Slice selection and T1 contrast in FLASH NMR imaging

JOURNAL

OF MAGNETIC

RESONANCE

77,6&74

( 1988)

Slice Selection and Tl Contrast in FLASH WOLFGANG

HI~NICKE,

KLAUS-DIETMAR

MERBOLDT,

NMR Imaging AND JENS FRAHM

Max-Planck-Institut fir biophysikalische Chemie, Postjach 2841, D-3400 Giittingen, Federal Republic of Germany Received April 3, 1987; revised September 9, 1987 This paper describes the signal intensity in rapid FLASH NMR imaging as a function of the repetition time, the NMR relaxation times, the flip angle, and the shape of the tailored RF pulses used for slice selection. In the absence or after elimination of signal contributions from transverse coherences the theoretical treatment may be confined to a steady state of the longitudinal magnetization. It turns out that deviations from a rectangular excitation profile due to imperfect pulse shapes strongly alter both the dynamic approach to steady-state conditions and the resulting saturation behavior as expected from theoretical expressions. As a consequence the signal-to-noise and image contrast become dependent on the actual slice profile. In Ti images calculated from series of FLASH images with different flip angles or repetition times qualitative relations between tissues with different r, values are borne out correctly, whereas the accuracy of Ti relaxation times may not be satisfactory. No restrictions are expected for 3D imaging using a spatially homogeneous RF excitation. Experiments have been carried out on phantoms and human volunteers using a Bruker 2.35 T 40 cm NMR system. 0 1988 Academic press, 1nc. INTRODUCTION FLASH NMR imaging allows the acquisition of cross-sectional images within seconds (I, 2) and three-dimensional data sets within minutes (3). The method employs RF excitation pulses with limited flip angles and detects gradient-recalled echoes. Typical repetition times are of the order of 20 ms. Since most tissues exhibit short T, relaxation times FLASH sequences cause the establishment of a steady state of the longitudinal magnetization and do not involve steady-state transverse magnetizations. If tissues with large T2 values such as CSF lead to residual transverse magnetizations these may be dealt with in two different ways (4). Using refocused FLASH sequences T2 coherences are properly included into the image only by refocusing of the phaseencoding gradient (5, 6). Further, more complex steady-state free precession (SSFP) Fourier imaging techniques have also been reported (7, 8). Since the resulting sequences exhibit image contrasts depending on the ratio Tz/T, (9, IO), a rapid T, evaluation from such images is not possible. On the other hand, T2 coherences may be eliminated from rapid images using spoiled FLASH sequences with variable spoiling gradients in the direction of the slice-selection gradient (4). In this case T, contrasts are maintained so that T, relaxation times may be determined from series of FLASH images with different flip angles or repetition times. This paper deals with both dynamic and steady-state saturation effects as observed for the slice profiles and signal intensities of FLASH images without contributions 0022-2364/88 $3.00 Copyright 0 1988 by Academic Press, Inc. Al1 rights of reproduction in any form reserved.

64

l-, CONTRAST

65

AND FLASH IMAGING

from transverse coherences. In contrast to previous treatments (11-17) the signal intensity and the accessible Ti contrast are described as a function of flip angle and repetition time including slice profile artifacts due to specific RF pulse shapes. It should be emphasized that steady-state slice profiles obtained for refocused FLASH sequences may differ from the present results. In fact, a description of steady-state conditions including contributions from transverse coherences requires an even more complex treatment. Similar arguments hold for ECG-synchronized versions as, e.g., used in tine heart studies. Also in these cases steady-state transverse magnetizations may interfere with the desired gradient echo because identical gradient switches are used for repetitive applications of the sequence within the same cardiac cycle. On the other hand, steady-state conditions may be efficiently disturbed by the presence of flow or motion which may be considered as biological “spoiling” mechanisms. THEORETICAL

CONSIDERATIONS

Neglecting signal contributions due to T2 coherences the observable magnetization in the steady state of a spoiled FLASH imaging experiment (4) yields (18, 19) 1 -

M(or, TR/Ti)

