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The Impact of Flip Angle and TR on the Enhancement Ratio of Dynamic Gadobutrol-enhanced MR Imaging:

In Vivo VX2 Tumor Model and Computer Simulation

Po-Chou CHEN1, Ding-Jie LIN1, Jo-Chi JAO2*, Chia-Chi HSIAO3, Li-Min LIN4,5, and Huay-Ben PAN3

1Department of Biomedical Engineering, I-SHOU University Kaohsiung 824, Taiwan, ROC

2Department of Medical Imaging and Radiological Sciences, Kaohsiung Medical University

3Department of Radiology, Kaohsiung Veterans General Hospital

4Department of Dentistry, Division of Oral Pathology, Kaohsiung Medical University Hospital

5School of Dentistry, College of Dental Medicine, Kaohsiung Medical University (Received April 18, 2014; Accepted December 10, 2014; published online March 31, 2015) Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is widely used to diagnose cancer and monitor therapy. The maximum enhancement ratio (ERmax) obtained from the curve of signal intensity over time could be a biomarker to distinguish cancer from normal tissue or benign tumors. We evaluated the impact of flip angle (FA) and rep- etition time (TR) on the ERmax values of dynamic gadobutrol-enhanced MR imaging, ob- taining T1-weighted (T1W) MR imaging of VX2 tumors using 2-dimensional fast spoiled gradient echo (2D FSPGR) with various FAs (30°, 60° and 90°) at 1.5 tesla before and after injection of 0.1 mmol/kg gadobutrol. In vivo study indicated significant differences be- tween ERmax values and area under the ER-time curve (AUC100) of VX2 tumors and mus- cle tissue, with the highest ERmax and AUC100 at FA 90°. Computer simulation also dem- onstrated the ER as a strictly increasing monotonic function in the closed interval [0°, 90°]

for a given TR when using T1W FSPGR, and the highest ER value always occurred at FA 90°. The FA for the highest ER differed from that for the highest signal-to-noise or con- trast-to-noise ratio. For long TR, the ER value increases gradually. However, for short TR, the ER value increases rapidly and plateaus so that the ER value changes little beyond a certain FA value. Therefore, we suggest use of a higher FA, near 90°, to obtain a higher ERmaxfor long TR in 2D SPGR or FSPGR and a smaller FA, much less than 90°, to reach an appropriate ERmax for short TR in 3D SPGR or FSPGR. This information could be helpful in setting the optimal parameters for DCE-MRI.

Keywords: fast spoiled gradient echo,flip angle, gadobutrol, repetition time, VX2 animal model

Introduction

Cancer incidence increases yearly, and early treatment based on early accurate diagnosis is very important. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has been used to detect lesions and monitor treatment. Administra-

tion of a contrast agent (CA) enables differentiation of enhancement patterns of tumors from those of normal tissues.1–5

Gadolinium-diethylenetriamine penta-acetic acid (Gd-DTPA; Magnevist, Schering, Berlin, Germa- ny) is the first CA approved by the U.S. Food and Drug Administration (FDA) since 1988 as a non- specific extracellular CA and has been widely used in DCE-MRI.6,7Since then, several novel CAs have also been approved for clinical use. Gadobutrol

*Corresponding author, Phone: +886-7-3121101 ext. 2356-14, Fax:+886-7-3113449, E-mail: jochja@kmu.edu.tw

©2015 Japanese Society for Magnetic Resonance in Medicine

MAJOR PAPER

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(Gadovist, Schering, Berlin, Germany) is a neutral, hydrophilic, and macrocyclic contrast agent that has become clinically available. Its higher relaxiv- ities compared to that of Gd-DTPA allows greater contrast between tumor and tissue.8–11

The enhancement ratio (ER), calculated from the MR signal intensity after injection of CA divided by that before CA injection, can be a biomarker to distinguish cancers from normal tissue. The rela- tive maximum ER (ERmax) can also differentiate malignant from benign masses in some tumors.12,13 ERmax varies with pulse sequence in addition to magnetic field, category of CA, injection dosage of CA, and time interval after injection of CA.10,14 A T1-weighted (T1W) spoiled gradient echo (SPGR) pulse sequence is most commonly used in DCE-MRI, and its signal intensity depends on such scanning parameters as flip angle (FA), repetition time (TR), proton density, and echo time (TE). We investigated the impact of FA and TR on the ER of dynamic gadobutrol-enhanced MR imag- ing.

