid artery longitudinal displacement is associated with thicker intima-media thickness. Longitudinal displacement may predict adverse coronary heart disease and cardiovascular disease events.

Effects of arterial blood flow on walls of the abdominal aorta: distributions of wall shear stress and oscillatory shear index determined by phase-contrast magnetic resonance imaging

Although abdominal aortic aneurysms (AAAs) occur mostly inferior to the renal artery, the mechanism of the development of AAA in relation to its specific location is not yet clearly understood. The objective of this study was to evaluate the hypothesis that even healthy volunteers may manifest specific flow characteristics of blood flow and alter wall shear or oscillatory shear stress in the areas where AAAs commonly develop. Eight healthy male volunteers were enrolled in this prospective study, aged from 24 to 27. Phase-contrast magnetic resonance imaging (MRI) was performed with electrocardiographic triggering. Flow-sensitive four-dimensional MR imaging of the abdominal aorta, with three-directional velocity encoding, including simple morphological image acquisition, was performed. Information on specific locations on the aortic wall was applied to the flow encodes to calculate wall shear stress (WSS) and oscillatory shear index (OSI). While time-framed WSS showed the highest peak of 1.14 ± 0.25 Pa in the juxtaposition of the renal artery, the WSS plateaued to 0.61 Pa at the anterior wall of the abdominal aorta. The OSI peaked distal to the renal arteries at the posterior wall of the abdominal aorta of 0.249 ± 0.148, and was constantly elevated in the whole abdominal aorta at more than 0.14. All subjects were found to have elevated OSI in regions where AAAs commonly occur. These findings indicate that areas of constant peaked oscillatory shear stress in the infra-renal aorta may be one of the factors that lead to morphological changes over time, even in healthy individuals.

Cardiovascular magnetic resonance phase contrast imaging

Cardiovascular magnetic resonance (CMR) phase contrast imaging has undergone a wide range of changes with the development and availability of improved calibration procedures, visualization tools, and analysis methods. This article provides a comprehensive review of the current state-of-the-art in CMR phase contrast imaging methodology, clinical applications including summaries of past clinical performance, and emerging research and clinical applications that utilize today's latest technology.

Quantifying errors in flow measurement using phase contrast magnetic resonance imaging: comparison of several boundary detection methods

Quantifying flow from phase-contrast MRI (PC-MRI) data requires that the vessels of interest be segmented. The estimate of the vessel area will dictate the type and magnitude of the error sources that affect the flow measurement. These sources of errors are well understood, and mathematical expressions have been derived for them in previous work. However, these expressions contain many parameters that render them difficult to use for making practical error estimates. In this work, some realistic assumptions were made that allow for the simplification of such expressions in order to make them more useful. These simplified expressions were then used to numerically simulate the effect of segmentation accuracy and provide some criteria that if met, would keep errors in flow quantification below 10% or 5%. Four different segmentation methods were used on simulated and phantom MRA data to verify the theoretical results. Numerical simulations showed that including partial volumed edge pixels in vessel segmentation provides less error than missing them. This was verified with MRA simulations, as the best performing segmentation method generally included such pixels. Further, it was found that to obtain a flow error of less than 10% (5%), the vessel should be at least 4 (5) pixels in diameter, have an SNR of at least 10:1 and have a peak velocity to saturation cut-off velocity ratio of at least 5:3.

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.

SIMULATION OF PULSATILE BLOOD FLOW THROUGH STENOTIC ARTERY CONSIDERING DIFFERENT BLOOD RHEOLOGIES: COMPARISON OF 3D AND 2D-AXISYMMETRIC MODELS