= Rosin 01 1

_

cos

e--TWT~ ,e-TRIT,

, e-TEfT2

with flip angle 01,repetition time TR, gradient echo time TE, spin-lattice relaxation time T1, effective spin-spin relaxation time TT , and initial magnetization MO. For very small flip angles, i.e., cos a! = 1, the signal intensity as given by Eq. [I] becomes proportional to M,,exp(-TE/T,*). Thus, for small flip angles and short echo times TE, image contrasts predominantly result from spin density differences. Increasing the TE value yields Tf -weighted images which for homogeneous magnets may lead to conventional “true” T2 contrasts in close analogy to “late” spin echoes (20). On the other hand, for high flip angles of the order of 90” with cos OLN 0 the signal intensity becomes proportional to MO[ 1 - exp(-TR/T,)] as known from saturation recovery techniques (21). In general, T1 contrasts may be selected by a variation of the repetition time and/or the flip angle. Equation [l] holds for magnetizations that are homogeneously excited. In NMR imaging, however, slice-selective excitation is achieved using RF pulses with tailored pulse shapes. After single application of a selective RF pulse in the presence of a sliceselection gradient the spatial characteristics of the NMR signal correspond to a distribution of flip angles as a function of distance from the slice center. Therefore, in accordance with Eq. [ 11, a rapid FLASH imaging experiment will establish spatially dependent steady states modifying the slice profile. Here the resulting excitation profiles and integrated signal intensities are calculated by means of numerical solutions of the Bloch equations (22) assuming homogeneous spin distributions within the slice. (i) Approach to steady state. In order to ensure true steady-state conditions, one must take care both experimentally and theoretically to employ a sufficient number of excitations. The dynamic approach to steady state in FLASH images is demonstrated in Fig. 1 for three different flip angles (lo”, 45”, and 90°) and two different pulse shapes (45”) using TR/Ti = 0.025 (muscle tissue). The curves represent transverse magnetizations as observed immediately after a pulse for the initial 30 excitations.

H.&NICKE,

MERBOLDT,

Number

of

AND FRAHM

Excitotlons

FIG. 1. Calculated transverse magnetizations as a function of the number of excitation pulses for three different flip angles and two different pulse shapes using TR/T, = 0.025 (muscle tissue). The curves represent the dynamic approach to steady-state conditions by means of the relative transverse magnetizations observed after the application of pulses with a 10” rectangular excitation profile ( ’ . . ), a 45” rectangular excitation profile (-), a 90” rectangular excitation profile (---), a 45” damped sine RF pulse shape (O-e), and a 45” Gaussian RF pulse shape (++X) respectively. The signal intensities for the shaped pulses are normalized to the area under the slice profile following a single 90” pulse of the same shape.

The intensities are proportional to the longitudinal magnetization immediateiy before the pulse by a factor of sin CL For 90’ flip angles, the first pulse excites all spins, while subsequent pulses only affect those longitudinal magnetizations that have been recovered by spin-lattice relaxation during the repetition interval. Accordingly, steady-state conditions are already reached after two pulses. On the other hand, the lower the flip angle the slower steady-state conditions are established. This may be easily verified by comparing the relative signal variations for 45’ and 10” excitations, respectively. While 45” pulses, although initially resulting in strong signal reductions, yield only a 6% change in the transverse magnetization from pulse No, 16 to No. 30, a 10” flip angle leads to a 12% variation for the same interval. For a flip angle of 45” the theoretical curve in Fig. 1 corresponding to a rectangular excitation profile is compared to the results obtained for two excitation profiles generated by a Gaussian and a damped sine pulse, respectively. The most obvious difference is due to a considerably higher signal intensity caused by the specific flip-angle distributions of the two pulse shapes (see below). Increased signal contributions from small flip-angle excitations are also responsible for a slower approach to steady state than expected for homogeneous excitation using the same flip angle. For example, the Gaussian pulse shape leads to an 18% change in the transverse magnetization from pulse No. 16 to No. 30, Based on these results all numerical calculations have been performed using 32 prescan excitations to establish a stable steady state. It should be noted that steady-state conditions are more rapidly approached for smaller TI relaxation times, i.e., for TR/T, > 0.025.

T, CONTRAST

67

AND FLASH IMAGING

(ii) Steady-state conditions. Figures 2 and 3 demonstrate the steady-state saturation effects on the slice profiles for a Gaussian pulse shape and a damped sine pulse shape using one side lobe, respectively. For small flip angles (Fig. 2) or large ratios TR/Ti (Fig. 3) i.e., in the absence of strong saturation, the slice profiles are close to the behavior expected from a Fourier transformation of the pulse shape. For high flip angles and/or low ratios TR/Ti , however, the slice profiles become distorted. This is due to the fact that the distribution of flip angles in the direction of the slice-selection gradient results in a distribution of steady-state signals that is characterized by almost complete saturation in the center of the slice and reduced saturation or relatively high signal intensities in its outer wings. Accordingly, the “effective” slice thickness measured as the full width at half-height increases with increasing flip angle or decreasing ratio TR/Tr . Under extreme conditions, i.e., 90” excitation pulses, short repetition times, and long ri relaxation times, the slice profiles may even degenerate into two slices separated by a distance of about their thickness. These findings have been experimentally demonstrated by others (12, 23). Of course, the interpretation of images with distorted slice profiles will be particularly difficult for inhomogeneous tissues because of severe partial volume effects for both signal and contrast. It should be noted that the slice distortions as shown in Figs. 2 and 3 strongly depend on the pulse shape employed. A comparison of the results obtained for a Gaussian pulse (Figs. 2a and 3a) and a damped sine pulse (Figs, 2b and 3b) indicates that pulse shapes approximating rectangular excitation profiles may reduce slice distortions. In fact, in the ideal case of a perfectly homogeneous excitation one would observe a b

