Effect of phase-encoding scheme on the relationshipbetween contrast agent concentration and signal intensityon inversion recovery turbo fast low-angle shot T1-weightedimages

Mahmood Nazarpoor

Received: 13 June 2013 / Revised: 20 January 2014 / Accepted: 21 January 2014

� Japanese Society of Radiological Technology and Japan Society of Medical Physics 2014

Abstract Previous studies have shown that the image

parameters such as the repetition time and inversion time

(TI) and image sequences can have an effect on the max-

imum linearity between signal intensity (SI) and concen-

tration. Our aim in this study was to investigate the effect

of a phase-encoding scheme (linear phase-encoding and

center out phase-encoding) at different TIs on the maxi-

mum linear relationship between contrast agent concen-

tration and SI using inversion recovery TurboFLASH

(turbo fast low angle shot) T1-weighted images in MRI. A

phantom was designed to hold 25 vials which contained

either different (between 0 and 19.77 mmol/L) or constant

(1.20 mmol/L) concentrations of contrast agent. The vials

of constant concentration were used for measurement of

coil non-uniformity. The vials of different concentrations

were used for the measurement of the maximum linear

relationship between SI and concentration and the effect of

a phase-encoding scheme on the linearity, where the

squared correlations (R2) between the corrected SI and the

concentration were equal to 0.95 and 0.99. The results

showed that the linear relationship between SI and con-

centration was dependent on the phase-encoding scheme

and on the TIs. The results also showed that the maximum

linearity with the linear phase-encoding acquisition was

higher than that with the center out phase-encoding

acquisition at the same R2. This study shows that the phase-

encoding scheme is an important parameter when the SI is

measured. These schemes can have an effect on the max-

imum linearity between SI and concentration.

Keywords T1-weighted image � Inversion recovery �Signal intensity � Concentration of contrast agent �Center out phase-encoding � Linear phase-encoding

1 Introduction

Gd-based MR contrast agents play an indirect role in the

MR signal by reducing the relaxation times of the sur-

rounding nuclear spins [1]. MRI is not able to directly

measure the concentration of the contrast agent. The con-

centration is measured indirectly from the signal intensity

(SI). If the relationship between SI and concentration can

be shown to be linear over a range of concentrations, then

relative changes in SI can be used for finding the

concentration.

Therefore, the SI–time curve can be used instead of the

concentration–time curve for the measurement of hemo-

dynamic parameters, such as organ blood flow and organ

blood volume [2].

Different publications suggested different values for the

maximum linearity between SI and concentration in the

stationary state and steady state [3–5]. For this reason, the

relationship between SI and concentration should be

investigated more thoroughly for determining the maxi-

mum concentration that yields a linear response.

Our previous studies showed that image parameters such

as the repetition time (TR) and inversion time (TI) and

image sequences can have an effect on the maximum lin-

earity between SI and concentration [6–8].

Our aim in this study was to investigate the effect of a

phase-encoding scheme (center out phase-encoding and

linear phase-encoding) at different TIs on the maximum

linear relationship between the contrast agent concentration

and SI after correction for coil non-uniformity. The squared

M. Nazarpoor (&)

Department of Radiology, Faculty of Paramedicine, Tabriz

University of Medical Sciences, Tabriz, Iran

e-mail: mnazarpoor@yahoo.co.uk; nazarpoorm@tbzmed.ac.ir

Radiol Phys Technol

DOI 10.1007/s12194-014-0260-7

correlation (R2) between the corrected SI and the concen-

tration was set to 0.95 and 0.99 by use of inversion

recovery TurboFLASH (turbo fast low-angle shot) T1-

weighted images.

2 Materials and methods

2.1 Phantom

For assessment of the relationship between SI and con-

centration in stationary vials, a phantom was designed to

hold vials which contained either different or constant

concentrations of a contrast agent. The shape of the

phantom was approximately cubic; it was made of Perspex.

Its length, width and height were 20, 18, and 20 cm,

respectively [6]. Figure 1 shows a coronal image of the

phantom, which contains the vials (glass tube, inner

diameter approximately 15 mm) with different contrast

agent concentrations. The position of the different con-

centrations inside the vials can be seen from the figure.

The phantom of different concentrations consisted of 25

vials, filled with different concentrations of Gd-DTPA

(Magnevist, Schering Health Care Ltd, West Sussex, UK).

