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Selective spin imaging in solids
JOURNAL
OF
MAGNETIC
RESONANCE
36, 269-272
(1979)
COMMUNICATIONS Selective Spin Imaging in Soli In 1373, Lauterbur demonstrated the possibility of detecting spatial distributions of spin densities and/or relaxation times using high-resolution NMR techniques in combination with magnetic field gradients (1). Since then, attention has been focused mainly on producing proton images in liquid-like materials. Several methods of imaging, which can be subdivided into overall and selective spin imaging, have been developed. In the first category, the whole object is observed, and two- or threedimensional images are obtained by projection reconstruction techniques (1) or by straightforward Fourier transformation (2). In the second method, only a particular region in a specimen is observed at any given time. The selective method has several advantages: (i) Considerable data storage and handling is avoided, (ii) image distortions due to inhomogeneities in the static and rf magnetic fields and due to nonlinearities in the field gradients are reduced, and (iii) a specific part of the body can be investigated without the necessity of handling data from the whole body. Selective spin imaging has been obtained using rf fields of low intensity (3-s) or fluctuating field gradients (6). The magnitude of the field gradient used in spin imaging depends on the desired spatial resolution and the linewidth of the NMR signal in the absence of a gradient. In liquid-like materials, the natural linewidth varies from less than one to a few hundred hertz. This means that for a spatial resolution of 0.5 mm, ~el~~ra~~ents inust be used with a frequency equivalence of -10 Hz/cm to 5 kHz/cm; these can easily be realized. In solid materials, the situation is much more difficult; the natural linewidth, usually caused by static dipolar interactions, is -10 to 50 kHz. For a resolution of 0.5 mm, this would demand gradients varying from 0.2 to 1 MHz/cm which are difficult to realize, especially for larger objects. The problem can be solved by the application of line-narrowing techniques (7), whereby the dipolar broadening can be reduced by a factor of 100 to 400. The offset produced by the gradients is also reduced, but this reduction factor is much smaller (depending on the specific line-narrowing program, this factor varies from 2”’ to 5 (7)). As a result, a spatial resolution of 0.5 mm can be obtained with gradients which can be one or two orders of magnitude smaller than the gradients needed if no line-narrowing were applied. In fact, the gradients become comparable to those used for liquid-like specimens. The first, and to our knowledge, only spin-imaging experiment in solids to date has een performed by Mansfield and Grannell(8). As a line-narrowing technique, th.ey used a specific sequence (9), by which the whole object is observed, so that this method can be regarded as an overall imaging experiment. Now in solids, as in 269
0022-2364/79/110269-54$02.50/O Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
270
COMMUNICATIONS
liquids, the same considerations hold for overall and selective spin imaging. Therefore, we considered it worthwhile to investigate the possibility of selective spin imaging in solids as well, and it is the purpose of this paper to describe such a metfiod. efore doing so, we note that in solids, selectivity cannot be obtained by rf fields of low intensity, because then line-narrowing effects would not be achieved. Furthermore, the application of fluctuating field gradients in combination with linenarrowing experiments is of doubtful general utility since the residual dipoiar broadening can be an asymmetrical function of the offset (10). The asymmetry would generate nonzero dc contributions from all the spins in an object. Therefore, we used another approach, and searched for a line-narrowing experiment where the residual broadening, and thus the signal amplitude, depends strongly on the resonance offset. The observed signal from an object in the presence of a field gradient is then mainly derived from a small region in the specimen (in spirit, this technique is similar to the EONAR method developed by Damadian et aE. (11) where the liquid state resonance is broadened by an inhomogeneous static gradient except in a smal1 region). By varying the static field or rf frequency, the spin image of the object can be constructed in a selective way. In order to be able to perform this construction it is necessary, of course, that the reduction factor of the offset as a function of offset is recisely known (and preferably constant). We applied the method developed by Yannoni and Vieth (12) as a line-narrowing technique, where a combination of rf irradiation and field modulation is used. For specific values of the rf amplitude, modulation frequency and index, and the offset from resonance (Aw), line-narrowing is obtained. In these experiments, a train of
Resonance
offset
lkHz1
FIG. 1. Lineshape properties of the proton signal of adamantane after line narrowing as a function of resonance offset. (a) Full width at half-maximum (FWHM); and (b) amplitude (in arbitrary units). Experimental conditions: T = 295 K, rf frequency, 23 MHz. The line-narrowing program consisted of a train of 142” pulses (pulse duration 3.8 psec) with equal times (7 = 9.56 ysec) between the leading edge of each pulse. Sinusoidal frequency modulation was used with a period 37 and a modulation index of 2.01. The phase of the modulation was locked to the rf pulse train, and was set such that the center of every (2 + 3n)th puise (n = 0,1,2, .) was close to a node of the sinusoid.
