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Zoom imaging using noise pulses
JOURNAL
OF MAGNETIC
RESONANCE
88,406-4
16 ( 1990)
Zoom Imaging Using Noise Pulses ALEXANDER
J.S. DECRESPIGNY,T. AND LAURANCE
ADRIAN D. HALL
CARPENTER,
Herchel Smith Laboratory for Medicinal Chemistry, Cambridge University School of Clinical Medicine, University Fowie Site, Robinson Way, Cambridge CB2 2PZ, United Kingdom Received January 18, 1990
It is often the case in nuclear magnetic resonance imaging that the features of interest within the object under examination are smaller than the whole imaged volume and good spatial resolution is necessary to resolve these small features ( l-3). Rather than acquire a high-resolution image of the whole sample, it is obviously preferable to image just the region of interest, thus saving time in the imaging procedure and making optimum use of the dynamic range of the NMR machine’s receiver system. If the region of interest (ROI) lies near the surface of the sample, then the localization achieved with a surface coil may restrict the field of view sufficiently; this has the additional advantage of a good signal-to-noise ratio due to the high filling factor. For deep-lying regions, however, acquisition of a zoomed image of the ROI by simply increasing the strengths of the B0 gradients used in the imaging sequence causes signal from the edges of the sample to be folded back into the image unless steps are taken to remove the contribution from spins outside the region of interest. We have recently introduced a new technique for spatial localization by outervolume saturation, ROISTER (4). This technique uses noise-modulated radiofrequency pulses (5, 6) combined with time-varying B0 gradients to achieve 2D or 3D localization of a convex volume in a single scan. A pulse sequence for 2D localized imaging is shown in Fig. 1, where the ROISTER sequence is simply added to the start of a standard spin-warp experiment. In this Communication we describe the application of this technique to reduced field-of-view imaging. Noise-modulated selective pulses aim to randomize magnetization everywhere outside the selected slice where spins are, ideally, undisturbed. A basic noise pulse was generated by inverse Fourier transformation of a sequence of 5 12 random complex numbers in which the central 25 points in the sequence were set to zero. The random numbers were generated on a SUN 4 / 150 workstation using the standard nonlinear additive feedback algorithm supplied with the machine to produce values uniformly distributed in the range 0 to 1 for the magnitude, and 0 to 2?r for the phase of each complex number. The plot of longitudinal magnetization in Fig. 2A shows the simulated response of a uniform spin system to this pulse, applied in the presence of a constant B. gradient. The large positive and negative variations in magnetization outside the “unexcited” slice average to zero across the sample as a whole. Thus, following the application of the noise pulse in the presence of a constant field gradient, a nonselective 90” pulse produces net signal only from the slice. This is of course only 0022-2364190 $3.00 Copyright 0 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.
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RF FIG. 1. A typical ROISTER imaging sequence with a 2D selective saturation sequence followed by a slice-selective spin echo.
true for uniform samples, which are rarely found in practice. The application of such a pulse, used as the sole means of slice selection, would only be useful for in vivo spectroscopy if the variation in magnetization produced is random on a sufficiently small scale to average out signal contributions from all regions within the sample. For imaging, the pixel size is an important factor when considering the outer-volume suppression achievable using noise pulses. This may be illustrated, for example,
-1L C FIG. 2. Plots of longitudinal
D
magnetization against frequency offset for selective noise pulses. Plot (A) shows the response to a simple noise pulse while (B) is the response to a pulse generated with a uniform amplitude in the frequency domain. (C) and (D) are the responses to the two optimized pulses used in the experiments.
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by preceding a spin-warp imaging sequence with a selective noise pulse applied in conjunction with a constant gradient. An image with a pixel size which is small compared to the pseudo-random variations in magnetization produced by the noise pulse would clearly show the large changes in signal intensity in the outer volume. Conversely, in an image with coarser spatial resolution, the random variation in longitudinal magnetization within each of the larger pixels will cause the resultant z magnetization in each pixel to be reduced, giving better apparent suppression. If a zoomed image is then made of the selected volume, the pixel size is of course reduced by the zoom factor. Outer-volume signal aliased back into the image may now not be random on a sufficiently small scale to cancel effectively within the smaller pixels. However, each pixel in the zoomed image may receive signal contributions from several areas in the outer volume, and these will tend to further average out, counteracting the reduction in cancellation due to the reduced pixel size. The transverse magnetization created by the noise pulse may be a problem if there is coherence within individual pixels. This may be refocused by the spin-echo sequence and appear as noisy degradation within the image, extending up to high spatial frequencies. The effect of transverse magnetization is particularly important when multiple noise pulses are used to achieve saturation, as described below. When using noise pulses in zoom imaging or localized spectroscopy, the objective is to reduce the net z component of the undesired magnetization to zero before the start of the imaging or spectroscopy sequence. To this end, the simple noise pulse needs to be optimized with respect to both the excitation null within the selected slice and the reduction of z magnetization outside. A pulse which is more efficient at reducing M, may be generated by defining the amplitude of its frequency spectrum to be constant (except in a central region which has zero intensity) while the phase remains random (6). Ideally this tips all the z magnetization outside the selected slice into the transverse plane with random phase. The simulated M, response to such a pulse is shown in Fig. 2B. As in Fig. 2A some magnetization is excited inside the slice largely due to the effect of pulse truncation, which causes a ringing at the slice boundary. To reduce this effect a simple linear iterative optimization procedure (4, 7) was used. A desired excitation profile was defined by 5 12 points, with uniform 90 flip angle and random phase, except for the central 25 points of zero excitation, which was then inverse Fourier transformed to produce an initial RF pulse envelope. This initial pulse shape was then zero-filled to 1024 points and Fourier transformed; this procedure is equivalent to performing sine function interpolation on the original frequency spectrum and illustrates the ringing at the slice edges due to the pulse truncation. The amplitude of this new frequency spectrum was then reset to the desired rectangular shape while the phase response was unaltered. After inverse transformation, 5 12 points were taken as the new pulse shape and the whole process was repeated until negligible improvement occurred in the frequency profile. After this, iteration was continued for a period where only the central 25 points in the spectrum were reset to zero each time. The spin response to such an optimized pulse is shown in Fig. 2C, where the total excitation bandwidth is defined to be less than the total pulse bandwidth in order to reduce the RF power requirements. Figure 2D shows the response to an optimized pulse with a slice width four times that shown in Fig. 2C; both these optimized pulses were used in the experiments described below.
