MAGNETIC RESONANCE IN MEDICINE
19, 321-326 (1991)
Anisotropy in Diffusion-Weighted MRI * MICHAELE. MOSELEY,JOHNKUCHARCZYK, HALEHS. ASGARI, AND DAVIDNORMAN Department of Radiology, University of California, Sun Francisco, California 94143 Received February I , 1991 Diffusional anisotropy of water protons, induced by nonrandom, directional barriers which hinder or retard water motion, is measurable by MRI. Faster water diffusion was observed when the diffusion-sensitizinggradient direction paralleled the long axes of white matter tracts, indicative of fewer bamers to water motion. Diffusion perpendicular to this 3xis was as much as four times slower. Anisotropy was seen pre- and postmortem in all axial, sagittal, and coronal planes, with and without cardiac gating. Ordering has also been observed in feline optic nerve and in human peripheral nerves. Utilization of this technique can greatly improve understanding and assessment of demyelinating disorders, of white matter infarcts and neoplasms, and of neonatal brain and spinal cord development. 0 1991 Academic Press, Inc.
INTRODUCTION
Measurement of diffusion using pulsed-gradient spin-echo ( Stejskal-Tanner ) NMR methods as well as the assessment of anisotropic-restricted diffusion was reported more than 20 years ago ( 1 , 2). In vivo diffusion MRI, which can map microscopic motion of water protons, has only recently been studied ( 3 - 8 ) . The lack of large gradient strengths (those exceeding 1 g/cm) and the problems created by excessive eddy currents inherent in large-bore magnet gradients have impeded these studies. Most diffusion-weighted MRI sequences have been modifications of the spin-echo paired-gradient Stejskal-Tanner ( ST) sequences. All spin dephasing caused by the first diffusion-sensitizing gradient pulse is refocused by the second diffusion-sensitizing gradient pulse for stationary spins. Moving incoherent spins will not completely refocus and will attenuate the observed signal. The observed echo intensity S(TR, TE, Gi) can be expressed as S(TR, TE, Gi)
= S(co, O,O)exp(-TE/T2)(
+ exp(-
1 - 2 exp(- (TR
-
TE/2)/T1)
TR/T1))exp(y2d2Gi2(A- d/3)ADC),
where S(co, 0,O) is the signal at TE = 0, TR = co . The terms TE, TI and T2 are the echo time and spin-lattice and spin-spin relaxation times, respectively, y is the gyromagnetic ratio, d and Gi are the duration and the amplitude of square diffusionsensitizing directional ST gradient pulses along i, A is the time interval between the * Presented at SMRM Workshop on Future Directions in MRI of Diffision and Microcirculation,Bethesda, MD, June 7 and 8, 1990. 32 I
0740-3 194/9 I $3.00 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.
322
MOSELEY ET AL.
leading edges of the diffusion-sensitizing gradients pulses and the term ADC is the proton apparent diffusion coefficient, which can be thus determined ( 1-4); In S(TE, Gi)/S(TE, 0) = -y2d2Gi2(A - d/3)ADC
=
-bADC,
where a gradient attenuation factor ( 3 , 4 )b is defined as y d2Gi’( A - d / 3 ) for square gradient pulses absent of gradient cross-terms ( I , 2). The direction of the diffusionsensitizing gradient pulses can be controlled and the apparent diffusion along the respective direction can be measured. Full assessment of anisotropy of diffusion requires measurement of the diffusion tensor ( a scalar diffusion rate as a function of direction). The presence of nonrandom barriers will impart anisotropic proton diffusion resulting in a slower ADC for protons along a more hindered direction compared to a direction in which the spins can translate freely along the observed mean pathlength. Stejskal-Tanner MR diffusion methods have been invaluable in determining the anisotropic (differing diffusional rates along one or more of the three magnet axes) diffusion behavior of small molecules in ordered or oriented matter ( 9- I I ) and of tissues in vitro (12-14). Anisotropy of diffusion was suggested as a possible explanation for the large regional differences in in vivo human white matter apparent diffusion coefficients by Thomsen et al. ( 7 ) . A more complete description of the existence of in vivo anisotropy was the topic of a review article by Rosen et al. (8). METHODS
