MAGNETIC RESONANCE IN MEDICINE 19,228-232
( 1991)
Diffusion and Perfusion in High Resolution NMR Imaging and Microscopy *,?
c. B. AHNAND z. H. CHOS Department of Radiological Sciences, University of California, Iwine, Irvine, California 9271 7 Received February I , 1991 Diffusion and perfusion phenomena under strong gradient fields ( - 100 G/cm) are examined in high resolution nuclear magnetic resonance (NMR) imaging and microscopy, where diffusion-associatedsignal attenuation predominates over T , and T, relaxation decays. Image contrast based on the diffusion and microcirculation is discussed with experimental results obtained with a 7.0-T microscopy system. Ultimate resolution limit due to diffusion 1991Academic Press, Inc. is investigated in high resolution NMR imaging and microscopy. INTRODUCTION
Diffusion is a transport process resulting from random molecular motion whose rate can be represented by the diffusion coefficient or diffusivity. Measurement of the diffusion coefficient by NMR techniques had been tried as early as the 1950s ( I , 2), and recently two-dimensional diffusion coefficient mapping in biological samples has been applied (3-5). Perfusion, on the other hand, is related to the microcirculation in biological system such as through capillaries, where blood motion in the capillary is coherent during the echo time, even though directions of capillaries in a voxel are distributed randomly. Thus perfusion may be modeled as an ensemble of randomly oriented coherent flows (6, 7). One similarity between diffusion and perfusion in NMR imaging is that both of them cause signal attenuations under a bipolar gradient, rather than affecting phases like coherent bulk flow in large arteries. One difference, however, is that recovery of the attenuated signal is possible in the perfusion due to the coherent motion in the capillary, e.g., by the acquisition of an even echo (6). Diffusion, however, is a pure Brownian random motion and therefore a perfect refocusing is impossible (8). Since the microcirculation in tissue is heavily dependent on the local tissue activity, tissue diffusion and perfusion may be useful parameters for organ functional imaging. Several experimental NMR pulse sequences for the measurements of diffusion and perfusion have been developed (3-7). Although perfusion fraction is an interesting parameter quantitatively related with tissue perfusion ( 7), the parameter is extremely sensitive to noise due to biexponential fit ( 9 ) .Perfusion imaging by the subtraction of flow-uncompensatedimage (first echo image) from flow-compensatedimage (second * Presented at SMRM Workshop on Future Directions in MRI of Diffusion and Microcirculation,Bethesda, MD, June 7 and 8, 1990. This work was supported in part by NIH Grant ROI H D 25390-01A 1. $ Also at the Department of Electrical Science, Korea Advanced Institute of Science, Seoul, Korea. 0740-3 194191 $3.00 Copyright Q 199 1 by Academic Press, Inc. All rights of reproduction in any form reserved.
228
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DIFFUSION AND PERFUSION IN NMR MICROSCOPY
echo image) is, however, less sensitive to noise than the biexponential fit thereby maximizing signal-to-noiseratio ( 6, 10). One of the major difficultiesin the application of perfusion imaging to in vivo human study is the relative small ratio of the capillary beds to stationary tissues ( I 1 ). Signal variation due to the diffusion is also less than the T I or T2 decays in the conventional imaging under gradient strength less than 0.5 G/cm. As will be discussed in the next section, the diffusion- and perfusion-related signal attenuations will determine image contrast dominantly in the high resolution NMR imaging and microscopy where employed gradient strength is in the order of 10-100 G / cm. Some features of microscopic imaging as well as diffusion-associated resolution degradation will be investigated with experimental results. IMAGE CONTRAST BY DIFFUSION AND PERFUSION IN NMR MICROSCOPY
One of the emerging applications of nuclear magnetic resonance imaging is microscopy which allows biological samples to be studied at the cellular or subcellular level noninvasively (12-16). Other major advantages of NMR microscopy are its nonionizing nature, inherent high resolution, and high contrast tomographic capability which may allow true in vivo three-dimensional imaging of cells. From the well-known diffusion formula ( 2 ) ,signal intensity affected by diffusion is given by I ( t ) = Z(O)exp(-y2DG2t3/3) with gyromagnetic ratio y,diffusion coefficient D ,gradient strength G, and time t . For a biological sample with a diffusion coefficient of 1.0 x 1 0 - ~cm2/s (diffusion coefficient for water is 2.2 x 1 0 - ~cm2/s), NMR signal intensities affected by the diffusion are plotted in Fig. 1 as a function of time for conventional imaging ( G = 0.5 G/cm) and microscopic imaging (G = 50 G/cm). Signal intensity affected by the T2relaxation ( T2 = 40 ms) is also shown for comparison. As shown in these plots, T2attenuation is much larger than the diffusionassociated attenuation in the conventional imaging, and thus T2 relaxation plays a 1 .o
in conventional imaging
0.8 W
U
3 .= 0.6 Q E,
-
0.4 CI) .-
v)
0.2
0.0 0
10
20
30
40
50
Time [ms]
FIG. 1 . Signal intensities affected by diffusion and T2relaxation in conventional imaging and microscopy.