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In the ROISTER experiment, desirable features are (i) short saturation sequence to reduce the effects of motion and T, relaxation during the sequence; (ii) low gradient strength to reduce eddy currents; (iii) large phase variation across pixels to prevent the refocusing of magnetization and to improve the resultant suppression; and (iv) low RF power. One compromise between these features is represented by the pulse response profiles in Figs. 2C and 2D. The relative importance of each of these features in practical cases will dictate the characteristics of the noise pulse, so that the ease and speed of generation of an optimized pulse is important. In the above examples, the optimization took 15 s of CPU time on the SUN workstation. Where noise pulses are used repeatedly to achieve selective saturation, the amount of magnetization excited by each pulse within its “null” slice is important since it can cause an artifactual modulation in intensity in the resulting “zoomed” image. Although the optimization procedure outlined above may not be perfect, it appears to yield pulses which excite only a small amount (3%) of magnetization within the selected slice, while the edges of the slice are sharp. Experimental work was carried out using an Oxford Research Systems Biospec I console with a 2 T, 3 1 cm bore Oxford Instruments superconducting magnet and a homebuilt, 20 cm i.d. gradient set. The phantom used for these studies was a cylindrical container of inner diameter 48 mm, containing glass tubes of various diameters and filled with water doped with MnC12 to give T, and T2 values of 882 and 84 ms, respectively. Figure 3A shows a 128 X 128 pixel image of a 5 mm slice through this phantom with a field of view of 53 mm, giving a pixel resolution of 420 pm. The standard spin-echo imaging sequence (TE = 24 ms) used to acquire this image was then preceded by two selective noise pulses applied with orthogonal gradients to select a square ROI, Fig. 3B. The slice gradients were left on for a period of 2 ms after each noise pulse to dephase the transverse magnetization produced. Figure 4 shows the sequence used to obtain this image, in which the noise pulse had the response profile shown in Fig. 2C. The pulse length (2.2 ms) and gradient strength ( 1.8 G/cm) resulted in a region of interest which filled a quarter of the field of view, and the image had sufficient resolution to show the structure in the longitudinal magnetization after application of the noise pulses. The RF power was set to achieve optimum reduction of signal from the outer volume; this meant that, in practice, the mean flip angle was close to 90” for each pulse. The amount of outer-volume suppression is generally good; however, some intensity can still be seen where spins in the outer volume lie within one of the unexcited slices. These stripes of signal occur at particular frequency offsets where there happens to be reduced excitation in the noise pulse spectrum. To illustrate the effect of pixel size on apparent outer-volume suppression, we may use pulses which produce a more rapid variation in excited magnetization across the sample. The image in Fig. 3C shows a region of interest which was selected using the noise pulse having the response profile Fig. 2D. This pulse has four times the null slice width of the pulse used to obtain Fig. 3B, but was applied for four times as long (with the same slice gradient) to select the same ROI. In this case, however, the more rapid variation of z magnetization across each pixel in the outer volume results in improved suppression, and less signal intensity is visible in the partially excited slices. We now consider the case where the single noise pulse, applied with each of the two gradient directions, is replaced by multiple applications of the same pulse, but with reduced flip angle. This illustrates the problem of coherent magnetization cre-
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FIG. 3. Image (A) shows the phantom used in the experiments, with a field of view of 53 mm, and (B) the square ROI selected with two applications of the optimized noise pulse (Fig. 2C). Improved outervolume suppression is achieved in (C) using a pulse with a wider slice width (Fig. 2D) applied to select the same ROI. Image (D) shows the ROI selected using a total of 20 noise pulses, each with a flip angle of 50”. Ten pulses were applied with the gradients in each of the x and y directions. The fuzzy areas of signal intensity above and below the ROI in this image are probably an effect of eddy currents in the magnet due to the long gradient pulses used in the presaturation sequence.
ated by the pulses. In the general case, the effect of a discrete RF pulse on a spin isochromat at some particular frequency offset (due either to chemical shift or displacement in a field gradient) may be considered to be a series of rotations about some time-varying axis in a frame rotating at the Larmor frequency. The net result is equivalent to a single rotation by some angle about some other axis in the rotating frame; both the rotation angle and the axis depend on the pulse shape, the power, and the frequency offset. The resulting longitudinal magnetization of the isochromat is then m, = mo( cos*O + sin28 cos 4) = mOcos (Y, where 13is the angle of the net rotation axis with respect to the z axis and 4 is the
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FIG. 4. A pulse sequence for selective imaging using just two noise pulses in the presaturation sequence, and spoiler gradients (dashed) to dephase the transverse magnetization they produce.
