1D spectroscopic imaging with rf echo planar (SIRFEN) methods

Magnetic

Resonance

Imaging.

1991

Vol. 9. pp. 909-916,

0730-725x/91 S3.oLl+ .oa Copyright 0 1991 Pergamon Press plc

Printed in the USA. Au rights reserved.

0 Original Contribution

1D SPECTROSCOPIC

IMAGING

WITH RF ECHO PLANAR

(SIRFEN) METHODS

R.V. MULKERN,* P.S. MELKI,? H.S. LILLY,% AND F.A. HOFFER* *Department of Radiology, Children’s Hospital, Boston, MA, USA, iDepartment of Radiology, Brigham and Women’s Hospital, Boston, MA, USA, and SGeneral Electric Medical Systems, Milwaukee, WI, USA A recently developed rf echo planar imaging method has been modified to rapidly generate spectroscopic information along one in-plane axis and spatial information along the other. The method allows the production of one-dimensional chemical shift images (1D CSIs) in acquisition times of 18 set or less. A specific phaseencode-reordering algorithm provides convenient manipulation of T2 weighting, yielding partial suppression of short T2 species lie muscle water. The method is demonstrated in phantoms and in vivo with 1D CSIs of human brain and limbs. Abnormal fat distribution is demonstrated in the calf of a patient with aggressive fibromatosis. The advantages of short acquisition times obtainable with SIRFEN are offset by limited spectral resolution, suggesting that primary.applications will be confined to rapid spatial mapping of major spectral components.

Keywords: Spectroscopic

imaging; rf echo planar; Fat-water

Developing in vivo proton spectroscopy as a clinically viable tool still represents a challenge to MR practitioners despite many demonstrations’-” with a variety of different methods.‘1-22 Lively discussions as to the merit of individual volume localization methods continue. 23,24Potential clinical applications of proton spectroscopy range from simple fat-water separation studies’*2 to the more difficult detection of low-concentration cerebral metabolites3-9 and long-T2 lipid moieties reported to accompany malignancy in a number of cancers.25’26 One-dimensional chemical shift images (1D CSIs) within a selected slice may be obtained with in-plane phase encoding and echo readout in the absence of applied gradients. To obtain such information with routine spin-echo sequences requires data-acquisition times that may be dramatically reduced with rf echo planar techniques. 27-29This approach underlies the spectroscopic imaging with rf _echo pla_nar (SIRFEN) principle. The method is illustrated below using the recently developed fast acquisition interleaved Spin-echo (FAISE) method, which provides convenient G contrast

RECEIVED

4/11/91;

ACCEPTED

MATERIALS

AND

METHODS

Experiments were performed with a GE Signa 1.5-T imaging system (General Electric Corporation, Milwaukee). The magnet had been previously shimmed to 22 Hz over a 20-cm diameter spherical volume. No additional shimming procedures were performed prior to the experiments. Images and 1D CSIs were generated by two-dimensional Fourier transformation (2D FT) followed by magnitude calculation. Studies were performed with the central slice frequency set to the water resonance. Phantom materials consisted of acetone (Aldrich Chemical Company, Milwaukee), a 3% by volume hydrogen peroxide water solution (Diamond Drug, West Haven, CT), a pH 7.4 aqueous buffer solution (Fisher Scientific Company, Fairlawn, NJ), and spectroscopic-grade tetramethylsilane (Wilmad Glass Company, Buena, NJ). Studies of human brain were

6/3/91.

to R.V. Mulkem,

RARE.

manipulation with a specific phase-encode-reordering algorithm.28 Preliminary demonstrations include phantom studies, in vivo human brain and limb studies of a healthy volunteer, and studies from a 9-year-old male patient with aggressive fibromatosis.

INTRODUCTION

Address correspondence

separation;

Radiology, Children’s Hospital, 300 Longwood Avenue, Department

of

Boston, 909

MA 02115, USA.