a 025.

025 a00

loo

000..

i -025.

-025~ 025

025

\ x c F 2 ,c

20°

2o"

oooZVI 5 -0.25. d‘j

000 1

-0251 025,

025

000 I

3o" (100

3o"

-0251

-025

025.

025 60'

J

-025. 025

029

9o”

ooo-15

-1

-05 Slice

0

05

AXIS /cm

1

15

9o”

000 -025 1

-025. -2

60'

ooo-

000

-025

100

2

-2

-15

-1

-05

0

05

Slice

Axis

/cm

1

15

2

FIG.2. Calculated slice profiles for FLASH NMR imaging as a function of flip angle for two different RF pulse shapes and TR/T, = 0.05. (a) Gaussian RF pulse (2.0 ms duration) in the presence of a slice-selection gradient of strength 7.5 mT m-l. (b) Damped sine pulse with one side lobe (2.5 ms duration) in the presence of a slice-selection gradient of strength 5.0 mT m-l.

HANICKE,

68

MERBOLDT,

AND FRAHM

b 0075

0.063 -0251 025,

0 050

\

1

aoo-a25. a25,

0038 000.. -Q25j 0.25 0.025 -025 000 I-2

-15

-1

-05 Slce

0

05

AXIS /cm

1

15

2

-2

-1.5

-1

-05

0

05

Slice

Axis

/cm

1

15

2

FIG. 3. Calculatedsliceprofilesfor FLASH NMR imagingasa function of TR/T, for two different RF pulseshapesand a flip angleof 30”. (a) and (b) asfor Fig. 2.

rectangular slice profile with no distortions induced by a variation of flip angle or TR/Ti . Similar conclusions may be dratin from the overall observable signal intensity in FLASH images derived from Figs. 2 and 3 by integration of the steady-state intensities over the slice thickness. As shown in Fig. 4 the effects of a Gaussian and a damped sine pulse are compared-to the behavior expected from Eq. [l] assuming homogeneous excitation (solid line). It turns out that the integrated signal intensity may be considerably higher than theoretically expected (compare also Fig. 1) because of the strong signal contributions from the edges of the slice in situations where its center part becomes heavily saturated. M:oreover, as anticipated from Fig. 2, the maximum signal is obtained at flip angles higher than the Ernst angle. This effect is more pronounced for the Gaussian pulse than for the sine pulse, whereas the signal behavior of a 3D imaging experiment using spatially homogeneous excitation should exactly match Eq. [I]. Assuming TR = 30 ms, the two ratios TR/Tr = 0.025 (Fig. 4a) and 0.075 (Fig. 4b) represent muscle tissue (Ti =: 1.2 s at 2.35 T) and adipose fat (Ti = 0.4 s at 2.35 T), respectively. Figure 5 depicts the contrast between both tissues defined as the difference between the corresponding signal strengths in Fig. 4. Again, there is a strong dependence on the pulse shape. First, the worse the RF pulse shape or the larger the deviations from homogeneous excitations, the more the maximum contrast is shifted from its theoretical value of about 30” toward higher flip angles. Second, in the case of Gaussian pulses almost no contrast variation is obtained for flip angles higher than 45 ‘. Finally, for both high and low flip angles the accessible contrast turns out to be a sensitive function of the slice profile, so that even small changes of the RF pulse shape as, e.g.,

T, CONTRAST

AND FLASH

69

IMAGING

a

OOOL,

10

,

,

20

30 Flip

,

,

,

LO 50 60 Angie / degree

I

I

#

70

80

90

FIG. 4. Signal intensities for FLASH NMR images integrated over the slice profiles as a function of flip angle for two ratios TR/T, and two RF pulse shapes. (a) TR/T, = 0.025, (b) TR/T, = 0.075. The dashed lines refer to a Gaussian (- - -) and a (damped sine (---) pulse shape, respectively, and have been calculated using profiles as shown in Figs. 2 and 3. The signal intensities are normalized to the area under the slice profile following a single 90” pulse of the same shape. The solid line refers to the behavior expected from Eq. [l] and corresponds to a truly rectangular excitation profile as, e.g., employed in most 3D imaging sequences.