rotation angle about this axis, as shown in Fig. 5A; (Yis the resultant flip angle, between the magnetization vector and the z axis. If one neglects relaxation and assumes no reduction in signal from the isochromat due to the dephasing effects of field gradients, multiple applications of the pulse in the presence of a constant field gradient will cause the magnetization vector to move in a circle so that m, varies periodically with the number of pulses. Figure 5C shows the variation of m, for the case 0 = 90”, 4 = 4.5”, where there is a zero in z magnetization after 20 pulses. If, however, there is a delay between the pulses during which the transverse magnetization in the isochromat dephases completely, then after 12pulses the longitudinal magnetization is given by m, = mOcosna, where the magnetization vector is pointing along the z axis at the end of each dephasing delay, shown in Fig. 5B. The longitudinal magnetization approaches zero asymptotically and Fig. 5D shows the case of a 37” flip angle where m, is reduced by 99% after 20 pulses. This latter case is more relevant to a discussion of the effect of noise pulses on spins lying outside the null slice: although larger flip angles are required, errors in flip angle will affect the resultant suppression less critically than in the case where there is no dephasing. Somewhere between these two extremes is the practical case, illustrated by the image of the ROI shown in Fig. 3D. To obtain this, the imaging sequence was preceded by a train of 10 noise pulses in each of the x and y gradient directions with a delay of 300 PS between each pulse (during which the slice gradient remains on) and a flip angle of 50”; the total duration of this presaturation sequence was 50 ms. Some of the transverse magnetization created by each noise pulse is dephased during the interpulse delay, while a certain amount is flipped back along the z axis where it needs to be resuppressed, which accounts for the requirement of a 50” flip angle. The use of
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mz
’ 0.8 0.6 0.4 0.2
..\\\
5
C
10
15
20
5
number of pulses
D
number of pulses
FIG. 5. (A) shows the magnetization trajectory for a single isochromat after application of a noise pulse where the isochromat lies outside the “null” slice. The net effect is to rotate the magnetization by some angle about some axis in the rotating frame. Multiple applications of the pulse cause the magnetization vector to follow a circular path, and m2 is periodic with time. (C) shows this for the case 8 = 90”, I$ = 4.5”, where the curve shape is a quarter cycle cosine waveform. In (B) the transverse magnetization is completely dephased by held gradients between applications of the noise pulse, so m, decreases monotonically. (D) illustrates this for the case 0 = 90”, 4 = 37”, where m, is reduced to 1o/oof m0 after 20 pulses.
longer dephasing delays or larger gradients would not necessarily eliminate this effect, but would produce a more rapid phase variation in the transverse magnetization across the sample so that the magnetization flipped back along the z axis is at a higher spatial frequency (8). The outer-volume suppression has improved in this image, probably because the excitation profile of the noise pulse is somewhat more uniform at lower flip angles. The fuzzy areas of signal intensity above and below the ROI are probably caused by eddy currents due to the long constant gradient pulses used in the presaturation sequence. Figure 6A shows an image of this region in which the gradient strengths in the imaging sequence were increased by a factor of 4 to zoom in on the ROI. This results in improved resolution with the new pixel size of 111 pm; however, insufficiently suppressed signal from the outer volume has aliased into the image and degraded the quality of it. It is possible to remove this aliasing in the “read” direction by reducing the bandwidth of the analog filter in the receiver section of the NMR machine. This
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FIG. 6. Image (A) shows the region of interest of Fig. 3D zoomed by a factor of 4, so that the pixel size is now 111 km. For (B), a circular region of interest was selected, centered at the same place, using a 19step ROISTER sequence of duration 47.5 ms, similar to that shown in Fig. 1. Image (C) shows this region zoomed by a factor of 4, and showing reduced contamination from remnant outer-volume signal, compared to (A). (D) shows the unzoomed ROI (B), displayed with the same number of pixels as the zoomed image (C) using bilinear interpolation, to illustrate the improvement in resolution obtained by acquiring a true zoomed image. No signal averaging was performed to acquire these images, but the gain of the NMR receiver was increased for the zoomed images.
