Mogneric Rezonance Imaging. Vol. 10, pp. 755-763, Printed in the USA. All rights reserved.

1992 Copyright 0

0730-725X/92 $5.00 + .oO 1992 Pergamon Press Ltd.

l Session: Plenary Lecture

NMR IMAGING

OF SOLIDS WITH MAGIC ANGLE SPINNING W.S.

VEEMAN AND G. BIJL

Physikalische Chemie FB 6, UniversiCit-GH-

Duisburg, Lotharstrasse

1, 4100 Duisburg 1, Germany

Different aspects of solid state NMR imaging are reviewed, with emphasis on imaging in combination with line narrowing, especially in combination with magic angle spinning. Experimental results obtained with the latter technique are discussed, along with the implications of magic angle spinning on slice selection. Keywords: NMR imaging; Solid state imaging; Imaging and line narrowing; Polymer blends; Solid state imaging and slice selection.

INTRODUCTION

intrinsic linewidth of the spins in the object is Aw and the applied gradient strength G. To distinguish points A and B in Fig. 1 we require that

Nuclear magnetic resonance (NMR) imaging is a wellestablished technique for use as a diagnostic tool in medicine and for the study of biological systems. For solid materials the technique is not yet as fully developed due to the fact that the large intrinsic NMR linewidth interferes with the encoding of the nuclear spins in different locations by the magnetic field gradient. Although fluids in these solid materials, naturally present or absorbed into it, can be imaged following the same techniques as used in medicine, imaging of the really rigid solid material requires special conditions. In this review first some basic techniques for the imaging of solids will be compared, and then our attempts to use magic angle sample spinning (MAS) in combination with imaging will be discussed.

AwryGAx

(1)

Since we shall later see that the smallest gradient in accordance with Eq. (1) has to be preferred, we find for the linear resolution Ax:

Ax=&

YG .

Clearly, Eq. (2) indicates that when the linewidth Aw increases, the gradient strength G also has to be increased, at least when the resolution Ax is to be kept constant. Let us now, again for a simple one-dimensional object, compare a case with small and large linewidth Aw (Figs. 2A and 2B). For constant Ax, in these two situations a small and large gradient G has to be employed. The spread in resonance frequencies is clearly greater for the larger gradient, and therefore the bandwidth (BW) of the NMR receiver has to be chosen in accordance with the gradient strength. The integrated signal intensity in the frequency spectra of Fig. 2 is constant and determined by the total number of spins in the object and by, of course, the number of repetitions of the experiment, or the number of scans (NS). When we assume the number of spins in the object fixed, then the integrated voltage signal-to-noise ratio S/N is proportional to

THE RELATION BETWEEN NMR LINEWIDTH, IMAGE RESOLUTION, AND IMAGE SIGNAL-TO-NOISE RATIO Figure 1 shows a simple one-dimensional object along the x axis. An image is required of this object with a spatial resolution Ax, while we assume that the

delta

.

x

S

N=m

Fig. I. A linear object along x. 755

NS

z&E

(3)

Magnetic Resonance Imaging l Volume 10, Number 5, 1992

756

a b

11 --I

Fig. 2. An idealized NMR spectrum of the object in Fig. 1 with (A) a small and (B) a large gradient.

where NS is the number of acquisitions and BW the receiver bandwidth, which is proportional to the gradient G. We adopted here the view that the noise is of thermal origin and proportional to X&W. For equal resolution Ax and equal S/N of an image we find: Experimental

time ot NMR linewidth

.

(4)

This important relation has been derived for a onedimensional imaging experiment. Since the effect of the increased bandwidth occurs only during the detection of the NMR signal, in principle the above result does not change when one considers two- or threedimensional imaging, employing Fourier transform or projection reconstruction techniques. This in contrast to the situation in which one wants to increase the resolution at the same signal-to-noise ratio. For instance, when in a one-dimensional imaging experiment one desires an improvement of the resolution by a factor of 2, the number of spins that contribute to the signal intensity of one pixel decreases with the same factor of 2, and to obtain the same signal-to-noise ratio, the experimental time has to increase by a factor of 4. For one dimension, therefore, the relation Experimental

time oc (resolution)-’

(5)

exists, when one defines the resolution as the minimum

distance that can be resolved. Now this relation is not independent of the dimensionality of the imaging experiment; for three dimensions the number of spins decreases with the volume of the resolved element and Experimental

time ot (resolution)-‘j

.

