Magneric Resonance Imaging, Vol. 10, pp. 799-808, Printed in the USA. All rights reserved.

0730-725X192 $5.00 + .M) Copyright Q 1992 Pergamon Press Ltd.

1992

0 Session: Plenary Lecture POTENTIAL INDUSTRIAL APPLICATIONS OF INHOMOGENEOUS BROADENING IMAGING DAVID Department

C. AILION

of Physics, University of Utah, Salt Lake City, UT 84112, USA

Variations in magnetic susceptibility at air-water interfaces can result in inhomogeneous broadening of the NMR line. By special asymmetrical imaging techniques, originally developed for lung imaging, images can be formed of only those molecules that experience this inhomogeneous broadening. The basic concepts and latest developments in inhomogeneous-broadening-imaging techniques are described. Potential industrial applications are also discussed. Keywords: Nuclear magnetic resonance; Imaging; Susceptibility; echo; Gradients; Lung.

INTERNAL

INHOMOGENEOUS

Inhomogeneous

broadening;

Linewidth; Spin

Lung, on the other hand, has a much shorter FID (-2-4 msec, depending on B0 and state of inflation). This very short FID is much less than that due to inhomogeneity in B0 and must be due to a mechanism internal to the lung. In our early work,2 we demonstrated that the signal loss arises from an inhomogeneous broadening mechanism, since we were able to recover the signal in an echo. We were able to show that the inhomogeneous broadening in lung is due to variations in magnetic susceptibility arising from alveolar air-tissue interfaces.3 The existence of these airtissue interfaces is a unique characteristic of lung that distinguishes it from all other organs.4 This phenomenon can be understood by considering the well-known behavior of a diamagnetic sphere in an otherwise uniform magnetic field. Calculations of the magnetic induction B using Maxwell’s equations result in a shift in the magnetic induction, but not a spread in its values. This can be seen from Fig. la, in which the lines of force are parallel within the sphere, though with a somewhat different density from those outside the sphere and far from it. However, for a diamagnetic spherical shell, there will be a spread in the values of B [since the lines of force in Fig. lb are no longer precisely parallel, since the magnetic induction will be reduced for those portions of the shell (top and bottom) that are approximately parallel to the field, but will be unaltered for those regions (middle) that are perpendicular]. This spread in B will result in a broadening of the NMR linewidth. The existence of this broadening has been observed experimentally in a spherical shell phantom consisting of two concentric

BROADENING

Broadening of an NMR line is a well-recognized source of decreased signal intensity in pulse NMR experiments and in MRI. In solids the NMR linewidth may be broadened by dipolar or quadrupolar interactions. In liquids and biological tissues these interactions are usually motionally narrowed,’ with the result that their contributions to the linewidth may be substantially less than that due to inhomogeneity in the applied static field B0 over the sample. In any case, the variations in internal (or external) fields over the sample cause the nuclear spins to precess at slightly different rates and thus to get out of phase in a time Tl that is inversely proportional to the linewidth. This phenomenon results in a decay (called the freeinduction decay, or FID) of the magnetization following a 90” pulse. If the broadening arises from static field variations, such as an inhomogeneous static field or a static quadrupolar interaction, then it is called inhomogeneous broadening and the signal lost in the FID can be recovered by the application of a 180” pulse, resulting in the formation of a spin echo. If, on the other hand, the FID is due to dipolar interactions, which are usually time-dependent, then the signal loss is irreversible and cannot be recovered; the corresponding line broadening is referred to as homogeneous broadening. Susceptibility Broadening Most biological tissues are characterized by an FID of duration several hundred milliseconds to 1 or 2 sec. 799

800

Magnetic Resonance Imaging 0 Volume 10, Number 5, 1992

(a)

(b)

Fig. 1. (a) Lines of force for sphere of water in an otherwise uniform magnetic field. (b) Lines of force for spherical shell of water in an otherwise uniform magnetic field.