of course does not stop aliasing in the phase-encoding direction and also modulates the resulting image by the transfer function of the filter. In all the experimental work in this paper, the analog filter was kept at a constant width so as to have no effect on the volume selection process. In the ROISTER experiment, each spin isochromat is at a different frequency offset for each application of a noise pulse, since the gradient direction varies with time. Thus, over the whole presaturation sequence an isochromat experiences a range of the noise pulse frequency spectrum, instead ofjust one point as in the constant gradient case above. This means that, since the magnetization vector is rotated by a differ-
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ent angle about a different (randomly varying) axis in the rotating frame at each step in the ROISTER sequence, there is a better chance of the resultant longitudinal magnetization averaging to zero. Figure 6B shows an image of a region in the phantom at the same position as the ROI selected above, acquired using a 2D ROISTER sequence (Fig. 1) with 19 noise pulses, and showing improved suppression over the constant gradient case. Here the total presaturation sequence lasted 47.5 ms and the noise pulse and flip angle were the same as those used for the multiple noise pulse experiment above. The modulus of the total gradient vector was 1.8 G/cm and described a circle in the x-y plane during the sequence. A delay of 300 I.LSbetween each noise pulse was necessary on our equipment in order to shift the transmitter frequency and thereby effect movement of the ROI away from the center of the gradients, and some dephasing of transverse magnetization would have occurred in this time. Figure 6C shows a zoomed image of this region with the same spatial resolution as that in Fig. 6A but with less contamination by signal from the outer volume. Some of the remaining contamination (which causes a mottled effect on the image) is due to signal from saturated spins relaxing back along the z axis during the delay between the ROISTER sequence and the start of the imaging sequence. In this case, with a delay of 5 ms, an average of 0.5% of magnetization would have relaxed back before the start of the spin-echo sequence. Exactly the same volume selection experiment was performed on a uniform phantom in order to measure the degree of outer-volume suppression achieved; this showed that the signal from the outer volume was reduced by 97.5%, with a 6% loss in signal from the selected volume, probably due to the small amount of magnetization excited by the noise pulses within the selected slice. These values (obtained by averaging pixel intensities from images with good signal-to-noise ratios (SNR)) take no account of the random phase variation of remnant magnetization over the outer volume which may give better suppression than indicated here when using ROISTER for localized spectroscopy, where spectral contamination is the vector sum of signal from all over the outer volume. An important feature of using time-varying gradients is the ability to generate conformal regions of interest; this property would be particularly useful for increasing signal in a localized spectroscopy experiment, but can easily be demonstrated by imaging. In Fig. 7A an irregular region of interest is drawn on the image of the phantom used in these experiments. The definition of this region was used to generate gradient waveforms in two dimensions along with the corresponding pulse frequency offsets. These were then used in a ROISTER sequence, with the same parameters as those for the images above, to select the nearest convex approximation to the desired region of interest, Fig. 7B. Figure 7D shows this region zoomed to three times the spatial resolution. A geometrical simulation of the selected region, Fig. 7C, shows the intensity variation around the ROI in the ideal case of complete dephasing of transverse magnetization between noise pulses. The same flip angle was assumed in the simulation as was used in the experiment, so that in the ideal case only 0.02% of magnetization remains, far away from the ROI. Although regions of interest may be defined anywhere within the sample, it is still necessary to display the image centered within the data matrix. In the above images, the region of interest was displaced from the center of the gradients in both the read and the phase-encoding directions. Shifting an image in the frequency domain to
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FIG. 7. An irregular region of interest (A) drawn on an image ofthe whole phantom was used to generate gradient waveforms and frequency offsets for the noise pulses in order to select this region of the sample (B). Image (C) shows the simulated shape of the ROI, calculated using idealized square slice profiles. A zoomed image of this region (D) was acquired with a pixel size of 148 Wm.
center it within the data matrix is equivalent to effecting the corresponding linear phase shifts in both directions in the time domain, prior to Fourier transformation. This may be achieved, in the read direction, simply by offsetting the receiver frequency by an amount equal to the displacement of the ROI from the gradient center, and in the phase-encoding direction by incrementing the receiver phase on each scan ( 1). The shifts in the phase-encoding direction can also of course be applied to the time data during postprocessing or, as was the case for the images presented here, simply by shifting the aliased image the correct amount using the display software on our SUN workstation. Field-of-view reduction may be used in a number of ways. If the region-of-interest dimension is a fraction 1 /n of the whole object dimension, then an image of this region with the same resolution and the same pixel signal-to-noise ratio as those for the whole sample may be acquired, using a conventional 2DFI technique, in 1/n
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times the time required for the whole image. Alternatively, an image of the region with n times the pixel resolution in each dimension but 1 /n2 times the SNR may be acquired in the same time, so that the same SNR as the original image could be achieved in n4 times the imaging time. The compromise made between resolution, acquisition and processing times, and SNR is also affected by the subjective effect of image processing, such as interpolation and filtering, which can improve the perception of small scale features in images. This can be seen in Fig. 6D, which shows an interpolated low-resolution image of the ROI (Fig. 6B) compared with a zoomed image (Fig. 6C) which clearly shows improved resolution, despite the decreased signal-to-noise ratio. The technique for single-shot 2D localization presented here could easily be followed by a fast imaging sequence such as EPI (9) or FLASH ( 10) to perform snapshot zoom imaging, with the possibility of multislice imaging along the selected column. The T2 independence of the technique should also make it useful in many circumstances. The coherent transverse magnetization created by each noise. pulse still limits the degree of saturation which can be achieved with this technique, but some particular combination of noise pulses which produce a more rapid variation in magnetization, “rotating” gradients, and dephasing delays or gradients may prove optimal. ACKNOWLEDGMENTS We thank (A.J.S.dC.).
Dr.
Herchel
Smith
for
an endowment
(L.D.H.
and
T.A.C.)
and
research
studentship
REFERENCES I. J. BRIAND 2. J. FRAHM,
AND L. D. HALL, J. Magn. Reson. 83,418 ( 1989). H. BRUHN. M. L. GYNGELL, K. D. MERBOLDT,
W. H;~NICKE,
AND R. SAUTER,
Magn.