The concentration of Gd-DTPA varied between 0 and

19.77 mmol/L (0.00, 0.30, 0.45, 0.60, 0.75, 0.90, 1.20,

1.50, 1.80, 2.10, 2.39, 2.69, 2.99, 3.28, 3.58, 3.98, 4.96,

5.95, 7.93, 9.90, 13.85, and 19.77 mmol/L).

A clinical head and neck coil was used with the phan-

tom. The phantom was located inside the coil. The vials

were set vertically, and the axes of the vials were per-

pendicular to the image plane (coronal image).

Two experiments were performed, one using vials with

different concentrations for measurement of the relation-

ship between SI and concentration and the other using vials

of a constant concentration for measurement of coil non-

uniformity. The vials in the phantom with constant con-

centration (1.20 mmol/L) were placed in exactly the same

positions as the vials with different concentrations [6].

One of the major sources of image non-uniformity in the

high-field MR scanners is the radio-frequency (RF) coil

inhomogeneity [9–11]. Therefore, for measuring the accurate

SI in an image, the response of the RF coils should be uniform.

The non-uniformity of the coil will be calculated from vials

with constant concentration. If the coil is uniform, the SI of the

vials with the constant concentration (1.20 mmol/L) for the

different parts of the phantom should be the same. As the coil

is not uniform, the SI was different. We chose the SI of one vial

in the center of the coil as reference SI (i.e., the vial with a

concentration of 1.20 mmol/L). Therefore, the SI of the vials

with the constant concentration should be equal to that of SI.

After normalization of the mean SI from the vials with con-

stant concentration, the correction factor due to the non-uni-

formity of the coil can be calculated for different parts of the

vials with different concentrations.

For calculating the corrected SI for different concen-

trations, the SI of each vial was multiplied by its correction

factor [7, 8].

2.2 Theory

In MRI, the acquired data actually represent the Fourier

transformation of the imaged object rather than the object

itself. In the other words, MRI acquires data in k-space, and

Fig. 1 Coronal image of the

phantom. The positions of

different concentrations inside

the vials can be seen from this

figure

M. Nazarpoor

a Fourier transformation will convert k-space data to image

data. The center of k-space determines the majority of the

image contrast, and the edges of k-space determine high-

resolution structural information on the image [12, 13].

For T1-weighted monitoring of the contrast agent, a

number of T1-weighted sequences are available [14]. The

inversion recovery sequence first uses a 180� pulse, which

is then followed by a 90� excitation pulse.

Figure 2 is a schematic representation of the inversion

recovery gradient echo TurboFLASH sequences. TE is the

echo time.

The standard inversion recovery sequence, which is

dependent on TI and TR, is described by the following

equation [7, 8]:

SðtÞ ¼ S0 1� 2 exp �TICðtÞ

Kþ 1

T1Pr e

� �� ��

þ exp �TRCðtÞ

Kþ 1

T1Pr e

� �� ��; ð1Þ

where S(t) and S0 are the SI after administration of a

contrast agent and the observed SI in the absence of any

magnetization preparation pre-pulses or contrast agent,

respectively. T1Pre is the longitudinal relaxation time

before contrast application. C(t) is the concentration of the

contrast agent at time t. K is a constant that depends on the

contrast medium.

The transverse relaxation time (T2) will also be influ-

enced at higher concentrations of the contrast medium.

Therefore, Eq. (1) should be multiplied by exp � TE

T2

� �at

higher concentrations of contrast agents [15, 16].

Two common acquisition strategies in MRI are linear

phase-encoding and center out phase-encoding [17]. As

stated by Jivan et al. [18], after an inversion pulse, which

occurs at time zero, as the longitudinal magnetization

recovers, images can be acquired by the TurboFLASH

image sequence. Each image can be formed by application

of a set of a pulses, each of which gives one k-space line.

The signal will decrease after each a to reach a steady-state

saturation level. After this step, it will be constant during

image acquisition.

The center out phase-encoding acquires the center of

k-space at time zero or the start of the RF pulses, and

most of the image contrast is determined by the central

views of k-space and a small number of flash lines of k-

space around the centre of k-space line. The linear

phase-encoding acquires the center of k-space at the time

from the inversion pulse to the mid-line of k-space when

the longitudinal magnetization recovery has reached a

steady-state level; this is usually called the effective TI

(see Fig. 3) [13].

TI in Eq. (1) is the TI for the center out phase-encoding

and the effective TI for the linear phase-encoding

acquisitions.