(6)

Eq. (2) makes clear that when the NMR linewidth is large, we can basically distinguish two different approaches to solid-state NMR imaging: (1) using large gradients or (2) using line-narrowing techniques in combination with imaging. In the case 1, Eq. (4) tells us that for a constant resolution the experimental time is proportional to the linewidth (or gradient) or that for the same experimental time one has to sacrifice resolution relative to approach 2.

A nice example of approach 1 is the STRAFI technique, ’ in which the huge field gradient (depending on the homogeneous field, up to 100 T/m) in a region outside but close to the magnet is employed. This gradient of course cannot be switched nor can its direction be changed. Therefore, the sample is rotated in this gradient in subsequent experiments and the back projection reconstruction technique is used. To enhance the signal-to-noise ratio, a spin-echo train is coadded. Although this technique seems to work very well, we feel that in view of the above consideration, it cannot be the experiment of choice if one wants to obtain the highest possible resolution in a rigid sample. In the worst case, the solid ‘H linewidth can be a factor of lOOO-10,000 times higher than the corresponding linewidth in a specimen with liquidlike spins. Another disadvantage of this technique is that it appears very difficult to obtain chemical shift information, and therefore chemical shift imaging seems to be impossible. Another ingenious example of the use of an imaging technique, which is straightforward in the sense that no line narrowing is applied, is formed by NMR imaging in combination with multiple quantum NMR.2 A multiple quantum coherence of order n evolves n times faster in a gradient than the usual single-quantum coherences. The effective gradient is therefore n times as large as the applied gradient. Since it is possible in rigid solids with strongly dipolar coupled spin systems to generate multiple quantum coherences with orders far beyond 10 or 20, a very large gradient can easily be generated. Although this technique by definition is very well suited for solid-state imaging, the disadvantage of course is that the signal intensity of these high-order multiple quantum coherences is lower than that of the single-quantum coherences, and it seems that what one gains in gradient strength one loses in signal intensity. A technique in many respects intermediate between the two abovementioned approaches has been proposed by Emid and Creighton. 3 For the other approach, the line-narrowing approach, many different techniques have been described. They all have in common that some kind of solid-state NMR line narrowing is used, and they can be most easily classified by the line-broadening interactions that are averaged out. NMR line broadening of solid amorphous or polycrystalline samples can be caused by the following interactions: 1. The dipolar coupling between spins 2. The anisotropy of the chemical shift 3. Quadrupole interactions for spins with magnetic quantum number I > 1

NMR of solids with magic angle spinning 0 W.S. VEEMAN AND G. BIJL

4. Bulk magnetic susceptibility 5. Distributions of isotropic chemical shifts. The last three causes for line broadening are not considered here since we limit ourselves to nuclei with Z = 4 and we assume that the line-broadening effects of the bulk susceptibility and possible distributions of the chemical shift are either negligible or are sufficiently averaged out by the line-narrowing techniques that are applied to eliminate the effect of one or both of interactions 1 and 2. The solid-state imaging techniques in combination with line narrowing can now be classified in three groups: l