glass spheres with water filling the space in between.3 Excellent agreement was obtained between the measured line shapes and theoretically calculated line shapes. A better model for the alveolar region of the lung consists of spheres of air with water in between. Using this model, we showed3 that the line breadth increases (though not precisely linearly) with the air percentage of the total volume. Furthermore, by calculating the Fourier transform of the line shape, we calculated the FID time constant to be 3.4 msec for 70% air at 40 MHz, in excellent agreement with our measurements on lung. A disadvantage of this model is that it cannot be used for large air-water ratios, since the spheres will touch and the model will break down when the percentage air reaches 74%. We have improved this model by using space-filling Wigner-Seitz polyhedra (Fig. 2) with rounded corners and with thickened walls, thereby accommodating any desired air-water ratio from 0 to 100%. This model gives a slightly asymmetrical line shape that has been observed experimentally in isolated rat lung.’ Figure 3a shows an image of an isolated excised rat lung, and Fig. 3b shows a schematic drawing of this same lung in which we have identified various small regions (voxels) within which we have obtained NMR line shapes. Figure 4a shows the set of line shapes that we obtained from the outer or alveolar (parenchymal) portion of the lung. The excellent agreement between experimental measurement and our theoretical model is illustrated by the results for voxel B, expanded and shown in the right-hand part of the figure. A very different model (cylinder) is needed for the central (nonparenchymal) region of the lung, containing bronchi and large blood vessels. For a cylinder of water, we found that the line is shifted but the shape is symmetricaL Furthermore, the NMR line shift de-

Fig. 2. Two-dimensional cross-section of the modified Wigner-Seitz foam with thickened boundaries. In this model for the alveoli, the air is in the polyhedral spaces and the water (representing alveolar wall tissue) is in the boundaries.

pends on the orientation

of the cylinder relative to the magnetic field (Fig. 5); the shift is largest for the cylinder’s long axis parallel to B. and smallest for the long axis perpendicular to BO. Figure 6 shows line shapes from the central portion of the lung. Voxel P is expanded, and the experimental shape can be fit as a superposition of parenchymal (Wigner-Seitz) and nonparenchymal (cylinder) lines. These results suggest that regional line shape measurements can distinguish different types of geometry in rat lung. Because of the obvious sensitivity of NMR line shape to water geometry, we have extended our theoretical investigations to other types of water geometry (slabs, cubes, cubical shells).6*7 A comparison of experimental measurements with theoretical line shapes is shown for various geometrical phantoms in Fig. 7. For the slabs, as with the cylinders, we found that the field shift depends on the orientation of the slab relative to the magnetic field direction, being maximum (--9 ppm) for B,, parallel to the face of the slab and minimum (close to zero) for B0 perpendicular. For cubes, the field shift is intermediate (--6 ppm) between these extremes and is comparable to that for a

Industrial applications of inhomogeneous broadening imaging 0 D.C. AILION

(a)

2DFT

(b)

image

801

Tracing

Fig. 3. Image of an excised rat lung: (a) Two-dimensional FT image. (b) Schematic drawing indicating, by the letters A-I in the outer (parenchymal) region and by the letters J-Q in the inner (nonparenchymal) region, voxels from which line shapes were measured.

A A A I

1 I

A

I I

I I I I I

&A

A

I

FIELD

,‘I I

(porn)

(b)

I

A

I

I

Ii I

I

Fig. 4. NMR line shapes from the outer, or alveolar, region of the excised rat lung. (a) Measured line shapes from voxels A-I; (b) expanded line shape for voxel B showing a comparison of measured with calculated line shape based on modified Wigner-Seitz model.

I

I I I I

-3 0

SHIFT

3 6

ppa

-3 0 3 6

PPa

Magnetic Resonance Imaging 0 Volume 10, Number 5, 1992

802

FIELD SHIFT (ppml

(a)

Parallel

FIELD SHIFT

to Bo

(b)

Perpendicular

Fig. 5. NMR line shapes for a cylinder of water (a) parallel to B, and (b) perpendicular

(ppm)

to Bo to B,.

Experimental

-LA-

-AI

-A!I

-10

I

I

AL

-3 0 3 6

PPB

-5

5 0 10 FIELD SHIFT @pm)

(b)

-3 0 3 6

solid sphere. However, unlike the sphere, the field inside a cube is not uniform, so that the cube shows some line broadening. The cubical shell for which B,, is perpendicular to one face has four faces that are parallel to the field and two that are perpendicular to it. These features appear in the figure. In summary, it appears that the NMR properties of water can be categorized on the basis of the aspect ratio in terms of

ppm

Fig. 6. NMR line shapes from the inner, or bronchial, regions of the excised rat lung of Fig. 4. (a) Measured line shapes from voxels J-Q; (b) expanded line shape for voxel P showing a comparison of measured with calculated line shape based on a superposition of Wigner-Seitz and cylindrical

models.