Reson. Med. 9,79 ( 1989). A. PRESS, D. G. AMARAL, AND L. R. SQUIRE, Nature (London) 341,54 ( 1989). J. DE CRESPIGNY, T. A. CARPENTER, AND L. D. HALL, J. Magn. Reson. 85,595 ( 1989). L. TOMLINSON AND H. D. W. HILL, J. Chem. Phys. 59, 1775 ( 1973). J. ORDIDGE, Mugn. Reson. Med. 5,93 (1987). TURNER AND K. HEDGES, “Works in Progress,” 1029,8th Society of Magnetic Resonance in Medicine Conference, Amsterdam, 1989. 8. 1. R. YOUNG, G. M. BYDDER, AND D. J. BRYANT, Magn. Reson. Med. 11, 127 ( 1989). 9. P. MANSFIELD AND L. PYKETT, J. Magn. Reson. 29,355 ( 1978). 10. A. HAASE, J. FRAHM, D. MATTAEI, W. H~NICKE, AND K. D. MERBOLDT, J. Magn. Resson.67,258 (1986). 3. 4. 5. 6. 7.
G. A. B. R. R.
OF MAGNETIC
RESONANCE
88,406-4
16 ( 1990)
Zoom Imaging Using Noise Pulses ALEXANDER
J.S. DECRESPIGNY,T. AND LAURANCE
ADRIAN D. HALL
CARPENTER,
Herchel Smith Laboratory for Medicinal Chemistry, Cambridge University School of Clinical Medicine, University Fowie Site, Robinson Way, Cambridge CB2 2PZ, United Kingdom Received January 18, 1990
It is often the case in nuclear magnetic resonance imaging that the features of interest within the object under examination are smaller than the whole imaged volume and good spatial resolution is necessary to resolve these small features ( l-3). Rather than acquire a high-resolution image of the whole sample, it is obviously preferable to image just the region of interest, thus saving time in the imaging procedure and making optimum use of the dynamic range of the NMR machine’s receiver system. If the region of interest (ROI) lies near the surface of the sample, then the localization achieved with a surface coil may restrict the field of view sufficiently; this has the additional advantage of a good signal-to-noise ratio due to the high filling factor. For deep-lying regions, however, acquisition of a zoomed image of the ROI by simply increasing the strengths of the B0 gradients used in the imaging sequence causes signal from the edges of the sample to be folded back into the image unless steps are taken to remove the contribution from spins outside the region of interest. We have recently introduced a new technique for spatial localization by outervolume saturation, ROISTER (4). This technique uses noise-modulated radiofrequency pulses (5, 6) combined with time-varying B0 gradients to achieve 2D or 3D localization of a convex volume in a single scan. A pulse sequence for 2D localized imaging is shown in Fig. 1, where the ROISTER sequence is simply added to the start of a standard spin-warp experiment. In this Communication we describe the application of this technique to reduced field-of-view imaging. Noise-modulated selective pulses aim to randomize magnetization everywhere outside the selected slice where spins are, ideally, undisturbed. A basic noise pulse was generated by inverse Fourier transformation of a sequence of 5 12 random complex numbers in which the central 25 points in the sequence were set to zero. The random numbers were generated on a SUN 4 / 150 workstation using the standard nonlinear additive feedback algorithm supplied with the machine to produce values uniformly distributed in the range 0 to 1 for the magnitude, and 0 to 2?r for the phase of each complex number. The plot of longitudinal magnetization in Fig. 2A shows the simulated response of a uniform spin system to this pulse, applied in the presence of a constant B. gradient. The large positive and negative variations in magnetization outside the “unexcited” slice average to zero across the sample as a whole. Thus, following the application of the noise pulse in the presence of a constant field gradient, a nonselective 90” pulse produces net signal only from the slice. This is of course only 0022-2364190 $3.00 Copyright 0 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.
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RF FIG. 1. A typical ROISTER imaging sequence with a 2D selective saturation sequence followed by a slice-selective spin echo.
true for uniform samples, which are rarely found in practice. The application of such a pulse, used as the sole means of slice selection, would only be useful for in vivo spectroscopy if the variation in magnetization produced is random on a sufficiently small scale to average out signal contributions from all regions within the sample. For imaging, the pixel size is an important factor when considering the outer-volume suppression achievable using noise pulses. This may be illustrated, for example,
-1L C FIG. 2. Plots of longitudinal
D
magnetization against frequency offset for selective noise pulses. Plot (A) shows the response to a simple noise pulse while (B) is the response to a pulse generated with a uniform amplitude in the frequency domain. (C) and (D) are the responses to the two optimized pulses used in the experiments.