230
AHN AND CHO
more important role in the image contrast. With increased gradient strength in high resolution imaging, however, the intensity variation by diffusion predominates over the T 2 decay. Furthermore due to increased relaxation times in high field imaging, together with excessive signal attenuation with long echo time, contrast based on the relaxation processes may no longer be an efficient way to obtain physiological information. Since the diffusion coefficient reflects physical characteristics of the tissue, it could be an important physiological parameter measurable by NMR microscopy. These facts are demonstrated in Fig. 2 with microscopic phantom images (2 mm diameter). They are acquired by the 3D spin-echo sequence (256 X 256 X 16) with repetition time of 500 ms and echo time of 9 ms. Large intensity variation (contrast) is observed due to diffusion which is controlled by the gradient durations; i.e., the dephasing and rephasing periods of the readout gradient are 2.5 and 3.5 ms for the lightly diffusion-weighted image and heavily diffusion-weighted image, respectively.
FIG. 2. Experimentally obtained microscopic phantom images containing water, DMSO, and glycerol with a 7.0-T microscopy system.
DIFFUSION AND PERFUSION IN NMR MICROSCOPY
23 1
Larger intensity variation is observed in the region containing higher diffusion coefficient (e.g., water) compared with those regions with lower diffusion coefficients (e.g., DMSO and glycerol). Diffusion coefficient map is also calculated from the two differently diffusion-weighted images. The effect of perfusion in biological tissue is dependent on the voxel size and average capillary size of the tissue. For example, a single capillary flow may be considered as a bulk flow if the voxel size is much smaller than the capillary size. Figure 3 shows experimentally obtained images of human liver biopsy (whole object size is ( 1.5 mm) 3, which is much smaller than 1 voxel in conventional imaging), where capillaries with diameters of about 30 p m are observed. Since the voxel size (8 X 8 X 50 pm) is less than the capillary diameter, the capillary flow would appear as a coherent bulk flow rather than perfusion as would be the case in conventional imaging. DIFFUSION-LIMITED RESOLUTION IN NMR MICROSCOPY
From basic NMR imaging formulas, it appears that the spatial resolution can be improved by increasing either the gradient strength or the acquisition time ( Taq);
FIG.3. Microscopic images of human liver biopsy obtained by the 3D spin-echo technique (256 X 256 X 32) with repetition time of 300 ms and echo time of 6 ms. Small capillaries with diameters of about 30
gm are observable (marked with white triangle) with image voxel size of 8 X 8 X 50 gm.