“thick” water (resulting in a narrow linewidth) and “thin” water (resulting in a broad linewidth whose field at the peak depends on the orientation of the thin water relative to the magnetic field. Chemical Shift Broadening In addition to the susceptibility broadening described above, there may be other sources of internal

Industrial applications of inhomogeneous lluckness

= 0.005"

EXPERIMENTAL

Field Shlfl @pm)

(b) Thickness = O.wO5”

(cl

(4

Fig. 7. Comparison of theoretical (solid) with experimental (dashed) NMR line shapes for various water geometries. (a) Water slab perpendicular to Bo;(b) water slab parallel to B,,; (c) water cube with face perpendicular to BO; and (d) cubical water shell with face perpendicular to BO.

inhomogeneous broadening. For example, fat and oil typically have a number of chemically shifted proton groups, which collectively can appear as an inhomogeneously broadened line. Accordingly, the FID for fat or oil should be shorter than that of bulk water. In addition, NMR spectra of typical fats and oils usually show two separated groups of lines: a narrow Hz0 line and a broadened bundle of chemically shifted alkyl lines.’ These two groups of lines will interfere in

.

(b)

such a way as to cause beats in the FID. For two narrow resonance lines M, and M2, separated by a frequency Aw, the resultant FID can be written as8 M=

(M:+M;+2M,M2cosAwt)1’2.

MOTOR

OIL

(1)

Thus, when t = ?T/Aw, M = Ml - M2, and the FID will

show a beat. The signal from fat can be separated from that of muscle by utilizing this beat phenomenon.’ Figure 8 shows line shape measurements of corn oil, motor oil, and water in identical containers. In Fig. 8a the spectrum of corn oil shows the strong alkyl peak and a weaker, but still noticeable, water peak. For motor oil (Fig. 7b), the water peak is barely discernible, since there is much less Hz0 here; also the linewidth is less than that of the corn oil sample. Figure 8c shows a pure water sample; note that the linewidth is considerably less than that of corn oil and motor oil. New

-

w WATER

FREQUENCY(Hz) __,

Fig. 8. Measured NMR line shapes at 1.O T for various liquids: (a) corn oil; (b) motor oil; and (c) water.

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Magnetic Resonance Imaging 0 Volume 10, Number 5, 1992

methods for separating the signals of oil and water will be presented in later parts of this paper. ASYMMETRICAL

IMAGING TECHNIQUE

Over the last 8 yr we have developed techniques for imaging the tissues that exhibit internal inhomogeneous broadening. These techniques involve pulse sequences that are temporally symmetrical or asymmetrical with respect to the time interval 7 between the 90” and 180” pulses and the time interval 7’ between the 180” pulse and the echo (see Fig. 9). With these techniques we can easily separate in an image the regions that are inhomogeneously broadened from those that are not. We typically apply a frequency-encoding magnetic field gradient G, in between the 90” and 180” pulses with a refocusing gradient following the 180” pulse. For an internally inhomogeneously broadened sample, there will be two sources of dephasing: (1) the dephasing due to the sample-induced inhomogeneous broadening, which will refocus at 27, and (2) the dephasing due to the external field gradient G,, which will refocus at a time (7 + 7’) when the area under the gradient following the 180” pulse equals the area under the gradient between the 90” and 180” pulses. The combined effects of these two sources of dephasing determines the amplitude of the spin echo. In a symmetrical sequence (7 = T’), these two dephasings will refocus at the same time (27) resulting in maximum echo height. In the asymmetrical sequence (7 # T’), the refocusing of the dephasing due to the internal field gradients will still

Symmetric

spin

echo

sequence

at 27 but will no longer be coincident with the refocusing of the dephasing due to the external field gradient G,, which will occur at 7 + 7’. Since these signals refocus at different times, the echo height with the asymmetrical sequence will be reduced compared with that with the symmetrical sequence. For a normal occur

(T =T ‘)

(b)

-r-

(4 Asymmetric spin 90”

echo

sequence

( T#

T ‘)

180”

rf

“&

I A uu

Fig. 9. Pulse sequences used in NMR images of lung: (a) symmetrical (7 = 7’); (b) asymmetrical (T # 7‘).