caused by instrumental instabilities while changing the RF power, may lead to contrast manipulations. EXPERIMENTAL

RESULTS

Experiments have been carried out using a Bruker Medspec imaging and spectroscopy system with a 2.35 T 40 cm magnet. Figure 6 shows transaxial FLASH images of the forearm of a healthy human volunteer using Gaussian RF pulses and flip angles ranging from 15’ to 90” in 15 c)increments. The repetition time was 30 ms. As expected from the behavior shown in Figs. 4a and 4b the signal intensities for fat and muscle tissue increase with flip angle to reach a maximum at relatively high flip angles. Moreover, the contrast between muscle and fat increases with increasing flip angle in accordance with Fig. 5. For low flip angles such as 15” (Fig. 6a) the contrast is mainly given by the spin density with almost no Tf weighting because of the short echo time of 10 ms. In fact, muscle and. fat appear iso-intense while blood vessels benefit from reflow phenomena (24). For high flip angles one obtains strong T1 contrasts which for the Gaussian pulse shape exhibit only minor changes for flip angles between 60” and 90” (Figs. 6d-6f). It should b’e especially emphasized that the surprisingly high signal intensities obtained for 90” flip angles are almost entirely due to the distorted slice

70

HANICKE,

MERBOLDT,

10

z

20

30

LO

Flip

Angle

AND FRAHM

50

60

70

80

90

/degree

FIG. 5. Contrast in FLASH NMR images as a function of flip angle. Here contrast is demonstrated as the difference of signal intensities for tissues with TR/T, = 0.075 and TR/T, = 0.025. These values refer to adipose fat and muscle tissue assuming TR = 30 ms and a field strength of 2.35 T. The contrast behavior has been derived from the signal intensities in Fig. 4 for a Gaussian pulse shape (- - -), a damped sine pulse shape (---), and a rectangular slice profile (-).

profiles providing signal contributions from two separated wings of the originally desired slice. In principle, a series of images as shown in Fig. 6 may be used to calculate a T, image. An attractive approach stems from reordering of Eq. [I] according to (25) !!+d

sin a!

=

M(a)

e-TR/T~

+

y,,f&

_

e-TR/T,)e-TE/7;

tan 01

and subsequent use of a linear least-squares fit. It turns out that the linearization procedure yields a good correlation even if the effects of the slice distortions are neglected. Figures 7a and 7b depict calculated T, images for a phantom comprising compounds with different T, values and for the human forearm shown in Fig. 6, respectively. Although calculated on a pixel by pixel basis without smoothing or averaging the images are very homogeneous. Long T, relaxation times are represented by bright image intensities. Qualitatively, the calculated images in Fig. 7 exhibit the correct T1 relationships either for muscle and fat or between the vials of doped water with T, values of 200, 420, 8 10, 1110, and 1730 ms, respectively, as determined by means of a spectroscopic inversion-recovery sequence with an accuracy of about +5%. Quantitatively, however, the image values calculated using Eq. [2] and assuming the nominal flip angles are incorrect by factors of 4- 10 when compared to the reference data. In order to account for the slice distortions and inhomogeneous excitation profiles, Fig. 4 has been used to determine semiempirical “effective” flip angles by projecting the measured intensities onto the theoretical signal behavior (solid line). For three different sets of effective flip angles assuming TR/T, = 0.025, 0.05, and 0.075, respectively, the corresponding Ti images look very similar to each other as well as to Fig. 7a again confirming the qualitative relationships. However, even in the best case the calculated T1 values of 220, 370, 630, 690, and 1390 ms are still not satisfactory, The remaining deviations may be explained by the extreme sensitivity of the quantitative evaluations to small

T, CONTRAST

FIG. 6. Rapid FLASH NMR images (2.35 the forearm of a normal volunteer have been TR = 30 ms and a spatial resolution of 128 The slice thickness was 5 mm. The flip angles The used RF pulses and gradients correspond

AND

FLASH

IMAGING

71

T) as a function of flip angle. The transaxial cross sections of recorded within a measuring time of about four seconds using X 256 complex data points (interpolated to 256’ for display). increase from about 15” (a) to about 90” (f) in steps of 15”. to the data shown in Fig. 2a.