l

l

Group Z Only the dipolar interaction is averaged to zero. To this group belong imaging techniques4-* that employ the same homonuclear line-narrowing techniques as are used for high-resolution solid-state NMR: multiple pulse NMR techniques like WAHUHA, MREV-8, and the Lee-Goldburg experiment. The chemical shift may be effected (scaled) by the line-narrowing techniques of this group, but the anisotropic and isotropic part are not averaged to zero. These techniques form the oldest approaches to solid-state imaging and were already applied by Mansfield and co-workers in 1973!4 In addition to the high-resolution techniques mentioned, other techniques that effectively narrow the dipolar linewidth also exist.9 Group ZZ The dipolar interaction is averaged out, and at the same time the total chemical shift (anisotropic and isotropic part) is eliminated. Since the Hamiltonians of the chemical shift and a gradient behave similarly, the gradient has to be modulated in time (oscillatory gradients or pulsed gradients) for the techniques in this group. When all interactions except the interaction with the gradient are suppressed, it seems that the time evolution of the spins has been halted; therefore, the name time suspension is used for these techniques. lo Group ZZZThe dipolar interaction and the anisotropic chemical shift is eliminated, leaving the isotropic chemical shift intact. This can be obtained by mechanical rotation of the object around an axis that makes the magic angle (54.7”) with the external magnetic field.” The limitation of this technique is that it can only effectiveIy remove the dipolar broadening when the spinning speed exceeds the dipolar linewidth. Although considerable progress is made with fast MAS, frequencies over 30 kHz are reported; for really rigid solids the MAS technique has to be combined with another means of eliminating the dipolar broadening. To eliminate the anisotropic part of the chemical shift, relatively modest

157

spinning speeds in general are sufficient. For solids with internal motions, for example, elastomers, where the dipolar interactions are partly averaged out by the molecular motions, the MAS technique is, as we shall show, capable of eliminating most of the line broadening. In the following we shall describe and discuss our attempts to combine imaging with MAS. IMAGING

AND MAS RESULTS

When MAS is applied to the sample in order to remove NMR line broadening, the unavoidable fact is that the object one wants to image is rotating fast around an axis that makes the magic angle with the external field. When an object is rotated through a static field gradient, spins in the object undergo the effect of an oscillating magnetic field, which cause the NMR intensity to spread out in a centerband and many spinning sidebands. Although imaging of rotating objects in a static gradient or of a static object in a rotating gradient has been described, 12-15we want to discuss here a technique that makes use of a gradient that rotates synchronously with the spinner. Although this makes the experimental setup somewhat more complicated, conceptually the imaging experiment is then very simple, since in a frame that rotates with the spinner the gradient is static and the imaging can proceed as usual. In addition, we shall see that the magic angle experiment in all but one aspect is very forgiving for experimental missettings, and therefore the experimental setup is not critical. The experimental setup is shown schematically in Figs. 3, 4, and 5.16,” Figure 3 shows how a rotating field gradient is composed from two linearly oscillating gradients along x and y. Figure 4 shows schemati-

dBz,dI’ lb dBz/dy

/’

,’ .’

,‘-

.------.._ 1 ‘.

‘,

,’

/

Y

‘\I \

/,’ ,’

‘~

,’

~.

‘.._

/-.

,’

i/:

Fig. 3. By combining an oscillatory field gradient along x and y, a rotary gradient in the xy plane is obtained.

758

Magnetic Resonance Imaging 0 Volume 10, Number 5, 1992

54.7

1850 Hz is sufficient to average both the dipolar and the chemical shift broadening. Figure 7 shows the image of two polyethylene particles. ” Since in polyethylene the dipolar broadening is severe, MAS alone is not sufficient to obtain the required line narrowing. In addition to the MAS, here MREV-8 is employed. The next example is an image of polybutadiene. Polybutadiene with MAS shows two resolved proton lines (Fig. 8), and due to these differences in chemical shift a severely distorted image is obtained (Fig. 9). The image of Fig. 10 results after a deconvolution procedure” in which data from three experiments are combined: an experiment without a gradient, an experiment with a positive gradient, and one with a negative gradient. This procedure is also applied to the applications displayed in the following figures. Figure 11 shows an image of polystyrene powder; due to the spinning the powder distributes itself more or less in a circle along the wall of the spinner. Figure 12 shows the image of a polyisoprene sample in which with a laser five holes with a diameter of about 200 pm at equidistant positions were burnt. As the image shows, the spinning at a rate of 5 kHz has a dramatic effect on the holes: the inner hole is enlarged while the two outer holes are no longer open due to the flow of mass. With a spinning frequency of 5 kHz the centrifugal acceleration is about IO’ g at the inner wall! Figure 13 shows the image of a polymer blend, polystyrenepolybutadiene. l9 Since only MAS is used for the line narrowing, the NMR line of the rigid polystyrene is not narrowed and the image is due to polybutadiene only. The image clearly shows that the blend is not compatible.

