In vivo wall shear stress measurements using phase-contrast MRI

A Pseudo-Spectral Method for Wall Shear Stress Estimation from Doppler Ultrasound Imaging in Coronary Arteries

PURPOSE

The Wall Shear Stress (WSS) is the component tangential to the boundary of the normal stress tensor in an incompressible fluid, and it has been recognized as a quantity of primary importance in predicting possible adverse events in cardiovascular diseases, in general, and in coronary diseases, in particular. The quantification of the WSS in patient-specific settings can be achieved by performing a Computational Fluid Dynamics (CFD) analysis based on patient geometry, or it can be retrieved by a numerical approximation based on blood flow velocity data, e.g., ultrasound (US) Doppler measurements. This paper presents a novel method for WSS quantification from 2D vector Doppler measurements.

METHODS

Images were obtained through unfocused plane waves and transverse oscillation to acquire both in-plane velocity components. These velocity components were processed using pseudo-spectral differentiation techniques based on Fourier approximations of the derivatives to compute the WSS.

RESULTS

Our Pseudo-Spectral Method (PSM) is tested in two vessel phantoms, straight and stenotic, where a steady flow of 15 mL/min is applied. The method is successfully validated against CFD simulations and compared against current techniques based on the assumption of a parabolic velocity profile. The PSM accurately detected Wall Shear Stress (WSS) variations in geometries differing from straight cylinders, and is less sensitive to measurement noise. In particular, when using synthetic data (noise free, e.g., generated by CFD) on cylindrical geometries, the Poiseuille-based methods and PSM have comparable accuracy; on the contrary, when using the data retrieved from US measures, the average error of the WSS obtained with the PSM turned out to be 3 to 9 times smaller than that obtained by state-of-the-art methods.

CONCLUSION

The pseudo-spectral approach allows controlling the approximation errors in the presence of noisy data. This gives a more accurate alternative to the present standard and a less computationally expensive choice compared to CFD, which also requires high-quality data to reconstruct the vessel geometry.

Predicting vulnerable carotid plaques by detecting wall shear stress based on ultrasonic vector flow imaging

OBJECTIVE

Carotid plaque vulnerability is a significant factor in the risk of cardiocerebrovascular events, with intraplaque neovascularization (IPN) being a crucial characteristic of plaque vulnerability. This study investigates the value of ultrasound vector flow imaging (V-flow) for measuring carotid plaque wall shear stress (WSS) in predicting the extent of IPN.

METHODS

We enrolled 140 patients into three groups: 53 in the plaque group (72 plaques), 23 in the stenosis group (27 plaques), and 64 in the control group. V-flow was used to measure WSS parameters, including the average WSS (WSS mean) and the maximum WSS (WSS max), across three plaque locations: mid-upstream, maximum thickness, and mid-downstream. Contrast-enhanced ultrasound examination was used in 76 patients to analyze IPN and its correlation with WSS parameters.

RESULTS

WSS max in the stenosis group was significantly higher than that in the control and plaque groups at the maximum thickness part (P < .05) and WSS mean in the stenosis group was significantly lower than that in the control group at the mid-upstream and mid-downstream segments (P < .05). WSS mean in the plaque group was significantly lower than that of the control group at all three locations (P < .05). Contrast-enhanced ultrasound examination revealed that plaques with neovascularization enhancement exhibited significantly higher WSS values (P < .05), with a positive correlation between WSS parameters and IPN enhancement grades, particularly WSS max at the thickest part (r = 0.508). Receiver operating characteristic curve analysis of WSS parameters for evaluating IPN showed that the efficacy of WSS max in evaluating IPN was better than that of WSS mean (P < .05), with an area under the curve of 0.7762 and 0.6973 (95% confidence intervals, 0.725-0.822 and 0.642-0.749, respectively). The cut-offs were 4.57 Pa and 1.12 Pa, sensitivities were 74.03% and 63.64%, and specificities were 75.00% and 68.18%.

CONCLUSIONS

V-flow effectively measures WSS in carotid plaques. WSS max provides a promising metric for assessing IPN, offering potential insights into plaque characteristics and showing some potential in predicting plaque vulnerability.

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.