VX2 tumors are hypervascular adenocarcinomas often used as a model for human disease and can be implanted in many organs for preclinical studies. In this study, we implanted VX2 tumor cells into one thigh of each of 18 New Zealand rabbits for imag- ing the thigh and there were no obvious motion ar- tifacts during DCE-MRI.15–17 We used the rabbit VX2 tumor to compare ERmax values obtained us- ing T1W FSPGR with various FAs. In addition, we examined the effects of FA and TR on the ER val- ues by computer simulation and explored the theo- retical approach of optimal FA for the highest ER.

Materials and Methods MR imaging of animals

Our institutional animal care and use committee approved the protocol for animal use.

We divided 18 rabbits into 3 groups of 6 animals each that were subjected to MR imaging using flip angles of 30°, 60°, or 90°. Each rabbit was implant- ed with VX2 tumor cells in a concentration of about 1© 106/mL that was injected intramuscular- ly into its left thigh using a 0.5 mL VX2 tumor cell suspension via a 19-gauge needle. The injected site was shaved and disinfected with ethanol and povi- done iodine. The cell suspension was prepared from a mass removed from a rabbit carrying a VX2 tu- mor and placed in a cell culture dish with normal saline. The tumor mass was washed 3 times, chop- ped into very small pieces, and digested with tryp- sin to form cell suspension.

Two weeks after tumor implantation, the rabbits

underwent MR examinations after being anesthe- tized with 16 mg/kg Zoletil 50 (VIRBAC Animal Health, Carros, France) and 14 mg/kg Rompun 2%

(Bayer Korea Ltd., Kyonggi-do, Korea) and insert- ed a 23-gauge butterfly needle into an ear vein for gadobutrol injection. All MR imaging studies were performed on a 1.5-tesla whole-body MR scanner (Signa HDxt, GE Medical Systems, Milwaukee, WI, USA) with an 8-channel knee coil. The rabbit’s left thigh was placed into a knee coil with the VX2 mass in the center.

A phantom of 2% agarose and a phantom of wa- ter were put aside the thigh for references. A 3- plane localizer scan was followed by a convention- al spin echo (CSE) pulse sequence for T1 and T2

measurement and a 2-dimensional (2D) FSPGR pulse sequence for DCE-MRI. The scanning pa- rameters for T1 measurement were: field of view (FOV), 16© 16 cm2; matrix size (MS), 256© 128;

slice thickness (ST), 5 mm; number of slices (NS), 8; bandwidth (BW), 15 kHz; number of excitations (NEX), one; TE, 14 ms; and TR, 270, 500, 1000, and 2000 ms. T2 measurement employed the same FOV, MS, ST, BW and NEX as those for T1meas- urement but different TR (2000 ms) and TEs (15, 30, 45 and 60 ms). The scanning parameters for DCE-MRI for each group were: TR, 100 ms; TE, 1.3 ms; BW, 31.3 kHz; and FA, 30°, 60°, or 90°.

The scan time for each image was 14 s.

Following acquisition of 4 precontrast images, each rabbit was administered 0.1 mmol/kg gadobu- trol by bolus injection through the ear vein that was flushed with one mL of saline. Scans were subse- quently performed continuously for 3 min, after which consecutive scans were performed with one scan per minute. The total scan time for DCE-MRI was 30 min. All acquired MR images were trans- ferred to an Advantage Window workstation for analysis.

For data analysis, several regions of interest (ROIs) were chosen from the rims of tumors, mus- cle, phantom, and background. Angiogenesis at the periphery of tumors resulted in stronger enhance- ment of the rims than cores of the tumors, and ac- cumulation of more gadobutrol in the rims of tu- mors enhanced the MR signal. The ROIs from the rims of tumors were selected according to the re- gions most enhanced in the second DCE images after injection of gadobutrol.

