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

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.

Fluid-structure interaction analysis of transcatheter aortic valve implantation

Transcatheter aortic valve implantation (TAVI) is a minimally invasive intervention for the treatment of severe aortic valve stenosis. The main cause of failure is the structural deterioration of the implanted prosthetic leaflets, possibly inducing a valvular re-stenosis 5-10 years after the implantation. Based solely on pre-implantation data, the aim of this work is to identify fluid-dynamics and structural indices that may predict the possible valvular deterioration, in order to assist the clinicians in the decision-making phase and in the intervention design. Patient-specific, pre-implantation geometries of the aortic root, the ascending aorta, and the native valvular calcifications were reconstructed from computed tomography images. The stent of the prosthesis was modeled as a hollow cylinder and virtually implanted in the reconstructed domain. The fluid-structure interaction between the blood flow, the stent, and the residual native tissue surrounding the prosthesis was simulated by a computational solver with suitable boundary conditions. Hemodynamical and structural indicators were analyzed for five different patients that underwent TAVI - three with prosthetic valve degeneration and two without degeneration - and the comparison of the results showed a correlation between the leaflets' structural degeneration and the wall shear stress distribution on the proximal aortic wall. This investigation represents a first step towards computational predictive analysis of TAVI degeneration, based on pre-implantation data and without requiring additional peri-operative or follow-up information. Indeed, being able to identify patients more likely to experience degeneration after TAVI may help to schedule a patient-specific timing of follow-up.

Effects of Pulsatility on Arterial Endothelial and Smooth Muscle Cells

Continuous flow ventricular assist device (CFVAD) support in advanced heart failure patients causes diminished pulsatility, which has been associated with adverse events including gastrointestinal bleeding, end organ failure, and arteriovenous malformation. Recently, pulsatility augmentation by pump speed modulation has been proposed as a means to minimize adverse events. Pulsatility primarily affects endothelial and smooth muscle cells in the vasculature. To study the effects of pulsatility and pulse modulation using CFVADs, we have developed a microfluidic co-culture model with human aortic endothelial (ECs) and smooth muscle cells (SMCs) that can replicate physiologic pressures, flows, shear stresses, and cyclical stretch. The effects of pulsatility and pulse frequency on ECs and SMCs were evaluated during (1) normal pulsatile flow (120/80 mmHg, 60 bpm), (2) diminished pulsatility (98/92 mmHg, 60 bpm), and (3) low cyclical frequency (115/80 mmHg, 30 bpm). Shear stresses were estimated using computational fluid dynamics (CFD) simulations. While average shear stresses (4.2 dynes/cm2) and flows (10.1 mL/min) were similar, the peak shear stresses for normal pulsatile flow (16.9 dynes/cm2) and low cyclic frequency (19.5 dynes/cm2) were higher compared to diminished pulsatility (6.45 dynes/cm2). ECs and SMCs demonstrated significantly lower cell size with diminished pulsatility compared to normal pulsatile flow. Low cyclical frequency resulted in normalization of EC cell size but not SMCs. SMCs size was higher with low frequency condition compared to diminished pulsatility but did not normalize to normal pulsatility condition. These results may suggest that pressure amplitude augmentation may have a greater effect in normalizing ECs, while both pressure amplitude and frequency may be required to normalize SMCs morphology. The co-culture model may be an ideal platform to study flow modulation strategies.

Blood Flow and Shear Stress Allow Monitoring of Progression and Prognosis of Tumor Diseases