Wall Shear Stress Measurements Based on Ultrasound Vector Flow Imaging: Theoretical Studies and Clinical Examples

Wall shear stress (WSS) is considered as a key factor for atherosclerosis development. Previous WSS research based on pulsed wave Doppler (PWD) showed limitations in complex flows. To improve accuracy for nonlaminar flow, a commercial ultrasound vector flow imaging (UVFI)-based WSS calculation is proposed. Errors for PWD are presented theoretically when flow is not laminar. Based on this, simulations of WSS calculations between PWD and UVFI were set up for different turbulent flows. Our simulations show that UVFI has obviously better performance than PWD in WSS calculations. Wall shear stress results in different flow conditions at carotid bifurcations are described.

Biomechanical Forces and Oxidative Stress: Implications for Pulmonary Vascular Disease

Significance: Oxidative stress in the cell is characterized by excessive generation of reactive oxygen species (ROS). Superoxide (O₂^-) and hydrogen peroxide (H₂O₂) are the main ROS involved in the regulation of cellular metabolism. As our fundamental understanding of the underlying causes of lung disease has increased it has become evident that oxidative stress plays a critical role. Recent Advances: A number of cells in the lung both produce, and respond to, ROS. These include vascular endothelial and smooth muscle cells, fibroblasts, and epithelial cells as well as the cells involved in the inflammatory response, including macrophages, neutrophils, eosinophils. The redox system is involved in multiple aspects of cell metabolism and cell homeostasis. Critical Issues: Dysregulation of the cellular redox system has consequential effects on cell signaling pathways that are intimately involved in disease progression. The lung is exposed to biomechanical forces (fluid shear stress, cyclic stretch, and pressure) due to the passage of blood through the pulmonary vessels and the distension of the lungs during the breathing cycle. Cells within the lung respond to these forces by activating signal transduction pathways that alter their redox state with both physiologic and pathologic consequences. Future Directions: Here, we will discuss the intimate relationship between biomechanical forces and redox signaling and its role in the development of pulmonary disease. An understanding of the molecular mechanisms induced by biomechanical forces in the pulmonary vasculature is necessary for the development of new therapeutic strategies.

Biomechanical Forces and Atherosclerosis: From Mechanism to Diagnosis and Treatment

The article provides an overview of current views on the role of biomechanical forces in the pathogenesis of atherosclerosis. The importance of biomechanical forces in maintaining vascular homeostasis is considered. We provide descriptions of mechanosensing and mechanotransduction. The roles of wall shear stress and circumferential wall stress in the initiation, progression and destabilization of atherosclerotic plaque are described. The data on the possibilities of assessing biomechanical factors in clinical practice and the clinical significance of this approach are presented. The article concludes with a discussion on current therapeutic approaches based on the modulation of biomechanical forces.

Electrostatic Steering Enables Flow-Activated Von Willebrand Factor to Bind Platelet Glycoprotein, Revealed by Single-Molecule Stretching and Imaging

Von Willebrand factor (VWF), a large multimeric blood protein, senses changes in shear stress during bleeding and responds by binding platelets to plug ruptures in the vessel wall. Molecular mechanisms underlying this dynamic process are difficult to uncover using standard approaches due to the challenge of applying mechanical forces while monitoring structure and activity. By combining single-molecule fluorescence imaging with high-pressure, rapidly switching microfluidics, we reveal the key role of electrostatic steering in accelerating the binding between flow-activated VWF and GPIbα, and in rapidly immobilizing platelets under flow. We measure the elongation and tension-dependent activation of individual VWF multimers under a range of ionic strengths and pH levels, and find that the association rate is enhanced by 4 orders of magnitude by electrostatic steering. Under supraphysiologic salt concentrations, strong electrostatic screening dramatically decreases platelet binding to VWF in flow, revealing the critical role of electrostatic attraction in VWF-platelet binding during bleeding.

Novel and facile criterion to assess the accuracy of WSS estimation by 4D flow MRI