Multislice diffusion-weighted ( Stejskal-Tanner ) spin-echo images (TR 1000- 1800, TE 80- 100) were acquired with diffusion-sensitizing gradient pulses of 0-6 G/cm resulting in gradient b values ( 3 , 4 ) of up to 14I3 s/ mm2 in the cat studies. For these studies utilizing large gradient strengths, self-shielded gradients were used ( 15-1 7). The direction of the applied diffusion-sensitizing gradient pulses was varied between the x,y , and z gradient axes. Because very strong diffusion-sensitizinggradient pulses were used with large resulting b values, much larger than those b values from the inherent frequency-encoding and slice-selection gradient pulses in the MRI sequence, they may play a significant role ( 1) . To assess the effect of cross terms ( 1, 18)between the diffusion-sensitizinggradients pulses and the slice-selective and frequency-encoding gradients, image acquisitions can be repeated with interchanging frequency- and phaseencoding gradients (swapping axes) or through careful calibration of the effective diffusion-sensitizing gradient b values using phantoms at a known temperature, or the gradient factor b can be determined either numerically or analytically ( 1 ). The diffusion-weighted images shown in this study are magnitude images containing T 1-,T2-, and diffusion-weighting. In a diffusion-weightedimage, relative faster apparent diffusion within a region will result in attenuation of that regional image intensity. Slower apparent diffusion will produce a smaller signal attenuation resulting in regional relative hyperintensity. The calculation of a “pure diffusion” image, in which the signal intensity is solely due to the diffusion effect, requires two or more images of varying b values ( 3 , 4, 7), in which the voxel intensity is related to the ADC. Visualization of anisotropic detail is often easier from diffusion-weighted images, which are devoid of CSF (which is very hyperintense on T2-diffusion and “pure diffusion” images).
PROTON DIFFUSION ANISOTROPY
323
RESULTS AND DISCUSSION
In cardiac-gated, coronal images from cats studied to date, the directional dependence of the white matter apparent diffusion (Fig. 1) was not observed in corresponding regions of gray matter. Within given regions of cortical white matter, the apparent diffusion coefficients were as low as 0.5 -t 0.1 (along the diffusion-sensitizinggradient cm2/s (z-gradient direction). The corpus x-direction) and as high as 1.O k 0.1 X callosum exhibited the largest pronounced dependence of ADC (an anisotropy ratio can be expressed as D (parallel)/D (perpendicular)) along the z and x axes (0.4 k 0.1 to 1.3 k 0.1 X cm2/s, respectively). From the observed image intensities and knowledge of the diffusion-sensitizinggradient direction, one can derive the orientation
FIG. I . Coronal diffusion-weighted spin-echo images of a cat (TR 1800 ms, TE 80 ms, NEX 4, 3 mm slice, FOV 80 mm). Gradient strengths are b 0 s/mm2 (upper left) and 1413 s/mm2 (other three). The direction of the applied diffusion-sensitizing gradient was varied among x (left-to-right direction in upper right image), y (top-to-bottom direction, lower left), and z (out-of-plane direction, lower right). When white matter tracts are oriented parallel to the direction of the applied diffusion gradient (such as the corpus callosum along x, upper right), fast directional (relatively unhindered or unrestricted) diffusion of water protons is indicated by regions of hypointensity. Water diffusion perpendicular to the applied gradient direction is slower (more hindered by the structure and orientation of the white matter bundles), which accounts for the high signal intensity of the corpus callosum along z (lower right).
-
324
MOSELEY ET AL.
of individual white matter tracts. Estimation of the translational distances traveled by water protons during ( A - 6 / 3 ) (6 to 11 pm, respectively, in the corpus callosum) suggests that axonal diameters may be determinable from such measurements, if diffusion is restricted. This orientational dependence of feline white matter signal intensity has also been observed in nongated premortem and in postmortem diffusion-weightedimages ( 1 9 ) . An analysis of the effect of the cross-terms between the inherent MRI gradient and the diffusion-sensitizing gradient pulses on the observed anisotropy implies that the anisotropic contrast in the image is due primarily to the diffusion-sensitizing gradient pulses at high b values ( 1 8 ) . The in vivo directionaldiffusion-weighted images indicate that water proton diffusion anisotropy is best observed in the large diameter, fast-conducting motor and somatosensory nerve fibers. In addition to the heavily myelinated proprioceptive axons, the optic nerves (Fig. 2), corpus callosum, and anterior and posterior commissures appear to be associated with significant anisotropic effects. This ordering of water motion most likely occurs along the axis of the individual neurofibrils as well as along or within the axons isolated by the myelin sheath. Despite relatively low signal-to-noise from the long TE times necessary for placement of the ST gradient pair, anisotropy has also been observed in the tibia1 nerve of human volunteers (Fig. 3 ) . Utilization of this MRI technique for determining the orientation of white matter through measurement of water proton apparent diffusion has the potential to greatly improve our understanding and assessment of demyelination disorders, white matter infarcts, neoplasms involving white matter tracts, and neonatal brain and spinal cord development.