Hemodynamic factors such as velocity distribution, pressure gradient and wall shear stress are thought to play an important role in the prognosis of symptomatic carotid occlusion. Although there are many studies about modeling the blood flow behavior in carotid, hemodynamic characteristics of blood flow in a stenosed carotid artery is still debatable. In this study a three-dimensional (3D) model of a symmetric stenosed common carotid artery (CCA) is developed and the simulation results of it are compared to the experimental data where subsequent agreement is confirmed. To study the accuracy of two-dimensional (2D) axisymmetric model, the result of it is compared to the result of the 3D model. Two non-Newtonian rheological models, namely Carreau and modified Power-law, as well as Newtonian model are used to realize the hemodynamical differences of 2D-axisymmetric and 3D models in pulsatile blood flow. Comparing the 3D simulated results with 2D-axisymmetric modeling results that were published in recent years indicates that the assumption of 2D-axisymmetric model cannot adequately predict the velocity profiles even for a symmetric stenotic artery. Although a symmetric stenotic artery is considered, the results indicate a nonsymmetric flow in poststenosis region that is detected by the presence of extensive secondary flows particularly at diastole. The existence of secondary flows that can only be detected in 3D modeling is the main reason for the differences in hemodynamic factors in 3D and 2D results.

Errors in the estimation of wall shear stress by maximum Doppler velocity

OBJECTIVE

Wall shear stress (WSS) is an important parameter with links to vascular (dys)function. Difficult to measure directly, WSS is often inferred from maximum spectral Doppler velocity (Vmax) by assuming fully-developed flow, which is valid only if the vessel is long and straight. Motivated by evidence that even slight/local curvatures in the nominally straight common carotid artery (CCA) prevent flow from fully developing, we investigated the effects of velocity profile skewing on Vmax-derived WSS.

METHODS

Velocity profiles, representing different degrees of skewing, were extracted from the CCA of image-based computational fluid dynamics (CFD) simulations carried out as part of the VALIDATE study. Maximum velocities were calculated from idealised sample volumes and used to estimate WSS via fully-developed (Poiseuille or Womersley) velocity profiles, for comparison with the actual (i.e. CFD-derived) WSS.

RESULTS

For cycle-averaged WSS, mild velocity profile skewing caused ±25% errors by assuming Poiseuille or Womersley profiles, while severe skewing caused a median error of 30% (maximum 55%). Peak systolic WSS was underestimated by ~50% irrespective of skewing with Poiseuille; using a Womersley profile removed this bias, but ±30% errors remained. Errors were greatest in late systole, when skewing was most pronounced. Skewing also introduced large circumferential WSS variations: ±60%, and up to ±100%, of the circumferentially averaged value.

CONCLUSION

Vmax-derived WSS may be prone to substantial variable errors related to velocity profile skewing, and cannot detect possibly large circumferential WSS variations. Caution should be exercised when making assumptions about velocity profile shape to calculate WSS, even in vessels usually considered long and straight.

Multicellularity and antibiotic resistance in Klebsiella pneumoniae grown under bloodstream-mimicking fluid dynamic conditions

BACKGROUND

While the importance of fluid dynamical conditions is well recognized in the growth of biofilms, their role during bacteremia is unknown. We examined the impact of physiological fluid shear forces on the development of multicellular aggregates of Klebsiella pneumoniae.

METHODS

Wild-type and O-antigen or capsular mutants of K. pneumoniae were grown as broth culture in a Taylor-Couette flow cell configured to provide continuous shear forces comparable to those encountered in the human arterial circulation (ie, on the order of 1.0 Pa). The size distribution and antibiotic resistance of aggregates formed in this apparatus were determined, as was their ability to persist in the bloodstream of mice following intravenous injection.

RESULTS

Unlike growth in shaking flasks, bacteria grown in the test apparatus readily formed aggregates, a phenotype largely absent in capsular mutants and to a lesser degree in O-antigen mutants. Aggregates were found to persist in the bloodstream of mice. Importantly, organisms grown under physiological shear were found to have an antibiotic resistance phenotype intermediate between that of fully planktonic and biofilm states.

CONCLUSIONS

When grown under intravascular-magnitude fluid dynamic conditions, K. pneumoniae spontaneously develops into multicellular aggregates that are capable of persisting in the circulation and exhibit increased antibiotic resistance.

