ORIGINAL PAPER

Optimization of MR phase-contrast-based flow velocimetryand shear stress measurements

Taeho Kim • Ji-Hyea Seo • Seong-Sik Bang •

Hyeon-Woo Choi • Yongmin Chang •

Jongmin Lee

Received: 16 October 2009 / Accepted: 18 December 2009 / Published online: 29 December 2009

� Springer Science+Business Media, B.V. 2009

Abstract 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 (R2 = 0.85 vs. 0.75, respectively).

The calculated mean shear stress had a significant

correlation with the physical measurements of mean

shear stress (R2 = 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 mea-

surements and was superior to a commercially avail-

able system.

Keywords Flow velocity � Shear stress �MRI � Phase-contrast MRI

Introduction

Deposition of fatty compounds on an arterial wall can

cause an abnormal increase in smooth muscle cells

and inflammatory cells, and can subsequently gener-

ate decreased elasticity of the thickened arterial wall.

Thus, arterial luminal stenosis and impairment of

blood flow can follow such changes. This patholog-

ical process is referred to as atherosclerosis [1]. The

clinical outcome of atherosclerosis includes ischemic

heart disease and cerebrovascular accidents, which

occur mainly during late adult life. However, the

process that leads to atherosclerosis starts during

adolescence [2]. Since atherosclerosis shows chronic

and slow progression, ranging from a subtle fatty

streak on an arterial wall to a fatal clinical outcome,

T. Kim � J.-H. Seo � S.-S. Bang � H.-W. Choi �Y. Chang � J. Lee (&)

Kyungpook National University Hospital, Daegu,

South Korea

e-mail: jonglee@knu.ac.kr

123

Int J Cardiovasc Imaging (2010) 26:133–142

DOI 10.1007/s10554-009-9572-9

early diagnosis is required for optimal treatment and

a better prognosis.

For the purpose of early detection of atheroscle-

rosis, measurements of intima-media thickness (IMT)

and distensibility have been suggested and reported in

the medical literature. These evaluation methods have

shown a significant correlation with risk factors

associated with atherosclerosis [3, 4]. In addition,

wall shear stress (WSS), a blood flow-driven force to

the vascular wall, has been frequently reported to

have a close relationship with the development of

atherosclerosis. Atherosclerosis has been observed

more commonly in zones of lower or oscillating WSS

compared to zones with higher steady WSS [5, 6].

Since the measurement of WSS depends on the flow

velocity, MRI with a velocity-encoded phase-contrast

sequence has been widely used for the non-invasive

evaluation of WSS [7].

WSS is the product of viscosity and the wall shear

rate (WSR). The WSR is the flow velocity divided by

the luminal diameter of the blood vessel. Therefore,

accurate and constant measurement of flow velocity

is necessary to calculate the WSS correctly. Although

MRI is a useful imaging modality for velocimetry,

consistent accuracy cannot be guaranteed, especially

for in vivo conditions where various factors confound

the results, such as turbulent flow and vascular wall

distensibility [7].

In order to develop a new and practical MR

velocimetry technique, a velocimetry technique was

optimized for a mechanical flow model based on the

size of the aortic lumen. Subsequently, the use of this

technique was confirmed and applied for the mea-

surement of shear stress on a pixel-by-pixel basis.

Materials and methods

Flow model systems

The initial phase-contrast MRI in vivo condition

measured flow velocity inconstantly in single subject

with the same condition. Moreover, due to periodic

vascular wall motion and pulsatile flow, motion

artifacts occurred (Fig. 1). Therefore, a flow model

was created to measure flow velocity constantly after

minimizing in vivo bias factors such as pulsatile

motion, different perivascular soft tissue bulk, and

various hemodynamic factors (Fig. 2).