degree

Fig. 4. A schematic drawing of the quadrature

coil set.

tally the arrangement of the quadrature coils. Figure 5 shows how from the optical sensing device that is usually used to count the spinner frequency, an audiofrequency is derived that drives, after amplification and phase splitting, two audio amplifiers (180 W each) connected to a set of quadrature gradient coils. The following figures show applications of the imaging technique in combination with a synchronously rotating field gradient. Figure 6 shows the image of two silicone rubber particles.r6 In this application two-dimensional Fourier imaging is used. The shift of the gradient over 90” from the evolution period to the detection period, as required for the Fourier imaging technique, corresponds in this case to a phase shift of the two audiofrequency signals that drive the quadrature coils. For silicone rubber the MAS frequency of

Drive Air valve

Spin Fix

Q

0

Gates

c ‘114 0

optic-

-

4 shifter

Low Pass -

go*+ Filter l80’@

0+360’in 5 12 steps

.2+20

kHz

+I+-1 in 5 12 steps

18OW D

l under computer

control

Fig. 5. The audiofrequency that drives the quadrature coils is derived from the signal obtained from the spinner optical sensor.

NMR

of solids with magic angle spinning 0 W.S. VEEW

2DFI

AND G. BUL

759

Silicone rubber

MAS 1850Hz t

-6

a

.

-4

-2

-

L

Omm

.

*

.

2 ’

.

4 -

-

6

.*

IO-

-6 -4

a-

m-2

4-

--4

t

I 2

1

. 4

Fig. 6. Two-dimensional

F2

&I

8

10

t

Fourier imaging of two silicone rubber particles.

THE IMPLICATION OF IMAGING AND LINE NARROWING Although the previous examples show that the combination of imaging, MAS, and multiple pulse linenarrowing functions rather well, we here want to discuss the advantages and limitations of this tech-

It is well-known that the use of multiple pulse decoupling during the imaging is limited due to the fact that the multiple pulse technique in a gradient suffers from its offset dependence.” At large offsets the decoupling power of such pulse sequences decreases, and therefore, for an object in a gradient, the line narrowing will not be uniform. We can define a maximum

nique.

Magnetic Resonance Imaging 0 Volume 10, Number 5, 1992

760

1 1

2

3

4

5mm

Fig. 7. The image of two polyethylene particles, obtained with MAS and MREV-8 line narrowing. 1

2

3

4mm

Fig. 10. The image of Fig. 9, deconvoluted. details.

See text for

offset frequency F above which the line narrowing is no longer acceptable. When the inner radius of our spinner is r, we then have the relation static

0

1

2

MAS 5kHz 3kHz

Fig. 8. The static and MAS narrowed ‘H spectrum of polybutadiene.

yGmaxr I F

(7)

At the same time the gradient is scaled by the multiple pulse technique, just as the chemical shift. Therefore the effective gradient is g =

Fig. 9. The image of a ring of polybutadiene in the spinner, distorted due to the presence of two chemically shifted resonance.

.

I

,

1

2

(8)

Gnax

I

3

I

4 mm

Fig. 11. The image of polystyrene powder.

NMR of

solids with magic angle spinning 0 W.S.

2mm 1.

Fig. 12. The image of a piece of polystyrene with five holes of about 200 pm. The spinning causes a flow of mass. See text for details.

where S is the scaling factor belonging to the particular pulse technique. With these relations and Eq. (2) we can calculate the resolution that one can hope to achieve with a multiple pulse sequence in a static gradient: Ax=

Aor -

VEEMAN AND G. BUL

761

these simple arguments show that the combination of multiple pulse NMR and imaging with static gradients, as we assumed so far, will never result in high-resolution solid-state imaging. By making the gradients timedependent, pulsed or oscillatory gradients, one can overcome these limitations. The combination of MAS, multiple pulse NMR, and pulsed or oscillatory gradients has not yet been made and will therefore not be considered here. With respect to the above-mentioned problems, imaging with MAS alone is relatively easy. The line narrowing by MAS is not offset-dependent, and the gradient is not scaled (see, however, the following section). The effect of the following hardware errors in the MAS imaging experiment have been investigated:2”22 The amplitude of the two quadrature field gradients are unequal, because of poor adjustment or imperfect coils. The coils do not generate perfectly perpendicular fields, because of hardware errors or a phase imbalance in the signals that drive the coils. The spinner center does not coincide with the center of the field. The phase difference between the rotating gradient and the spinner is not constant in time.