Four-dimensional flow magnetic resonance imaging (4D flow MRI) is a versatile tool to obtain hemodynamic information and anatomic information simultaneously. The wall shear stress (WSS), a force exerted on a vessel wall in parallel, is one of the hemodynamic parameters available with 4D flow MRI and is thought to play an important role in clinical applications such as assessing the development of atherosclerosis. Nevertheless, the accuracy of WSS obtained with 4D flow MRI is rarely evaluated or reported in literature, especially in the in vivo studies. We propose a novel and facile criterion called Reynolds resolution to assess the accuracy of WSS estimation in 4D flow MRI studies. Reynolds resolution consists of a spatial resolution, encoding velocity, kinematic viscosity of a working fluid, and signal-to-noise ratio, which are readily accessible information in 4D flow MRI measurements. We explored the relationship between Reynolds resolution and the WSS error. To include diverse and extensive cases, we measured three circular tubing flows with a diameter of 40, 8, and 2 mm. The 40 mm tubing flow was measured by 3 Tesla (T) human MR scanner with a knee coil and spatial resolution of 0.5 mm. The 8 and 2 mm tubing flows were both measured by 4.7 T MR scanner, but the scans were performed with a conventional birdcage coil (8 mm tubing) and a custom-made solenoid coil (2 mm tubing), respectively. The spatial resolution was varied from 0.2, 0.4 or 0.8 mm for the 8 mm tubing flow, but was fixed at 0.090 mm for 2 mm tubing flow. In addition, the near-wall velocity gradient, required to be determined prior to the WSS, was calculated using two methods; these included assuming a linear velocity profile or quadratic velocity profile near wall. The accuracy of WSS obtained using each method and tubing flow was evaluated against the theoretical WSS value. As a result, we found that Reynolds resolution is in logarithmic relation to the WSS error.

Vascular smooth muscle cell contraction and relaxation in the isolated aorta: a critical regulator of large artery compliance

Over the past few decades, isometric contraction studies of isolated thoracic aorta segments have significantly contributed to our overall understanding of the active, contractile properties of aortic vascular smooth muscle cells (VSMCs) and their cross-talk with endothelial cells. However, the physiological role of VSMC contraction or relaxation in the healthy aorta and its contribution to the pulse-smoothening capacity of the aorta is currently unclear. Therefore, we investigated the acute effects of VSMC contraction and relaxation on the isobaric biomechanical properties of healthy mouse aorta. An in-house developed set-up was used to measure isobaric stiffness parameters of periodically stretched (10 Hz) aortic segments at an extended pressure range, while pharmacologically modulating VSMC tone and endothelial cell function. We found that the effects of α1-adrenergic stimulation with phenylephrine on the pressure-stiffness relationship varied in sensitivity, magnitude and direction, with the basal, unstimulated NO production by the endothelium playing a pivotal role. We also investigated how arterial disease affected this system by using the angiotensin-II-treated mouse. Our results show that isobaric stiffness was increased and that the aortic segments demonstrated a reduced capacity for modulating the pressure-stiffness relationship. This suggests that not only increased isobaric stiffness at normal pressure, but also a reduced capacity of the VSMCs to limit the pressure-associated increase in aortic stiffness, may contribute to the pathogenesis of this mouse model. Overall, this study provides more insight in how aortic VSMC tone affects the pressure-dependency of aortic biomechanics at different physiological and pathological conditions.

Flow-induced elongation of von Willebrand factor precedes tension-dependent activation

Von Willebrand factor, an ultralarge concatemeric blood protein, must bind to platelet GPIbα during bleeding to mediate hemostasis, but not in the normal circulation to avoid thrombosis. Von Willebrand factor is proposed to be mechanically activated by flow, but the mechanism remains unclear. Using microfluidics with single-molecule imaging, we simultaneously monitored reversible Von Willebrand factor extension and binding to GPIbα under flow. We show that Von Willebrand factor is activated through a two-step conformational transition: first, elongation from compact to linear form, and subsequently, a tension-dependent local transition to a state with high affinity for GPIbα. High-affinity sites develop only in upstream regions of VWF where tension exceeds ~21 pN and depend upon electrostatic interactions. Re-compaction of Von Willebrand factor is accelerated by intramolecular interactions and increases GPIbα dissociation rate. This mechanism enables VWF to be locally activated by hydrodynamic force in hemorrhage and rapidly deactivated downstream, providing a paradigm for hierarchical mechano-regulation of receptor–ligand binding.

Von Willebrand factor (VWF) is a blood protein involved in clotting and is proposed to be activated by flow, but the mechanism is unknown. Here the authors show that VWF is first converted from a compact to linear form by flow, and is subsequently activated to bind GPIbα in a tension-dependent manner.

A novel set-up for the ex vivo analysis of mechanical properties of mouse aortic segments stretched at physiological pressure and frequency

KEY POINTS

Cyclic stretch is known to alter intracellular pathways involved in vessel tone regulation. We developed a novel set-up that allows straightforward characterization of the biomechanical properties of the mouse aorta while stretched at a physiological heart rate (600 beats min^-1 ). Active vessel tone was shown to have surprisingly large effects on isobaric stiffness. The effect of structural vessel wall alterations was confirmed using a genetic mouse model. This set-up will contribute to a better understanding of how active vessel wall components and mechanical stimuli such as stretch frequency and amplitude regulate aortic mechanics.

