The Sensitivity of Low Flip Angle RARE Imaging
`
`David C. Alsop
`
`It is demonstrated that the stability of the Carr-Purcell-Mei-
`boom-Gill (CPMG) sequence reflects the existence of a steady
`state solution to the Bloch equations in the absence of T2 and
`T, decay. The steady state theory is then used to evaluate the
`performance of low flip angle RARE imaging sequences with
`both constant and optimally varied refocusing flip angles. The
`theory is experimentally verified in phantoms and then opti-
`mized, single shot, low flip angle RARE is used to obtain
`artifact-free images from the brain of a normal volunteer.
`Key words: RARE; fast imaging; magnetic resonance imaging.
`
`INTRODUCTION
`RARE imaging (1) is a method to increase the speed of
`spin-echo imaging by acquiring a series of spin echoes
`with different phase encodings after each excitation. Be-
`cause the technique offers either shorter scan times or
`higher signal-to-noise ratio than standard spin-echo im-
`aging while producing similar contrast (2, 3), RARE im-
`aging has become a clinical success. The faster speed of
`RARE imaging has allowed increased flexibility in choos-
`ing TR for optimal contrast and has improved the feasi-
`bility of inversion recovery preparation (4). In clinical
`applications, usually fewer than 16 echoes are employed,
`although in specialized applications where long T2 fluid
`is being imaged, such as MR cholangiography (5), longer
`echo trains are feasible.
`It is straightforward to further increase the speed of
`RARE imaging by acquiring a larger number of spin ech-
`oes but this approach eventually leads to several prob-
`lems. One major concern is RF power deposition within
`the subject. A long series of compact 180’ pulses can
`readily introduce more RF heating than is acceptable
`according to normal safety guidelines, particularly if
`multiple slices are being acquired. A long train of 180°
`pulses also increases the interaction between neighbor-
`ing slices and can lead to undesirable loss of contrast and
`signal. At the power levels employed in long echo train
`RARE imaging, magnetization transfer saturation (6) is
`quite significant and can increase the effective slice in-
`teraction. Finally, unless all the echoes are acquired
`within a time on the order of T2, significant distortion of
`the point spread function of the image will occur (I,?’, 8).
`This requirement places a strong restriction on the length
`of an echo train.
`
`MRM 37~176-184 (1997)
`From the Department of Radiology, University of Pennsylvania Medical
`Center, Philadelphia, Pennsylvania.
`Address correspondence to: David Alsop, Ph.D., Department of Radiology,
`University of Pennsylvania Medical Center, 3400 Spruce Street, Philadel-
`phia, PA 19104-4283.
`Received July 16. 1996; revised September 24, 1996; accepted September
`26, 1996.
`This research was supported in part by a Biomedical Engineering Research
`Grant from the Whitaker Foundation.
`0740-31 94/97 $3.00
`Copyright 0 1997 by Williams & Wilkins
`All rights of reproduction in any form reserved.
`
`These limitations of RARE imaging were recognized by
`one of its inventors (9) and the use of reduced flip angles
`for the refocusing pulses was proposed as a solution.
`When these reduced flip angle pulses are used, the echo
`amplitude becomes a complex combination of stimulated
`echoes and spin echoes. It was demonstrated with nu-
`merical simulations and experiments in long T2 speci-
`mens that the spin echo amplitude approaches a tempo-
`rary steady state which then slowly decays due to T2 and
`TI relaxation. Because the “steady state” is actually only
`temporary, it will be referred to as a pseudosteady state.
`The empirically determined pseudosteady state echo am-
`plitude was well approximated by the sine of half the
`refocusing flip angle. The use of a reduced flip angle
`dramatically decreases the power deposited by the se-
`quence and also reduces the slice interaction.