FIG.2 . Axial diffusion-weightedimages of the cat at the level of the optic nerve shown without application of the diffusion-sensitizing gradients (T2) and along the x and z directions (see arrows). Water apparent diffusion is faster along the axis of the nerve (hypointense along z ) than across ( hyperintense along x).
PROTON DIFFUSION ANISOTROPY
325
FIG. 3. Axial diffusion-weightedimages of a human volunteer at the level of the ankle (insert with zoom box shown) shown without application of the diffusion-sensitizing gradients (T2) and along the x (upper right image), y (lower left image), and z (lower right) directions (see arrows). The low SNR within the nerve reflects a relatively short T2 relaxation time. Observed hypointensity within the nerve as the diffusionsensitizing gradient is applied along z (lower right image) suggests faster proton diffusion along the nerve than across ( x and y directions).
REFERENCES 1. E. 0. STEJSKAL AND J. E. TANNER, J. Chem. Phys. 42,288 ( 1965). 2. E. 0. STEJSKAL, J. Chem. Phys. 43, 3597 (1965). 3. D. LEBIHAN,E. BRETON, D. LALLEMAND, P. GRENIER, E. CABANIS, AND M. LAVAL-JEANTET, Radiology 161,401 (1986). 4. D. LE BIHAN,E. BRETON,D. LALLEMAND, M-I. AUBIN,J. VIGNAUD, AND M. LAVAL-JEANTET, Radiology 168,497 (1988). 5. K.-D. MERBOLDT, H. BRUHN,J. FRAHM,M. H. GYNGELL, W. HANICKE, AND M. DEIMLING, Mug. Reson. Med. 9,423 (1989). 6. R. TURNER, D. LE BIHAN,J. DELANNOY, AND J. PEKAR,in “Book of Abstracts, Society of Magnetic Resonance in Medicine (SMRM), 8th Annual Meeting, 1989.” 7. c. THOMSEN, 0. HENRIKSEN, AND P. RING, AClU Rudiol. 28, ( 1987); c . THOMSEN, P.RING,AND 0. HENRIKSEN, in “Book of Abstracts, Society of Magnetic Resonance in Medicine (SMRM), 7th Annual Meeting, 1988.” 8. B. R. ROSEN,J. W. BELLIVEAU, AND D. CHIEN,Mugn. Reson. Q. 5,263 ( 1989). 9. P. STILBS,Prog. NMR Spectrosc. 19: ( 1987) and references cited therein. 10. G. LINDBLOM, Acta Chem. Scand. B35,61 (1981).
326
MOSELEY ET AL.
11. J. E. TANNER,in “Magnetic Resonance in Colloid and Interface Science” (H. A. Resing and C. G. Wade, Eds.), Vol. 34, pp. 16-29, 1976.
12. R. L. COOPER,D. B. CHANG,A. C. YOUNG,C. J. MARTIN,AND B. ANCKER-JOHNSON, Biophys. J. 14, 161 (1974). 13. J. R. HANSEN,Biochrm. Biophy,P. Acta 230,482 (1971). 14. G. G. CLEVELAND, D. C. CHANG,C. F. HAZELWOOD, AND H. E. RORSCHACH, Biophys. J . 16, 1043 (1976). 15. P. MANSFIELD AND B. CHAPMAN, J. Phys. E 19,540 (1986). 16. R. TURNERAND R. M. BOWLEY,J. Phys. E 19, 876 (1986). 17. P. B. ROEMER,W. A. EDELSTEIN,AND J. S. HICKEY,in “Book of Abstracts, Society of Magnetic Resonance in Medicine, 5th Annual Meeting, 1986,” p. 1087. 18. M. NEEMAN, J. P. FREYER,AND L. 0. SILLERUD, in “Book of Abstracts, Society of Magnetic Resonance in Medicine (SMRM), 9th Annual Meeting, 1990.” 19. M. E. MOSELEY, J. KUCHARCZYK, J. MINTOROVITCH, Y. COHEN,J. KURHANEWICZ, N. DERUGIN, H. ASGARI,AND D. NORMAN,Radiology 176,439 (1990).