The T1and T2values of tumor and muscle were obtained by least squares fitting to the values of ROIs of tumor and muscle according to Eqs. [1]

and [2] respectively using commercial software (Sigmaplot, version 9.01, Systat Software, San Jose, CA, USA.18

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S ¼ Mð1  2eðTR0:5TEÞ=T1þ eTR=T1Þ; ½1

and

S ¼ MeTE=T2; ½2

where S is the MR signal intensity and M is a con- stant. Because the spin echo signal can be ex- pressed as18:

S ¼ M0ð1  2eðTR0:5TEÞ=T1þ eTR=T1ÞeTE=T2; ½3

where M0is magnetization combined with the elec- tric gain, and M0can be determined by dividing M by eTE=T2 according to Eqs. [1] and [3] once T1

and T2 are obtained. Afterwards, we obtained the average T1, T2, and M0 of tumor and muscle of the 18 rabbits and used the data for computer simula- tion.

The ER value was calculated according to Eq. [4]:

ER ¼Spost

Spre

; ½4

where Spre and Spost are the MR signal intensity normalized with the 2% agarose phantom and ob- tained before (Spre) and after (Spost) gadobutrol in- jection. We averaged the signal intensities from 4 MR images obtained before gadobutrol injection to determine the MR signal intensity before gadobu- trol injection.

We could obtain the ER-time curve for each ROI and determine the ERmax for each ER-time curve.

The area under the curve of each ER-time curve (AUC100) was calculated according to Eq. [5]:

AUC100 ¼Xj

1

1 2

 

 ðtn tn1Þ  ðERnþ ERn1Þ;

½5

where ftng was the time series of dynamic scans, tn

was the nth term and ERnwas the ER obtained at tn

after gadobutrol injection. ER0was obtained before gadobutrol injection at t0= 0 s and was equal to one. AUC100 was obtained by summing every tra- pezoid area under the ER-time curve from 0 to 100 s ( j = 6).

We used nonparametric Wilcoxon test for the statistical analysis of T1, T2, ERmax, and AUC100

between the tumor and muscle; P< 0.05 was con- sidered to represent significant difference. We used nonparametric Kruskal-Wallis test to compare ER values obtained from each of the 3 groups (scanned with FA of 30°, 60°, or 90°). There was a signifi- cant difference in the ERmax or AUC100 among these 3 groups if P< 0.05.

After acquisition of the ER, we calculated the

concentration, C, of gadobutrol according to Eq. [6]:

C ¼ 1

r1TRln 1  B  ER

1  B  ER cosðFAÞ 1

r1T10; ½6

where B ¼ ð1  eTR=T10Þ

ð1  cosðFAÞeTR=T10Þ and the r1value is 4.7 mM¹1s¹1.19 Then, we determined the average maximum concentrations of tumor (Cmax_t) and muscle (Cmax_m) of the 18 rabbits. The average noise (·) of the DCE-MRI was obtained by averag- ing the standard deviation of background signal measured from the 18 rabbits. Cmax_t, Cmax_m, and

· were used for computer simulation.

After experiments were completed, rabbits were sacrificed under deep anesthesia with CO2. The left thigh with implanted VX2 tumor was then removed andfixed in 10% formalin. Paraffin-embedded sec- tions were stained with hematoxylin and eosin for visualization of VX2 tumors under a microscope.

Computer simulation

The signal-to-noise ratio (SNR), ER, and con- trast-to-noise ratio (CNR) values for SPGR were calculated according to Eqs. [7] through [10]20,21:

S ¼ M0 sinðFAÞð1  eTR=T1Þ

ð1  cosðFAÞeTR=T1ÞeTE=T2

 

; ½7

SNR ¼ S=; ½8

ER ¼ sinðFAÞð1  eTR=T1Þ

ð1  cosðFAÞeTR=T1ÞeTE=T2

 

. sinðFAÞð1  eTR=T10Þ

ð1  cosðFAÞeTR=T10ÞeTE=T20

 

; ½9

and

CNR ¼ SNRt SNRm; ½10

where SNRtis the SNR of tumor, and SNRm, that of muscle.