910

Magnetic Resonance Imaging 0 Volume 9, Number 6, 1991

formed with the approval of the Committee on Clinical Investigation of the Children’s Hospital, Boston. The pulse sequences consisted of either an f&echo or a 16-echo Carr-Purcell-Meiboom-Gill (CPMG) train with slice-selective rf pulses. In order to obtain chemical shift information, 33-msec echo readouts were performed in the absence of any applied gradients. The resulting spectral bandwidth was +4000 Hz with a 31-Hz/pixel resolution. Spatial localization along one in-plane axis was accomplished by phase encoding individual echoes within the individual echo trains with distinct phase-encode gradients27-29 immediately prior to readout. The phase-encode information was “unwound” immediately following echo readout. This procedure results in the acquisition of several kspace lines each repetition interval TR.30 The order in which phase-encode gradients are applied to individual echoes within individual echo trains may be manipulated to vary the T2 weighting.27-29 A specific phase-encode reordering algorithm, applicable to the acquisition of NYphase-encode values using N, “shots” of echo trains containing N, echoes (NY = N,N,J has been used for this purpose.28 It permits both FAISE images or the 1D CSIs reported below to have T2 weightings represented by pseudoecho times (pTEs), which may be set to be integral multiples of the echo spacing 27 in the CPMG sequence. The signal intensities of 1D CSIs versus pTE were compared with signal intensity versus conventional TE by generating 2D FT images from each echo of the “skeletal”

Fig. 1. A 1D CSI of a three-component mixture of tetramethylsilane (top horizontal line), acetone (middle line), and water (bottom line). A TR of 2.5 set was used with the 16echo, &shot sequence to acquire the 128 x 256 image matrix from a 5-mm slice in 22 set (time includes a baseline shot). The vertical axis is the frequency (chemical shift axis), while the horizontal axis is the spatial axis. The ceramic cup holding the components is 8 cm in diameter. Note the susceptibility shift. of the three spectral components at the edges of the cup.

performed with a healthy volunteer using a quadrature transmit-receive head coil. A linear transmit-receive extremity coil was used for calf studies of a healthy volunteer, while both calves of a patient with aggressive fibromatosis were studied with the quadrature transmit-receive body coil. Human studies were per-

AAAAAAAAAAAAAA

0

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Time,

300

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500

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Fig. 2. Closed symbols represent signal intensities versus pseudoecho time (pTE) obtained from 1D CSIs of acetone (triangles) and 3% hydrogen peroxide water solution (circles). Open symbols are the signal intensities measured in each phantom as a function of echo time TE, from a 16-echo CPMG imaging sequence data set.

Imaging with SIRFEN methods 0 R.V.

CPMG imaging sequences SIRFEN methods.

underlying

all the FAISE-

RESULTS Figure 1 is a 1D CSI of a ceramic cup containing a pH 7.4 aqueous buffer solution, acetone, and tetramethylsilane. This 128 x 256 1D CSI was acquired in 22 set with the 16-echo, 8-shot sequence. The three spectral components are tetramethylsilane (top), ace-

MULKERN ET AL.

911

tone, and water (bottom) at 0, 2.2, and 4.7 ppm, respectively.31 A set of 128 x 256 ID CSIs of an acetone phantom and a hydrogen peroxide water solution phantom were acquired with the 16-echo, S-shot sequence for pTE values ranging from 45 to 720 msec. Acquisition time for each 1D CSI was 18 set (TR = 2 set). Signal intensities from the acetone line and the water line were measured as a function of pTE, and the results are plotted in Fig. 2. Both phantoms were also imaged

Fig. 3. (A) An in vivo 1D CSI (top) and corresponding FAISE image of a IO-mm slice of human brain. The 256 x 256 1D CSI was acquired in 66 set with an 8-echo, 32-shot sequence utilizing a 2-set TR. The pTE was 45 msec. The 256 x 256 FAISE image was also acquired in 66 set using the &echo, 32-shot sequence. The pTE of the FAISE image was 30 msec. Note how the fat component (top horizontal spectral line of 1D CSI) correlates with the anatomy of the FAISE image with high fat signal intensities from tissue columns composed of subcutaneous fat at the left- and right-hand edges of the head and two central regions corresponding to tissue columns containing retrobulbar fat. (B) Same as in (A) but from a slice IO-mm inferior (three slices were simultaneously collected for both the 1D CSI data and the FAISE image data). Note the lack of retrobulbar fat signal intensities in the 1D CSI of this slice.