The flow model system consisted of two water

tanks, a main water-flowing tube, a bypass tube, pump,

and manometers. Each water tank stored a maximum

of 50 liters of water. The lower and upper water tanks

were designed to supply and to drain water flow

through the tube. The pump (PU-359M; Wilo Pumps,

Seoul, Korea) generated steady flow from the lower

tank toward the upper tank. A blocking valve and

Fig. 1 A three-tesla magnetic resonance phase-contrast image

of a human aorta. Due to pulsatile motion of the heart and aorta

as well as pulsatile flow within the cardiac chambers and aortic

lumen, a motion artifact (arrow) occurs over the descending

aorta and heart along the direction of phase encoding

Fig. 2 A scheme of the straight flow model is presented. For

measurement of exact flow velocity, this flow model was

developed by minimizing in vivo confounding factors. The

pump generates steady flow in the direction from the lower to

upper water tanks. A bypass valve controls flow velocity within

the main tube. A differential manometer was installed to

measure wall shear stress. The diameter and length of the tube

were 3 cm and 30 m, respectively. The measurement interval

of differential pressure was 1 m

134 Int J Cardiovasc Imaging (2010) 26:133–142

123

protractor were assembled in the bypass unit that

controlled flow velocity within the main tube. The

angles of the blocking valve ranged from 0� to 90�.

A lower angle of the valve lever allowed higher flow

velocity in the main tube. The size of the main tube

was 3 cm and 30 m for the inner diameter and length,

respectively. To measure the pressure gradient

between the inlet and outlet of a target segment of

the main tube, a digital manometer (490-1 Wet/Wet

Handheld Digital Manometer; Dwyer Instruments,

Michigan City, IN., USA) was installed at both ends of

the target zone with 1-cm diameter tubes. The pressure

gradient measurement using the manometer ranged

from 0 to 103 kPa with a standard error of ±0.5%.

A pressure gradient was measured for a 1-m distance.

Components of the flow model system installed within

the MR gantry room were made of non-metallic

materials. The scanning target segment of the main

tube was wrapped with a gelatin pack for similar image

contrast between intravascular and perivascular

spaces, as found under in vivo conditions.

As the flow model was a single tube model without

a diverting flow and contained laminar steady flow, as

a reference standard, the mean flow velocity was

physically measured using the following formula:

v ¼ Q=A ð1Þ

where Q (L/sec) is the physically measured volume

flow rate, v (cm/sec) is the mean velocity and A (cm2)

is the cross-sectional area of the water-flowing tube.

Since the flowing media within the flow model

was normal water (known as Newtonian fluid with

viscosity (l) of 0.9548 centipoises at 22�C) and the

tube had round cross-sectional morphology, the WSS

could be calculated using the following formula:

sw ¼8 � V

Dð2Þ

where sw is WSS, D is the diameter of the water-

flowing tube and V is the mean velocity of the

flowing media [8].

However, as formula (2) is a function of the mean

velocity and luminal diameter, the correlation between

the calculated and physically measured velocity

should be the same as the correlation coefficient for

the comparison of the velocity. In addition, the WSS

determined by the formula (2) is a global value without

local information for the region of interest. Therefore,

the shear rate based on pixels was measured from a

velocity-encoded MR phase-contrast image. Subse-

quently, the standard reference value of shear stress

was measured using formulas 3 and 4, based on a

physically measured pressure gradient.

DP� pD2

4¼ sw � pD� L ð3Þ

sw ¼DP� D

4Lð4Þ

where DP is the pressure difference between two

points for a pressure measurement, sw is the WSS,

D is the diameter of the water-flowing tube and L is

the distance between two points of the pressure

measurement [9].

To analyze the flow pattern between the inside and

outside zones of the curved tube, a curved flow model

system was developed by simple bending of the main

tube. Two types of curved model systems were

constructed based on the degree of curvature. The

MR scanning planes were at the midpoint of the

curved segment (Fig. 3). The structure of the other

components, except for the curved segment, was the

same as for the straight flow model system. Using the

curved flow model system, shifting of the peak

velocity and shear stress were analyzed.