In the presence of tumor angiogenesis, blood flow must increase, leading to an elevation of blood flow velocities (BFVels) and wall shear stress (WSS) in upstream native arteries. An adaptive arterial remodeling is stimulated, whose purpose lies in the enlargement of the arterial inner diameter, aiming for normalization of BFVels and WSS. Remodeling engages delayed processes that are efficient only several weeks/months after initiation, independent from those governing expansion of the neovascular network. Therefore, during tumor expansion, there is a time interval during which elevation of BFVels and WSS could reflect disease progression. Conversely, during the period of stability, BFVels and WSS drop back to normal values due to the achievement of remodeling processes. Ovarian peritoneal carcinomatosis (OPC), pseudomyxoma peritonei (PMP), and superficial arteriovenous malformations (AVMs) are diseases characterized by the development of abnormal vascular networks developed on native ones. In OPC and PMP, preoperative blood flow in the superior mesenteric artery (SMA) correlated with the per-operative peritoneal carcinomatosis index (OPC: n = 21, R = 0.79, p < 0.0001, PMP: n = 66, R = 0.63, p < 0.0001). Moreover, 1 year after surgery, WSS in the SMA helped in distinguishing patients with PMP from those without disease progression [ROC-curve analysis, AUC = 0.978 (0.902-0.999), p < 0.0001, sensitivity: 100.0%, specificity: 93.5%, cutoff: 12.1 dynes/cm²]. Similarly, WSS in the ipsilateral afferent arteries close to the lesion distinguished stable from progressive AVM [ROC-curve analysis, AUC: 0.988, (0.919-1.000), p < 0.0001, sensitivity: 93.5%, specificity: 95.7%; cutoff: 26.5 dynes/cm²]. Blood flow volume is indicative of the tumor burden in OPC and PMP, and WSS represents an early sensitive and specific vascular marker of disease progression in PMP and AVM.

High-Frame Rate Vector Flow Imaging Technique: Initial Application in Evaluating the Hemodynamic Changes of Carotid Stenosis Caused by Atherosclerosis

Objective: To investigate the value of high-frame rate vector flow imaging technique (V flow) in evaluating the hemodynamic changes of carotid stenosis caused by atherosclerotic plaques.

Methods and Materials: In this prospective study, patients with stenosis rate (diameter) ≥30% caused by carotid atherosclerotic plaques were included. Degrees of carotid stenosis were graded according to North American Symptomatic Carotid Endarterectomy Trial criteria: moderate (30–69%) or severe (70–99%). Mindray Resona 7s ultrasound machine with a linear array transducer (3–11 MHz) was used for ultrasound examinations. The mean WSS value of carotid arteries was measured at the proximal, narrowest region and distal of carotid stenosis. The mean WSS values were correlated with peak systolic velocity (PSV) measured by color Doppler flow imaging and stenosis degree detected by digital subtraction angiography (DSA). The vector arrows and flow streamline detected by V flow dynamic imaging were analyzed. Imaging findings of DSA in carotid arteries were used as the gold standard.

Results: Finally, 51 patients were included. V flow measurements were performed successfully in 17 patients (100%) with moderate-grade stenosis and in 30 patients (88.2%) with severe-grade stenosis. Dynamic V flow imaging showed yellow or red vectors at the stenotic segment, indicating fast speed blood flow (up to 260.92 cm/s). Changes of streamlines were detected in the stenotic segment. The mean WSS value measured at the narrowest region of the carotid artery had a moderately positive correlation with stenosis degree (r = 0.58, P < 0.05) and PSV value (r = 0.54, P < 0.05), respectively. Significant difference was detected in mean WSS value at the narrowest region of the carotid artery between severe carotid stenosis (1.47 ± 0.97 Pa) and moderate carotid stenosis (0.96 ± 0.44 Pa) (P < 0.05).

Conclusion: The hemodynamic changes detected by V flow of the carotid stenosis might be a potential non-invasive imaging tool for assessing the degree of carotid stenosis.

An unexpected paradox: wall shear stress in the aorta is less in patients with severe atherosclerosis regardless of obesity

BACKGROUND

Obesity is a widespread condition that is more prevalent in Western countries compared to others. Aortic atherosclerosis (AA) is a condition that frequently has been associated with obesity. An obesity paradox, where morbidly obese decedents had either no or minimal AA compared to nonobese decedents, recently has been described by some of us. The explanation for this almost counterintuitive paradox has yet to be determined, but a number of hypotheses were advanced, including hemodynamic factors producing aortic wall shear stress (WSS). The purpose of the present study was to determine if there was a relationship between AA and WSS, as determined by postmortem measurement of aortic wall diameters.

METHODS

Circumferences of the aorta at the levels of the ascending, thoracic and abdominal aorta were measured in 274 consecutive autopsies over 2-year period of time. AA was assessed using a previously described grading scale as either mild or severe. Circumferences were mathematically converted to diameters and WSS was calculated using the Hagen-Poiseuille formula. Two different methods to estimate cardiac output were used, both based on literature methods, one of which was body mass index (BMI) dependent, and the other BMI independent. Univariate and multivariable analyses of the relationship between WSS, age, BMI, gender, race and severity of AA were performed.