`A method for optimizing the flip angles of the first few
`refocusing pulses to achieve a constant amplitude echo
`train was later presented by LeRoux and Hinks (10). They
`demonstrated that beginning the RF pulse train with
`higher amplitude pulses that slowly decrease and ap-
`proach a constant, or asymptotic, flip angle can produce
`a constant echo amplitude from the very first echo. Al-
`though this work was primarily focused on stabilizing
`the signal when large flip angle, slice selective pulses
`were employed, the approach also eliminated the pri-
`mary drawback of constant flip angle, low flip angle
`RARE: the large number of echoes which have to be
`discarded until the pseudosteady state is reached. In
`addition, the optimized flip angle approach produced
`pseudosteady state echo amplitudes that were consider-
`ably higher than when a corresponding constant flip
`angle RF train was employed.
`The dependence of the pseudosteady state echo ampli-
`tude on the flip angles of the early pulses in the RF pulse
`train raises two questions whose answers will determine
`the quality and utility of low flip angle RARE imaging:
`What is the highest pseudosteady state echo amplitude
`attainable for a given asymptotic flip angle and what RF
`pulse trains can achieve this amplitude? Below an ana-
`lytical solution for the pseudosteady state spin echo train
`is derived that provides an upper limit for the attainable
`pseudosteady state echo amplitude. The solution is then
`employed to assess the efficiency of different RF pulse
`trains for producing magnetization in the pseudosteady
`state condition and to evaluate the utility of low flip
`angle RARE imaging. Finally the conclusions are evalu-
`ated experimentally in both phantoms and a normal vol-
`unteer.
`
`THEORY
`Pseudosteady State Solution
`A steady state solution to the Bloch equation has been
`derived for the short TR gradient echo sequence by fol-
`lowing the evolution of the magnetization from one ex-
`176
`
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`

`
`The Sensitivity o/ Low Flip Angle RARE Imaging
`
`citation to the next and requiring that the net change is
`zero (11). A similar method will be used below for the
`spin echo pseudosteady state. Because the spin echo
`pseudosteady state is not stable against T, and T2 decay,
`terms involving T,, T, and consequently M, in the Bloch
`equations will be ignored. Because RF pulses cause only
`rotation, the effect of the RF pulse can be expressed in
`terms of three Euler angles: a rotation around the z axis of
`angle p followed by a rotation around the y axis of angle
`a, and finally a rotation around the z axis of angle 6. This
`can be written in matrix form (12) as
`
`i;
`
`cos2- exp i (p + 6)
`a
`
`sin a
`exp ip
`
`I
`
`cy
`-sin'- exp -i(p - 6) -sin a exp i6
`2
`a
`cosz- exp -i(p + 6) - sin a exp -i6
`2
`sin cy
`2 ___ exp -ip
`
`cos a
`
`where M, is the complex transverse magnetization given
`by
`
`Mt = M, + iMy
`121
`Define the magnetization as equal to M at echo 1. The
`magnetization experiences a phase rotation of 412 fol-
`lowed by the RF pulse and a second rotation of 412 before
`echo 2. The phase rotation, 4, is caused by applied slice
`select and readout gradients as well as frequency offset
`from the transmitter frequency. This can be written as
`
`131
`
`is equal to
`The steady state requirement demands that
`M. This system of equations can be solved directly, see
`Appendix, to yield
`M*, = -exp i(p - 6)M,
`
`[41
`
`i s i n a e x p i ( y ) s i n ( P + S + + )
`i sina exp i ( 7 ) sin (
`)
`
`P + S + +
`
`P - 6
`
`177
`
`M, =
`
`(1 - coscy)
`
`Equation [4] determines the phase of the echo as a func-
`tion of the phase of the RF pulse and is a statement of the
`Meiboom-Gill condition (13) for the stability of a spin
`echo train. Equation [5] determines the fraction of the
`magnetization along the longitudinal direction. If one
`assumes that all of the equilibrium magnetization, M,,,
`has been placed in the pseudosteady state condition,
`then the transverse magnetization is given by, see Ap-
`pendix,
`
`-7 'I i
`
`(1 - cosa)
`
`\
`
`+
`The echo amplitude is given by averaging this expression
`over 4. This average can be easily performed numerically
`but by making use of special functions and integral tables
`(14). one can also find an analytical solution. see Appen-
`dix,
`
`Me,,,, = +-i Mo exp -i
`
`1
`
`where P is a Legendre function.