2.3 Image acquisition

The phantom was positioned within the head and neck coil.

All studies were carried out with a 1.5-T clinical MR

scanner (Vision, Siemens Medical, Erlangen, Germany).

We used T1-weighted TurboFLASH images to measure SI

TE

Centre of K space

180 degree inversion pulse

Effective TI

180 degree inversion pulse

Echo

α α α α α α1 20 n−3 n−2 n−1

Time

TI set

TR for one FLASH line

TurboFLASH

Inversion recovery TurboFLASH

TR for one TurboFLASH image

Fig. 2 Inversion recovery gradient echo TurboFLASH for one

image. This is an inversion recovery TurboFLASH with n a pulses,

where the n/2th line traverses the center of k-space (for linear phase-

encoding). ‘‘TI set’’ is the time between the 180� inversion pulse and

the first a excitation pulse. The effective TI is the time from the

inversion pulse to the mid-line of k-space n/2nd. TE and TR are the

echo time and repetition time, respectively. Imaging gradients are not

shown in this diagram

Effect of phase-encoding scheme

in the vials with different and constant concentrations. For

investigation of the effect of the phase-encoding scheme on

SI, the two acquisitions were preformed for the inversion

recovery (IR) sequence.

The TurboFLASH imaging parameters were as follows:

matrix size = 128 9 128, time for one FLASH

line = 8.5 ms, echo time (TE) = 4 ms, TR = 3 ms,

effective TI varied between 744 and 2944 ms (744, 844,

944, 1044,1144, 1244, 1344,1444, 1544, 1744, 1944, 2144,

2344, 2544, 2744, and 2944 ms) for the linear phase-

encoding, and TI varied between 700 and 1600 ms (700,

800, 900, 1000, 1200, 1400 and 1600 ms) for the center out

phase-encoding. Because one aim of this study was to

investigate the effect of the two phase-encoding schemes

on the maximum linearity between SI and contrast agent

concentration, the TI and effective TI values were differ-

ent. Each image was repeated 10 times (TR for one Tur-

boFLASH image) in the MR scanner with a slice thickness

of 10 mm, a pixel size of 2 9 2 mm, and a flip angle of

15�.

2.4 Image analysis

The image data were transferred from the MR scanner to a

Unix workstation. The image-processing software Interac-

tive Data Language (IDL, Research Systems, Inc., http://

www.rsinc.com) was used for processing.

Programs were written to calculate automatically:

– The mean image of 10 acquisitions, to improve the

signal to noise ratio.

M+

M−

Timea

TI

Effective TI

c

Before the start of image acquisition

End of image acquisition

Ideal longitudinal magnetization recovery

Real longitudinal magnetization recovery

128 α degree pulses

b

Fig. 3 Schematic representation of the magnetization during the T1-

weighted TurboFLASH sequence, showing the ideal and the real

shape of the longitudinal magnetization recovery. M- and M? are

the longitudinal magnetization values before and after the inversion

pulse. After applying an inversion pulse, which occurs at time zero, as

the longitudinal magnetization recovers, images can be acquired.

Each image is formed by application of radiofrequency (RF)

(a = 15�) pulses, each of which gives one k-space line. Point a

shows the start of the RF pulses. The amplitude of the signal after the

first a is higher than the other a. The time from the inversion pulse

(TI) to the mid-line of k-space is usually called the effective TI. The

effective TI (b) is placed at TI ? 64 9 8.5 ms for a typical

128 9 128 matrix size image and for one FLASH line (8.5 ms).

The center out phase-encoding acquires the center of k space at point

a and the linear phase-encoding acquires the center of k space at point

b. c is the end of image acquisition

M. Nazarpoor

– The mean SI of the 9 innermost pixels of each vial with

different and constant concentrations to avoid partial

volume effects.

– The correction factors with respect to coil non-unifor-

mity. The SI of the vials with different concentrations

was then multiplied by these factors.

– The best-fit curve of concentration versus SI curve

based on Eq. (1).

– The maximum concentration, where the R2 values

between the corrected SI and the concentration were

equal to 0.95 or 0.99 from the best-fit curve for all

experiments.