RESULTS

Of the 274 decedents, 140 had mild and 134 had moderate to severe AA. BMI <35 was associated with moderate to severe AA. WSS was inversely correlated with AA in all these segments of the aorta in each BMI subgroup with the exception of the ascending aorta for decedents with BMI ≤35 kg/m². Contrary to what we had hypothesized, WSS was not a determinant of the obesity paradox. However, among all the variables analyzed, a history of hypertension, diabetes mellitus and age were significant factors for developing AA (relative risk [RR] 0.35, P = .039; RR 1.51, P = .0006, RR 1.19, P = .0001, respectively).

CONCLUSIONS

Our data demonstrate that WSS was unexpectedly lower in decedents with moderate and severe AA as compared to those with mild AA. This observation, which requires further investigations, was seen in all BMI ranges and was confirmed by 2 methods to calculate WSS.

Phase-contrast magnetic resonance imaging for analyzing hemodynamic parameters and wall shear stress of pulmonary arteries in patients with pulmonary arterial hypertension

OBJECTIVE

To investigate flow-related parameters in pulmonary arteries of patients with pulmonary arterial hypertension (PAH).

MATERIALS AND METHODS

Eleven PAH patients and twelve control participants were recruited. PAH and controls had similar age and gender distribution. 2D phase-contrast MRI (PC-MRI) was performed in the main, right, and left pulmonary artery (MPA, RPA, and LPA). The flow velocity, wall shear stress (WSS), and oscillatory shear index (OSI) were measured.

RESULTS

PAH patients displayed prolonged acceleration time (T_acce) and increased ratio of flow change to acceleration volume in pulmonary arteries (both P < 0.001). The temporally averaged WSS values of MPA, RPA, and LPA in PAH patients were significantly lower than those of control participants (P < 0.001). The OSI in the pulmonary arteries was higher in PAH patients than control participants (P < 0.05). The ROC analysis indicated the ratio of maximum flow change to acceleration volume, WSS, and T_acce exhibited sufficient sensitivity and specificity to detect patients with PAH. The WSS demonstrated strong correlations with T_acce and the ratio value in the two groups (R² = 0.78-0.96).

CONCLUSIONS

We used a clinically feasible 2D PC-MRI sequence with a reasonable scanning time to compute aforementioned indices. The quantitative parameters provided sufficient information to differentiate PAH patients from control participants.

Cardiac Magnetic Resonance Imaging of Mechanical Cavopulmonary Assistance

Mechanical circulatory support (MCS) options are limited for patients with dysfunctional single ventricle physiology. To address this unmet clinical need, we are developing an axial-flow blood pump to provide mechanical assistance to the cavopulmonary circulation. In this study, we investigate the use of high-resolution cardiac magnetic resonance imaging (MRI) to visualize the complex fluid flow conditions of mechanical circulatory assist in two patient-specific Fontan anatomies. A three-bladed axial-flow impeller coupled to a supportive cage with a four-bladed diffuser was positioned in the inferior vena cava (IVC) of each Fontan anatomy. Cardiac magnetic resonance (CMR) imaging and power efficiency studies were conducted at physiologic relevant parameters with cardiac outputs of 2, 3, and 4 L/min with impeller rotational speeds of 2000 and 4000 rpm. The axial-flow impeller was able to generate improved flow in the total cavopulmonary connection (TCPC). The higher rotational speed was able to redistribute flow in the TCPC anastomosis aiding in removing stagnant blood. No retrograde flow was observed or measured in the superior vena cava (SVC). As an extension of the CMR data, a scalar stress analysis was performed on both models and found a maximum scalar stress of approximately 42 Pa for both patient anatomies. The power efficiency experiments demonstrated a maximum energy gain of 8.6 mW for TCPC Anatomy 1 and 12.58 mW for TCPC Anatomy 2 for a flow rate of 4 L/min and at 4000 rpm. These findings support the continued development of axial blood pumps for mechanical cavopulmonary assist.