Intraoperative handheld optical coherence tomography forward-viewing probe: physical performance and preliminary animal imaging

A prototype intraoperative hand-held optical coherence tomography (OCT) imaging probe was developed to provide micron resolution cross-sectional images of subsurface tissue during open surgery. This new ergonomic probe was designed based on electrostatically driven optical fibers, and packaged into a catheter probe in the form factor of clinically accepted Bayonet shaped neurosurgical probes. Optical properties of the probe were measured to have a ~20 μm spot size, 5 mm working distance and 4 mm field of view. Feasibility of this probe for structural and Doppler shift imaging was tested on porcine femoral blood vessel imaging.

Two-dimensional flow study in a stenotic artery phantom using ultrasonic particle image velocimetry

Blood flow dynamics has an important role in atherosclerosis initiation, progression, plaque rupture and thrombosis, and it is important to investigate the flow characteristics in the context of a mild stenotic artery. In this paper, tissue-equivalent ultrasound phantoms of artery stenosis were fabricated, and ultrasonic particle image velocimetry (EchoPIV) method was applied for two-dimensional flow study. A flow circuit was established and steady flow was provided by the gear pump. Flow at the inlet and the stenosis region were researched with EchoPIV method and ultrasound Doppler technique. The detailed 2D two-component velocity vectors were determined with EchoPIV method, and the measuring accuracy outweighs that of Ultrasound Doppler by comparing to the theoretical values of Poiseuille flow.

In vitro and preliminary in vivo validation of echo particle image velocimetry in carotid vascular imaging

Noninvasive, easy-to-use and accurate measurements of wall shear stress (WSS) in human blood vessels have always been challenging in clinical applications. Echo particle image velocimetry (Echo PIV) has shown promise for clinical measurements of local hemodynamics and wall shear rate. Thus far, however, the method has only been validated under simple flow conditions. In this study, we validated Echo PIV under in vitro and in vivo conditions. For in vitro validation, we used an anatomically correct, compliant carotid bifurcation flow phantom with pulsatile flow conditions, using optical particle image velocimetry (optical PIV) as the reference standard. For in vivo validation, we compared Echo PIV-derived 2-D velocity fields obtained at the carotid bifurcation in five normal subjects against phase-contrast magnetic resonance imaging (PC-MRI)-derived velocity measurements obtained at the same locations. For both studies, time-dependent, 2-D, two-component velocity vectors; peak/centerline velocity, flow rate and wall shear rate (WSR) waveforms at the common carotid artery (CCA), carotid bifurcation and distal internal carotid artery (ICA) were examined. Linear regression, correlation analysis and Bland-Altman analysis were used to quantify the agreement of different waveforms measured by the two techniques. In vitro results showed that Echo PIV produced good images of time-dependent velocity vector maps over the cardiac cycle with excellent temporal (up to 0.7 ms) and spatial (∼0.5 mm) resolutions and quality, comparable with optical PIV results. Further, good agreement was found between Echo PIV and optical PIV results for velocity and WSR measurements. In vivo results also showed good agreement between Echo PIV velocities and phase contrast MRI velocities. We conclude that Echo PIV provides accurate velocity vector and WSR measurements in the carotid bifurcation and has significant potential as a clinical tool for cardiovascular hemodynamics evaluation.

Endothelial shear stress: a critical determinant of arterial remodeling and arterial stiffness in humans--a carotid 3.0-T MRI study

BACKGROUND

Low endothelial shear stress (ESS) elicits endothelial dysfunction. However, the relationship between ESS and arterial remodeling and arterial stiffness is unknown in humans. We developed a 3.0-T MRI protocol to evaluate the contribution of ESS to arterial remodeling and stiffness.