The R2 gives the strength of the linear relationship

between SI and concentration. When R2 is 0.95, this indi-

cates that 95 % of the variation in SI is explained by the

variation in the concentration [19]. A computer program

calculated R2 from the first n points in the fitted data of SI

versus concentration. As n was increased, including more

data points, the value of R2 decreased. The value of n, and

hence the concentration, that gave an R2 value of 0.95 or

0.99 was found. This concentration is known as the max-

imum value that gives a linear relationship with the SI.

These programs could be run from either a UNIX

workstation or a personal computer.

3 Results

3.1 Center out phase-encoding acquisition

Figure 4 shows a typical result from the corrected SI (the

non-uniformity of the coil) versus concentration by use of

the center out phase-encoding acquisition. The corrected SI

was measured from mean SI of the 9 innermost pixels of

each vial. The mean non-uniformity coil correction factors

were calculated as 0.90, 0.93, 1.00, 0.95, 0.89, 0.94, 1.00,

0.96, 0.86, 0.97, 0.88, 1.00, 0.93, 0.90, 0.97, 1.03, 0.94,

0.96, 0.95, 0.99, 1.02, and 0.97 for the vials with concen-

trations of 0.00, 0.30, 0.45, 0.60, 0.75, 0.90, 1.20, 1.50,

1.80 (top left), 2.10, 2.39, 2.69, 2.99, 3.28, 3.58, 3.98, 4.96,

5.95, 7.93, 9.90, 13.85, and 19.77 mmol/L, respectively.

The error bars show the standard deviation for each vial.

The dashed lines show the curve fit of the data. The figure

shows that SI decreased at high concentrations due to the

T2-shortening effect on the SI.

The maximum linear relationship between concentra-

tions and corrected SI for the center out phase-encoding

that gave R2 values equal to 0.95 and 0.99 was 2.02 and

1.25 mmol/L, respectively, at TI = 1000 ms.

Figure 5 shows the maximum concentration versus TI

by use of the center out phase-encoding acquisition with 7

different TIs.

The linear relationship between SI and concentration

was up to 3.03 and 1.23 mmol/L for the short TI (700 ms)

and long TI (1600 ms), respectively, where R2 = 0.95. In

Fig. 4 Mean corrected SI from the 9 innermost pixels of the vials

versus the concentration of contrast agent for the center out phase-

encoding acquisition. The maximum linear relationship between

concentrations and corrected SI that gave squared correlations (R2)

equal to 0.95 and 0.99 was 2.02 and 1.25 mmol/L, respectively, at

TI = 1000 ms. The error bars show the standard deviation for each

vial

Fig. 5 The maximum concentration that gives R2 = 0.95 and 0.99

versus TI with the center out phase-encoding acquisition. The linear

relationship between SI and concentration is up to 3.03 and

1.23 mmol/L for the short TI (700 ms) and long TI (1600 ms),

respectively, where R2 = 0.95. In addition, these values reduce to

1.65 and 0.71 mmol/L for these inversion times where R2 = 0.99

Effect of phase-encoding scheme

addition, these values reduce to 1.65 and 0.71 mmol/L for

these TIs when R2 = 0.99. The R2 was measured from the

best-fit curve for each TI, similar to that obtained from

Fig. 5.

As can be seen from Fig. 5, an increase in TI is asso-

ciated with a decrease in the maximum concentration.

3.2 Linear phase-encoding acquisition

Figure 6 shows a typical result for the corrected SI versus

concentration for the linear phase-encoding acquisition.

The corrected SI was measured from the mean SI of the 9

innermost pixels of each vial, which was obtained after a

non-uniformity correction. The mean non-uniformity coil

correction factors were calculated as 0.89, 0.93, 0.99, 0.96,

0.89, 0.93, 1.00, 0.95, 0.90, 0.93, 0.90, 1.01, 0.94, 0.91,

0.98, 1.05, 0.97, 0.98, 0.95, 0.99, 1.06, and 0.99 for the vials

with concentrations of 0.00, 0.30, 0.45, 0.60, 0.75, 0.90,

1.20, 1.50, 1.80 (top left), 2.10, 2.39, 2.69, 2.99, 3.28, 3.58,

3.98, 4.96, 5.95, 7.93, 9.90, 13.85, and 19.77 mmol/L,

respectively. The error bars show the standard deviation for

each vial. The dashed lines show the curve fit of the data.

The figure shows that the T1-shortening effect is dominant

at low concentrations of Gd-DTPA, based on Eq. (1), and

the T2-shortening effect is dominant at high concentrations

and leads to a decrease in the SI.