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by preceding a spin-warp imaging sequence with a selective noise pulse applied in conjunction with a constant gradient. An image with a pixel size which is small compared to the pseudo-random variations in magnetization produced by the noise pulse would clearly show the large changes in signal intensity in the outer volume. Conversely, in an image with coarser spatial resolution, the random variation in longitudinal magnetization within each of the larger pixels will cause the resultant z magnetization in each pixel to be reduced, giving better apparent suppression. If a zoomed image is then made of the selected volume, the pixel size is of course reduced by the zoom factor. Outer-volume signal aliased back into the image may now not be random on a sufficiently small scale to cancel effectively within the smaller pixels. However, each pixel in the zoomed image may receive signal contributions from several areas in the outer volume, and these will tend to further average out, counteracting the reduction in cancellation due to the reduced pixel size. The transverse magnetization created by the noise pulse may be a problem if there is coherence within individual pixels. This may be refocused by the spin-echo sequence and appear as noisy degradation within the image, extending up to high spatial frequencies. The effect of transverse magnetization is particularly important when multiple noise pulses are used to achieve saturation, as described below. When using noise pulses in zoom imaging or localized spectroscopy, the objective is to reduce the net z component of the undesired magnetization to zero before the start of the imaging or spectroscopy sequence. To this end, the simple noise pulse needs to be optimized with respect to both the excitation null within the selected slice and the reduction of z magnetization outside. A pulse which is more efficient at reducing M, may be generated by defining the amplitude of its frequency spectrum to be constant (except in a central region which has zero intensity) while the phase remains random (6). Ideally this tips all the z magnetization outside the selected slice into the transverse plane with random phase. The simulated M, response to such a pulse is shown in Fig. 2B. As in Fig. 2A some magnetization is excited inside the slice largely due to the effect of pulse truncation, which causes a ringing at the slice boundary. To reduce this effect a simple linear iterative optimization procedure (4, 7) was used. A desired excitation profile was defined by 5 12 points, with uniform 90 flip angle and random phase, except for the central 25 points of zero excitation, which was then inverse Fourier transformed to produce an initial RF pulse envelope. This initial pulse shape was then zero-filled to 1024 points and Fourier transformed; this procedure is equivalent to performing sine function interpolation on the original frequency spectrum and illustrates the ringing at the slice edges due to the pulse truncation. The amplitude of this new frequency spectrum was then reset to the desired rectangular shape while the phase response was unaltered. After inverse transformation, 5 12 points were taken as the new pulse shape and the whole process was repeated until negligible improvement occurred in the frequency profile. After this, iteration was continued for a period where only the central 25 points in the spectrum were reset to zero each time. The spin response to such an optimized pulse is shown in Fig. 2C, where the total excitation bandwidth is defined to be less than the total pulse bandwidth in order to reduce the RF power requirements. Figure 2D shows the response to an optimized pulse with a slice width four times that shown in Fig. 2C; both these optimized pulses were used in the experiments described below.
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In the ROISTER experiment, desirable features are (i) short saturation sequence to reduce the effects of motion and T, relaxation during the sequence; (ii) low gradient strength to reduce eddy currents; (iii) large phase variation across pixels to prevent the refocusing of magnetization and to improve the resultant suppression; and (iv) low RF power. One compromise between these features is represented by the pulse response profiles in Figs. 2C and 2D. The relative importance of each of these features in practical cases will dictate the characteristics of the noise pulse, so that the ease and speed of generation of an optimized pulse is important. In the above examples, the optimization took 15 s of CPU time on the SUN workstation. Where noise pulses are used repeatedly to achieve selective saturation, the amount of magnetization excited by each pulse within its “null” slice is important since it can cause an artifactual modulation in intensity in the resulting “zoomed” image. Although the optimization procedure outlined above may not be perfect, it appears to yield pulses which excite only a small amount (3%) of magnetization within the selected slice, while the edges of the slice are sharp. Experimental work was carried out using an Oxford Research Systems Biospec I console with a 2 T, 3 1 cm bore Oxford Instruments superconducting magnet and a homebuilt, 20 cm i.d. gradient set. The phantom used for these studies was a cylindrical container of inner diameter 48 mm, containing glass tubes of various diameters and filled with water doped with MnC12 to give T, and T2 values of 882 and 84 ms, respectively. Figure 3A shows a 128 X 128 pixel image of a 5 mm slice through this phantom with a field of view of 53 mm, giving a pixel resolution of 420 pm. The standard spin-echo imaging sequence (TE = 24 ms) used to acquire this image was then preceded by two selective noise pulses applied with orthogonal gradients to select a square ROI, Fig. 3B. The slice gradients were left on for a period of 2 ms after each noise pulse to dephase the transverse magnetization produced. Figure 4 shows the sequence used to obtain this image, in which the noise pulse had the response profile shown in Fig. 2C. The pulse length (2.2 ms) and gradient strength ( 1.8 G/cm) resulted in a region of interest which filled a quarter of the field of view, and the image had sufficient resolution to show the structure in the longitudinal magnetization after application of the noise pulses. The RF power was set to achieve optimum reduction of signal from the outer volume; this meant that, in practice, the mean flip angle was close to 90” for each pulse. The amount of outer-volume suppression is generally good; however, some intensity can still be seen where spins in the outer volume lie within one of the unexcited slices. These stripes of signal occur at particular frequency offsets where there happens to be reduced excitation in the noise pulse spectrum. To illustrate the effect of pixel size on apparent outer-volume suppression, we may use pulses which produce a more rapid variation in excited magnetization across the sample. The image in Fig. 3C shows a region of interest which was selected using the noise pulse having the response profile Fig. 2D. This pulse has four times the null slice width of the pulse used to obtain Fig. 3B, but was applied for four times as long (with the same slice gradient) to select the same ROI. In this case, however, the more rapid variation of z magnetization across each pixel in the outer volume results in improved suppression, and less signal intensity is visible in the partially excited slices. We now consider the case where the single noise pulse, applied with each of the two gradient directions, is replaced by multiple applications of the same pulse, but with reduced flip angle. This illustrates the problem of coherent magnetization cre-
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FIG. 3. Image (A) shows the phantom used in the experiments, with a field of view of 53 mm, and (B) the square ROI selected with two applications of the optimized noise pulse (Fig. 2C). Improved outervolume suppression is achieved in (C) using a pulse with a wider slice width (Fig. 2D) applied to select the same ROI. Image (D) shows the ROI selected using a total of 20 noise pulses, each with a flip angle of 50”. Ten pulses were applied with the gradients in each of the x and y directions. The fuzzy areas of signal intensity above and below the ROI in this image are probably an effect of eddy currents in the magnet due to the long gradient pulses used in the presaturation sequence.
