Easy Improvement of Signal-to-Noise in RARE-SequencesWith Low Refocusing Flip Angles

Jurgen Hennig* and Klaus Scheffler

It is demonstrated that the signal intensity in a RARE (TSE,FSE. . .)-sequence with low refocusing flip angle a can be sig-nificantly increased by setting the flip angle of the first refocus-ing pulse to 90°1a/2. In addition to the gain in signal intensity,the initial signal modulations over the first few echoes arereduced compared to a CPMG-echo train with constant a.Magn Reson Med 44:983–985, 2000. © 2000 Wiley-Liss, Inc.

Key words: RARE; TSE; FSE

With the current rapid development of MR-scanners withfield strength of 3 T and beyond new interest has arisen forthe use of RARE (TSE, FSE. . .)-sequences with low refo-cusing flip angles. It is clear that protocols and conceptsfrom lower field strength cannot be directly and easilytransferred to applications on high-field systems. Suscep-tibility effects and RF power deposition problems set newboundary conditions for clinically useful imaging proto-cols. The increased susceptibility effects lead to more se-vere artifacts and distortions when sequences based ongradient reversal (gradient echo, EPI) are used. Spin-echobased techniques (RARE, TSE, FSE. . .) avoid these prob-lems but at the cost of drastically increased RF powerdeposition. It has been noted that using refocusing pulseswith flip angles a ,180° can be used in CPMG-sequences,which will yield a pseudosteady-state intensity propor-tional to sin(a/2) compared to perfect refocusing (1). Theterm pseudosteady-state is used because a steady state isonly achieved when relaxation effects are neglected.

Different approaches have been used to optimize thesignal amplitudes in such an echo train (2,3). Alsop (3) hasshown in his very elegant article that using optimized andvariable refocusing flip angles not only reduces the signalmodulations, but even leads to a further increase in thepseudosteady-state intensity. A practical implementationproblem for making use of this algorithm is the fact that theoptimized flip angles depend in a straightforward but com-putationally complex way on the refocusing flip angle forwhich the pseudosteady-state is to be reached. The pur-pose of this note is to present a simple way by which a veryclose approximation to the optimized pseudosteady-statecan be achieved with a single refocusing pulse of appro-priate flip angle at the start of the echo train.

THEORY

An extensive discussion on the pseudosteady-statereached in an echo train with constant refocusing pulse ais given in (4). In this article it was demonstrated that the

pseudosteady-state is not unique for each a, but that aninfinite number of pseudosteady-states can be reached foreach a depending on the initial state of the magnetizationat the beginning of the echo train. A closer look at thebehavior of the isochromats in such a pseudosteady-statereveals that a steady-state is indeed reached only withrespect to the total observable magnetization, whereaseach isochromat will show a periodic modulation. Thisinfinite number of pseudosteady-states can therefore beregarded as dynamic pseudosteady-states. The staticpseudosteady-state, in which each isochromat returns ex-actly to the same coordinates Mss 5 (Mssx,Mssy,Mssz) aftereach refocusing pulse is unique for each a.

This static pseudosteady-state can be calculated veryeasily based on a straightforward geometrical argument.As shown in Fig. 1, it is obvious that the precession anglef 5 v*TE of isochromats with off-resonance frequency varound the z-axis for each isochromat between two refo-cusing pulses separated by TE has to be reversed by therotation angle a around the x-axis caused by the refocusingpulse. Therefore, the following trigonometric relationsapply:

tan~f/2! 5 Mssy/Mssx [1.1]

tan~a/2! 5 Mssy/Mssz [1.2]

Mssx2 1 Mssy

2 1 Mssz2 5 1. [1.3]

The magnetization vector Mse(v) at the time of the echowill then be derived by rotation of Mss around z by f/2.Note that the y-coordinate at the echo time will be zero,i.e., Mse(v) as a function of v will be distributed on a circlein the x–z-plane. It is equally clear that all Mss(v) will lieon a circle which is tilted by a/2 with respect to the x-axis.

This particular configuration has led us to speculate thata reasonable approximation of the static pseudosteady-state might be reached by using a refocusing flip angle90°1a/2 for the first refocusing pulse. This will rotate themagnetization, which has been distributed evenly in thex-y-plane after excitation, into the same plane required forMss. The created magnetization Mos(v) will be unequal toMss(v), since precession by f/2 after the excitation pulsedoes not deliver the isochromats to the proper position inthe circle. Figure 2 shows that the magnetization thusprepared is quite close to the true steady-state magnetiza-tion. By vector addition Mos can be decomposed into:

Mos~v! 5 Mss~v! 1 r~v!, [2]

where r is a residue vector representing the differencebetween Mss and Mos, which is antiphasic to Mos andMss. The echo amplitude in the subsequent refocusing

Abt. Rontgendiagnostik, Section of Medical Physics, Freiburg, Germany.*Correspondence to: Prof. Dr. Jurgen Hennig, Hugstetterstr. 55, 79106Freiburg, Germany. E-mail: hennig@nz11.ukl.uni-freiburg.deReceived 11 May 2000; revised 10 July 2000; accepted 12 July 2000.