ABSTRACT

Cyclic stretch is a major contributor to vascular function. However, isolated mouse aortas are frequently studied at low stretch frequency or even in isometric conditions. Pacing experiments in rodents and humans show that arterial compliance is stretch frequency dependent. The Rodent Oscillatory Tension Set-up to study Arterial Compliance is an in-house developed organ bath set-up that clamps aortic segments to imposed preloads at physiological rates up to 600 beats min^-1 . The technique enables us to derive pressure-diameter loops and assess biomechanical properties of the segment. To validate the applicability of this set-up we aimed to confirm the effects of distension pressure and vascular smooth muscle tone on arterial stiffness. At physiological stretch frequency (10 Hz), the Peterson modulus (E_P ; 293 (10) mmHg) for wild-type mouse aorta increased 22% upon a rise in pressure from 80-120 mmHg to 100-140 mmHg, while, at normal pressure, E_P increased 80% upon maximal contraction of the vascular smooth muscle cells. We further validated the method using a mouse model with a mutation in the fibrillin-1 gene and an endothelial nitric oxide synthase knock-out model. Both models are known to have increased arterial stiffness, and this was confirmed using the set-up. To our knowledge, this is the first set-up that facilitates the study of biomechanical properties of mouse aortic segments at physiological stretch frequency and pressure. We believe that this set-up can contribute to a better understanding of how cyclic stretch frequency, amplitude and active vessel wall components influence arterial stiffening.

Stiff substrates enhance monocytic cell capture through E-selectin but not P-selectin

The stiffening of blood vessel walls is associated with inflammatory diseases, including atherosclerosis, diabetes, and obesity. These diseases are driven by the excessive recruitment of inflammatory leukocytes out of the bloodstream and into tissues, but whether vascular stiffening plays a direct role in this process is not clear. In this study, we investigated the possibility that leukocyte capture from blood flow is enhanced on stiffer substrates. We modeled blood flow in vitro by perfusing monocytic cells over hydrogels that matched the stiffness of healthy and diseased arteries. The hydrogels were coated with either E-selectin or P-selectin, which are the endothelial adhesion proteins known to mediate immune cell capture from flow. Interestingly, we discovered that cell attachment to P-selectin coated gels was not dependent on substrate stiffness, while attachment through E-selectin was enhanced on stiffer gels. Specifically we found that on E-selectin coated gels, cells attached in greater numbers, remained attached for longer time periods, and rolled more slowly on stiff gels than soft gels. These results suggest that vascular stiffening could promote leukocyte adhesion to vessel walls where E-selectin is expressed, but may have less of an effect when P-selectin is also present.

Atrial fibrillation pacing decreases intravascular shear stress in a New Zealand white rabbit model: implications in endothelial function

Atrial fibrillation (AF) is characterized by multiple rapid and irregular atrial depolarization, leading to rapid ventricular responses exceeding 100 beats per minute (bpm). We hypothesized that rapid and irregular pacing reduced intravascular shear stress (ISS) with implication to modulating endothelial responses. To simulate AF, we paced the left atrial appendage of New Zealand White rabbits (n = 4) at rapid and irregular intervals. Surface electrical cardiograms were recorded for atrial and ventricular rhythm, and intravascular convective heat transfer was measured by microthermal sensors, from which ISS was inferred. Rapid and irregular pacing decreased arterial systolic and diastolic pressures (baseline, 99/75 mmHg; rapid regular pacing, 92/73; rapid irregular pacing, 90/68; p < 0.001, n = 4), temporal gradients ([Formula: see text] from 1,275 ± 80 to 1,056 ± 180 dyne/cm(2) s), and reduced ISS (from baseline at 32.0 ± 2.4 to 22.7 ± 3.5 dyne/cm(2)). Computational fluid dynamics code demonstrated that experimentally inferred ISS provided a close approximation to the computed wall shear stress at a given catheter to vessel diameter ratio, shear stress range, and catheter position. In an in vitro flow system in which time-averaged shear stress was maintained at [Formula: see text] , we further demonstrated that rapid pulse rates at 150 bpm down-regulated endothelial nitric oxide, promoted superoxide (O 2 (.-) ) production, and increased monocyte binding to endothelial cells. These findings suggest that rapid pacing reduces ISS and [Formula: see text] , and rapid pulse rates modulate endothelial responses.