ySF ’

With the values r = 1.75 mm, linewidth Ao = 200 Hz, S = 4~6 for MREV-8, and F = 3000 Hz, we find a maximum resolution of 250 pm. Although one can argue that the value of F has been estimated somewhat too low, the other values are realistic, and therefore

4-

3-

The effect of most of these errors is not very dramatic. Mainly spinning sideband images at a frequency 2w, are developed, where o, is the spinning frequency. In addition, the spinning sideband images are averaged out when the RF pulsing is not synchronized with the spinner. In some cases small frequency shifts of the centerband image can occur. The only critical part of the experiment is the last error, phase jitter between the rotating gradient and the spinner. It can be calculated that with a jitter between the spinner and the gradient of 10” the resolution at the site of the inner radius of the spinner is about 150 pm. Such a jitter can exist due to the noise of the signal derived from the optical spinning speed-counting device. In order to really obtain a resolution of 50 pm or better over the whole sample, this jitter should be less than 3”.

2-

mm

SLICE SELECTION

AND MAS

l-

-!

Oo

I

1

2mm

3

4

Fig. 13. The image of a blend of polystyrene and polybutadiene. Because only MAS is applied, only the polybutadiene is imaged, since the polystyrene dipolar line broadening is too large.

The images shown above are all two-dimensional images of a slice of material of approximately 0.5 mm thickness. Electronic slice selection would clearly be preferable. We attempted to do so with a cylindrical gradient coil, symmetrically placed with respect to the stator of the magic angle assembly. Figure 14 schematically shows the setup of the rotor and gradient coil

MagneticResonanceImaging0 Volume10, Number5, 1992

162

-Ti

I

Hi

A

B

c

//\

,’

/

\

/’

/‘,z

4?y,;’ \

< -( ,,,/

F

/’

C/

,/’

/

b/H’

Fig. 15. The effect of small unwanted gradient fields in the magic angle setup. See text for details. Fig. 14. Schematic presentation of the magnetic field directions in the rotor due to a z gradient.

and the directions of the magnetic field due to the gradient coil at six sites in the rotor. On the rotor axis these fields are parallel to this axis and form a perfect gradient; however, off-axis the fields have the tendency to point toward the rotor axis. For the dimensions that correspond to our experimental configuration, at 1.5 mm off-axis at the ends of the spinner the angle between the gradient fields and the rotor axis is about 10”. This has important consequences for the slice selection, as is indicated in Fig. 15. In this figure two situations are indicated. On the left side of this figure the rotor axis and gradient axis are parallel to the magnetic field direction. The gradient field direction is indicated in three positions: A, B, and C. It happens that the components of these fields parallel to the external field are approximately equal; the perpendicular components can be neglected. This situation changes when the rotor axis makes the magic angle with the external field (see the right side of Fig. 15). Now the components parallel to the external field are very unequal: when the fields in A and C make an angle of 10” with the rotor axis, then the field component in A, parallel to the external field, is 0.75 times this component in B and the corresponding component in C is 1.22 times the field in B. So the slight errors in the gradient field, which normally can be neglected when the gradient coil has its axis parallel to the external field, have a strong effect here. When the rotor rotates around the magic angle, strong spinning sidebands are generated due to these errors. A more serious effect is