Optimization of flow measurement techniques

MR imaging was performed using a 3.0 tesla MR

system (Excite HD; GE Healthcare, Milwaukee, WI

USA). The pulse sequence was a velocity-encoded

phase-contrast sequence. The repetition time, echo

time, size of the field of view, slice thickness,

reconstructed matrix, and number of excitations were

7.7 ms, 3.2 ms, 15 cm, 6 mm, 256 9 128, and 1,

respectively. The velocity encoding value was tailored

for each case and ranged from 210 to 255 cm/sec.

Twenty MR image acquisitions were performed for 10

different flow velocity measurements each. Since

steady flow was maintained during the MR acquisi-

tion, 20-phase MR images at each velocity setting

were averaged to measure the mean pixel-by-pixel and

whole-region velocity. The flow measurement was

performed using one straight tube and two types of

curved tubes.

For an MR phase-contrast image, the velocity can

be theoretically calculated using the following

formula:

Int J Cardiovasc Imaging (2010) 26:133–142 135

123

v ¼ D/180�

� venc ð5Þ

where v is the flow velocity, D/ is the phase shift (�)

and venc is the velocity encoding value (cm/sec) [10].

The phase shift D/ can be expressed in either radians

or degrees. If D/ is expressed in degrees, the range of

D/ is -180� to 180�. The velocity encoding value

venc is an arbitrarily defined velocity range based on

the assumed peak velocity of target flow. If venc is

100 cm/sec, the velocity range for an MR phase-

contrast image is -100 to 100 cm/sec [11]. If venc is

set lower than the real peak velocity, an aliasing

artifact occurs and peak velocity is underestimated.

By contrast, if venc is set higher than the real peak

velocity, the accuracy of the velocity estimation

decreases. Therefore, it is important to set an optimal

venc value for the accurate evaluation of velocity

[10, 11].

In this study, to develop a proper mathematical

formula for velocity estimation from the phase-

contrast MR image data, systematic correction of

confounding factors was performed. At first, the

standard reference mean flow velocity for the use of

the straight steady flow model system was measured

from the physically measured flow volume during the

pump running time. The reference velocity ranged

from 137 to 188 cm/sec and showed good reversed

correlation with the opening angle of the stopcock

valve (R2 = 0.979) (Fig. 4).

Second, the theoretical velocimetry equation [for-

mula (5)] was confirmed based on physically mea-

sured flow velocity using a straight flow model

system. Since the grey scale of phase images of

phase-contrast imaging theoretically reflect the phase

shift of flow, D/ was replaced with signal intensity.

Subsequently, linear regression analysis between the

mean signal intensity (SI) and physically measured

mean velocity (MV) was performed. However, the

comparison between SI and MV demonstrated a poor

correlation (R2 = 0.009) (Fig. 5a). In addition, the

calculated velocity using formula (5) showed a poor

correlation with the physically measured velocity

(R2 = 0.063) (Fig. 5b). This discrepancy was ana-

lyzed and was found to originate from the different

strength or homogeneity of background magnetiza-

tion (B0) for each evaluation.

To normalize the background magnetization, the

variable D/ was replaced with ‘SI of the phase

image/SI of the magnitude image.’ D/ was expressed

Fig. 3 A scheme of the curved flow model is presented. This

flow model was used to evaluate variations in the wall shear

stress between the inner and the outer surface of the curved

segment. a Curved flow model type1 has completely circular

tube within scanning zone. b Curved flow model type 2 has

semicircular tube for less centrifugal flow than type 1

Fig. 4 The correlation between the valve opening angle and

physically measured reference velocity reveals good correla-

tion (R2 = 0.979, P \ 0.001)

136 Int J Cardiovasc Imaging (2010) 26:133–142

123

in radians, where the constant 1808 was replaced by

p. By the addition of a fitting constant to the

physically measured mean velocity, a dedicated flow

velocity formula for the flow model was developed as

the following:

v ¼ PCSI

MSI� 1

p� venc � a ð6Þ

where PCSI is the signal intensity of a phase image,

MSI is the signal intensity of a magnitude image, v is

the estimated velocity, venc is the velocity encoding

value and a is the fitting constant for the physically

measured velocity (0.3 in this flow model).