19, 321-326 (1991)
Anisotropy in Diffusion-Weighted MRI * MICHAELE. MOSELEY,JOHNKUCHARCZYK, HALEHS. ASGARI, AND DAVIDNORMAN Department of Radiology, University of California, Sun Francisco, California 94143 Received February I , 1991 Diffusional anisotropy of water protons, induced by nonrandom, directional barriers which hinder or retard water motion, is measurable by MRI. Faster water diffusion was observed when the diffusion-sensitizinggradient direction paralleled the long axes of white matter tracts, indicative of fewer bamers to water motion. Diffusion perpendicular to this 3xis was as much as four times slower. Anisotropy was seen pre- and postmortem in all axial, sagittal, and coronal planes, with and without cardiac gating. Ordering has also been observed in feline optic nerve and in human peripheral nerves. Utilization of this technique can greatly improve understanding and assessment of demyelinating disorders, of white matter infarcts and neoplasms, and of neonatal brain and spinal cord development. 0 1991 Academic Press, Inc.
INTRODUCTION
Measurement of diffusion using pulsed-gradient spin-echo ( Stejskal-Tanner ) NMR methods as well as the assessment of anisotropic-restricted diffusion was reported more than 20 years ago ( 1 , 2). In vivo diffusion MRI, which can map microscopic motion of water protons, has only recently been studied ( 3 - 8 ) . The lack of large gradient strengths (those exceeding 1 g/cm) and the problems created by excessive eddy currents inherent in large-bore magnet gradients have impeded these studies. Most diffusion-weighted MRI sequences have been modifications of the spin-echo paired-gradient Stejskal-Tanner ( ST) sequences. All spin dephasing caused by the first diffusion-sensitizing gradient pulse is refocused by the second diffusion-sensitizing gradient pulse for stationary spins. Moving incoherent spins will not completely refocus and will attenuate the observed signal. The observed echo intensity S(TR, TE, Gi) can be expressed as S(TR, TE, Gi)
= S(co, O,O)exp(-TE/T2)(
+ exp(-
1 - 2 exp(- (TR
-
TE/2)/T1)
TR/T1))exp(y2d2Gi2(A- d/3)ADC),
where S(co, 0,O) is the signal at TE = 0, TR = co . The terms TE, TI and T2 are the echo time and spin-lattice and spin-spin relaxation times, respectively, y is the gyromagnetic ratio, d and Gi are the duration and the amplitude of square diffusionsensitizing directional ST gradient pulses along i, A is the time interval between the * Presented at SMRM Workshop on Future Directions in MRI of Diffision and Microcirculation,Bethesda, MD, June 7 and 8, 1990. 32 I
0740-3 194/9 I $3.00 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.
322
MOSELEY ET AL.
leading edges of the diffusion-sensitizing gradients pulses and the term ADC is the proton apparent diffusion coefficient, which can be thus determined ( 1-4); In S(TE, Gi)/S(TE, 0) = -y2d2Gi2(A - d/3)ADC
=
-bADC,
where a gradient attenuation factor ( 3 , 4 )b is defined as y d2Gi’( A - d / 3 ) for square gradient pulses absent of gradient cross-terms ( I , 2). The direction of the diffusionsensitizing gradient pulses can be controlled and the apparent diffusion along the respective direction can be measured. Full assessment of anisotropy of diffusion requires measurement of the diffusion tensor ( a scalar diffusion rate as a function of direction). The presence of nonrandom barriers will impart anisotropic proton diffusion resulting in a slower ADC for protons along a more hindered direction compared to a direction in which the spins can translate freely along the observed mean pathlength. Stejskal-Tanner MR diffusion methods have been invaluable in determining the anisotropic (differing diffusional rates along one or more of the three magnet axes) diffusion behavior of small molecules in ordered or oriented matter ( 9- I I ) and of tissues in vitro (12-14). Anisotropy of diffusion was suggested as a possible explanation for the large regional differences in in vivo human white matter apparent diffusion coefficients by Thomsen et al. ( 7 ) . A more complete description of the existence of in vivo anisotropy was the topic of a review article by Rosen et al. (8). METHODS