ated by the pulses. In the general case, the effect of a discrete RF pulse on a spin isochromat at some particular frequency offset (due either to chemical shift or displacement in a field gradient) may be considered to be a series of rotations about some time-varying axis in a frame rotating at the Larmor frequency. The net result is equivalent to a single rotation by some angle about some other axis in the rotating frame; both the rotation angle and the axis depend on the pulse shape, the power, and the frequency offset. The resulting longitudinal magnetization of the isochromat is then m, = mo( cos*O + sin28 cos 4) = mOcos (Y, where 13is the angle of the net rotation axis with respect to the z axis and 4 is the
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FIG. 4. A pulse sequence for selective imaging using just two noise pulses in the presaturation sequence, and spoiler gradients (dashed) to dephase the transverse magnetization they produce.
rotation angle about this axis, as shown in Fig. 5A; (Yis the resultant flip angle, between the magnetization vector and the z axis. If one neglects relaxation and assumes no reduction in signal from the isochromat due to the dephasing effects of field gradients, multiple applications of the pulse in the presence of a constant field gradient will cause the magnetization vector to move in a circle so that m, varies periodically with the number of pulses. Figure 5C shows the variation of m, for the case 0 = 90”, 4 = 4.5”, where there is a zero in z magnetization after 20 pulses. If, however, there is a delay between the pulses during which the transverse magnetization in the isochromat dephases completely, then after 12pulses the longitudinal magnetization is given by m, = mOcosna, where the magnetization vector is pointing along the z axis at the end of each dephasing delay, shown in Fig. 5B. The longitudinal magnetization approaches zero asymptotically and Fig. 5D shows the case of a 37” flip angle where m, is reduced by 99% after 20 pulses. This latter case is more relevant to a discussion of the effect of noise pulses on spins lying outside the null slice: although larger flip angles are required, errors in flip angle will affect the resultant suppression less critically than in the case where there is no dephasing. Somewhere between these two extremes is the practical case, illustrated by the image of the ROI shown in Fig. 3D. To obtain this, the imaging sequence was preceded by a train of 10 noise pulses in each of the x and y gradient directions with a delay of 300 PS between each pulse (during which the slice gradient remains on) and a flip angle of 50”; the total duration of this presaturation sequence was 50 ms. Some of the transverse magnetization created by each noise pulse is dephased during the interpulse delay, while a certain amount is flipped back along the z axis where it needs to be resuppressed, which accounts for the requirement of a 50” flip angle. The use of
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mz
’ 0.8 0.6 0.4 0.2
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FIG. 5. (A) shows the magnetization trajectory for a single isochromat after application of a noise pulse where the isochromat lies outside the “null” slice. The net effect is to rotate the magnetization by some angle about some axis in the rotating frame. Multiple applications of the pulse cause the magnetization vector to follow a circular path, and m2 is periodic with time. (C) shows this for the case 8 = 90”, I$ = 4.5”, where the curve shape is a quarter cycle cosine waveform. In (B) the transverse magnetization is completely dephased by held gradients between applications of the noise pulse, so m, decreases monotonically. (D) illustrates this for the case 0 = 90”, 4 = 37”, where m, is reduced to 1o/oof m0 after 20 pulses.
longer dephasing delays or larger gradients would not necessarily eliminate this effect, but would produce a more rapid phase variation in the transverse magnetization across the sample so that the magnetization flipped back along the z axis is at a higher spatial frequency (8). The outer-volume suppression has improved in this image, probably because the excitation profile of the noise pulse is somewhat more uniform at lower flip angles. The fuzzy areas of signal intensity above and below the ROI are probably caused by eddy currents due to the long constant gradient pulses used in the presaturation sequence. Figure 6A shows an image of this region in which the gradient strengths in the imaging sequence were increased by a factor of 4 to zoom in on the ROI. This results in improved resolution with the new pixel size of 111 pm; however, insufficiently suppressed signal from the outer volume has aliased into the image and degraded the quality of it. It is possible to remove this aliasing in the “read” direction by reducing the bandwidth of the analog filter in the receiver section of the NMR machine. This
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FIG. 6. Image (A) shows the region of interest of Fig. 3D zoomed by a factor of 4, so that the pixel size is now 111 km. For (B), a circular region of interest was selected, centered at the same place, using a 19step ROISTER sequence of duration 47.5 ms, similar to that shown in Fig. 1. Image (C) shows this region zoomed by a factor of 4, and showing reduced contamination from remnant outer-volume signal, compared to (A). (D) shows the unzoomed ROI (B), displayed with the same number of pixels as the zoomed image (C) using bilinear interpolation, to illustrate the improvement in resolution obtained by acquiring a true zoomed image. No signal averaging was performed to acquire these images, but the gain of the NMR receiver was increased for the zoomed images.