Impact of Patient-Specific Inflow Velocity Profile on Hemodynamics of the Thoracic Aorta

Computational fluid dynamics (CFD) provides a noninvasive method to functionally assess aortic hemodynamics. The thoracic aorta has an anatomically complex inlet comprising of the aortic valve and root, which is highly prone to different morphologies and pathologies. We investigated the effect of using patient-specific (PS) inflow velocity profiles compared to idealized profiles based on the patient's flow waveform. A healthy 31 yo with a normally functioning tricuspid aortic valve (subject A), and a 52 yo with a bicuspid aortic valve (BAV), aortic valvular stenosis, and dilated ascending aorta (subject B) were studied. Subjects underwent MR angiography to image and reconstruct three-dimensional (3D) geometric models of the thoracic aorta. Flow-magnetic resonance imaging (MRI) was acquired above the aortic valve and used to extract the patient-specific velocity profiles. Subject B's eccentric asymmetrical inflow profile led to highly complex velocity patterns, which were not replicated by the idealized velocity profiles. Despite having identical flow rates, the idealized inflow profiles displayed significantly different peak and radial velocities. Subject A's results showed some similarity between PS and parabolic inflow profiles; however, other parameters such as Flowasymmetry were significantly different. Idealized inflow velocity profiles significantly alter velocity patterns and produce inaccurate hemodynamic assessments in the thoracic aorta. The complex structure of the aortic valve and its predisposition to pathological change means the inflow into the thoracic aorta can be highly variable. CFD analysis of the thoracic aorta needs to utilize fully PS inflow boundary conditions in order to produce truly meaningful results.

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.

Functional assessment of thoracic aortic aneurysms - the future of risk prediction?

INTRODUCTION

Treatment guidelines for the thoracic aorta concentrate on size, yet acute aortic dissection or rupture can occur when aortic size is below intervention criteria. Functional imaging and computational techniques are a means of assessing haemodynamic parameters involved in aortic pathology.

SOURCES OF DATA

Original articles, reviews, international guidelines.

AREAS OF AGREEMENT

Computational fluid dynamics and 4D flow MRI allow non-invasive assessment of blood flow parameters and aortic wall biomechanics.

AREAS OF CONTROVERSY

Aortic valve morphology (particularly bicuspid aortic valve) is associated with aneurysm of the ascending aorta, although the exact mechanism of aneurysm formation is not yet established.

GROWING POINTS

Haemodynamic assessment of the thoracic aorta has highlighted parameters which are linked with both clinical outcome and protein changes in the aortic wall. Wall shear stress, flow displacement and helicity are elevated in patients with bicuspid aortic valve, particularly at locations of aneurysm formation.

AREAS TIMELY FOR DEVELOPING RESEARCH

With further validation, functional assessment of the aorta may help identify patients at risk of aortic complications, and introduce new haemodynamic indices into management guidelines.

Does altered aortic flow in marfan syndrome relate to aortic root dilatation?

Purpose

To examine possible hemodynamic alterations in adolescent to adult Marfan syndrome (MFS) patients with aortic root dilatation.

Materials and Methods

Four‐dimensional flow MRI was performed in 20 MFS patients and 12 age‐matched normal subjects with a 3T system. The cross‐sectional areas of 10 planes along the aorta were segmented for calculating the axial and circumferential wall shear stress (WSS_axial, WSS_circ), oscillatory shear index (OSI_axial, OSI_circ), and the nonroundness (NR), presenting the asymmetry of segmental WSS. Pearson's correlation analysis was performed to present the correlations between the quantified indices and the body surface area (BSA), aortic root diameter (ARD), and Z score of the ARD. P < 0.05 indicated statistical significance.

Results

Patients exhibited lower WSS_axial in the aortic root and the WSS_circ in the arch (P < 0.05–0.001). MFS patients exhibited higher OSI_axial and OSI_circ in the sinotubular junction and arch, but lower OSI_circ in the descending aorta (all P < 0.05). The NR values were lower in patients (P < 0.05). The WSS_axial or WSS_circ exhibited moderate to strong correlations with BSA, ARD, or Z score (R² = 0.50–0.72) in MFS patients.

Conclusion

The significant differences in the quantified indices, which were associated with BSA, ARD, or Z score, in MFS were opposite to previous reports for younger MFS patients, indicating that altered flows in MFS patients may depend on the disease progress. The possible time dependency of hemodynamic alterations in MFS patients strongly suggests that longitudinal follow‐up of 4D Flow is needed to comprehend disease progress. J. Magn. Reson. Imaging 2016;44:500–508.

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.

Shear rate specific blood viscosity and shear stress of carotid artery duplex ultrasonography in patients with lacunar infarction

Background

This study describes a new method for determining site-specific vascular shear stress using dynamic measures of shear rate and blood viscosity (BV) in the carotid arteries, and examines characteristics of carotid arterial shear stress among patients with lacunar infarction.