Multislice diffusion-weighted ( Stejskal-Tanner ) spin-echo images (TR 1000- 1800, TE 80- 100) were acquired with diffusion-sensitizing gradient pulses of 0-6 G/cm resulting in gradient b values ( 3 , 4 ) of up to 14I3 s/ mm2 in the cat studies. For these studies utilizing large gradient strengths, self-shielded gradients were used ( 15-1 7). The direction of the applied diffusion-sensitizing gradient pulses was varied between the x,y , and z gradient axes. Because very strong diffusion-sensitizinggradient pulses were used with large resulting b values, much larger than those b values from the inherent frequency-encoding and slice-selection gradient pulses in the MRI sequence, they may play a significant role ( 1) . To assess the effect of cross terms ( 1, 18)between the diffusion-sensitizinggradients pulses and the slice-selective and frequency-encoding gradients, image acquisitions can be repeated with interchanging frequency- and phaseencoding gradients (swapping axes) or through careful calibration of the effective diffusion-sensitizing gradient b values using phantoms at a known temperature, or the gradient factor b can be determined either numerically or analytically ( 1 ). The diffusion-weighted images shown in this study are magnitude images containing T 1-,T2-, and diffusion-weighting. In a diffusion-weightedimage, relative faster apparent diffusion within a region will result in attenuation of that regional image intensity. Slower apparent diffusion will produce a smaller signal attenuation resulting in regional relative hyperintensity. The calculation of a “pure diffusion” image, in which the signal intensity is solely due to the diffusion effect, requires two or more images of varying b values ( 3 , 4, 7), in which the voxel intensity is related to the ADC. Visualization of anisotropic detail is often easier from diffusion-weighted images, which are devoid of CSF (which is very hyperintense on T2-diffusion and “pure diffusion” images).
PROTON DIFFUSION ANISOTROPY
323
RESULTS AND DISCUSSION
In cardiac-gated, coronal images from cats studied to date, the directional dependence of the white matter apparent diffusion (Fig. 1) was not observed in corresponding regions of gray matter. Within given regions of cortical white matter, the apparent diffusion coefficients were as low as 0.5 -t 0.1 (along the diffusion-sensitizinggradient cm2/s (z-gradient direction). The corpus x-direction) and as high as 1.O k 0.1 X callosum exhibited the largest pronounced dependence of ADC (an anisotropy ratio can be expressed as D (parallel)/D (perpendicular)) along the z and x axes (0.4 k 0.1 to 1.3 k 0.1 X cm2/s, respectively). From the observed image intensities and knowledge of the diffusion-sensitizinggradient direction, one can derive the orientation
FIG. I . Coronal diffusion-weighted spin-echo images of a cat (TR 1800 ms, TE 80 ms, NEX 4, 3 mm slice, FOV 80 mm). Gradient strengths are b 0 s/mm2 (upper left) and 1413 s/mm2 (other three). The direction of the applied diffusion-sensitizing gradient was varied among x (left-to-right direction in upper right image), y (top-to-bottom direction, lower left), and z (out-of-plane direction, lower right). When white matter tracts are oriented parallel to the direction of the applied diffusion gradient (such as the corpus callosum along x, upper right), fast directional (relatively unhindered or unrestricted) diffusion of water protons is indicated by regions of hypointensity. Water diffusion perpendicular to the applied gradient direction is slower (more hindered by the structure and orientation of the white matter bundles), which accounts for the high signal intensity of the corpus callosum along z (lower right).
-
324
MOSELEY ET AL.
of individual white matter tracts. Estimation of the translational distances traveled by water protons during ( A - 6 / 3 ) (6 to 11 pm, respectively, in the corpus callosum) suggests that axonal diameters may be determinable from such measurements, if diffusion is restricted. This orientational dependence of feline white matter signal intensity has also been observed in nongated premortem and in postmortem diffusion-weightedimages ( 1 9 ) . An analysis of the effect of the cross-terms between the inherent MRI gradient and the diffusion-sensitizing gradient pulses on the observed anisotropy implies that the anisotropic contrast in the image is due primarily to the diffusion-sensitizing gradient pulses at high b values ( 1 8 ) . The in vivo directionaldiffusion-weighted images indicate that water proton diffusion anisotropy is best observed in the large diameter, fast-conducting motor and somatosensory nerve fibers. In addition to the heavily myelinated proprioceptive axons, the optic nerves (Fig. 2), corpus callosum, and anterior and posterior commissures appear to be associated with significant anisotropic effects. This ordering of water motion most likely occurs along the axis of the individual neurofibrils as well as along or within the axons isolated by the myelin sheath. Despite relatively low signal-to-noise from the long TE times necessary for placement of the ST gradient pair, anisotropy has also been observed in the tibia1 nerve of human volunteers (Fig. 3 ) . Utilization of this MRI technique for determining the orientation of white matter through measurement of water proton apparent diffusion has the potential to greatly improve our understanding and assessment of demyelination disorders, white matter infarcts, neoplasms involving white matter tracts, and neonatal brain and spinal cord development.