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with the 16-echo CPMG sequence, and the signal intensities from both materials were measured as a function of TE. The results are also plotted in Fig. 2. The values of T2calculated from the latter decay curves were 2869 msec (acetone) and 58 msec (hydrogen peroxide water solution). These are in good agreement with the “T2"values of 2451 and 56 msec obtained from the signal intensity decay with pTE in the 1D CSI data sets. Figure 3 presents 1D CSIs and corresponding FAISE images of two slices of the brain of a healthy volunteer. The 256 x 256 1D CSIs were acquired in 66 set with the g-echo, 32-shot sequence (three slices total). The 256 x 256 FAISE images of these slices were also acquired in 66 set with the g-echo, 32-shot sequence but with a 27 spacing of 15 msec. The pTEs were 45 and 30 msec for the 1D CSIs and FAISE images, respectively. Figure 4(A) is a FAISE image through the calf of a healthy volunteer. An g-echo, 32-shot sequence was used to generate 1D CSIs of this slice at pTE values of 90 msec and then 270 msec. Each 256 x 256 1D CSI was acquired in 66 set using a TR of 2 sec. The 90msec pTE 1D CSI is presented in Fig. 4(B). Figure 5 presents spectra obtained from frequency axis profiles at the spatial locations depicted by the arrows in

Fig. 4(B). One location was chosen to yield spectra from primarily subcutaneous fat while the other was chosen to yield spectra from a heterogeneous tissue column containing subcutaneous fat, bone marrow, and muscle. The spectra have been plotted on a partsper-million scale based on extrapolation from the frequency location of the tetramethylsilane peak at 0 ppm in Fig. 1. Figure 6(A) is a conventional proton-densityweighted spin-echo image (TR/TE = 2000/20) of both calves from a patient with aggressive fibromatosis of the left popliteal fossa. Figure 6(B) is a 128 x 256 1D CSI from this slice acquired in 42 set with the 16-echo, g-shot sequence but employing two signal averages and a 2.5-set TR. The pTE was 270 msec.

(A)

(B)

DISCUSSION Brown et al. suggested that reasonable resolutions and imaging times might be achieved if there were “some way to sample different k values while simultaneously refocussing the spins. . . .“‘I This work presents such a method within the framework of rf echo planar imaging schemes. *‘FanOther groups have demonstrated rapid spectroscopic imaging with the use of gradient-recalled echoes,20*21and an extensive discussion has been provided by Matsui et al.**

Fig. 4. (A) A FAISE image through the calf of a healthy volunteer (lo-mm slice thickness) from which 1D CSIs were acquired. (B) 1D CSI with a 90-msec pTE from the slice depicted in (A). Another 1D CSI was also acquired from this slice but with a pTE of 270 msec (data not shown). The 1D CSIs were acquired with the &echo, 32-shot sequence using a TR of 2 set (dataacquisition time = 66 set, image matrix = 256 x 256). The chemical shift axis is again vertical, but the frequency direction is reversed from that of the brain 1D CSIs, making the lipid component the lower spectral line. The arrows in (B) depict the spatial locations of 4-pixel-wide columns from which profiles along the frequency direction (e.g., spectra) were obtained.

Imaging with SIRFEN methods 0 R.V. lE4

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Fig. 5. Magnitude calculated spectra from the spatial locations depicted in Fig. 4(B) as referenced with respect to tetramethylsilane at 0 ppm (extrapolation from frequency location in Fig. 1). Spectra on the left were acquired with a pTE of 90 msec while those on the right were acquired with a pTE of 270 msec. The top two spectra are from a tissue column containing primarily subcutaneous fat, while the lower two spectra are from a heterogeneous tissue column containing subcutaneous fat, muscle, and bone marrow. Two lipid peaks between 0 and 2.6 ppm are resolved. The muscle water peak at 4.8 ppm in the lower left panel (pTE = 90 msec) becomes significantly suppressed with respect to the major lipid peak in the 270-msec pTE spectra (lower right panel).