Here, the M0, T10, T20of tumor and muscle and were determined from the MR imaging study men- tioned above. Ignoring the impact offield inhomo- geneity, we assumed T2* = T2.22 The T1 and T2

values of tumor and muscle after gadobutrol injec- tion were calculated according to Eqs. [11] and [12]23:

1 T1 ¼ 1

T10þ r1C; ½11

and

1 T2 ¼ 1

T20þ r2C; ½12

where C is the concentration of the contrast agent, r1 is longitudinal relaxivity, r2 is transverse relax-

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ivity, T1 is the longitudinal relaxation time and T2, the transverse relaxation time after CA injection, and T10 is the longitudinal relaxation time and T20, the transverse relaxation time in the absence of CA.

Concentrations Cmax_t and Cmax_m were also ob- tained from the in vivo MR imaging studies men- tioned above. In the calculation, we used the value 4.7 mM¹1s¹1 for r1 and 6.8 mM¹1s¹1 for r2.19 We evaluated the SNR, ER, and CNR values of tumor and muscle for various FAs (one to 90°) and TRs (5 to 100 ms) with concentrations of Cmax_tand Cmax_m

and those of tumor with 0.5 mM gadobutrol con- centration.

Results

MR imaging of animals

Figure 1 shows CSE images for T1 measure- ments and Fig. 2, those for T2measurements of tu- mor and muscle. MR signal intensity increased with TR for a given TE and decreased with TE for a given TR. There were 2 phantoms; one was water and the other was 2% agarose. The water phantom was used to double-check whether the water con- tent in the agarose phantom evaporated. The differ- ent inherent proton density and relaxation times of these 2 phantoms yielded different MR signal in- tensities. In particular, the SNR of water was high- er than that of 2% agarose (Fig. 2), which was ex- pected because of the higher proton density and T2

relaxation time of water. The T10 values of tumor were 1812« 257 ms and of muscle, 1517 « 133 ms. The T20 values of tumor were 59.17« 8.43 ms and of muscle, 31.37« 3.43 ms. There were signif- icant differences of T10and T20 values between tu- mor and muscle (P< 0.01). The average value of M0 for tumor was 7456 and for muscle, 5352.

Figure 3 shows several representative dynamic gadobutrol-enhanced MR images from one rabbit.

The contrast between tumor and muscle was low before gadobutrol injection. Right after the bolus injection of gadobutrol, the MR signal intensity of the tumor increased more than that of muscle, and consequently, the contrast between tumor and mus- cle increased. The contrast increased with time, reached a maximum value, and gradually decreased with time as a result of the excretion of gadobutrol.

Figure 4a shows the ER-time curves of tumor and muscle obtained with FA/TR/TE = 90°/100 ms/

1.3 ms using an FSPGR pulse sequence. The ER of the tumor was higher than that of muscle. Figure 4b shows the ER values of tumor obtained from the same TR/TE (100 ms/1.3 ms), but with various FA (30°, 60°, and 90°). The ERmaxobtained with a 90°

FA was larger than that obtained with FAs of 60° or 30°. Table lists the ERmax and AUC100 values ob- tained with various FAs. ERmax and AUC100 values in the tumor differed significantly from these val- ues in the muscle among the 3 groups scanned with various FAs (P< 0.05).

Fig. 1. Conventional spin echo (CSE) magnetic res- onance (MR) images of a rabbit thigh with VX2 tumor (arrows) obtained with echo time (TE) of 14 ms and repetition times (TR) of (a) 270, (b) 500, (c) 1000, and (d) 2000 ms for the T1 measurement.