FIG.2 . Axial diffusion-weightedimages of the cat at the level of the optic nerve shown without application of the diffusion-sensitizing gradients (T2) and along the x and z directions (see arrows). Water apparent diffusion is faster along the axis of the nerve (hypointense along z ) than across ( hyperintense along x).
PROTON DIFFUSION ANISOTROPY
325
FIG. 3. Axial diffusion-weightedimages of a human volunteer at the level of the ankle (insert with zoom box shown) shown without application of the diffusion-sensitizing gradients (T2) and along the x (upper right image), y (lower left image), and z (lower right) directions (see arrows). The low SNR within the nerve reflects a relatively short T2 relaxation time. Observed hypointensity within the nerve as the diffusionsensitizing gradient is applied along z (lower right image) suggests faster proton diffusion along the nerve than across ( x and y directions).
REFERENCES 1. E. 0. STEJSKAL AND J. E. TANNER, J. Chem. Phys. 42,288 ( 1965). 2. E. 0. STEJSKAL, J. Chem. Phys. 43, 3597 (1965). 3. D. LEBIHAN,E. BRETON, D. LALLEMAND, P. GRENIER, E. CABANIS, AND M. LAVAL-JEANTET, Radiology 161,401 (1986). 4. D. LE BIHAN,E. BRETON,D. LALLEMAND, M-I. AUBIN,J. VIGNAUD, AND M. LAVAL-JEANTET, Radiology 168,497 (1988). 5. K.-D. MERBOLDT, H. BRUHN,J. FRAHM,M. H. GYNGELL, W. HANICKE, AND M. DEIMLING, Mug. Reson. Med. 9,423 (1989). 6. R. TURNER, D. LE BIHAN,J. DELANNOY, AND J. PEKAR,in “Book of Abstracts, Society of Magnetic Resonance in Medicine (SMRM), 8th Annual Meeting, 1989.” 7. c. THOMSEN, 0. HENRIKSEN, AND P. RING, AClU Rudiol. 28, ( 1987); c . THOMSEN, P.RING,AND 0. HENRIKSEN, in “Book of Abstracts, Society of Magnetic Resonance in Medicine (SMRM), 7th Annual Meeting, 1988.” 8. B. R. ROSEN,J. W. BELLIVEAU, AND D. CHIEN,Mugn. Reson. Q. 5,263 ( 1989). 9. P. STILBS,Prog. NMR Spectrosc. 19: ( 1987) and references cited therein. 10. G. LINDBLOM, Acta Chem. Scand. B35,61 (1981).
326
MOSELEY ET AL.
11. J. E. TANNER,in “Magnetic Resonance in Colloid and Interface Science” (H. A. Resing and C. G. Wade, Eds.), Vol. 34, pp. 16-29, 1976.
12. R. L. COOPER,D. B. CHANG,A. C. YOUNG,C. J. MARTIN,AND B. ANCKER-JOHNSON, Biophys. J. 14, 161 (1974). 13. J. R. HANSEN,Biochrm. Biophy,P. Acta 230,482 (1971). 14. G. G. CLEVELAND, D. C. CHANG,C. F. HAZELWOOD, AND H. E. RORSCHACH, Biophys. J . 16, 1043 (1976). 15. P. MANSFIELD AND B. CHAPMAN, J. Phys. E 19,540 (1986). 16. R. TURNERAND R. M. BOWLEY,J. Phys. E 19, 876 (1986). 17. P. B. ROEMER,W. A. EDELSTEIN,AND J. S. HICKEY,in “Book of Abstracts, Society of Magnetic Resonance in Medicine, 5th Annual Meeting, 1986,” p. 1087. 18. M. NEEMAN, J. P. FREYER,AND L. 0. SILLERUD, in “Book of Abstracts, Society of Magnetic Resonance in Medicine (SMRM), 9th Annual Meeting, 1990.” 19. M. E. MOSELEY, J. KUCHARCZYK, J. MINTOROVITCH, Y. COHEN,J. KURHANEWICZ, N. DERUGIN, H. ASGARI,AND D. NORMAN,Radiology 176,439 (1990).