The spectral decomposition of the three-component phantom (Fig. 1) demonstrates how SIRFEN methods yield typical 1D CSI dataI in time periods of 20 set or less with standard image matrix sizes and a moderate chemical shift resolution of 31 Hz/pixel. The ability to manipulate T2 weighting with the phaseencode-reordering algorithm introduced in the FAISE technique28 is demonstrated in Fig. 2, in which the decay curves obtained from the 1D CSI experiments and the CPMG imaging experiments are closely correlated. The short T2 of the hydrogen peroxide solution is most probably due to the presence of paramagnetic oxygen. The 1D CSIs of human brain in Fig. 3 may be cor-

related with the anatomy of the corresponding FAISE images. The fat component in Fig. 3(A) divides itself into roughly four sections along the spatial axis. The strong fat signal at each end is attributed to subcutaneous fat along the left- and right-hand sides of the head as collapsed into one dimension. The two centrally located fat signals in Fig. 3(A) correspond to retrobulbar fat, an observation supported by the fact that intense central fat regions are unobserved in the 1D CSI of the slice acquired below the orbits [Fig. 3(B)]. One or more chemical shift components between the two major spectral peaks are observed at roughly the spatial center of the brain 1D CSIs. Whether this signal intensity arises from unsaturated

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Magnetic Resonance Imaging 0 Volume 9, Number 6, 1991

Fig. 6. (A) Conventional proton-density-weighted image of both calves of a patient with aggressive fibromatosis. Fatty infiltration of muscle mass is apparent in the left leg of the patient (right-hand side of image). (B) 1D CSI of the slice shown in (A). The lipid line is the upper spectral component along the vertical axis in this ID CSI. The arrow demarcates region of increased signal intensity from this component at a spatial location corresponding to the tissue column in the patient’s left leg which contains the fatty infiltrate. A 16-echo, 8-shot sequence with a 2.5-set TR and two signal averages per phase encode was used to acquire the 128 x 256 1D CSI in 42 set with a pTE of 270 msec.

lipid protons’7 or major spectral components that are susceptibility shifted is undetermined (see the slight curvature of all three spectral components at the edges of the ceramic cup in Fig. 1 for evidence of susceptibility shifts). Examining the 1D CSI from healthy calf tissue [Fig. 4(B)] reveals that more than two spectral components (e.g., saturated lipid and water protons) can be resolved with the moderate spectral resolution employed. In particular, a low-resolution splitting of the lipid component is apparent. Figure 5 demonstrates this explicitly for spectra taken from subcutaneous fat

and from the heterogeneous tissue column containing bone marrow, muscle, and subcutaneous fat. The major spectral component in the l- to 2-ppm region is attributed to saturated lipid protons, primarily -(CHP)groups. The smaller peak around 2.3 ppm is attributed to protons from =CH-CA,--CH= and O=C--CH2-(CH,), groups, as reported previously in localized in vivo proton spectra of healthy calvesI and femoral bone marow. lo The appearance of two peaks between 4 and 6 ppm in the 270-msec pTE spectra of subcutaneous fat is attributed to water protons at 4.7 ppm and vinyl protons (H-C=C-H)

Imaging with SIRFEN methods 0 R.V. MULKERN

around 5.8 ppm.” The influence of Tz weighting may be appreciated in the spectra obtained from the heterogeneous tissue column. These spectra demonstrate how lengthening the pTE value from 90 to 270 msec substantially reduces the short T2 muscle water spectral component at 4.8 ppm with respect to the two resolved lipid resonances between 0 and 2.5 ppm.32 A clinical example of SIRFEN application is provided in Fig. 6. The fatty infiltration of muscle in the left calf is obvious in the spin-echo image [Fig. 6(A)]. The ID CSI study confirms the presence of increased lipid signal from this region ]Fig. 6(B)]. The healthy right leg demonstrates high fat signal intensities at locations corresponding to subcutaneous fat at the lateral and medial aspects and through the column containing bone marrow. The primary difference between the healthy-leg lipid component and the diseased-leg lipid component is the region of increased signal intensity observed at the spatial location corresponding to the tissue column containing fatty infiltration of the muscle [arrow in Fig. 6(B)]. The SIRFEN principle demonstrated above may be extended to 2D CSI acquisitions by applying two phase-encode gradients. “Acquisition times for 2D CSI data sets using a second phase-encode gradient and a 16-echo CPMG train repeated eight times to gather 128 phase-encode steps would require some 17 min, with a 1-set TR. Smaller spatial matrices might be more useful in practice with a 64 x 64 x 256 data acquisition performed in approximately 5 min. Despite the rapid data acquisition, the SIRFEN method described above suffers from limited spectral resolution. Furthermore, to increase the spectral resolution to 4 Hz/pixel with SIRFEN would require 250-msec echo readouts, resulting in excessively long echo spacings within the CPMG trains. In this case, the method offers little or no advantage over more conventional CSI methods. As a consequence, potential applications of the SIRFEN method will probably be largely confined to rapid 1D or 2D mapping of major spectral components.