WSS is determined by multiplication of the

viscosity of flowing fluid with the wall shear rate

(WSR) as the following [7]:

sw ¼ lou

orð7Þ

where sw is WSS, l is the viscosity of fluid and qu/qr

is the WSR.

The pixel-by-pixel shear rate was calculated from

the velocity divided by the distance of the pixel from

the inner wall [12]. The pixel-by-pixel velocity using

the optimized velocimetry technique and subsequent

mean shear stress were evaluated and were verified

by the use of self-developed PC-based software. The

dedicated analysis program performed automated

segmentation of the region-of-interest (ROI) based

on both magnitude and phase images.

Data analysis

The calculated velocity determined using formula (6)

was compared with the physically measured velocity

determined using formula (1). Since the physically

measured velocity was the mean velocity, the calcu-

lated pixel-by-pixel velocity was averaged for the

comparison. To verify the suggested velocimetry

formula (6) for the straight steady flow model,

calculated and physically measured velocities were

compared. In addition, the flow velocity of the same

straight flow model was also estimated using a

commercial flow analysis system (Report Card 4.0;

GE Healthcare) and the results were compared with

the results of formula (6) based on the physically

measured data.

Based on the physically measured WSS, the

calculated shear stress using formula (4) and formula

(7) were compared. Since the physically measured

WSS was calculated to a mean value, the calculated

pixel-by-pixel shear stress was averaged for the

comparison. The confirmation of the shear stress

measurement was also based on the data from the

straight and steady flow models.

For the curved steady flow model, based on the

expectation of flow redistribution in the curved tube,

the peak velocity zone and mean shear stress were

estimated. These two parameters were compared

between the inner and outer half areas of the curved

flow. The mean shear stress discrepancy between the

Fig. 5 A plot showing the correlation among physically

measured mean velocity, mean signal intensity and calculated

mean velocity is presented. a The correlation between the

mean signal intensity of a phase-contrast MR image and the

physically measured mean velocity using data from the straight

flow model is shown. b The correlation between the physically

measured velocity and calculated velocity using the modified

velocity calculation formula (5) is shown

Int J Cardiovasc Imaging (2010) 26:133–142 137

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inner and outer zones of the curved tube was quanti-

tatively analyzed.

For statistical analysis, the acquired velocity and

shear stress were compared with standard reference

data using linear regression analysis, as these param-

eters showed a linear relationship by simple plotting.

For the linear regression analysis, an R2 greater than

0.65 and a P-value less than 0.05 were regarded as

statistically significant. For the mean shear stress

comparison in the curved flow model system, t-test

was used to determine the difference between inner

and outer areas of flow. If a P-value was lower than

0.05, the mean shear stress was regarded as signif-

icantly different.

Results

To confirm the application of the suggested veloci-

metry formula (6), phase-contrast MRI data from the

straight flow model was analyzed (Fig. 6). The flow

velocity profile graphs, with steady flow within the

straight tube, showed a laminar bullet pattern of flow

for both the highest and the lowest flow velocity

settings (Fig. 7a–d). The physically measured mean

velocity and calculated mean velocity using formula

(6) showed a good correlation (R2 = 0.848, P \0.001) (Fig. 8a). The use of the commercial flow

analysis system also showed a good correlation

(R2 = 0.748, P \ 0.001) (Fig. 8b). However, the

use of formula (6) had a better correlation with the

standard reference compared to the commercial flow

analysis program.

Verification of shear stress was also analyzed by

linear regression. For the linear regression, the

calculated mean shear stress derived from formula

(6) and the physically measured WSS using formula

(7) were compared. This data was acquired from the

straight flow model. The calculated mean shear stress

showed good correlation with the physically mea-

sured WSS (R2 = 0.95, P \ 0.001).