Fig. 10. NMR image of thorax of intact dead rat: (a) symmetrical; (b) asymmetrical; and (c) difference. (Modified from Ref. 4, with permission.)

Industrial applications of inhomogeneous broadening imaging 0 D.C.

tissue, such as liver, which shows no internal inhomogeneous broadening, the signals obtained with the symmetrical and the asymmetrical sequences will be equal. In contrast, the asymmetrical signal in inflated lung, which shows considerable internal inhomogeneous broadening due to the air-water interfaces, will be considerably reduced compared with the symmetrical signal. Thus, by subtracting voxel-by-voxel the asymmetrical from the symmetrical image, we can form a difference image representing only those regions exhibiting internal inhomogeneous broadening (Fig. 10).

AILION

805

SPIN ECHO AMPLITUDE M(T + T’) = MO

exp(-(Av*)z.*/

2) exp(+

DEGASED

+ T’) I T2 )

RAT LUNG

A-------A

A

NEW TECHNIQUES FOR IMAGING LINE BROADENING

Linewidth Imaging Because of the valuable information obtainable from the linewidth, we have been particularly interested in developing techniques for determining the regional variation of the linewidth. Using the asymmetrical imaging technique described above, we have recently developed a new kind of image (a linewidth imagelO~l’), in which the local intensity within a voxel is proportional to the linewidth within the voxel, rather than the water density. Since the linewidth characterizes the nature of the water, rather than the density of the water, such an image can provide information not easily obtained from the usual proton density images. We have calculated, assuming a Gaussian line shape, that the signal echo amplitude M( 7 + 7’) arising in the asymmetrical imaging sequence (Fig. 9) from a voxel at 7 + 7’ is given by M(7 + 7’) = M,exp[

-(‘z

“)]exp[

-cA~‘7’]

(2) where MO is the equilibrium magnetization, 7, = 7 7’ is the asymmetry time, and (Au*) is the contribution to the second moment of the NMR line within a voxel arising from internal inhomogeneous broadening. The quantity (Av2) can be obtained for each voxel by measuring the spin-echo amplitude for different asymmetry times but at fixed 7 + 7’. Equation (2) predicts that a plot of In M versus 7: should be a straight line of negative slope. We have verified this feature in a number of systems (Fig. 11) and have obtained excellent agreement between (A v*> determined from the slopes in an imaging experiment and the linewidth of the resonant line, determined by the width at half-maximum, in a nonimaging experiment. To demonstrate the power of this technique, we constructed a phantom (Fig. 12a) of the thorax con-

\”

I 5

I 10

I

I

15

20

ra Note:

In(M) is proportional

1

25

2 hs2)

to -2,2

Fig. 11. Semilog plot of magnetization for various samples exhibiting internal broadening.

vs. T: measured inhomogeneous

sisting of two sponges (simulating the lungs) of slightly different water content [sponge 1 (13% water by volume) and sponge 2 (18% water)], which were individually sealed in separate plastic containers and then immersed in water (simulating the chest wall). Figure 12b shows a normal proton density image (symmetrical spin-echo image). Even though the regions of higher water density in the bottom and in sponge 2 appear somewhat brighter, it is very difficult to determine the boundary between the sponges (broad-line water) and the bulk water at the bottom (narrow-line water). In the linewidth image (Fig. 12~) voxels having a narrow linewidth appear darker than voxels exhibiting inhomogeneous broadening. Accordingly, the bulk water at the bottom is easily distinguished from water in the sponges. We have recently applied this technique to rat lungs. Phase Imaging As described earlier, fats and oils typically exhibit inhomogeneous broadening, as well as beats in the FID, due to the various chemically shifted alkyl groups. It is often desirable to separate these in an image. We produced two cylindrical sample vials containing oil (motor oil and corn oil) floating on water. Figure 13 shows symmetrical, asymmetrical (7, = 3 msec), and a difference signal for each. As can be seen, the difference image shows good contrast for the