REFERENCES

ton NMR spectroscopy using stimulated echoes: Initial applications to human brain in vivo. Magn. Reson. Med. 9:79-93; 1989. 4. Bruhn, H.; Frahm, J.; Gyngell, M.L.; Merboldt, K.D.;

Hanicke, W.; Sauter, R. Cerebral metabolism in man after acute stroke: New observations using localized proton NMR spectroscopy. Magn. Reson. Med. 9:126131; 1989. 5. Arnold, D.L.; Matthews, P.M.; Francis, C.; Antel, J. Proton magnetic resonance spectroscopy of human brain in vivo in the evaluation of multiple sclerosis: Assessment of the load of the disease. Magn. Reson. Med. 14:154-159; 1990. 6. Alger, J.R.; Frank, J.A.; Bizzi, A.; Fulham, M.J.; DeSouza, B.X.; Duhaney, M.O. ; Inscoe, S.W.; Black, J.L.; van Zijl, P.C.M.; Moonen, C.T.W.; Di Chiro, G. Metabolism of human gliomas: Assessment with H-l MR spectroscopy and F-l 8 fluorodeoxyglucose PET. Radiology 177:633-641; 1990. 7. Van Hecke, P.; Marchal, G.; Johannik,

8.

9.

10.

11.

12.

K.; Demaerel, P.; Wilms, G.; Carton, H.; Baert, A.L. Human brain proton localized NMR spectroscopy in multiple sclerosis. Magn. Reson. Med. 18:199-206; 1991. Frahm, J.; Bruhn, H.; Gyngell, M.L.; Merboldt, K.D.; Hanicke, W.; Sauter, R. Localized proton NMR spectroscopy in different regions of the human brain in vivo. Relaxation times and concentrations of cerebral metabolites. Magn. Reson. Med. 11:47-63; 1989. Luyten, P.R.; den Hollander, J.A. Observation of metabolites in the human brain by MR spectroscopy. Radiology 161:795-798; 1986. Ballon, D.; Jakubowski, A.; Gabrilove, J.; Graham, M.C.; Zakowski, M.; Sheridan; Koutcher, J.A. In vivo measurements of bone marrow cellularity using volumelocalized proton NMR spectroscopy. Magn. Reson. Med. 19:85-95; 1991. Brown, T.R.; Kincaid, B.M.; Ugurbil, K. NMR chemical shift imaging in three dimensions. Proc. Natl. Acad. Sci. USA 79:3523-3526; 1982. Sepponen, R.E.; Sipponen, J.T.; Tanttu, J.I. A method for chemical shift imaging: Demonstration of bone marrow involvement with proton chemical shift imaging. J. Comput. Assist. Tomogr. 8:585-587;

13. Dixon, diology 14. Frahm, proton

Magn. Reson. Imaging 8:779-789;

1990.

Rosen, B.R.; Fleming, D.M.; Kushner, D.C.; Zaner, K.S.; Buxton, R.B.; Bennet, W.P.; Wismer, G.L.; Brady, T. J. Hematoiogic bone marrow disorders: Quantitative chemical shift MR imaging. Radiology 169:799804; 1988.

Frahm, J.; Bruhn, H.; Gyngell, M.L.; Merboldt, K.D.; Hanicke, W.; Sauter, R. Localized high-resolution pro-

1984.

W.T. Simple proton spectroscopic imaging. Ra153:189-194; 1984. J.; Merboldt, K.D.; Hanicke, W.J. Localized spectroscopy using stimulated echoes. Magn.

Reson. 72:502-508;

Jensen, K.E.; Jensen, M.; Grundtvig, P.; Thomsen, C.; Karle, H.; Henriksen, 0. Localized in vivo proton spectroscopy of the bone marrow in patients with leukemia.