`In Fig. 1, the theoretical pseudosteady state function,
`Eq. [7], is compared with the empirical formula for the
`amplitude when a constant flip angle RF pulse train is
`employed (9). The theoretical echo amplitude is larger
`than the constant flip angle echo amplitude for all flip
`angles. This discrepancy arises from the major unjusti-
`fied assumption in the theoretical derivation: that all of
`the equilibrium longitudinal magnetization is transferred
`to the pseudosteady state. There is an inefficient transi-
`tion to the pseudosteady state when a constant flip angle
`RF pulse train is used. It is possible to derive the echo
`amplitude produced by a constant flip angle RF pulse
`train by assuming that all magnetization not initially
`aligned with the pseudosteady state condition eventually
`dissipates. The 90° excitation pulse produces a purely
`transverse magnetization. Assuming the phase of the ex-
`citation pulse is chosen to satisfy the Meiboom-Gill con-
`dition (13), Eq. [4], the component of the excited magne-
`tization along the pseudosteady state solution
`is
`determined by the angle between the pseudosteady state
`solution, M"", and the transverse plane.
`
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`
`

`
`178
`
`Alsop
`
`best to consider optimization of efficiency and stabiliza-
`tion of the echo amplitude simultaneously.
`The method of Hennig (9) for calculating the echo
`amplitudes of an arbitrary RF pulse train was imple-
`mented. Following LeRoux and Hinks (lo), the method
`was modified so that the flip angle of each subsequent RF
`pulse could be determined by specification of the desired
`amplitude of the echo produced by the pulse. To make
`possible the specification of other than constant echo
`amplitudes, an iterative determination of the flip angle
`was used in place of the exact solution developed by
`LeRoux and Hinks for the constant echo amplitude case.
`Beginning with the first echo, an initial guess for the flip
`angle was chosen. The amplitude of the echo was deter-
`mined and then the guess for the flip angle was revised
`based on an iterative root finding algorithm. For simplic-
`ity only nonselective pulses were considered in the cal-
`culations. Figure 1 summarizes the results of the calcu-
`lations. The theoretical pseudosteady state solution
`provides an upper bound to the attainable efficiency. The
`constant flip angle approach is clearly less efficient, es-
`pecially at low flip angles. Amplitude stabilized echo
`trains, on the other hand, are highly efficient. An RF
`pulse train designed to produce a constant echo ampli-
`tude generates a signal very close to the optimal value at
`moderate to high asymptotic flip angles but the efficiency
`starts to drop at low asymptotic flip angles. The relatively
`high efficiency of the amplitude stabilized train can be
`attributed to the gradual decrease of the flip angle from
`angles near 180' at the first echo to the lower, constant
`flip angle used at large echo numbers. An example of an
`optimized RF pulse train is plotted in Fig. 2.
`Intuitively, one would expect that increasing the flip
`angle of the first few RF pulses would further improve
`the efficiency of the echo train because the transition
`from transverse to pseudosteady state angles would be
`even more gradual. This can be achieved by specifying
`larger echo amplitudes for the first few echoes. RF pulse
`
`i
`
`- b- - Stab\lhzed, w l t h Ramp
`0 Stabilized, no Ramp
`
`a
`.- -
`L L
`
`0
`
`5
`
`10
`Echo Number
`
`15
`
`20
`
`FIG. 2. Examples of echo amplitude stabilized RF pulse trains
`designed to achieve amplitudes of 0.4 Mo. The constant echo
`amplitude RF pulse train, open squares, is slightly less efficient
`than the RF pulse train designed for an initial downward ramp in
`echo amplitude, open triangles, so a slightly larger asymptotic flip
`angle is required to achieve the same echo amplitude. Because of
`the initial downward ramp in echo amplitude, the ramp stabilized
`RF pulse train begins with a larger flip angle.