METHODS AND RESULTS

Fifteen young (aged 26 ± 3 years) and 15 older (aged 57 ± 3 years) healthy volunteers as well as 15 patients with cardiovascular disease (aged 63 ± 10 years) were enrolled. Phase-contrast MRI of the common carotid arteries was used to derive ESS data from the spatial velocity gradients close to the arterial wall. ESS measurements were performed on 3 occasions and showed excellent reproducibility (intraclass correlation coefficient, 0.79). Multiple linear regression analysis accounting for age and blood pressure revealed that ESS was an independent predictor of the following response variables: carotid wall thickness (regression coefficient [b], -0.19 mm(2) per N/m(2); P=0.02), lumen area (b, -15.5 mm(2) per N/m(2); P<0.001), and vessel size (b, -24.0 mm(2) per N/m(2); P<0.001). Segments of the artery wall exposed to lower ESS were significantly thicker than segments exposed to higher ESS within the same artery (P=0.009). Furthermore, ESS was associated with arterial compliance, accounting for age, blood pressure, and wall thickness (b, -0.003 mm(2)/mm Hg per N/m(2); P=0.04).

CONCLUSIONS

Our carotid MRI data show that ESS is an important determinant of arterial remodeling and arterial stiffness in humans. The data warrant further studies to evaluate use of carotid ESS as a noninvasive tool to improve the understanding of individual cardiovascular disease risk and to assess novel drug therapies in cardiovascular disease prevention.

The critical role of hemodynamics in the development of cerebral vascular disease

Atherosclerosis and intracranial saccular aneurysms predictably localize in areas with complex arterial geometries such as bifurcations and curvatures. These sites are characterized by unique hemodynamic conditions that possibly influence the risk for these disorders. One hemodynamic parameter in particular has emerged as a key regulator of vascular biology—wall shear stress (WSS). Variations in geometry can change the distribution and magnitude of WSS, thus influencing the risk for vascular disorders. Computer simulations conducted using patient-specific data have suggested that departures from normal levels of WSS lead to aneurysm formation and progression. In addition, multiple studies indicate that disturbed flow and low WSS predispose patients to extracranial atherosclerosis, and particularly to carotid artery disease. Conversely, in the case of intracranial atherosclerosis, more studies are needed to provide a firm link between hemodynamics and atherogenesis. The recognition of WSS as an important factor in cerebral vascular disease may help to identify individuals at risk and guide treatment options.

Non-invasive hemodynamic state monitoring using ultrasound

Hemodynamic monitoring provides vital information for diagnosing and treating patients in acute clinical settings. A method is investigated to non-invasively monitor changes in the hemodynamic state. The approach utilizes short-axis ultrasound color flow imaging and processing methods to produce simultaneous waveforms for the arterial area and flow. Beat-to-beat measurements of the mean area, peak volumetric flow rate, and heart rate are extracted, and the distribution of these parameters is used to define the hemodynamic state. Changes in the hemodynamic state are detected by calculating a distance between new measurements and the current hemodynamic state, and then comparing this distance to an adaptive threshold. The distribution was modeled as a multivariate normal distribution characterized by a mean vector and a covariance matrix, and the Mahalanobis distance was used as the distance metric. The threshold level was adapted to produce a constant probability of false positives based on the current distribution. The method was evaluated by observing pharmacologically induced changes in the hemodynamic state during an in vivo animal experiment. The ultrasound-based measurements provided sufficient accuracy to discriminate between the hemodynamic states before, during and after infusion of a vasodilator. The ability to detect an acute change in the hemodynamic state was demonstrated in the transient period at the start of the infusion.

Association between wall shear stress and carotid atherosclerosis in patients with never treated essential hypertension

BACKGROUND

Wall shear stress (WSS) has been shown to be a critical determinant of vessel diameter implicated in vascular remodeling and atherogenesis. Carotid intima-media thickness (IMT), resistive index (RI), and pulsatility index (PI) have been used as relevant indictors for carotid atherosclerosis. The study aimed to investigate the relationship between hemodynamic parameters in the common carotid artery (CCA) and the severity of carotid atherosclerosis in untreated hypertensive patients.