COMMUNICATIONS Liquid
Solid
II
“Sensitive Region”
“Sensitive Region”4 A
FIG. 2. (a) Fourier transform of the proton FID signal from two tubes of water doped with Fe3+ in the presence of a field gradient of 19 kHz/cm; (b), ( c ) , and (d) Fourier transforms of the decays observed during line-narrowing of the proton signal from two tubes of adamantane in the presence of a field gradient of 19 kHz/cm for three different values of the static field. The experimental conditions were the same as given in the caption of Fig. 1. The horizontal scales are corrected for the offset reduction factor of 5.5, and are the same for all the spectra.
identical rf pulses with equal spacings was used and the field modulation was replaced by frequency modulation (1.2). It was found that line-narrowing could be obtain for many values of the different parameters. Different reduction factors for t dipolar broadening and offset as well as different dependences of these factors on the offset resulted. Figure 1 shows the amplitude and full width at half-maximum (FWI-IM) of the narrowed proton signal of adamantane as a function of Ao under the experimental conditions given in the caption. We observe that for Ahw/27r = 21 kHz, the residual linewidth is 40 Hz, corresponding to a reduction factor of -300, and that indeed the linewidth rapidly increases for other values of Aw. The offset was uced by a factor 5.5, independent of the actual value of Aw (this is not shown in the figure). It follows that a sensitive region is selected with a width of - 1 kEIz, so that a field gradient of 20 kHz/cm is sufficient to obtain a spatial resolution of 0.5 mm. An example of selective imaging is given in Fig. 2. As an object we used two parallel tubes with an inner diameter of 1 mm, separated by 3.2 mm. This object subjected to a field gradient of 19 kHz/cm, oriented parallel to the static field parallel to the plane through the tubes. Figure 2a shows the Fourier transform of the proton free induction decay when the tubes were filled with water doped with Fe3+. Figures 2b to d show the result of the line-narrowing method described above applied to the proton signal from two tubes of adamantane at three values of the static field. These values were chosen in such a way that the sensitive region is shifted from the left tube, to a point in between the tubes, to the right tube. The possibility of
272
COMMUNICATIONS
performing selective spin imaging in this way follows clearly from the figure, an full one-dimensional image can easily be obtained by repeating the experiment for more values of the static field. For the construction of two- or three-dimensional images, the field gradients have to be switched into two or three directions during the line-narrowing experiment If the above narrowing technique is used during the whole experiment, the spin density at a “point” in the object is measured (sensitive point method (6)). If, during the last gradient an overall line-narrowing method is used like the one described in Ref. (9)? the spin density of a “line” is detected (sensitive line method (1.3)). A full image is again obtained by changing the value of either the static. field or the rf frequency after each experiment. Since we could apply a field gradient in one direction only, this i could not be investigated further. ACKNOWLEDGMENTS The authors acknowledge the skillful assistance of R. D. Kendrick. authors (R.A.W.) was Summer Faculty Visitor at the IBM Research like to acknowledge the financial support of IBM Holland.
This work Laboratory,
was done while one of the San Jose, and be would
REFERENCES 3. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13.