The maximum linear relationships between concentra-

tions and corrected SI that gave R2 values equal to 0.95 and

0.99 were 2.14 and 0.93 mmol/L, respectively, at TI set at

400 ms (effective TI = TI ? 64 9 8.5 = 944 ms).

Figure 7 shows the maximum concentration that gives

R2 values equal to 0.95 and 0.99 versus effective TI for the

linear phase-encoding acquisition at 16 different TI values.

The linear relationship between SI and concentration

was up to 2.64 and 0.89 mmol/L, for short effective TI

(744 ms) and long effective TI (2944 ms), respectively

(R2 = 0.95). In addition, these values were reduced to 1.15

and 0.38 mmol/L for these effective TIs where R2 = 0.99.

Figure 7 indicates that an increase in the effective TI is

associated with a decrease in the maximum concentration.

The R2 was measured from the best-fit curve for each TI,

similar to that obtained from Fig. 5.

4 Discussion

MRI is unable to measure the concentration of contrast

within the region of interest of an organ; it is measured

indirectly from the SI. At high concentrations, both T1 and

T2 can be affected as the SI response becomes nonlinear,

with an unsteady plateau. Therefore, to calculate the con-

centration from the SI, one should measure the maximum

concentration for linearity between SI and the

concentration.

Fig. 6 Mean corrected SI from the 9 innermost pixels of the vials

versus concentration of contrast agent for the linear phase-encoding

acquisition. The maximum linear relationship between concentrations

and corrected SI that gave R2 equal to 0.95 and 0.99 was 2.14 and

0.93 mmol/L, respectively, at TI set at 400 ms (effective inversion

time = TI ? 64 9 8.5 = 944 ms). The error bars show the standard

deviation for each vial

Fig. 7 Maximum concentration that gives R2 = 0.95 and 0.99 versus

effective TI. The linear relationship between SI and concentration is

up to 2.64 and 0.89 mmol/L for short effective TI (744 ms) and long

effective TI (2944 ms), respectively (R2 = 0.95). In addition, these

values reduce to 1.15 and 0.38 mmol/L for these effective inversion

times when R2 = 0.99 with the linear phase-encoding acquisition

M. Nazarpoor

The correlation between MR SI values on T1-weighted

TurboFLASH and the concentration of Gd-DOTA (Gado-

terate, 0.5 mol/mL) was reported by Canet et al. [4]. They

showed that the SI increase on T1-weighted images was

linearly proportional to the Gd chelate concentration at low

concentrations (B0.8 mmol/L) with TI = 300 ms (effec-

tive TI = 716 ms); however, the SI response becomes

nonlinear at higher concentrations.

In this study, the SI was corrected by the correction

factor of the non-uniformity of the coil.

The present results, which used the inversion recovery

TurboFLASH sequence (linear phase-encoding), from the

vials, indicated that an increase in TI was associated with a

decrease in the maximum linear concentration when the R2

was equal to 0.95 or 0.99. The result (see Fig. 7) also

shows that, at long TI (2944 ms), the maximum linear

relationship between SI and concentration was up to

0.89 mmol/L when R2 = 0.95, or up to 0.38 mmol/L when

R2 = 0.99. These values can increase at short TI. In

addition, our result (see also Fig. 7) when we used the Gd-

DTPA contrast agent under Canet’s conditions was about

2.64 (R2 = 0.95) or 1.15 mmol/L (R2 = 0.99). It should be

noted that the two contrast agents have roughly the same

relaxivity [20].

The non-uniformity of the coils can affect the SI, and this

contributes a large error to the measured SI [11]. Because

Canet did not mention any correction of the non-uniformity

of the coil, the difference between the present study and that

of Canet et al.’s. report may be due to the non-uniformity of

the coil. Another reason may be the use of a different TR by

Canet, or a different value of R2 was used for finding the

maximum linear relationship between SI and concentration.

Neither of these values was cited by Canet.

Fritz-Hansen et al. [21] found linearity between signal

changes and tracer concentrations up to 1.0 mmol/L

(R2 = 0.999), and an effective TI of 720 ms when using

the IR TurboFLASH sequence (linear phase-encoding)

(TR, time for one FLASH line = 6.5 ms, TE = 3.0 ms,

flip angle = 12�, effective TI varying between 170 and

2000 ms). They did not mention the actual TR. Our image

parameters are slightly different from Fritz-Hansen’s

image parameters. The present study (see Fig. 7) showed

that the maximum linearity was about 1.20 at R2 = 0.99, at

an effective TI of 720. The difference between the present

study and that of Fritz-Hansen et al. may be due to the use

of different TE, TR, and flip angle, or it may be due to the

effect of non-uniformity of the coil [11].