Magnetic Resonance in Medicine 44:983–985 (2000)

© 2000 Wiley-Liss, Inc. 983

periods will then be given by the amplitude of the truesteady-state minus whatever part of r(v) will be refocusedat the echo time. Figure 3 shows that this preparation witha single first refocusing pulse keeps magnetization veryclose to the static steady-state. It is quite astonishing to seethat a single refocusing pulse dramatically alters the fate ofall subsequent echoes.

RESULTS

All experiments were performed on a 1.5 T scanner (Sie-mens Sonata; Siemens Medical Systems, South Iselin, NJ).A single-shot RARE-sequence with echo interval TE 59.4 ms was used throughout. Calibration measurements

FIG. 1. Geometrical demonstration of the steady-state magnetiza-tion Mss for an isochromat precessing by f 5 v TE betweenrefocusing pulses with flip angle a: a steady-state is achieved ifprecession around the z-axis by v and subsequent rotation aroundx by the refocusing pulse brings magnetization back to Mss. Sym-metry requires that all Mss(v) will lie an a plane which is tilted by a/2with respect to the x–z-plane. Mse indicates the position of themagnetization vector at the time of the echo which will be in thex–z-plane for all v.

FIG. 4. Theoretical steady-state echo amplitude I (full line) andamplitude reached in a multiecho experiment with constant refo-cusing flip angle a (dotted line) compared to that achieved by a90°-(90°1a/2)-[a-]n-experiment. Asterisk shows experimental val-ues with the conventional sequence, full circles indicate experimen-tal amplitudes of the optimized sequence.

FIG. 2. Distribution of isochromats after the 90°1a/2-pulse witha 5 90° (Mosx and Mosz, dotted line) compared to the distributionrequired for the true static steady-state Mssx and Mssz (thick lines)and the residues representing the differences between both.

FIG. 3. Distribution of the isochromats for spin-echo sequencesusing a constant refocusing flip angle of a 5 90° (a,b) and for anoptimized sequence using a first refocusing pulse with flip angle90°1a/2 5 135° (c,d). The first (a,c) and the 20th (b,d) echo areshown. The thick circle segment in d shows the distribution ofisochromats for the static pseudosteady-state.

984 Hennig and Scheffler

were performed with a single-shot experiment on a purewater phantom with T1 5 T2 . 2 sec. For the refocusingpulses simple Gaussian-shaped pulses (duration 1.28 ms)were used.

Figure 4 shows that the echo intensities achieved bysuch a 90°-(90°1a/2)-[a-]n-sequence is very close to thetheoretical values of the static pseudosteady-state. It alsoshows the excellent agreement of the signal intensitiesmeasured with a single-shot RARE-sequence with the cal-culated values. Exhaustive numerical calculation of thesignal intensity for integral values of a1 and a in a 90°-(a1)-[a-]n-sequence shows that the maximum intensity isindeed reached at a1 5 90°1a/2.

In addition to the gain in signal amplitude, the signalmodulations over the first few echoes are reduced, but nottotally avoided (Fig. 5). Especially for slice selective refo-cusing, where the observed signal is a summation over theslice profile, this residual modulation effect will, however,be insignificant.

CONCLUSION

Using a first refocusing pulse with flip angle 90°1a/2offers an easy way to significantly improve S/N and imagequality of RARE (TSE, FSE. . .)-sequences with low refo-cusing flip angle.

REFERENCES1. Hennig J. Multiecho imaging sequences with low refocusing flip angles.

J Magn Reson 1988;78:397–407.2. Le Roux P, Hinks RS. Stabilization of echo amplitudes in FSE se-

quences. Magn Reson Med 1993;30:183–190.3. Alsop DC. The sensitivity of low flip angle RARE imaging. Magn Reson

Med 1997;37:176–184.4. Hennig J. Echoes—how to generate, recognize, use or avoid them in

MR-imaging sequences. Conc Magn Reson 1991;3:125–143.

FIG. 5. Signal amplitude I(ne) for a conventional CPMG-sequence(dotted line) and the corresponding optimized sequence as a func-tion of the number of echoes, ne, after excitation for a 5 90° anda 5 120°.

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