Fig. 2. Conventional spin echo (CSE) magnetic res- onance (MR) images of a rabbit thigh with VX2 tumor (arrows) obtained with repetition time (TR) of 2000 ms and echo times (TE) of (a) 15, (b) 30, (c) 45, and (d) 60 ms for the T2measurement.

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The noise value, , was 17.57; the Cmax_t was 0.13 « 0.04 mM; and the Cmax_m was 0.03« 0.01 mM. The VX2 tumor was verified by hematoxylin and eosin staining (Fig. 5).

Computer simulation

Figure 6 shows SNR values of tumor and muscle as a function of TR and FA. The SNR of tumor was higher than that of muscle for any TR and FA, and the concentration of gadobutrol was 0.13 mM in tu- mor and 0.03 mM in muscle. The SNR increased with TR for a given FA for both tumor and muscle.

However, SNR values increased with FA first and then decreased for some given TR. There was an optimal FA for the maximum SNR (SNRmax), and

the optimal FA increased with TR as well. Tumor also had higher ER than muscle for each corre- sponding TR and FA (Fig. 7). The ER values de- creased with TR but increased with FA for both tu- mor and muscle. Figure 9a shows the CNR values as a function of TR and FA. CNR first increased with FA and then decreased for a given TR. The optimal FA was basically defined as that corre- sponding to the maximum value of SNR, CNR, and ER for each TR (Figs. 7–9). There was an op-

Fig. 4. Enhancement ratio (ER)-time curves of dy- namic contrast-enhanced magnetic resonance imaging (DCE-MRI) from (a) tumor and muscle with 90o flip angle (FA) and (b) tumor with variable FAs using fast spoiled gradient echo (FSPGR) pulse sequences (rep- etition time [TR]/echo time [TE], 100/1.3 ms).

Table. Maximum enhancement ratio (ERmax) and area under the ER-time curve (AUC100) with various flip angles (FA)

Tumor Muscle

FA 30° FA 60° FA 90° FA 30° FA 60° FA 90°

ERmax 1.60« 0.13 1.81« 0.20 2.22« 0.31 1.16« 0.07 1.23« 0.04 1.24« 0.05 AUC100 142.1 « 10.5 158.6 « 18.4 198.2 « 24.4 107.1 « 3.2 109.9 « 3.5 111.1 « 3.1 Fig. 3. Dynamic gadobutrol-enhanced images of a

rabbit thigh with VX2 tumor (arrows) obtained (a) be- fore, (b) 14 s, and (c) one, (d) 3, (e) 10, and (f ) 30 min after gadobutrol injection with 90° flip angle (FA), repetition time (TR) of 100 ms, and echo time (TE) of 1.3 ms.

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timal FA for the maximum CNR (CNRmax), and the optimal FA increased with TR as well. The optimal FA for CNRmax differed from that for SNRmax. SNRmax, ERmax and CNRmax for given TR and FA values were higher for a tumor with a higher con- centration of gadobutrol (0.5 mM) than a tumor with a concentration of 0.13 mM gadobutrol (Figs.

8 and 9b).

Discussion

In this study, we investigated the impact of FA and TR on the ERmaxof FSPGR T1-weighted gado- butrol-enhanced MR imaging using an in vivo VX2 tumor model and computer simulation. In general, FA and TR are the 2 dominant factors that influence the MR signal intensity of SPGR T1W images.

Fig. 6. Computer simulation: (a) Signal-to-noise ra- tio (SNR) of tumor (SNRt) and (b) muscle (SNRm) (tumor, 0.13 mM; muscle, 0.03 mM).

Fig. 5. Microscopic image of VX2 cells. T, VX2 tu- mor cells; N, normal muscle cells.

Fig. 7. Computer simulation: (a) Enhancement ratio (ER) of tumor (ERt) and (b) muscle (ERm) (tumor, 0.13 mM; muscle, 0.03 mM).

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There were significant differences in ERmax and AUC100of ER-time curves between the tumor and muscle. The ERmax value increased with FA (0°– 90°) for a given TR for both computer simulation and single dosage gadobutrol-enhanced MR imag- ing. Furthermore, computer simulations demon- strated increased ERmax values with a higher con- centration of gadobutrol (0.5 mM).