that on excitation with an infinitely narrow excitation frequency, practically the whole spinner is excited because during the spinner rotation most of the spins sample a range of gradient fields. Although one might think that this problem does not exist when the gradient coil is not parallel to the spinner assembly but aligned along the external field axis, this is not true. We tried to solve this problem with an extra coil. Since the field component in Fig. 15 perpendicular to the plane of B and the rotor axis z is harmless, we can with a field gradient in the plane of B and z, perpendicular to z, compensate the unwanted components. The improvement we reached is about a factor 10, but nevertheless by selective excitation a slice of approximately 0.5-mm thickness is still excited. This is not sufficient, and other methods have to be found in order to combine selective excitation and MAS. CONCLUSIONS For high-resolution solid-state imaging some form of line narrowing has to be applied. For solids with a small or moderate dipolar interaction, MAS is an excellent technique to combine with imaging. The combination with slice selection, however, poses problems that have yet to be solved. REFERENCES 1. Sarnoilenko, A.A.; Zick, K. Stray field imaging of solids (STRAFT). Bruker Reports 1:40-41; 1990. 2. Garroway, A.N.; Baum, J.; Munowitz, M.G.; Pines, A. NMR imaging in solids by multiple-quantum resonance. J. Magn. Reson. 60:337-341; 1984.

NMR

of solids with magic angle spinning 0

3. Emid, S.; Creighton, J.H.N. High resolution NMR imaging in solids. Physica 128B:81-83; 1985. 4. Mansfield, P.; Grannell, P.K. Diffraction and microscopy in solids and liquids by NMR. Phys. Rev. B 12: 36183634; 1975. 5. Wind, R.A.; Yannoni, C.S. Selective spin imaging in solids. J. Magn. Reson. 36:269-272; 1979. 6. Chingas, G.C.; Miller, J.B.; Garroway, A.N. NMR images of solids. .I Magn. Reson. 66:530-535; 1986. 7. De Luca, F.; Maraviglia, B. Magic angle NMR imaging in solids. J. Magn. Reson. 67:169-172; 1986. 8. De Luca, F.; Nuccetelli, C.; De Simone, B.C.; Maraviglia, B. NMR imaging of a solid by the magic angle rotating frame method. .I Magn. Reson. 69:496-500; 1986. 9. McDonald,

P. J.; Attard, J. J.; Taylor, D.G. A new approach to the NMR imaging of solids. J. Magn. Reson. 72:224-229;

1987.

10. Cory, D.G.; Miller, J.B.; Garroway, A.N. Time suspension multiple pulse sequences: Application to solid state imaging. .I. Magn. Reson. 90:205-213; 1990. 11. Andrew, E.R. The narrowing of NMR spectra of solids by high-speed specimen rotation and the resolution of chemical shift and spin multiplet structures for solids. Prog. NMR Spectroscopy 8: l-39; 197 1. 12. Matsui, S.; Kohno, H. NMR imaging with a rotating field gradient. J. Magn. Reson. 70: 157-162; 1986. 13. Matsui, S.; Sekihara, K.; Shiono, H.; Kohno, H. A

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G.

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static NMR image of a rotating object. J. Magn. Reson. 77:182-186; 1988. 14. Ogura, Y.; Sekihara, K. Static imaging of a rotating object, image quality improvement using J2 synthesis. J. Magn. Reson. 88:359-363; 1990. 15. Ogura, Y.; Sekihara, K. Static imaging of a rotating object. J. Magn. Reson. 92:490-503; 1991.

16. Cory, D.G.; van OS, J.W.M.; Veeman, W.S. NMR images of rotating solids. J. Magn. Reson. 76:543-547; 1988. 17. Cory, D.G.; Reichwein, A.M.; van OS, J.W.M.; Veeman, W.S. NMR images of rigid solids. Chem. Phys. Lett. 143:467-470; 1988. 18. Cory, D.G.; Reichwein, A.M.; Veeman, W.S. Removal of chemical shift effects in NMR imaging. .I, Magn. Reson. 80:259-267; 1988. 19. Cory, D.G.; de Boer, J.C.; Veeman, W.S. MAS ‘H

NMR imaging of polybutadiene/polystyrene Macromolecules

22:1618-1621;

blends.

1989.

20. Garroway, A.N.; Mansfield, P.; Stalker, D.C. Limits to resolution in multiple pulse NMR. Phys. Rev. 11: 121-

138; 1975. 21. Cory, D.G.; Veeman, W.S. Magnetic field gradient imperfections in NMR imaging of rotating solids. J. Magn. Reson. 82:374-381; 1989. 22. Veeman, W.S.; Cory, D.G. ‘H NMR imaging of solids with magic angle spinning. Adv. Magn. Reson. 13:4355; 1989.