For the curved flow models, the phase images

showed slightly lower signal intensity in the inner area

of the flow (Figs. 9, 10). The calculated mean shear

stress of the outer half area of the flow was significantly

higher compared to the inner half area (1.04 ± 0.14 Pa

vs. 0.81 ± 0.13 Pa, respectively) with a statistically

significant difference (P \ 0.0001). The two-dimen-

sional and three-dimensional plots showed that the

calculated pixel-by-pixel shear stress was consistently

higher in the outer zone of curved flow at both the

highest and lowest velocity settings (Fig. 7e, f).

Discussion

To determine the optimal technique for velocimetry,

we used a large and straight steady flow model that

was free from variable in vivo confounding factors

such as flow pulsatility, vascular wall elasticity, and

heterogeneous perivascular structures and motion

artifacts. In clinical practice, confounding factors

are encountered such as a non-perpendicular imaging

plane to flow, inappropriately expected maximum

velocity, erroneous reconstruction of the MR signal

and limited spatial and temporal resolution [13].

Although the optimized velocimetry technique was

Fig. 6 Phase-contrast MR images for the use of the straight

flow model are shown. The velocity was calculated at the

region of the tube (arrows). A magnitude image (a) and phase-

contrast image (b) are shown

138 Int J Cardiovasc Imaging (2010) 26:133–142

123

solely dedicated for the use of the flow models, by the

addition of individual confounding factors, the

velocimetry technique may be useful for in vivo

imaging. The next step of this consecutive velocime-

try study will be the use of a straight pulsatile flow

model the size of the aorta.

The confirmation of MR velocity imaging has been

performed continuously from the time this technology

was introduced. Walker et al. [14] validated the

relationship between the mean projected intensity of

total flow area and flow velocity using the in vitro

steady parabolic laminar flow model; the mean

velocity of total flow to within 10% of the measured

value over a wide range of flow rates was determined.

However, the velocimetry on a pixel-by-pixel basis

was not evaluated. Firmin et al. [15] validated the MR

velocity imaging technique by comparing the left

ventricular stroke volume obtained by geometric

measurement of the ventricular area using a modified

Simpson’s method and the stroke output derived from

the velocity map of the ascending aorta. The stroke

output was measured based on the mean signal

intensity of aortic flow; a significantly high correlation

was identified by this comparison (r = 0.97, P \0.001) and the standard error estimate was reported as

3.2 ml. Using the velocimetry technique based on

averaged signal intensity of the velocity map, Tar-

nawski et al. [16] measured the time-averaged flow

volume of the carotid artery and validated the

technique based on Doppler ultrasound values (r =

0.52, P \ 0.01).

The limitations of velocimetry, using the MR

velocity-encoded phase-contrast imaging, have been

reported. The blood flow-related motion artifact

decreases the accuracy of MR velocimetry [7]. The

severity of the motion artifact is more severe with

higher magnetic field strength, such as with a 3-Tesla

MR scanner (Fig. 1). The velocity and volume of

blood flow may be underestimated if the vessel of

interest is not imaged in a plane exactly perpendicular

to the direction of flow [17]. Aliasing, or erroneous

reconstruction of the MR signal, may occur if the

Fig. 7 Calculated velocity and shear stress are displayed in

two-dimensional and three-dimensional color-mapped images.

The velocity and the shear stress can be estimated by color

scales. Two-dimensional axial image for the high velocity

profile (a) shows more red color scale than the low velocity

profile (b). Three-dimensional plotting for velocity profiles

reveals higher amplitude in the high velocity model (c) than the

low velocity model (d). In high velocity model, shear stress

plotting using color scale on axial image (e) reveals the highest

shear stress along the wall. Three-dimensional plotting of shear

stress (f) shows quantitative values of wall shear stress

Int J Cardiovasc Imaging (2010) 26:133–142 139

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expected maximum velocity is lower than the actual

peak velocity, at any time during the cardiac cycle. In

addition, the evaluation of very small vessels with

velocity-encoded cine MR imaging is suboptimal

because such vessels are involved in relatively few

pixels [13]. Furthermore, pressure gradient measure-

ments are subject to error because they are calculated

on the basis of the peak velocity, which may be

underestimated when temporal resolution is lower

than in real time [18].