`
`2 0.4
`Ln
`x
`U
`
`. I
`
`o . o & , ,
`0
`
`,
`
`.
`
`,
`
`,
`
`,
`
`,
`
`~
`
`,
`
`- - - - - -
`-
`,
`,
`50
`100
`Steody State Flip Angle (degrees)
`
`Steady State Theory
`Stabilized, w i t h Romp
`StobiLzed. no Romp
`Constant Flip Angle
`.
` , 1
`L
`,
`150
`
`,
`
`,
`
`FIG. 1. Pseudosteady state RARE echo amplitudes as a function
`of the asymptotic refocusing flip angle. The theoretical pseudoste-
`ady state amplitude, solid line, represents the maximum possible
`amplitude achievable. The asymptotic echo amplitudes for a con-
`stant flip angle RF pulse train, a train optimized for constant echo
`amplitude, and one optimized for a short downward ramp in echo
`amplitude followed by constant echo amplitude are also plotted.
`The optimized RF pulse trains come closest to producing the
`optimal echo amplitude.
`
`= M o 1 + i i
`
`sina sin ( e ~ l ) j - '
`
`(1 -cosa)
`The average of this complex expression over all 4 is
`simply given by (14)
`
`in agreement with the earlier empirical result (9) .
`
`Optimization of Echo Amplitudes
`In the previous paragraph it was shown that the ineffi-
`ciency of the constant flip angle RF pulse train reflects
`the difference in angular orientation of spins in the
`pseudosteady state condition compared with the spins
`placed in the transverse plane by the excitation pulse.
`One way to improve this efficiency is to slowly lower the
`flip angle of the RF pulse train from 180°, for which the
`pseudosteady state solution is in the transverse plane, to
`the desired asymptotic angle so the difference between
`the angle of the actual spins and the pseudosteady state
`solution is minimized. Because the flip angles used at the
`beginning of the echo train also have an impact on vari-
`ations in the spin echo amplitude from echo to echo, it is
`
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`
`

`
`The Sensitivity of Low Flip Angle RARE Imaging
`
`179
`
`trains were therefore also calculated to produce a linear
`decrease in signal amplitude from echo one to echo three
`and an echo amplitude equal to the third echo amplitude
`for subsequent echoes. The slope of this amplitude ramp
`was chosen such that the amplitude of echo zero, if it
`existed, would be M,,. An example of such a ramp opti-
`mized RF pulse train is plotted in Fig. 2. The pseudoste-
`ady state echo amplitude achieved with this optimiza-
`tion approach is also plotted in Fig. 1 but it is so nearly
`identical to the theoretical optimum that it is partially
`obscured. Ramp optimized RF pulse trains are more ef-
`ficient than constant optimized RF pulse trains but the
`higher echo amplitudes of the first two echoes must be
`magnitude corrected prior to image reconstruction.
`
`Effects of T2 and T, Decay
`The echo trains produced with multiple spin echoes are
`not truly in a steady state because T, and T, ultimately
`cause the decay of the signal. For perfect 180' pulses,
`only T, affects the amplitude but when lower flip angles
`are used, TI decay also plays a role because stimulated
`echoes are present. Once an RF pulse train has been
`selected, it is straightforward to insert T, and T, decay
`into the calculation of echo amplitudes. The echo ampli-
`tudes of the resulting echo trains do not decay as a
`perfect exponential. The effective T, for the decay, Tzeff,
`was therefore defined as
`
`-\-, *
`
`where S(t, T2, T,, a ) is the echo amplitude as a function
`of time, T2, T, and the refocusing flip angle, a. This
`definition for TZeff was chosen as the most appropriate
`for the discussion of signal-to-noise ratio which follows,
`and also yields the correct relaxation rate for an expo-
`nential decay. In Fig. 3, the ratio of TZeff to T, is plotted
`versus the ratio of T, to T2 for several constant optimized
`RF pulse trains with different asymptotic flip angles.
`When T , is long compared with T,, TZeff is longer than T,
` '
`' 1
`
`5 L "
`
`.