A correlation between the SI and the concentration of

Gd-DTPA on T1-weighted imaging with use of the satu-

ration recovery sequence was also reported by Takeda et al.

[5] and Vallee et al. [22]. Because the image sequence was

different, it is not possible to compare Takeda’s and Val-

lee’s results with ours.

In addition, Dean et al. [23] and Unger et al. [20]

reported that the linearity between SI and concentration

was 1 mmol/L, but they did not mention in detail how they

found this value for comparison with the results of the

present study.

As mentioned above, different papers have reported

different values for the maximum linear relationship

between SI and the concentration of the contrast agent in

T1-weighted imaging. These values were varied between

0.8 and 1 mmol/L concentration for the IR sequence [4, 5,

20, 23].

The linear relationship between SI and the concentration

of the contrast agent was investigated in our previous study

(center out phase-encoding, TR = 2 s) [7]. That study

showed that the linear relationship between SI and con-

centration extended up to 5.34 and 2.46 mmol/L for the

short TI (400 ms) and long TI (800 ms), respectively,

where R2 = 0.95. In addition, these values were reduced to

2.63 and 1.57 mmol/L for these TIs, where R2 = 0.99. The

slightly difference between the present study (see Fig. 5)

and the previous study is due to the use of a different TR.

For finding this linearity, the value of R2 which gives the

strength of the linear relationship between SI and concen-

tration is important. The use of R2 for measuring the lin-

earity is mentioned with different values in different

papers. Takeda et al. [5] accepted the value of 0.76 for the

linearity. Bourke et al. [24] and Fritz-Hansen et al. [21]

also stated that R2 = 0.74 and R2 = 0.999 show a rea-

sonably strong association between SI and concentration,

respectively. In this study, the maximum linearity was

calculated for both R2 = 0.95 and 0.99, which indicates a

far higher degree of linearity.

In summary, our results (see Figs. 5, 7) show that there

is a difference between the maximum linearity of the

concentration and the SI with the different phase-encoding

schemes. The figures show that the maximum linearity with

the linear phase-encoding acquisition was higher than with

the center out phase-encoding acquisition at the same R2.

The difference in values of the maximum linearity between

the two phase-encoding schemes is due to the different

methods of sampling k-space. In particular, the time at

which the center of the k-space is acquired, the linear

phase-encoding acquisition will have experienced multiple

FLASH lines before the center of k-space is reached,

making the image more sensitive to T1 effects compared to

the center out phase-encoding acquisition [18].

In other words, before the initial a pulse in the IR gra-

dient echo TurboFLASH sequence, the protons of the

liquid inside the slice are unsaturated and emitted a very

strong signal. After the initial a, the slice contains saturated

protons and gives a signal lower than that before the initial

a. After the second a, the slice contains more saturated

protons than after the first a and gives a signal weaker than

Effect of phase-encoding scheme

that from the first a. The unsaturated protons give a

stronger signal than the saturated protons. Therefore, the

center out phase-encoding acquisition started from before

the initial a pulse and emits a very strong signal. In addi-

tion, after the n/2th a pulses (n = 128 and a = 15� for this

study), the amplitude of the signal should be constant (the

linear phase-encoding acquisition) and gives a signal

weaker than that from before the first a (the center out

phase-encoding acquisition) [13].

In spite of phase acquisition and R2 = 0.95 or 0.99, at a

typical effective TI = 800 ms, which is normally used for

in vivo perfusion, as at this time the blood has not signal at

1.5 T, the maximum linearity is about twice that previously

reported (i.e., 0.8 mmol/L) for measuring the perfusion

parameters on T1-weighted imaging [2, 25, 26].

Our previous study showed that the results of this study

can be used for in vivo study if all image parameters are the

same as in the in vitro study [27].

5 Conclusion

In conclusion, our previous studies showed that the image

parameters such as TR and TI and image sequences can

have an effect on the maximum linearity between SI and

concentration. This study shows that the phase-encoding

scheme is an important parameter when the SI is measured.

These schemes can have an effect on the maximum

linearity.

Conflict of interest The authors declare that there is no conflict of

interest.

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