Computer simulation demonstrated that the ER value also increased with FA for a given TR in the closed interval [0, 90°] in tumors with a higher concentration of gadobutrol (0.5 mM). After inject- ing 0.1 mmol/kg gadobutrol, we obtained a Cmaxof gadobutrol of 0.13 mM in tumor. A higher injected dosage is expected to yield a higher concentration of gadobutrol in tumor. We assumed a gadobutol concentration of 0.5 mM in tumor with an injected dosage higher than 0.1 mmol/kg. From the result of

simulation, we demonstrated the same tendency for monotonic increase of ERmaxin the interval [0, 90°]

for concentrations of both 0.13 and 0.5 mM. There- fore, it is expected that the tendency of optimal FA is similar for tumor concentration between 0.13 to 0.5 mM. The common routine dosages used clini- cally are 0.1 mmol/kg or sometimes 0.2 mmol/kg.

A tumor concentration of 0.5 mM far exceeds clin- ically used double-dosage injection. Therefore, an estimated dosage of 0.5 mM is sufficient.

The scanning time of the T1W SPGR pulse se- quence is shorter, and the sequence has been wide- ly used in DCE-MRI. The acquired MR signal in- tensity, shown in Eq. [7], depends on TR, TE, FA, T1, T2, and proton density. T1, T2, and proton den- sity are the intrinsic properties of tissues and are independent of MR imaging pulse sequences. TE usually is set to the minimum value in the T1W Fig. 8. Computer simulation: (a) Signal-to noise ra-

tio of tumor (SNRt) and (b) enhancement ratio of tu- mor (ERt) (tumor, 0.5 mM; muscle, 0.03 mM).

Fig. 9. Computer simulation: (a) Contrast-to-noise ratio of tumor (CNRt) (tumor, 0.13 mM; muscle, 0.03 mM) and (b) CNRt (tumor, 0.5 mM; muscle, 0.03 mM).

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SPGR pulse sequence, and the item eTE=T2 eTE=T20 is close to one. Therefore, the ER can be expressed approximately as:

ER ¼ sinðFAÞð1  eTR=T1Þ ð1  cosðFAÞeTR=T1Þ

 

. sinðFAÞð1  eTR=T10Þ ð1  cosðFAÞeTR=T10Þ

 

: ½13

Equation [13] is a strictly monotonic increasing function in the closed interval [0°, 90°], in which the highest ER value always occurs at an FA of 90°.

This result agrees with those of in vivo study and computer simulation. The FA for the ERmax is al- ways 90°, which may not be optimal for SNRmaxor CNRmax.24,25

The ER value increases gradually with FA for longer TR and increases rapidly and plateaus for short TR. Consequently, ER values change little beyond some FA for a short TR. The 3-dimentional (3D) SPGR sequence is commonly used to cover a large volume of interest. A short TR and small FA are often used in 3D SPGR to shorten scan time.

However, 2-dimensional (2D) SPGR is more suit- able than 3D SPGR for fewer slices of interest. A shorter TR yields a low SNR with small coverage.

Therefore, a longer TR is often used in 2D SPGR than that in 3D SPGR, which produces a more sig- nificant effect of FA on ER. In general, the choice of a larger FA will help increase ER in 2D SPGR, even in 3D SPGR.26,27

Angiogenesis generally produces greater blood flow in tumor than normal tissue. Use of a larger FA increases the effect of inflow, and the inflow effect could help to differentiate tumor from normal tis- sue. However, use of a larger FA increases the spe- cific absorption rate (SAR), so the decision to use a larger FA to achieve a higher ER requires consid- eration of whether the SAR is within the permitted limitation. Nevertheless, the SAR of SPGR with FA 90° is less than that of fast spin echo (FSE) with FA 90° and 180°. Therefore, the SAR of SPGR with FA 90° is acceptable.