Methods

Vascular shear stress measurements were conducted in 37 patients (17 lacunar infarction patients and 20 control subjects) using duplex ultrasonography. Vessel wall diameters and velocities were measured in each arterial segment at peak-systolic (PS) and end-diastolic (ED) phases, for calculation of PS/ED shear rates. PS/ED shear stresses [dyne/cm²] were determined with PS/ED shear rates and shear-rate dependent BV values. For comparison, both values of hematocrit-derived BV and BV measurements at 300 s^-1 were used for calculation of shear stress.

Results

All cardiovascular disease (CVD) risk factors including BV values were similar between the two groups. In both common carotid arteries, PS and ED shear stresses were significantly lower in the patients with lacunar infarction than in controls in multivariate models that included age, sex, and other major CVD risk factors. PS and ED shear stresses using the shear rate specific BV were 4.5% lower and 7.3% higher than those using the two other BVs, respectively.

Conclusion

Lacunar infarction was associated with reduced carotid arterial shear stress. The use of estimated BV for calculating carotid arterial shear stress provides more accurate assessment of the hemodynamic contribution of shear stress than previous models that have arbitrarily assigned a constant value to this dynamic flow property.

Influence of bicuspid valve geometry on ascending aortic fluid dynamics: a parametric study

Bicuspid aortic valve (BAV) predisposes to aortic aneurysms with a high prevalence. A first hypothesis for this phenomenon is related to fibrillin deficiency (genetic hypothesis). The present article focused on a complementary, hemodynamic hypothesis stating that it is the peculiar fluid dynamics of blood in the ascending aorta of patients with BAV configurations that leads to aneurysm formation. To corroborate this hypothesis, a parametric study was performed based on numerical simulations of ascending aorta hemodynamics with different configurations of orifice area and valve orientation. The resulting wall shear stress (WSS) distributions and degree of asymmetry of the blood jet were investigated, and surrogate indices introduced. The results showed that WSS was more pronounced in subjects with BAV morphologies, also in the nonstenotic case. In particular, a maximum WSS of 3Pa was found (vs. 1.5Pa in subjects with a tricuspid configuration). It is localized at the mid-ascending aorta, the segment more prone to dilate as shown by the index related to maximum WSS (0.869 in BAV vs. 0.322 in tricuspid). Moreover, the asymmetry of the blood flow was found larger for decreasing valve area, the related index at mid-ascending aorta being more than three times higher than that found for tricuspid configuration (0.70 vs. 0.20). Further, WSS and flow asymmetry were higher also at the sinus of Valsalva and sinotubolar junction for a latero-lateral (LL) BAV configuration in keeping with the clinical observation on association between BAV configurations and different aortic aneurysm morphology. These findings may help explain the higher risk of aneurysm formation in BAV patients. The proposed indices will require validation prior to application in clinical settings.

Optimization of MR phase-contrast-based flow velocimetry and shear stress measurements

This study was designed to measure the pixel-by-pixel flow velocity and shear stress from phase-contrast MR images. An optimized method was suggested and the use of the method was confirmed. A self-developed, straight steady flow model system was scanned by MRI with a velocity-encoded phase-contrast sequence. In-house developed software was used for the pixel-by-pixel flow velocity and shear stress measurements and the measurements were compared with physically measured mean velocity and shear stress. A comparison between the use of the in-house velocimetry software and a commercial velocimetry system was also performed. Curved steady flow models were scanned by phase-contrast MRI. Subsequently, velocity and shear stress were measured to confirm the shifted peak flow velocity and shear stress toward the outer side of the lumen. Peak velocity and shear stress were calculated for both the inner and outer half of the lumen and were statistically compared. The mean velocity measured with the use of in-house software had a significant correlation with the physical measurements of mean velocity; in addition, the measurement was more precise compared to the commercial system (R(2) = 0.85 vs. 0.75, respectively). The calculated mean shear stress had a significant correlation with the physical measurements of mean shear stress (R(2) = 0.95). The curved flow model showed a significantly shifted peak velocity and shear stress zones toward the outside of the flow (P < 0.0001). The technique to measure pixel-by-pixel velocity and shear stress of steady flow from velocity-encoded phase-contrast MRI was optimized. This technique had a good correlation with physical measurements and was superior to a commercially available system.