P. 6. LAUI-ERBUR, Nature 242, 190 (1973). A. KUMAR,D. WELTI? AND R. R. ERNST,~ Magn. Reson. la,69 (1975). A. N.GARROWAY,P.K.GRANNELL,AND P.MANSFIELD,J. Phys.C 7,L.457 (1974). P.C.LAUTERBUR,D.M.KRAMER,W.V.HOUSE,AND C.-N.CHENG,J. Amer. Chem.Soc.91, 6866 (1975). P.MANSFIELD AND A.A.MAuDsLEY,J. Phys. C 9,L409(1976). W. S. HINSHAW, J. Appl. Phys. 47,3709 (1976). M. MEHRING, “High Resolution NMR Spectroscopy in Solids,” Springer-Verlag, Berlin, 1976. P.MANSFIELD AND P.K.GRANNELL,F%~s. Rev.B 12,3618 (1975). P.MANSFIELD,M.J.ORCHARD,D.C.STALKER,ANDK.H.B.RICHARDS, Phys.Rev.B 7,9O (1973). A.N. GARROWAY,P. MANSFIELD, AND D. C. STALKER,%~S. Rev.B 11,121(1975);W.-K. RHIM,D.D.ELLEMAN,AND R.W.VAUGHAN,J. Chem.Phys.59,3740 (1973). R.DAMADIAN,L.MINKOFF,M.GOLDSMITH,M.STANFORD,ANDJ.KOUTCHER,~~'"P~~~~~~ings of the XIXth Congress Ampere, Heidelberg, September 1976,” p. 253. C. S. YANNONI AND H.-M. VIETH, Phys. Rev. Leff. 37,123O (1976); in “Proceedings of the XIX& Colloque Ampere, Heidelberg, September 1976,” p. 437. P.MANSFIELD, A. A.MAUDSLEY,ANDT.BAINES,J. Phys.E 9,271(1976).
IBM Research Laboratory 5400 Cottle Road San Jose, California 95193 eceived March 15, 1979; revised June 25, 1979 * Permanent address, Department Delft 2600 GA, The Netherlands.
of Applied
Physics,
Technical
University
Delft,
PG.
Box
5046,
OF
MAGNETIC
RESONANCE
36, 269-272
(1979)
COMMUNICATIONS Selective Spin Imaging in Soli In 1373, Lauterbur demonstrated the possibility of detecting spatial distributions of spin densities and/or relaxation times using high-resolution NMR techniques in combination with magnetic field gradients (1). Since then, attention has been focused mainly on producing proton images in liquid-like materials. Several methods of imaging, which can be subdivided into overall and selective spin imaging, have been developed. In the first category, the whole object is observed, and two- or threedimensional images are obtained by projection reconstruction techniques (1) or by straightforward Fourier transformation (2). In the second method, only a particular region in a specimen is observed at any given time. The selective method has several advantages: (i) Considerable data storage and handling is avoided, (ii) image distortions due to inhomogeneities in the static and rf magnetic fields and due to nonlinearities in the field gradients are reduced, and (iii) a specific part of the body can be investigated without the necessity of handling data from the whole body. Selective spin imaging has been obtained using rf fields of low intensity (3-s) or fluctuating field gradients (6). The magnitude of the field gradient used in spin imaging depends on the desired spatial resolution and the linewidth of the NMR signal in the absence of a gradient. In liquid-like materials, the natural linewidth varies from less than one to a few hundred hertz. This means that for a spatial resolution of 0.5 mm, ~el~~ra~~ents inust be used with a frequency equivalence of -10 Hz/cm to 5 kHz/cm; these can easily be realized. In solid materials, the situation is much more difficult; the natural linewidth, usually caused by static dipolar interactions, is -10 to 50 kHz. For a resolution of 0.5 mm, this would demand gradients varying from 0.2 to 1 MHz/cm which are difficult to realize, especially for larger objects. The problem can be solved by the application of line-narrowing techniques (7), whereby the dipolar broadening can be reduced by a factor of 100 to 400. The offset produced by the gradients is also reduced, but this reduction factor is much smaller (depending on the specific line-narrowing program, this factor varies from 2”’ to 5 (7)). As a result, a spatial resolution of 0.5 mm can be obtained with gradients which can be one or two orders of magnitude smaller than the gradients needed if no line-narrowing were applied. In fact, the gradients become comparable to those used for liquid-like specimens. The first, and to our knowledge, only spin-imaging experiment in solids to date has een performed by Mansfield and Grannell(8). As a line-narrowing technique, th.ey used a specific sequence (9), by which the whole object is observed, so that this method can be regarded as an overall imaging experiment. Now in solids, as in 269