of course does not stop aliasing in the phase-encoding direction and also modulates the resulting image by the transfer function of the filter. In all the experimental work in this paper, the analog filter was kept at a constant width so as to have no effect on the volume selection process. In the ROISTER experiment, each spin isochromat is at a different frequency offset for each application of a noise pulse, since the gradient direction varies with time. Thus, over the whole presaturation sequence an isochromat experiences a range of the noise pulse frequency spectrum, instead ofjust one point as in the constant gradient case above. This means that, since the magnetization vector is rotated by a differ-
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ent angle about a different (randomly varying) axis in the rotating frame at each step in the ROISTER sequence, there is a better chance of the resultant longitudinal magnetization averaging to zero. Figure 6B shows an image of a region in the phantom at the same position as the ROI selected above, acquired using a 2D ROISTER sequence (Fig. 1) with 19 noise pulses, and showing improved suppression over the constant gradient case. Here the total presaturation sequence lasted 47.5 ms and the noise pulse and flip angle were the same as those used for the multiple noise pulse experiment above. The modulus of the total gradient vector was 1.8 G/cm and described a circle in the x-y plane during the sequence. A delay of 300 I.LSbetween each noise pulse was necessary on our equipment in order to shift the transmitter frequency and thereby effect movement of the ROI away from the center of the gradients, and some dephasing of transverse magnetization would have occurred in this time. Figure 6C shows a zoomed image of this region with the same spatial resolution as that in Fig. 6A but with less contamination by signal from the outer volume. Some of the remaining contamination (which causes a mottled effect on the image) is due to signal from saturated spins relaxing back along the z axis during the delay between the ROISTER sequence and the start of the imaging sequence. In this case, with a delay of 5 ms, an average of 0.5% of magnetization would have relaxed back before the start of the spin-echo sequence. Exactly the same volume selection experiment was performed on a uniform phantom in order to measure the degree of outer-volume suppression achieved; this showed that the signal from the outer volume was reduced by 97.5%, with a 6% loss in signal from the selected volume, probably due to the small amount of magnetization excited by the noise pulses within the selected slice. These values (obtained by averaging pixel intensities from images with good signal-to-noise ratios (SNR)) take no account of the random phase variation of remnant magnetization over the outer volume which may give better suppression than indicated here when using ROISTER for localized spectroscopy, where spectral contamination is the vector sum of signal from all over the outer volume. An important feature of using time-varying gradients is the ability to generate conformal regions of interest; this property would be particularly useful for increasing signal in a localized spectroscopy experiment, but can easily be demonstrated by imaging. In Fig. 7A an irregular region of interest is drawn on the image of the phantom used in these experiments. The definition of this region was used to generate gradient waveforms in two dimensions along with the corresponding pulse frequency offsets. These were then used in a ROISTER sequence, with the same parameters as those for the images above, to select the nearest convex approximation to the desired region of interest, Fig. 7B. Figure 7D shows this region zoomed to three times the spatial resolution. A geometrical simulation of the selected region, Fig. 7C, shows the intensity variation around the ROI in the ideal case of complete dephasing of transverse magnetization between noise pulses. The same flip angle was assumed in the simulation as was used in the experiment, so that in the ideal case only 0.02% of magnetization remains, far away from the ROI. Although regions of interest may be defined anywhere within the sample, it is still necessary to display the image centered within the data matrix. In the above images, the region of interest was displaced from the center of the gradients in both the read and the phase-encoding directions. Shifting an image in the frequency domain to
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FIG. 7. An irregular region of interest (A) drawn on an image ofthe whole phantom was used to generate gradient waveforms and frequency offsets for the noise pulses in order to select this region of the sample (B). Image (C) shows the simulated shape of the ROI, calculated using idealized square slice profiles. A zoomed image of this region (D) was acquired with a pixel size of 148 Wm.
center it within the data matrix is equivalent to effecting the corresponding linear phase shifts in both directions in the time domain, prior to Fourier transformation. This may be achieved, in the read direction, simply by offsetting the receiver frequency by an amount equal to the displacement of the ROI from the gradient center, and in the phase-encoding direction by incrementing the receiver phase on each scan ( 1). The shifts in the phase-encoding direction can also of course be applied to the time data during postprocessing or, as was the case for the images presented here, simply by shifting the aliased image the correct amount using the display software on our SUN workstation. Field-of-view reduction may be used in a number of ways. If the region-of-interest dimension is a fraction 1 /n of the whole object dimension, then an image of this region with the same resolution and the same pixel signal-to-noise ratio as those for the whole sample may be acquired, using a conventional 2DFI technique, in 1/n
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times the time required for the whole image. Alternatively, an image of the region with n times the pixel resolution in each dimension but 1 /n2 times the SNR may be acquired in the same time, so that the same SNR as the original image could be achieved in n4 times the imaging time. The compromise made between resolution, acquisition and processing times, and SNR is also affected by the subjective effect of image processing, such as interpolation and filtering, which can improve the perception of small scale features in images. This can be seen in Fig. 6D, which shows an interpolated low-resolution image of the ROI (Fig. 6B) compared with a zoomed image (Fig. 6C) which clearly shows improved resolution, despite the decreased signal-to-noise ratio. The technique for single-shot 2D localization presented here could easily be followed by a fast imaging sequence such as EPI (9) or FLASH ( 10) to perform snapshot zoom imaging, with the possibility of multislice imaging along the selected column. The T2 independence of the technique should also make it useful in many circumstances. The coherent transverse magnetization created by each noise. pulse still limits the degree of saturation which can be achieved with this technique, but some particular combination of noise pulses which produce a more rapid variation in magnetization, “rotating” gradients, and dephasing delays or gradients may prove optimal. ACKNOWLEDGMENTS We thank (A.J.S.dC.).
Dr.
Herchel
Smith
for
an endowment
(L.D.H.
and
T.A.C.)
and
research
studentship
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