errors in the nominal flip angle and the assumed slice profile. For example, a 10% uncertainty of the flip angle causes T, variations of about 50%. A similar behavior has been observed for nonlinear fit procedures replacing Eq. [2]. On the other hand, a more accurate experimental determination of both the flip angle and the slice profile in our case failed because of instrumental uncertainties such as nonlinearities of the RF amplifiers. In general, similar findings for the influence of inhomogeneous excitation profiles on variations of the slice shape, signal intensity, and contrast behavior as a function

72

H;iNICKE,

MERBOLDT,

AND FRAHM

FIG3. 7. T, images calculated from series of FLASH NMR images with different flip angles. (a) Pha ntom corn] ksing tubes of water having different r, values. Ten images have been recorded with flip angles ra ngiw from 9” to 90” using linear increments. (b) Transaxial r, image of the human forearm calculated fro] nthe series; of six images shown in Fig. 6.

offl ip angle and/or TR/Tr apply to all partial saturation techniques (26). Accu rate T1 i mages without these problems may be expected from inversion-recovery and stim :ulated echo imaging techniques using long repetition times. Of course, also spat ially bon togeneous excitation in three-dimensional FLASH images (3) circumvents the

T, CONTRAST

AND FLASH

IMAGING

13

described difficulties at the expense of measuring time. T, determinations from rapid cross-sectional images will only become reliable if the excitation profiles could be made homogeneous or at least perfectly predictable. CONCLUSION

Slice profiles, signal intensities, and contrast capabilities of rapid FLASH images recorded without contributions from transverse coherences have been demonstrated to be sensitive functions of the RF pulse shape and the extent of saturation. In practice, tailored RF pulses with inhomogeneous excitation profiles lead to a strong variation of the steady-state slice profile as a function of flip angle and/or TR/Ti . This variation causes deviations from the theoretical saturation behavior and manipulates both the signal-to-noise and the contrast of cross-sectional FLASH images. Accordingly, a calculation of Tr relaxation times from T1-weighted images with different flip angles and/ or repetition times yields only qualitatively reliable relationships between tissues with different Ti values, while quantitative determinations would require a perfect knowledge of the actual steady-state excitation profile. The access to arbitrary Ti contrasts is an important aspect of rapid FLASH NMR imaging. In order to guarantee a well-defined contrast behavior, RF pulse shapes, sliceselection gradients, and the corresponding hardware may be further optimized to generate approximately rectangular as well as predictable slice profiles. Even in spite of the problems with quantitative evaluations the recording of series of differently Ti-weighted FLASH images may provide an attractive tool because of the short investigational times and the diagnostic need for qualitative discriminations. Alternative approaches to highly accurate T1 information are given by stimulated echo techniques (27, 28) providing either global T, images within conventional measuring times (2933) or local T, relaxation times within several seconds using localized ‘H NMR spectroscopy (34). ACKNOWLEDGMENTS Financial support by the Bundesminister fur Forschung und Technologie (BMFT) of the Federal Republic of Germany (Grant 01 VF 242) is gratefully acknowledged. Part of the calculations has been performed using the facilities of the Gesellschaft ftir wissenschaftliche Datenverarbeitung Giittingen (NAG-software). REFERENCES 1. A. HAASE, J. FRAHM, D. MATTHAEI, W. HWNICKE, AND K. D. MERBOLDT, J. Magn. Reson. 67,258 (1986). 2. J. FRAHM, A. HAASE, AND D. MATTHAEI, Magn. Reson. Med. 3,32 1 (1986). 3. J. FRAHM, A. HAASE, AND D. MATTHAEI, J. Comput. Assist. Tomogr. 10,363 (1986). 4. J. FRAHM, W. H.&NICKE,AND K. D. MERBOLDT, J. Magn. Reson. 72,307 (1987). 5. M. L. GYNGELL, G. L. NAYLER, N. D. PALMER, AND M. PALEY, Magn. Reson. Imaging 4,101(1986). 6. F. W. WEHRLI, “Introduction to Fast-Scan Magnetic Resonance,” General Electric, 1986. 7. A. OPPELT, R. GRAUMANN, H. BARFUSS,H. FISCHER,W. HARTL, AND W. SCHAJOR,Electromedica 54, 15 (1986). 8. M. L. GYNGELL, N. D. PALMER, AND L. M. EAST~CKID, “Society of Magnetic Resonance in Medicine, 5th Annual Meeting, Montreal, Book of Abstracts, 666, 1986.” 9. H. Y. CARR, Phys. Rev. 112, 1693 (1958). 10. W. S. HINSHAW, J. Appl. Phys. 47, 3709 (1976).

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HANICKE,

MERBOLDT,

AND

FRAHM

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