0022-2364/79/110269-54$02.50/O Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
270
COMMUNICATIONS
liquids, the same considerations hold for overall and selective spin imaging. Therefore, we considered it worthwhile to investigate the possibility of selective spin imaging in solids as well, and it is the purpose of this paper to describe such a metfiod. efore doing so, we note that in solids, selectivity cannot be obtained by rf fields of low intensity, because then line-narrowing effects would not be achieved. Furthermore, the application of fluctuating field gradients in combination with linenarrowing experiments is of doubtful general utility since the residual dipoiar broadening can be an asymmetrical function of the offset (10). The asymmetry would generate nonzero dc contributions from all the spins in an object. Therefore, we used another approach, and searched for a line-narrowing experiment where the residual broadening, and thus the signal amplitude, depends strongly on the resonance offset. The observed signal from an object in the presence of a field gradient is then mainly derived from a small region in the specimen (in spirit, this technique is similar to the EONAR method developed by Damadian et aE. (11) where the liquid state resonance is broadened by an inhomogeneous static gradient except in a smal1 region). By varying the static field or rf frequency, the spin image of the object can be constructed in a selective way. In order to be able to perform this construction it is necessary, of course, that the reduction factor of the offset as a function of offset is recisely known (and preferably constant). We applied the method developed by Yannoni and Vieth (12) as a line-narrowing technique, where a combination of rf irradiation and field modulation is used. For specific values of the rf amplitude, modulation frequency and index, and the offset from resonance (Aw), line-narrowing is obtained. In these experiments, a train of
Resonance
offset
lkHz1
FIG. 1. Lineshape properties of the proton signal of adamantane after line narrowing as a function of resonance offset. (a) Full width at half-maximum (FWHM); and (b) amplitude (in arbitrary units). Experimental conditions: T = 295 K, rf frequency, 23 MHz. The line-narrowing program consisted of a train of 142” pulses (pulse duration 3.8 psec) with equal times (7 = 9.56 ysec) between the leading edge of each pulse. Sinusoidal frequency modulation was used with a period 37 and a modulation index of 2.01. The phase of the modulation was locked to the rf pulse train, and was set such that the center of every (2 + 3n)th puise (n = 0,1,2, .) was close to a node of the sinusoid.
COMMUNICATIONS Liquid
Solid
II
“Sensitive Region”
“Sensitive Region”4 A
FIG. 2. (a) Fourier transform of the proton FID signal from two tubes of water doped with Fe3+ in the presence of a field gradient of 19 kHz/cm; (b), ( c ) , and (d) Fourier transforms of the decays observed during line-narrowing of the proton signal from two tubes of adamantane in the presence of a field gradient of 19 kHz/cm for three different values of the static field. The experimental conditions were the same as given in the caption of Fig. 1. The horizontal scales are corrected for the offset reduction factor of 5.5, and are the same for all the spectra.