`
`'
`
`"
`
`'
`
`"
`
`"
`
`'
`
`
`
`" 1
`
`'
`
`'
`
`0
`
`50
`100
`Flip Angle ( degrees )
`
`150
`
`FIG. 4. The calculated signal-to-noise ratio versus asymptotic flip
`angle calculated by using Eq. [ll] and the TZe,;s plotted in Fig. 3.
`Signal-to-noise ratio decreases only very slowly with the refocus-
`ing flip angle.
`
`but still relatively independent of T, except at very small
`asymptotic flip angles. When T, becomes comparable
`with T,, the contribution of T, to TZeff is considerable.
`
`Signal-to-Noise Ratio of Low Flip Angle RARE
`Although the use of lower flip angles in RARE imaging
`necessarily reduces the acquired echo amplitude, the
`signal-to-noise ratio need not decrease proportionately.
`Because the TZeff of low flip angle RARE is longer than
`that of T,, there is more time to acquire signal. Conse-
`quently, signal averaging of echoes or, alternatively, nar-
`rower bandwidth acquisitions can be used to reduce the
`measured noise. Employing the matched filter approach
`of Ernst and Anderson (11), the relative signal-to-noise
`ratio of low flip angle RARE is given by
`
`1
`
`The definition of Tzeff was chosen so that this expression
`would be true. This function is plotted in Fig. 4 for
`several different T, values. For objects with TI to T2
`ratios of 10, which is typical for tissues at moderate to
`high field, the signal-to-noise ratio decreases only very
`slowly with asymptotic flip angle. This argues that low
`flip angle RARE may be very competitive with other
`acquisition methods.
`Equation 1111 has neglected the effect of the acquisition
`time on the time available for signal recovery prior to
`another excitation. Many of the applications for low flip
`angle RARE, including fast T, and proton density imag-
`ing, require TR to be much longer than T I . In these
`applications, the effect of the slightly longer acquisition
`on signal-to-noise ratio should be small but will depend
`on the TR selected for the application
`
`84 degrees
`
`-
`
`1
`0
`
`5
`
`.
`
`I
`10
`T 1 / 7 2
`
`.
`
`.
`
`.
`
`,
`15
`
`.
`
`.
`
`.
`
`.
`
`
`
`20
`
`FIG. 3. The decay rate of the echo amplitudes, TZeff, is plotted
`versus the ratio of T, to T2 for several RF pulse trains with different
`asymptotic flip angles. The TZeff was calculated from simulations
`of constant echo amplitude optimized RF pulse trains.
`
`METHODS
`To experimentally verify the theory and evaluate the
`image quality, the low flip angle RARE sequence was
`
`General Electric Co. 1004 - Page 4
`
`

`
`180
`
`Alsop
`
`implemented on a clinical GE SIGNA 1.5 Tesla scanner
`equipped with a prototype gradient system. The gradient
`system could achieve gradient amplitudes of 23 mT/m
`and gradient switching speeds of 100 ps. The strong and
`fast gradients made possible very compact echo trains.
`To further compress the echoes, a Hamming windowed
`1.6 ms sinc pulse that was truncated at the first zero
`crossing was employed. With a 64 kHz acquisition band-
`width and a 256 frequency matrix, echo spacings of
`slightly under 5 ms were achievable.
`Single-shot images were acquired by using ramp opti-
`mized RF pulse trains. An acquisition matrix of 256 X 80,
`an FOV of 24 X 15 cm, and a slice thickness of 5 rnm
`were employed. To avoid artifacts in the reconstruction
`due to the higher amplitudes of the first two echoes, a
`total of 82 echoes were acquired and the first two were
`discarded. The phase encode ordering of Melki et 01. (2)
`was used for all imaging. The acquisition of a single
`image required 410 ms.
`To confirm the theoretical calculations, images of a
`uniform long T, phantom were acquired with the phase
`encoding gradient turned off. The amplitude of each echo
`was then calculated. Such data were obtained for trains
`with asymptotic flip angles ranging from 180" to 1 7 O . For
`comparison to the nonselective pulse theory, the ampli-
`tude of the slice select gradient for the refocusing pulses
`was reduced by a factor of four to achieve a more uniform
`flip angle across the slice. To avoid artifacts, the crusher
`gradients in the slice select direction were increased.