Magnetic Resonance Imaging 0 Volume 10, Number 5, 1992

806

SPONGE

PHANTOM

PROTON

DENSITY IMAGE

LINEWIDTH IMAGE

Fig. 12. Images of thorax phantom consisting of two moist sponges (Sl and S2) representing the lungs, and water representing the chest wall. (a) Drawing of phantom. (b) Symmetrical proton density image (brightness is proportional to local water density). (c) Linewidth image (brightness is proportional to the local NMR linewidth). Sl = 13% water; S2 = 18% water; W = water.

SYMMETRIC

ASYMMETRIC

(3mscc)

DIFPERENCE

CORN OIL WATER (a)

M1DTOR OIL WATER (b)

Fig. 13. NMR images of cross-sections of cylindrical tubes of oils floating on water. (a) Corn oil on water; (b) motor oil on water. From left to right are symmetrical, asymmetrical (ra = 3 msec), and difference images, respectively. The gap at the top is due to a small air bubble. Note the poor contrast in the difference image of the motor oil-water mixture. The NMR line shapes of the component liquids are shown in Fig. 8.

Industrial applications of inhomogeneous broadening imaging 0 D.C.

sample of corn oil floating on water. However, the motor oil has a narrower linewidth (see Fig. 8) than that of corn oil and even approaches the narrow linewidth of water; as a result, there is poor contrast between the motor oil and water. However, by increasing r, to a much larger value, say 10 msec, we have obtained improved contrast. In order to obtain improved contrast between narrow-line systems like motor oil and water, K. Ganesan and I have developed a technique based on phase imaging. Previously, phase imaging has been used to assist in field shimmingi and in mapping the susceptibility13 in biological systems. Even though the motor oil’s linewidth is not very large compared with that of water, it is significantly shifted in frequency (see Fig. 8). Accordingly, with the asymmetrical sequence, the signal from the oil will not have completely refocused at the time of the water echo, even though the two signals will refocus at the same time with the symmetrical sequence. Since the relative phase can be easily measured for each voxel, we can obtain an image of the spatial variation of the relative phase. Figure 14 shows such an image. Note that we now obtain excel-

SYMMETRIC IMAGE

AILION

807

lent contrast, both for the motor oil-water and for the corn oil-water samples with the asymmetrical imaging technique. POTENTIAL

INDUSTRIAL

APPLICATIONS

The most obvious applications of the techniques presented is in the medical area, particularly in the study of lungs. Since the NMR linewidth is very sensitive to the degree of inflation (aeration), our linewidth techniques are well suited to studying diseases of the lung that are associated with variations in the degree of inflation as well as variations in the alveolar structure. A particularly nice feature of these techniques is that they are capable of determining alveolar geometry without requiring alveolar resolution (-70 pm). In particular, such diseases as pulmonary edema and emphysema appear to be amenable to study by our techniques. Also, the effects of various chemicals and drugs on the lung may appear as variations in linewidth as well as in local water density. This area of application has yet to be thoroughly investigated.

ASYMMETRIC IMAGE

(3msec)

Fig. 14. Relative phase images of cylindrical tube samples used in Fig. 13: (a) corn oil-water; (b) motor oil-water. The images on the left are symmetrical and those on the right are asymmetrical (7, = 3 msec). Note the improved contrast, especially for the motor oil-water sample.

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Magnetic Resonance Imaging 0 Volume 10, Number 5, 1992

Another area of medical application is in contrasting fat from other tissues. A lot of work has already been done in utilizing the technique, independently developed by our group*,’ and Dixon,’ for using the water-alkyl beats to separate fat from tissue in MRI. However, relatively little work has been done to exploit the broader linewidths of fat in asymmetrical imaging sequences. The use of phase imaging to separate oil and water has applications beyond the medical area. An area of possible industrial importance is in separating oil from water in oil shale. An advantage of the NMR imaging techniques described above is that they are completely nondestructive. The susceptibility broadening described in this paper can apply, not only to air-water interfaces as in the lung, but also to any interfaces between water and material of different susceptibility (e.g., Si02). As a result, they might be particularly useful in studying the nature of water deposits in porous media. Acknowledgments-This research was supported by the U.S. National Institutes of Health under Grants HL31216 and CA44972. Particular thanks go to Dr. K. Ganesan for his great help in preparing the figures for this manuscript and for critically reading it. The research described in this paper represents the combined work of the author and his colleagues and students listed here: J. Bertolina, D.D. Blatter, T.A. Case, R.A. Christman, A.G. Cutillo, C.H. Durney, K. Ganesan, K.C. Goodrich, S. Hasbemi, S. Johnson, A.H. Morris, and S. Shioya.