identical rf pulses with equal spacings was used and the field modulation was replaced by frequency modulation (1.2). It was found that line-narrowing could be obtain for many values of the different parameters. Different reduction factors for t dipolar broadening and offset as well as different dependences of these factors on the offset resulted. Figure 1 shows the amplitude and full width at half-maximum (FWI-IM) of the narrowed proton signal of adamantane as a function of Ao under the experimental conditions given in the caption. We observe that for Ahw/27r = 21 kHz, the residual linewidth is 40 Hz, corresponding to a reduction factor of -300, and that indeed the linewidth rapidly increases for other values of Aw. The offset was uced by a factor 5.5, independent of the actual value of Aw (this is not shown in the figure). It follows that a sensitive region is selected with a width of - 1 kEIz, so that a field gradient of 20 kHz/cm is sufficient to obtain a spatial resolution of 0.5 mm. An example of selective imaging is given in Fig. 2. As an object we used two parallel tubes with an inner diameter of 1 mm, separated by 3.2 mm. This object subjected to a field gradient of 19 kHz/cm, oriented parallel to the static field parallel to the plane through the tubes. Figure 2a shows the Fourier transform of the proton free induction decay when the tubes were filled with water doped with Fe3+. Figures 2b to d show the result of the line-narrowing method described above applied to the proton signal from two tubes of adamantane at three values of the static field. These values were chosen in such a way that the sensitive region is shifted from the left tube, to a point in between the tubes, to the right tube. The possibility of
272
COMMUNICATIONS
performing selective spin imaging in this way follows clearly from the figure, an full one-dimensional image can easily be obtained by repeating the experiment for more values of the static field. For the construction of two- or three-dimensional images, the field gradients have to be switched into two or three directions during the line-narrowing experiment If the above narrowing technique is used during the whole experiment, the spin density at a “point” in the object is measured (sensitive point method (6)). If, during the last gradient an overall line-narrowing method is used like the one described in Ref. (9)? the spin density of a “line” is detected (sensitive line method (1.3)). A full image is again obtained by changing the value of either the static. field or the rf frequency after each experiment. Since we could apply a field gradient in one direction only, this i could not be investigated further. ACKNOWLEDGMENTS The authors acknowledge the skillful assistance of R. D. Kendrick. authors (R.A.W.) was Summer Faculty Visitor at the IBM Research like to acknowledge the financial support of IBM Holland.
This work Laboratory,
was done while one of the San Jose, and be would
REFERENCES 3. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13.
P. 6. LAUI-ERBUR, Nature 242, 190 (1973). A. KUMAR,D. WELTI? AND R. R. ERNST,~ Magn. Reson. la,69 (1975). A. N.GARROWAY,P.K.GRANNELL,AND P.MANSFIELD,J. Phys.C 7,L.457 (1974). P.C.LAUTERBUR,D.M.KRAMER,W.V.HOUSE,AND C.-N.CHENG,J. Amer. Chem.Soc.91, 6866 (1975). P.MANSFIELD AND A.A.MAuDsLEY,J. Phys. C 9,L409(1976). W. S. HINSHAW, J. Appl. Phys. 47,3709 (1976). M. MEHRING, “High Resolution NMR Spectroscopy in Solids,” Springer-Verlag, Berlin, 1976. P.MANSFIELD AND P.K.GRANNELL,F%~s. Rev.B 12,3618 (1975). P.MANSFIELD,M.J.ORCHARD,D.C.STALKER,ANDK.H.B.RICHARDS, Phys.Rev.B 7,9O (1973). A.N. GARROWAY,P. MANSFIELD, AND D. C. STALKER,%~S. Rev.B 11,121(1975);W.-K. RHIM,D.D.ELLEMAN,AND R.W.VAUGHAN,J. Chem.Phys.59,3740 (1973). R.DAMADIAN,L.MINKOFF,M.GOLDSMITH,M.STANFORD,ANDJ.KOUTCHER,~~'"P~~~~~~ings of the XIXth Congress Ampere, Heidelberg, September 1976,” p. 253. C. S. YANNONI AND H.-M. VIETH, Phys. Rev. Leff. 37,123O (1976); in “Proceedings of the XIX& Colloque Ampere, Heidelberg, September 1976,” p. 437. P.MANSFIELD, A. A.MAUDSLEY,ANDT.BAINES,J. Phys.E 9,271(1976).
IBM Research Laboratory 5400 Cottle Road San Jose, California 95193 eceived March 15, 1979; revised June 25, 1979 * Permanent address, Department Delft 2600 GA, The Netherlands.
of Applied
Physics,
Technical
University
Delft,
PG.
Box
5046,