915

ET AL.

1987.

15. Webb, P.; Spielman, D.; Macovski, A. A fast spectroscopic imaging method using a blipped phase encode gradient. Magn. Reson. Med. 12:306-315; 1989. phase-encoded spectral 16. Ford, J.J. Gradient-amplitude (GRAPES) imaging. A novel approach to spin-echo chemical-shift imaging. J. Magn. Reson. 87:346-351; 1990.

17. Jackson, E.F.; Narayana, P.A.; Flamig, D.P. One dimensional spectroscopic imaging with stimulated echoes: Phantom and human leg studies. Magn. Reson. Zmaging 8:153-159;

1990.

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18. Ordidge, R. J. ; Connelly, A.; Lohman, J.A.B. Image selected in vivo spectroscopy (ISIS). A new technique for spatially selective NMR spectroscopy. J. Mugn. Res. 77: 283-294; 1986. 19. Luyten, P.R.; Marian, A.J.H.; Sijtsma, B.; den Hollander, J.A. Solvent suppressed spatially resolved spectroscopy: An approach to high resolution NMR on a whole body MR system. J. Mugn. Reson. 67:148-155; 1986. 20. Twieg, D.B. Multiple-output chemical shift imaging (MOCSI): A practical technique for rapid spectroscopic imaging. Mugn. Reson. Med. 12:64-73; 1989. 21. Guilfoyle, D.N.; Blamire, A.; Chapman, B.; Ordidge, R. J.; Mansfield, P. PEEP -A rapid chemical-shift imaging method. Mugn. Reson. Med. 10:282-287; 1989. 22. Matsui, S.; Sekihara, K.; Kohno, H. Spatially resolved NMR spectroscopy using phase-modulated spin-echo trains. J. Magn. Reson. 67:476-490; 1986. 23. Pan, J.W.; Shulman, R.G. In vivo human localized ‘H spectroscopy. Magn. Reson. Med. 12:257-258; 1989. 24. Narayana, P.A.; Jackson, E.F.; Hazle, J.D.; Fotedar, L.K.; Kulkarni, M.V.; Flamig, D.P. In vivo localized proton spectroscopic studies of human gastrocnemius muscle. Mugn. Reson. Med. 12:259-260; 1989. 25. Mountford, C.E.; Saunders, J.K.; May, G.L.; Holmes, K.T.; Williams, P.G.; Fox, R.M.; Tattersall, M.H.N.; Barr, J.R.; Russell, P.; Smith, I.C.P. Classification of

26.

27.

28.

29.

human tumours by high-resolution magnetic resonance spectroscopy. Lance? 315:651-653; 1986. Bradamante, S.; Barchiesi, E.; Pilotti, S.; Borasi, G. High resolution ‘H NMR spectroscopy in the diagnosis of breast cancer. Magn. Reson. Med. 8:440-449; 1988. Hennig, J.; Naureth, A.; Friedburg, H. RARE imaging: A fast imaging method for clinical MR. Magn. Reson. Med. 3:823-833; 1986. Melki, P.S.; Mulkern, R.V.; Panych, L.P.; Jolesz, EA. Comparing the FAISE method with conventional dual echo sequences. J. Magn. Reson. Imug. 1:3 19-326; 1991. Mulkern, R.V.; Wong, S.T.S.; Winalski, C.; Jolesz, EA. Contrast manipulation and artifact assessment of 2D and 3D RARE sequences. Magn. Resort Imaging 8:

557-566; 1990. 30. Twieg, D.B. The k-space trajectory

formulation of the NMR imaging process with applications in analysis and imaging methods. Med. Phys. 10:610-621; 1983. 3 1. Pavia, D.L.; Lampman, G.M.; Kriz, G.S. Introduction to Spectroscopy: A Guide to Students of Organic Chemistry. Saunders Golden Sunburst Series. Saunders College Publishing/Halt, Rinehart, & Winston; 1979. 32. Adzamli, I.K.; Jolesz, F.A.; Bleier, A.R.; Mulkern, R.V.; Sandor, T. The effect of gadolinium DTPA on tissue water compartments in slow and fast twitch rabbit muscles. Mugn. Reson. Med. 11:172-180; 1989.