`To assess the image quality, in vivo single-shot images
`were obtained in the brain of a normal volunteer. Flip
`angles from 90" to 17" were evaluated. At these flip
`angles, the images could be acquired with a TR of 500 ms
`without exceeding manufacturers safety limits on heat-
`ing. Higher flip angles were not evaluated in vivo.
`
`RESULTS
`Phantom measurements confirmed the validity of the
`theory. Echo amplitudes are plotted in Fig. 5 for several
`different asymptotic flip angles. The initial amplitudes of
`
`0.0
`0
`
`10
`
`20
`Echo Number
`
`30
`
`40
`
`FIG. 5. Experimental echo amplitudes from a long T2 phantom
`using RF pulse trains optimized for a ramp down to a constant
`echo amplitude. Echo amplitudes from RF pulse trains with as-
`ymptotic flip angles of 1 B O O , go", 60", 30", and 17" are plotted.
`
`the echo trains are in excellent agreement with the the-
`ory. Also apparent in the figure is the excellent stability
`of echo amplitude that is possible with optimized RF
`pulse trains.
`Axial single-shot images of the brain of a normal vol-
`unteer are shown in Fig. 6. The images demonstrate high
`signal-to-noise ratio and good spatial resolution. As ex-
`pected, the image signal intensity for short TE images
`decreases with refocusing flip angle but signal-to-noise
`ratio is still fairly high with 30" refocusing pulses. T2-
`weighted images are also shown, demonstrating the flex-
`ibility in selecting T2 contrast with the RARE sequence.
`Differences in the degree of T2 weighting are apparent in
`the images. This is best illustrated in Fig. 7 where Tzeff
`decay is shown for both 90" and 17" asymptotic refocus-
`ing flip angles. The short TE images were windowed for
`identical appearance but longer TE images show much
`more T, weighting for the 90" flip angle than the 17"
`images. This is consistent with the increase in TZoff ex-
`pected in tissues with T, much longer than T2.
`
`DISCUSSION
`A theory for the pseudosteady state signal amplitude in
`spin echo trains has been presented that provides a the-
`oretical optimum signal intensity against which practical
`implementations can be compared. This theory sheds
`new light on the stability of CPMG (13, 15) echo trains
`and allows derivation of the asymptotic signal amplitude
`as a function of refocusing flip angle for such echo trains.
`For the specific purpose of optimizing low flip angle
`RARE imaging, the theory has shown that constant am-
`plitude low flip angle echo trains are inefficient at trans-
`ferring signal intensity into the pseudosteady state con-
`dition. This inefficiency adds to the problems associated
`with the gradual approach of the echo amplitudes to the
`pseudosteady state. Flip angle optimized RF pulse trains
`are clearly superior both at producing a pseudosteady
`state rapidly and converting transverse magnetization
`into the pseudosteady state. RF pulse trains optimized
`for constant echo amplitude produce nearly the theoret-
`ical maximum signal amplitude at intermediate to high
`asymptotic flip angles but at lower asymptotic flip an-
`gles, the efficiency begins to drop. The efficiency at lower
`flip angles can be increased to nearly 100% by optimiz-
`ing RF pulse trains for a downward ramp in echo ampli-
`tude from the 180" echo amplitude to the desired asymp-
`totic echo amplitude. Experimental implementation of
`this approach (Fig. 5) confirmed the exceptionally high
`efficiency of these RF pulse trains. While this approach
`does improve sensitivity, it requires magnitude correc-
`tion of the first few echoes prior to image reconstruction
`to avoid image artifact.