232
AHN AND CHO
molecular diffusion,however, will ultimately limit the resolution in N M R microscopy. Considering the fact that the diffusion-dependent root-mean-square phase variation should be less than the encoded phase by gradient, the diffusion-limited resolution is given by ( 1 3 ) .This is the inherent resolution limit due to the physical characteristics of the sample (diffusion coefficient) in micrometer size N M R imaging. Another important resolution-limiting factor in microscopy is the line broadening due to the diffusion-induced signal attenuation (8, 1 7 ) .This is due to the exponential decay of the signal amplitude associated with diffusion, which results in a line spread in the image domain. The line spread function obtained by the Fourier transform of the diffusion-affected signal amplitude could be a major resolution degradation factor in N M R microscopy for many biological samples.
v
m
CONCLUSION
Diffusion and perfusion in high resolution NMR imaging and microscopy are discussed with experimental results obtained with a 7.0-T microscopy system. Under strong gradient fields ( 10- 100 G/cm) diffusion appears to be a dominant tissue contrast parameter. Since the diffusion coefficient reflects physical status of the tissue, it can be an important physiological contrast parameter in N M R microscopy. The effect of perfusion in high resolution imaging is, however, dependent on the image voxel size and average capillary size; for example, a single capillary flow may be considered as a bulk flow if the voxel size is much less than the capillary size. The ultimate resolution in N M R microscopy is limited by diffusion due to both random phase and the line spread by the diffusion-associated amplitude variation. REFERENCES 1. E. L. HAHN,Phys. Rev. 80, 580 (1950). 2. H. Y. CARRAND E. M. PURCELL,Phys. Rev. 94,630 (1954). 3. G. E. WESBEY,M. A. MOSELEY, AND R. L. EHMAN,Invest. Radiol. 19,491 ( 1984).
4. D. LE BIHAN,E. BRETON,D. LALLEMAND, P.GRENIER,E. A. CABANIS,AND M. LAVAL-JEANTET, Radiology 161,401 (1986). 5. C. B. AHN,S. Y. LEE,0. NALCIOGLU, AND Z. H. CHO,Med. Phys. 13,789 (1986). 6. C. B. AHN,S. Y. LEE,0. NALCIOGLU, AND Z. H. CHO,Med. Phys. 14,43 (1987). 7. D. LE BIHAN,E. BRETON,D. LALLEMAND, M. L. AUBIN,J. VIGNAUD,AND M. LAVAL-JEANTET, Radiology 168, 497 ( 1988). 8. C . B. AHNAND Z. H. CHO,Med. Phys. 16,22 (1989). 9. C. T. W. MOONEN,J. PEKAR,AND P. C. M. VAN ZUL, in “Book of Abstracts, SMRM,” p. 384, 1990. 10. N. FUJITA,K. HARADA, K. SAKURAI, Y. AKAI, K. NAKANISHI, s. W. KIM.,AND T. KOZUKA,in “Book of Abstracts, SMRM,” p. 315, 1990. 11. Z. H. CHOAND C. B. AHN,Med. Phys. 14, 1092 ( 1987). 12. J. B. AGUAYO,S. J. BLACKBAND, J. SCHOWNIGER, M. A. MATTINGLY, AND M. HINTERMANN, Nature 322, 190 (1986). 13. Z. H. CHO,C. B. AHN,S. C. JUH,H. K. LEE,R. E. JACOBS,S. LEE,J. H. Yr, AND J. M. Jo, Med. Phys. 15,815 (1988). 14. R. A. MEYERAND T. R. BROWN,J. Magn. Reson. 76, 393 (1988). 15. C. B. AHN,J. A. ANDERSON, S. C. JUH,I. KIM, W. H. GARNER,AND Z. H. CHO,Invest. Ophthalmol. Vis. Sci. 30, 1612 (1989). 16. Z. H. CHO, C. B. AHN, S. C. JUH, R. M. FRIEDENBERG, R. E. JACOBS,AND S . E. FRASER,J. Visual Commun. Image Represent 1, 56 (1990). 17. P. T. CALLAGHAN AND C. D. ECCLES,J. Magn. Reson. 78, 1 ( 1988).