REFERENCES Slichter, C.P. Principles of magnetic resonance, 3d ed. Berlin: Springer-Verlag, 1990. D.C.; Case, T.A.; Blatter, D.D.; Morris, A.H.; Cutillo, A.G.; Durney, C.H.; Johnson, S.A. Applications of NMR spin imaging to the study of lungs. Bull. Mugn. Reson. 6:130-139; 1984. Case, T.A.; Durney, C.H.; Ailion, D.C.; Cutillo, A.G.; Morris, A.H. A mathematical model of diamagnetic line broadening in lung tissue and similar heterogeneous systems: Calculations and measurements. .Z.Mugn. Reson. 73:304-314; 1987. Ailion,

4. Morris, A.H.; Blatter, D.D.; Case, T.A.; Cutillo, A.G.; Ailion, D.C.; Durney, C.H.; Johnson, S.A. A new nuclear magnetic resonance property of lung. J. Appf. Physiol. 58:759-762; 1985. 5. Christman, R.A.; Case, T.A.; Ailion, D.C.; Shioya, S.; Cutillo, A.G.; Durney, C.H.; Morris, A.H. Comparison of calculated and experimental NMR spectral broadening for lung tissue. Unpublished. 6. Durney, C.H.; Bertolina, J.A.; Ailion, D.C.; Christman, R.A.; Cutillo, A.G.; Morris, A.H.; Hashemi, S. Calculation and interpretation of inhomogeneous line broadening in models of lungs and other heterogeneous systems. J. Mugn. Resonan. 85:554-570; 1989. 7. Bertolina, J.A.; Durney, C.H.; Ailion, D.C.; Cutillo, A.G.; Morris, A.H.; Goodrich, K.C. Experimental verification of inhomogeneous line broadening calculations in lung models and other inhomogeneous structures. .Z. Magn. Resonan. (in press). 8. Blatter, D.D.; Morris, A.H.; Ailion, D.C.; Cutillo, A.G.; Case, T.A. Asymmetric spin echo sequences: A simple new method for obtaining NMR ‘H spectral images. Invest. Rudiol. 20:845-853; 1985. 9. Dixon, W.T. Simple proton spectroscopic imaging. Radiology 153:189-194; 1984. 10. Ganesan, K.; Ailion, D.C. Spin echo calculation for the asymmetric spin echo imaging sequence. In: Book of abstracts: Eighth Annual Meeting of the Society of Magnetic Resonance in Medicine. Amsterdam: Society of Magnetic Resonance in Medicine; 1989:810. 11. Ganesan, K.; Goodrich, K.C.; Ailion, D.C.; Cutillo, A.G.; Durney, C.H.; Morris, A.H. A new technique for obtaining NMR linewidth images in lung and other inhomogeneously broadened systems. In: Book of abstracts: Tenth Annual Meeting of the Society of Magnetic Resonance in Medicine. San Francisco: SMRM; 1991: 206. 12. Sekihara, K.; Matsui, S.; Kohno, H. A new method of measuring static field distribution using modified FOUrier NMR imaging. J. Phys. E: Sci. Znstrum. 18:224227; 1985.

13. Cox, I.J.; Bydder, G.M.; Gadian, D.G.; Young, I.R.; Proctor, E.; Williams, S.R.; Hart, I. The effect of magnetic susceptibility variations in NMR imaging and NMR spectroscopy 168; 1986.

in vivo. J. Mugn. Resonun. 70:163-

Potential industrial applications of inhomogeneous broadening imaging.

Variations in magnetic susceptibility at air-water interfaces can result in inhomogeneous broadening of the NMR line. By special asymmetrical imaging ...
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