With the support of high spatial resolution and

signal-to-noise ratio (SNR) in the high field MR

scanner, signal intensity measurements in pixels with

enough SNR for quantitative measurement became

possible. In this study, we performed velocimetry on

a pixel-by-pixel basis for the purpose of calculating

the shear rate or stress on a pixel-by-pixel basis.

However, as shown in our preliminary study, theo-

retical formula (5) could not convert the signal

intensity to a statistically acceptable velocity. Since

no technique to convert signal intensity of pixels to

velocity has been reported, we optimized the veloc-

imetry technique on a pixel-by-pixel basis.

When strong pressure is continuously loaded onto a

vessel wall, the tunica intima will be injured. Subse-

quently, an immediate self-healing process (athero-

sclerotic change) will be initiated. During the response

to endothelial damage, the elasticity of the vessel wall

gradually decreases and the damping function of the

vessel wall against pulsatile flow weakens. For the

early diagnosis of atherosclerosis, several studies have

evaluated the WSS, which has a significant relation-

ship with the pathogenesis of atherosclerosis. These

studies have used MRI for the WSS measurement.

MRI has been reported to be useful for WSS evalu-

ation, as MRI can provide information about both in

vivo blood flow and the vascular anatomy in a non-

invasive manner [5, 19, 20].

To measure the WSS, Oyre et al. [11] developed a

three-dimensional paraboloid (3DP) method using

phase-contrast MRI. This method was based on two

assumptions. The velocity distribution was assumed

to have rotational circumferential symmetry and the

arteries were assumed to be perfectly circular in

shape. Therefore, if these assumptions could not be

satisfied due to in vivo confounding factors, the 3DP

results may not be reliable. The confounding factors

may include pulsatile flow, flow turbulence, and

irregular vascular morphology.

Another method to measure the WSS was the

micro particle image velocimetry (lPIV), which is an

image processing technique based on tracing particles

in the blood flow [21]. After injection of fluorescent

dye, flow information can be evaluated using the

signal from a moving tracer particle in the blood flow.

Using this method, Poelma et al. [22] evaluated the

WSS in a chicken embryo artery.

In summary, we have developed an aorta-sized

mechanical flow model with the intention of

Fig. 8 The correlation between the physically measured mean

velocity and calculated mean velocity is shown. a The

physically measured velocity and calculated velocity based

on the self-developed formula (6) shows good correlation with

R2 value of 0.848. b The measured velocity and calculated

velocity using a commercial flow analysis system (Report Card

4.0) shows worse correlation than using a self-developed

system (R2 = 0.748)

140 Int J Cardiovasc Imaging (2010) 26:133–142

123

minimizing in vivo confounding factors. The veloc-

imetry technique for phase-contrast MRI was mod-

ified. We measured the pixel-by-pixel velocity from

phase-contrast MR images. The in-house velocimetry

technique showed high precision with a greater

correlation coefficient compared to a commercial

Fig. 9 Phase-contrast MR images from curved flow models

are presented. The magnitude image (a) and phase image (b)

from the type 1 curved flow model and the magnitude image

(c) and phase image (d) from the type 2 curved flow model are

shown. In phases images from both models, inside of the

curved flow (arrow) shows lower signal intensity than outside

of the flow

Fig. 10 Three-dimensional color-mapped plottings of calculated wall shear stress from the type 1 (a) and the type 2 (b) curved flow

models show difference between the inside and outside of the lumen of the curved tubes

Int J Cardiovasc Imaging (2010) 26:133–142 141

123

flow analysis program. The determination of esti-

mated mean shear stress was also feasible and the

results were statistically significant.

Acknowledgments ‘‘This work was supported by the Korea

Research Foundation (KRF) grant funded by the Korea

government (MEST).’’ (No. 2009-0071901).

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