P-selectin glycoprotein ligand-1 plays a crucial role in the selective recruitment of leukocytes into the atherosclerotic arterial wall

Leukocyte recruitment to the arterial vessel wall is the first step in the development of atherosclerotic lesions. Leukocyte homing in this event proceeds through a well-defined adhesion cascade, which includes tethering, rolling, adhesion, and transmigration. Selectins, including the P-, E-, and L-selectins, and their ligands mediate the initial tethering and rolling. Interactions between selectins and their ligands serve as a braking system to decelerate fast-flowing leukocytes from the central blood stream and enable them to adhere to and transmigrate underneath the activated endothelium. The best characterized ligand for selectins is P-selectin glycoprotein ligand-1, an extended homodimeric mucin on leukocytes that binds to all three selectins. Recent studies show that differential expression or glycosylation of P-selectin glycoprotein ligand-1 in different leukocytes mediates selective recruitment of different subsets of monocytes or lymphocytes to atherosclerotic arteries.

Magnetic [corrected] resonance imaging [corrected] features of the disruption-prone and the disrupted carotid plaque

Stroke is a leading cause of long-term disability and is the third most common cause of death in the U.S. and western countries. Twenty percent of strokes are thought to arise from the carotid artery. Histopathological studies have suggested that plaque disruption is a key factor in the etiology of carotid-related ischemic events. Features associated with plaque disruption include intraplaque hemorrhage, large necrotic cores with thin overlying fibrous caps, plaque neovasculature, and inflammatory cell infiltrate. In vivo high-spatial-resolution, multicontrast-weighted cardiac magnetic resonance (CMR) has been extensively evaluated using histology as the gold standard, and has documented reliability in the identification of these key carotid plaque features. This pictorial essay illustrates the capability of CMR for identifying features of disruption-prone and disrupted atherosclerotic carotid plaques.

Optimum fuzzy filters for phase-contrast magnetic resonance imaging segmentation

PURPOSE

To develop and validate a multidimensional segmentation and filtering methodology for accurate blood flow velocity field reconstruction from phase-contrast magnetic resonance imaging (PC MRI).

MATERIALS AND METHODS

The proposed technique consists of two steps: (1) the boundary of the vessel is automatically segmented using the active contour approach; and (2) the noise embedded within the segmented vector field is selectively removed using a novel fuzzy adaptive vector median filtering (FAVMF) technique. This two-step segmentation process was tested and validated on 111 synthetically generated PC MRI slices and on 10 patients with congenital heart disease.

RESULTS

The active contour technique was effective for segmenting blood vessels having a sensitivity and specificity of 93.1% and 92.1% using manual segmentation as a reference standard. FAVMF was the superior technique in filtering out noise vectors, when compared with other commonly used filters in PC MRI (P < 0.05). The peak wall shear rate calculated from the PC MRI data (248 +/- 39 sec(-1)), was significantly decreased to (146 +/- 26 sec(-1)) after the filtering process.

CONCLUSION

The proposed two-step segmentation and filtering methodology is more accurate compared to a single-step segmentation process for post-processing of PC MRI data.

P-selectin glycoprotein ligand-1 is highly expressed on Ly-6Chi monocytes and a major determinant for Ly-6Chi monocyte recruitment to sites of atherosclerosis in mice

BACKGROUND

Ly-6C(hi) monocytes are key contributors to atherosclerosis in mice. However, the manner in which Ly-6C(hi) monocytes selectively accumulate in atherosclerotic lesions is largely unknown. Monocyte homing to sites of atherosclerosis is primarily initiated by rolling on P- and E-selectin expressed on endothelium. We hypothesize that P-selectin glycoprotein ligand-1 (PSGL-1), the common ligand of P- and E-selectin on leukocytes, contributes to the preferential homing of Ly-6C(hi) monocytes to atherosclerotic lesions.