`The use of low flip angles in the RF pulse train mixes
`both spin and stimulated echo components in the echo
`amplitudes. The decay rate of the echo amplitudes is
`thus determined by an effective T,, Tzeff, which is a
`mixture of T, and T2. For many tissues, Tl is much
`greater than T2. In these tissues, TZeff is longer than T, but
`is still relatively insensitive to the value of Tl. For very
`low flip angle RF pulse trains or in tissues such as fat
`where TI is not much longer than T,, T, also has an
`
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`

`
`The Sensitivity of Low Flip Angle RARE Imaging
`
`181
`
`FIG. 6. Axial, single-shot RARE
`images through the brain of a nor-
`mal volunteer. Images were ob-
`tained with ramp optimized RF
`pulse trains with asymptotic flip an-
`gles of 90" (left), 60" (center), and
`30" (right). The images in the upper
`row were obtained with an effective
`TE of 18 ms, the lower row with an
`effective TE of 83 ms.
`
`impact on contrast. In many pathologies, T, and TI
`change in the same direction. In such pathologies, the
`mixture of TI and I", decay should not strongly influence
`contrast, as long as a longer TEeff is used to compensate
`for the longer TZeff. In other pathologies, it is possible that
`Tzeff contrast will be poorer than T, contrast.
`Although the use of low refocusing flip angles does
`reduce the amplitude of the measured signal, the signal-
`to-noise ratio need not necessarily reduce proportion-
`ately. Accounting for the longer time available for imag-
`ing due to the longer TZeff shows that the signal-to-noise
`ratio is nearly unchanged until asymptotic angles of un-
`der 60" are reached (Fig. 4). Practical applications of low
`flip angle RARE will have an even slower decrease in
`signal-to-noise ratio than in the figure because the anal-
`ysis does not include the variation of data acquisition
`efficiency with bandwidth. For example, in the present
`implementation, a 64 kHz bandwidth was used that ac-
`quired a line of k space in 2 ms. The remaining 3 ms of
`the echo spacing were required for applying gradients
`and the pulse. At a lower flip angle where TZoff is twice
`Tz, a 10-ms echo spacing could instead be used. Since the
`RF and gradient timing is unchanged, the entire addi-
`tional 5 ms could be used for data acquisition by decreas-
`ing the bandwidth to 18 kHz. The practical reduction of
`noise is a factor of 1.9, rather than the 1.4 assumed in the
`theoretical considerations above, because the data acqui-
`sition efficiency increases from 40-70%.
`Single-shot images in the brain of a normal volunteer
`demonstrate excellent image quality and the expected
`changes in signal amplitude and contrast with refocusing
`flip angle. Long echo-train imaging with reduced refocus-
`ing flip angles reduces the power deposition of the se-
`
`quence dramatically. By employing 30" flip angles, for
`example, the signal amplitude is decreased by a factor of
`2, the signal-to-noise ratio by 30%, yet the power depo-
`sition is reduced by a factor of 36 relative to a 180" train.
`In practical application, and in the in vivo images
`shown in Figs. 6 and 7, slice selective refocusing pulses
`must be used and the imperfect slice profile will have
`implications for sensitivity and contrast. The methods of
`LeRoux and Hinks (10) for stabilizing the echo ampli-
`tudes when slice selective pulses are used can easily be
`applied to lower asymptotic flip angle RF pulse trains. As
`can be seen in Figs. 6 and 7, naive use of the nonselective
`pulse theory to tailor the amplitudes of selective pulses
`can produce images of excellent quality even though
`poorly selective pulses were used. Accurately accounting
`for the effects of slice selection will likely slightly alter
`the optimized RF pulse amplitudes and slightly increase
`the TZnff relative to the nonselective pulse theory. Since
`the RF power in low flip angle RARE is lower than when
`180" pulses are used, RF pulses with better slice profiles
`but that deposit more RF power might be employed. This
`would lead to more uniformity of contrast across the
`slice.
`The variation of RF amplitude, which typically occurs
`within a practical RF coil, has been neglected in this
`work. Experience with the standard head coil, in which
`the amplitude variations are of the order of lo%, and
`with the body coil, in which amplitude variation can be
`considerably higher than the head coil, suggests that RF
`inhomogeneity is not a major problem for this method.