METHODS

Duplex ultrasound was performed in 64 untreated hypertensive patients and 16 age-matched normotensive control subjects. Morphologic and hemodynamic parameters of CCA, including peak and mean WSS, RI, PI, and IMT were calculated after measuring internal diameter (ID) and flow velocity of CCA.

RESULTS

Subjects with hypertension had lower peak and mean WSS than did normotensive control subjects (P < 0.05). Both carotid RI and PI were found to correlate inversely with mean WSS in hypertensive subjects. There was no correlation between carotid IMT and WSS. Stepwise multiple regression analysis for carotid RI and PI after adjustment for age, carotid IMT, and high sensitivity C-reactive protein (hsCRP) showed that mean WSS was an independent determinant of RI and PI.

CONCLUSIONS

High carotid atherosclerotic indexes as expressed by both RI and PI are associated with low WSS in CCA. These findings indicate that local shear stress is associated with altered vascular pulsatility and resistance. Consequent alteration in local vascular dynamics could be an underlying mechanism for the progression of atherosclerosis.

In vivo non-invasive high resolution MR-based method for the determination of the elastic modulus of arterial vessels

The mechanical properties of arterial walls have long been recognized to play an essential role in the development and progression of cardiovascular disease (CVD). Early detection of variations in the elastic modulus of arteries would help in monitoring patients at high cardiovascular risk stratifying them according to risk. An in vivo, non-invasive, high resolution MR-phase-contrast based method for the estimation of the time-dependent elastic modulus of healthy arteries was developed, validated in vitro by means of a thin walled silicon rubber tube integrated into an existing MR-compatible flow simulator and used on healthy volunteers. A comparison of the elastic modulus of the silicon tube measured from the MRI-based technique with direct measurements confirmed the method's capability. The repeatability of the method was assessed. Viscoelastic and inertial effects characterizing the dynamic response of arteries in vivo emerged from the comparison of the pressure waveform and the area variation curve over a period. For all the volunteers who took part in the study the elastic modulus was found to be in the range 50-250 kPa, to increase during the rising part of the cycle, and to decrease with decreasing pressure during the downstroke of systole and subsequent diastole.

Sub-piexl methods for improving vector quality in echo PIV flow, imaging technology

Developments of many cardiovascular problems have been shown to have a close relationship with arterial flow conditions. An ultrasound-based particle image velocimetry technique(Echo PIV) was recently developed to measure multi-component velocity vectors and local shear rates in arteries and opaque fluid flows by identifying and tracking flow tracers (ultrasound contrast microbubbles) within these flow fields. To improve the measurement accuracy, sub-pixel calculation method was adopted in this paper to maximize the ultrasound RF signal and B mode image correlation accuracy and increase the image spatial resolution. This algorithm is employed in processing both computer-generated particle image patterns and the B-mode images of microbubbles in rotating flows obtained by a high frame rate (up to 1000 frames per second) ultrasound imaging system. The results show the correlation of particle patterns and individual flow vector quality are improved and the overall flow mappings are also improved significantly. This would help the Echo PIV system to provide better multi-component velocity accuracy.

Micro-ultrasound biofluid imaging and multi-component velocity measurement with micro echo particle image velocimetry technique

This paper presents a high-resolution microscale ultrasonic particle image velocimetry technique (termed as Micro-EPIV) for measuring multi-component velocity vectors in microscale opaque flows such as blood and biofluid flow in microvessel. The method was tested by in vitro flow imaging and in vivo small animal blood flow imaging studies. The bioflow and blood flow were seeded with ultrasound contrast microbubbles, and were "illuminated" acoustically by 50 MHz and 30 MHz ultrasound, respectively. B-mode images obtained at imaging frame rate of 10 frames per second (fps) and 110 fps were constructed from back-scattered RF signals from bubbles. Then, consecutive images were processed with optimized PIV algorithm, to acquire multi-component velocity vectors. The results were in good agreement with analytical solutions and the velocities measured by ultrasound Doppler technique.