( 1991)
Diffusion and Perfusion in High Resolution NMR Imaging and Microscopy *,?
c. B. AHNAND z. H. CHOS Department of Radiological Sciences, University of California, Iwine, Irvine, California 9271 7 Received February I , 1991 Diffusion and perfusion phenomena under strong gradient fields ( - 100 G/cm) are examined in high resolution nuclear magnetic resonance (NMR) imaging and microscopy, where diffusion-associatedsignal attenuation predominates over T , and T, relaxation decays. Image contrast based on the diffusion and microcirculation is discussed with experimental results obtained with a 7.0-T microscopy system. Ultimate resolution limit due to diffusion 1991Academic Press, Inc. is investigated in high resolution NMR imaging and microscopy. INTRODUCTION
Diffusion is a transport process resulting from random molecular motion whose rate can be represented by the diffusion coefficient or diffusivity. Measurement of the diffusion coefficient by NMR techniques had been tried as early as the 1950s ( I , 2), and recently two-dimensional diffusion coefficient mapping in biological samples has been applied (3-5). Perfusion, on the other hand, is related to the microcirculation in biological system such as through capillaries, where blood motion in the capillary is coherent during the echo time, even though directions of capillaries in a voxel are distributed randomly. Thus perfusion may be modeled as an ensemble of randomly oriented coherent flows (6, 7). One similarity between diffusion and perfusion in NMR imaging is that both of them cause signal attenuations under a bipolar gradient, rather than affecting phases like coherent bulk flow in large arteries. One difference, however, is that recovery of the attenuated signal is possible in the perfusion due to the coherent motion in the capillary, e.g., by the acquisition of an even echo (6). Diffusion, however, is a pure Brownian random motion and therefore a perfect refocusing is impossible (8). Since the microcirculation in tissue is heavily dependent on the local tissue activity, tissue diffusion and perfusion may be useful parameters for organ functional imaging. Several experimental NMR pulse sequences for the measurements of diffusion and perfusion have been developed (3-7). Although perfusion fraction is an interesting parameter quantitatively related with tissue perfusion ( 7), the parameter is extremely sensitive to noise due to biexponential fit ( 9 ) .Perfusion imaging by the subtraction of flow-uncompensatedimage (first echo image) from flow-compensatedimage (second * Presented at SMRM Workshop on Future Directions in MRI of Diffusion and Microcirculation,Bethesda, MD, June 7 and 8, 1990. This work was supported in part by NIH Grant ROI H D 25390-01A 1. $ Also at the Department of Electrical Science, Korea Advanced Institute of Science, Seoul, Korea. 0740-3 194191 $3.00 Copyright Q 199 1 by Academic Press, Inc. All rights of reproduction in any form reserved.
228
229
DIFFUSION AND PERFUSION IN NMR MICROSCOPY
echo image) is, however, less sensitive to noise than the biexponential fit thereby maximizing signal-to-noiseratio ( 6, 10). One of the major difficultiesin the application of perfusion imaging to in vivo human study is the relative small ratio of the capillary beds to stationary tissues ( I 1 ). Signal variation due to the diffusion is also less than the T I or T2 decays in the conventional imaging under gradient strength less than 0.5 G/cm. As will be discussed in the next section, the diffusion- and perfusion-related signal attenuations will determine image contrast dominantly in the high resolution NMR imaging and microscopy where employed gradient strength is in the order of 10-100 G / cm. Some features of microscopic imaging as well as diffusion-associated resolution degradation will be investigated with experimental results. IMAGE CONTRAST BY DIFFUSION AND PERFUSION IN NMR MICROSCOPY
One of the emerging applications of nuclear magnetic resonance imaging is microscopy which allows biological samples to be studied at the cellular or subcellular level noninvasively (12-16). Other major advantages of NMR microscopy are its nonionizing nature, inherent high resolution, and high contrast tomographic capability which may allow true in vivo three-dimensional imaging of cells. From the well-known diffusion formula ( 2 ) ,signal intensity affected by diffusion is given by I ( t ) = Z(O)exp(-y2DG2t3/3) with gyromagnetic ratio y,diffusion coefficient D ,gradient strength G, and time t . For a biological sample with a diffusion coefficient of 1.0 x 1 0 - ~cm2/s (diffusion coefficient for water is 2.2 x 1 0 - ~cm2/s), NMR signal intensities affected by the diffusion are plotted in Fig. 1 as a function of time for conventional imaging ( G = 0.5 G/cm) and microscopic imaging (G = 50 G/cm). Signal intensity affected by the T2relaxation ( T2 = 40 ms) is also shown for comparison. As shown in these plots, T2attenuation is much larger than the diffusionassociated attenuation in the conventional imaging, and thus T2 relaxation plays a 1 .o
in conventional imaging
0.8 W
U
3 .= 0.6 Q E,
-
0.4 CI) .-
v)
0.2
0.0 0
10
20
30
40
50
Time [ms]
FIG. 1 . Signal intensities affected by diffusion and T2relaxation in conventional imaging and microscopy.