`Errors in the amplitude of the RF pulse train will cause
`slight amplitude fluctuations in the first few echoes.
`These fluctuations could produce subtle artifacts, espe-
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`FIG. 7. Comparison of apparent T,
`decay in images obtained using
`ramp optimized RF pulse trains
`with asymptotic flip angles of 90"
`(top), and 17" (bottom). The differ-
`ence of T, decay in the images ob-
`tained at TFs of 18 ms (left), 83 rns
`(center), and 157 m s (right) is
`clearly apparent.
`
`cially in proton density images where the center of k-
`space is scanned in the first echoes. Discarding the first
`few echoes may be sufficient to eliminate these artifacts.
`Contrast will also be slightly affected by RF inhomoge-
`neity because TZeff will be longer when the RF amplitude
`is weaker.
`The major disadvantage of long echo-train imaging is
`the increased acquisition time required for each slice.
`This reduces the number of slices that can be acquired in
`a given repetition time and can lead to inefficiency in
`data acquisition. In this respect, long echo-train RARE
`imaging is similar to fast gradient-echo imaging. Long
`echo-train RARE imaging will most likely be optimal in
`applications where fast or motion insensitive imaging is
`required or in 3-dimensional sequences. The extension of
`the number of echoes made possible by low flip angle RF
`pulse trains may make it possible to acquire %dimen-
`sional T, images without the use of multiple slab acqui-
`sitions (16) that can suffer from slab boundary artifacts.
`Reduced flip angle echo trains need not be limited to
`long echo train acquisitions. In multiple slice interleaved
`RARE acquisitions at high field, power deposition can
`restrict the number of slices that can be acquired. In such
`circumstances, reduced flip angles can be used, although
`the signal-to-noise ratio will decrease more like the echo
`amplitude plotted in Fig. 1 rather than the signal-to-noise
`ratio plotted in Fig. 4 because the extended acquisition
`time available in each slice was not used for data acqui-
`sition.
`The single-shot images in Figs. 6 and 7 invite compar-
`ison with other single shot techniques including echo
`planar (17), GRASE (18), and prepared gradient echo
`sequences (19). Single-shot RARE does not suffer from
`
`the distortion and ghosting artifacts that plague echo-
`planar imaging so it may be competitive with echo-pla-
`nar imaging for motion insensitive T, and proton density
`imaging. However, echo-planar imaging can be operated
`in low flip angle gradient echo mode, allowing for higher
`temporal resolution than is feasible with RARE, and echo
`planar acquisitions are generally a factor of 2 to 4 times
`faster than RARE acquisitions. Because the CPMG con-
`dition is required, the RARE acquisition is also harder to
`prepare with contrasts such as T,* and diffusion, al-
`though approaches to overcoming these problems have
`been discussed (7). Low flip angle RARE is directly com-
`patible with the acquisition of multiple gradient echoes
`per echo train as are used in GRASE. Optimized RF pulse
`trains have previously been suggested as an approach to
`reduce the T2 decay artifacts in GRASE (20). As dis-
`cussed earlier, the use of low refocusing flip angles in
`RARE does make possible data acquisition efficiencies of
`70%, which are comparable with those of GRASE (21).
`with the better point spread function of RARE (22).
`The existence of a pseudosteady state and the use of
`low flip angle RF pulse trains in a RARE sequence seem
`to blur the distinction between fast gradient-echo and
`RARE imaging. In truth, there is little difference between
`RARE and prepared gradient echo sequences where the
`signal due to T , recovery during the acquisition is
`crushed by applied gradients (23) except that the theory
`for RARE explicitly takes into account the multiple spin
`and stimulated echoes that can occur in such sequences.
`There is a major difference between RARE and equilib-
`rium fast gradient echo sequences, however, because T,
`recovery of magnetization plays a major role in such
`gradient echo sequences. For long echo train, low flip
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`i i
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`If it is assumed that all of the equilibrium magnetization,
`M,, has been transferred to the pseudosteady state then
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