Circumferential strain in the wall of the common carotid artery: comparing displacement-encoded and cine MRI in volunteers

The walls of conduit arteries undergo cyclic stretching from the periodic fluctuation of arterial pressure. Atherosclerotic lesions have been shown to localize to regions of excessive stretching of the arterial wall. We employed a displacement encoding with stimulated echoes (DENSE) sequence to image the motion of the common carotid artery wall and map the two-dimensional (2D) circumferential strain. The sequence utilizes a fully-balanced steady-state free-precession (SSFP) readout with 0.60 mm in-plane resolution. Preliminary results in volunteers at 1.5T (N = 4) and 3.0T (N = 17) are compared to measurements of the lumen circumference from cine images. The agreement between the two independent measurements at both field strengths (P < or = 0.001) supports the use of DENSE as a means to map the pulsatile strain in the carotid artery wall.

Wall shear stress as measured in vivo: consequences for the design of the arterial system

Based upon theory, wall shear stress (WSS), an important determinant of endothelial function and gene expression, has been assumed to be constant along the arterial tree and the same in a particular artery across species. In vivo measurements of WSS, however, have shown that these assumptions are far from valid. In this survey we will discuss the assessment of WSS in the arterial system in vivo and present the results obtained in large arteries and arterioles. In vivo WSS can be estimated from wall shear rate, as derived from non-invasively recorded velocity profiles, and whole blood viscosity in large arteries and plasma viscosity in arterioles, avoiding theoretical assumptions. In large arteries velocity profiles can be recorded by means of a specially designed ultrasound system and in arterioles via optical techniques using fluorescent flow velocity tracers. It is shown that in humans mean WSS is substantially higher in the carotid artery (1.1–1.3 Pa) than in the brachial (0.4–0.5 Pa) and femoral (0.3–0.5 Pa) arteries. Also in animals mean WSS varies substantially along the arterial tree. Mean WSS in arterioles varies between about 1.0 and 5.0 Pa in the various studies and is dependent on the site of measurement in these vessels. Across species mean WSS in a particular artery decreases linearly with body mass, e.g., in the infra-renal aorta from 8.8 Pa in mice to 0.5 Pa in humans. The observation that mean WSS is far from constant along the arterial tree implies that Murray’s cube law on flow-diameter relations cannot be applied to the whole arterial system. Because blood flow velocity is not constant along the arterial tree either, a square law also does not hold. The exponent in the power law likely varies along the arterial system, probably from 2 in large arteries near the heart to 3 in arterioles. The in vivo findings also imply that in in vitro studies no average shear stress value can be taken to study effects on endothelial cells derived from different vascular areas or from the same artery in different species. The cells have to be studied under the shear stress conditions they are exposed to in real life.

Flow-area relationship in internal carotid and vertebral arteries

Subject-specific computational and experimental models of hemodynamics in cerebral aneurysms require the specification of physiologic flow conditions. Because patient-specific flow data are not always available, researchers have used 'typical' or population average flow rates and waveforms. However, in order to be able to compare the magnitude of hemodynamic variables between different aneurysms or groups of aneurysms (e.g. ruptured versus unruptured) it is necessary to scale the flow rates to the area of the inflow artery. In this work, a relationship between flow rates and vessel areas is derived from phase-contrast magnetic resonance measurements in the internal carotid arteries and vertebral arteries of normal subjects.

In vivo wall shear stress measurements using phase-contrast MRI

There is growing evidence to suggest that endothelial biology and atherosclerosis depend on arterial wall shear stress (WSS). We review the existing literature on in vivo measurements of WSS in healthy individuals using phase-contrast MRI, which is a promising, noninvasive technique for determining various blood flow characteristics. WSS data exist for the following arteries: carotid, brachial, aorta and femoral. Measured values indicate that WSS is site specific, a finding which opposes the notion that physiological WSS values are maintained at a constant magnitude in all parts of the arterial system. Among the WSS values obtained at the same site by different investigators there is qualitative agreement; however, differences exist in absolute values mainly due to the dependence on the method used to obtain WSS values from velocity data.