Compared to Gd-DTPA, gadobutrol has the ben- efit of less injection volume because of its high concentration formula. Images are sharper with ga- dobutrol than images obtained with Gd-DTPA in angiography.21,28 Gadobutrol can be applied in tu- mor diagnosis as well. Its higher relaxivity than that of Gd-DTPA can produce higher ERs than those with Gd-DTPA.29,30 In addition, gadobutrol has a good safety profile.31In the future, CAs with higher relaxivity will be helpful for increasing ER.

The computer simulation method of this study

can be applied in humans with any kind of Gd- based contrast agent once the T10 and r1 values of human organs are known. In this study, we used a conventional spin echo pulse sequence to measure T10 values because CSE can produce high quality images and take less scan time than conventional inversion recovery (CIR) pulse sequences. Though other fast imaging pulse sequences, such as Look- Locker or SPGR with various flip angles, can be used to obtain T10 in shorter scan time,32,33 their image quality is worse than that with conventional spin echo. Many factors, including temperature, main field strength, and tissue type, may influence r1values, and acquisition of the actual r1 in vivo is difficult. In this study, r1in the tissue is assumed to equal that in plasma in vitro at 37°C for 1.5T.21 However, acquisition of an accurate r1 in vivo re- mains a challenge. Nevertheless, even with such an approximation, the effect of FA and TR on ER can be estimated. The different assumption of r1values may change the values of SNR, CNR, AUC100, and ERmax but will not change the behavior of the ERmax value versus the FA, i.e., the increased ERmaxwith FA for a given TR in the closed interval [0, 90°].

Conclusions

DCE-MRI is popular for diagnosing lesions and monitoring therapy. The ERmax and AUC100 ob- tained from ER-time curves could differentiate tu- mor from normal tissue. The maximum ERmax oc- curs at FA 90° according to in vivo study, computer simulation, and theoretical calculation. For short TR, the ER value was shown to increase rapidly with FA and then plateau. In conclusion, a higher FA, close to 90°, can obtain a higher ERmaxfor long TR in 2D SPGR or FSPGR, and a smaller FA, much less than 90°, can still reach appropriate ER values for short TR in 3D SPGR or FSPGR.

Acknowledgement

This work was supported by a grant from the Na- tional Science Council of Taiwan, R.O.C. (NSC 99- 2221-E-214-008).

Appendix: Derivation of Eq. [6]

The enhancement ratio (ER) can be expressed as ER ¼ ð1  eTR=T1Þ

ð1  cosðFAÞeTR=T1Þ eTE=T

2

 

. ð1  eTR=T10Þ

ð1  cosðFAÞeTR=T10Þ eTE=T

20

 

; [A1]

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where FA is theflip angle, TR is the repetition time, TE is the echo time, T1 is the longitudinal relaxa- tion time, T2 is the effective transverse relaxation time after CA injection, and T10 is the longitudinal relaxation time and T20 is the effective transverse relaxation time in the absence of CA. For T1- weighted image,ðeTE=T2Þ=ðeTE=T20Þ  1, Eq. [A1]

can be reduced to

ER ¼ ð1  eTR=T1Þ ð1  cosðFAÞeTR=T1Þ

 

. ð1  eTR=T10Þ ð1  cosðFAÞeTR=T10Þ

 

: [A2]

Substituting B ¼ ð1  eTR=T10Þ

ð1  cosðFAÞeTR=T10Þ into Eq.

[A2] and rearranging it yields

½1  B  ER cosðFAÞeTR=T1 ¼ 1  B  ER [A3]

The natural logarithm of

eTR=T1 ¼ 1  B  ER

1  B  ER cosðFAÞ [A4]

multiplied by 1

TR on each side yields 1

T1 ¼1

TRln 1  B  ER

1  B  ER cosðFAÞ: [A5]

1 T1 ¼ 1

T10þ r1C; [A6]

where C is the concentration of the contrast agent and r1 is the longitudinal relaxivity.

Therefore, the concentration can be expressed as C ¼ 1

r1TRln 1  B  ER

1  B  ER cosðFAÞ 1

r1T10: [A7]

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