METHODS AND RESULTS

To test this hypothesis, we examined the expression and function of PSGL-1 on Ly-6C(hi) and Ly-6C(lo) monocytes from wild-type mice, ApoE(-/-) mice, and mice lacking both ApoE and PSGL-1 genes (ApoE(-/-)/PSGL-1(-/-)). We found that Ly-6C(hi) monocytes expressed a higher level of PSGL-1 and had enhanced binding to fluid-phase P- and E-selectin compared with Ly-6C(lo) monocytes. Under in vitro flow conditions, more Ly-6C(hi) monocytes rolled on P-, E-, and L-selectin at slower velocities than Ly-6C(lo) cells. In an ex vivo perfused carotid artery model, Ly-6C(hi) monocytes interacted preferentially with atherosclerotic endothelium compared with Ly-6C(lo) monocytes in a PSGL-1-dependent manner. In vivo, ApoE(-/-) mice lacking PSGL-1 had impaired Ly-6C(hi) monocyte recruitment to atherosclerotic lesions. Moreover, ApoE(-/-)/PSGL-1(-/-) mice exhibited significantly reduced monocyte infiltration in wire injury-induced neointima and in atherosclerotic lesions. ApoE(-/-)/PSGL-1(-/-) mice also developed smaller neointima and atherosclerotic plaques.

CONCLUSIONS

These data indicate that PSGL-1 is a new marker for Ly-6C(hi) monocytes and a major determinant for Ly-6C(hi) cell recruitment to sites of atherosclerosis in mice.

Measurement of systolic and diastolic arterial wall shear stress in the ascending aorta

PURPOSE

Wall shear stress (WSS) appears to contribute significantly in the initiation and progression of atherosclerotic disease. The purpose of this work is to present in vivo systolic and diastolic WSS calculations in the human ascending aorta by the application of three straightforward methodologies based on Poiseuille's theory of flow.

MATERIALS AND METHODS

Blood flow measurements were performed retrospectively in the ascending aorta of 20 non-atherosclerotic patients using phase-contrast MRI. WSS calculations were performed assuming Poiseuille's theory of flow based on average flow volume, average flow velocity and maximum flow velocity. Systolic and diastolic WSS values were calculated and compared with the calculated maximum and minimum values of WSS throughout the cardiac cycle.

RESULTS

Systolic WSS values calculated by average flow volume, average flow velocity and maximum flow velocity were similar (0.4+/-0.2N/m(2), 0.4+/-0.3N/m(2)and 0.4+/-0.2N/m(2), respectively). Diastolic WSS values calculated by maximum flow velocity were significantly higher (11.6+/-7.0x10(-2)N/m(2)) compared to values calculated by average flow volume (0.3+/-0.9x10(-2)N/m(2)) and average flow velocity (0.3+/-1.0x10(-2)N/m(2)). Comparison of systolic and diastolic WSS values with maximum and minimum WSS values showed that time instances of maximum and minimum blood flow velocities do not coincide with time instances of maximum and minimum blood flow volume.

CONCLUSION

In vivo calculation of WSS in the ascending aorta is feasible by phase-contrast MRI flow measurements and straightforward methodologies based on Poiseuille's theory of flow. However, measurements based on maximum flow velocity show larger deviations compared to measurements based on mean flow volume or mean flow velocity.

Wall shear stress calculation in ascending aorta using phase contrast magnetic resonance imaging. Investigating effective ways to calculate it in clinical practice

INTRODUCTION

There is growing evidence that atherosclerosis, as well as endothelial biology, depend on arterial wall shear stress (WSS). Several methods of WSS calculation with varying degrees of complexity have been proposed. This study aimed at investigating whether the most straightforward and easier to apply of these methods give comparable results in clinical practice.

METHODS

Complete velocity encoding measurements using phase contrast magnetic resonance imaging were performed in 20 patients at a level perpendicular to the long axis of the ascending aorta approximately 2cm above the aortic valve. WSS was calculated at this location on maximum systole. MR imaging was accomplished on a 1.5T scanner. Four methods were applied to calculate WSS; three of them are based on the predictions of Poiseuille's theory of flow, while the last one is based on calculations resulting by the application of the definition of WSS.

RESULTS

WSS calculated with the above mentioned methods was found to be in the range 4.2+/-1.8 to 3.5+/-1.7dynes/m(2). The velocity profile at the site of measurements can be described with a parabolic equation of the form u=ar(2)+br+c with an average r(2)=0.83, which is in good agreement with Poiseuille's theory of flow. Comparison of the results shows no statistically significant differences between WSS measurements calculated with these methods.

DISCUSSION

The four methods are equivalent in calculating WSS at the ascending aorta when blood flow velocities have a good parabolic distribution.