230
AHN AND CHO
more important role in the image contrast. With increased gradient strength in high resolution imaging, however, the intensity variation by diffusion predominates over the T 2 decay. Furthermore due to increased relaxation times in high field imaging, together with excessive signal attenuation with long echo time, contrast based on the relaxation processes may no longer be an efficient way to obtain physiological information. Since the diffusion coefficient reflects physical characteristics of the tissue, it could be an important physiological parameter measurable by NMR microscopy. These facts are demonstrated in Fig. 2 with microscopic phantom images (2 mm diameter). They are acquired by the 3D spin-echo sequence (256 X 256 X 16) with repetition time of 500 ms and echo time of 9 ms. Large intensity variation (contrast) is observed due to diffusion which is controlled by the gradient durations; i.e., the dephasing and rephasing periods of the readout gradient are 2.5 and 3.5 ms for the lightly diffusion-weighted image and heavily diffusion-weighted image, respectively.
FIG. 2. Experimentally obtained microscopic phantom images containing water, DMSO, and glycerol with a 7.0-T microscopy system.
DIFFUSION AND PERFUSION IN NMR MICROSCOPY
23 1
Larger intensity variation is observed in the region containing higher diffusion coefficient (e.g., water) compared with those regions with lower diffusion coefficients (e.g., DMSO and glycerol). Diffusion coefficient map is also calculated from the two differently diffusion-weighted images. The effect of perfusion in biological tissue is dependent on the voxel size and average capillary size of the tissue. For example, a single capillary flow may be considered as a bulk flow if the voxel size is much smaller than the capillary size. Figure 3 shows experimentally obtained images of human liver biopsy (whole object size is ( 1.5 mm) 3, which is much smaller than 1 voxel in conventional imaging), where capillaries with diameters of about 30 p m are observed. Since the voxel size (8 X 8 X 50 pm) is less than the capillary diameter, the capillary flow would appear as a coherent bulk flow rather than perfusion as would be the case in conventional imaging. DIFFUSION-LIMITED RESOLUTION IN NMR MICROSCOPY
From basic NMR imaging formulas, it appears that the spatial resolution can be improved by increasing either the gradient strength or the acquisition time ( Taq);
FIG.3. Microscopic images of human liver biopsy obtained by the 3D spin-echo technique (256 X 256 X 32) with repetition time of 300 ms and echo time of 6 ms. Small capillaries with diameters of about 30
gm are observable (marked with white triangle) with image voxel size of 8 X 8 X 50 gm.
232
AHN AND CHO
molecular diffusion,however, will ultimately limit the resolution in N M R microscopy. Considering the fact that the diffusion-dependent root-mean-square phase variation should be less than the encoded phase by gradient, the diffusion-limited resolution is given by ( 1 3 ) .This is the inherent resolution limit due to the physical characteristics of the sample (diffusion coefficient) in micrometer size N M R imaging. Another important resolution-limiting factor in microscopy is the line broadening due to the diffusion-induced signal attenuation (8, 1 7 ) .This is due to the exponential decay of the signal amplitude associated with diffusion, which results in a line spread in the image domain. The line spread function obtained by the Fourier transform of the diffusion-affected signal amplitude could be a major resolution degradation factor in N M R microscopy for many biological samples.
v
m
CONCLUSION
Diffusion and perfusion in high resolution NMR imaging and microscopy are discussed with experimental results obtained with a 7.0-T microscopy system. Under strong gradient fields ( 10- 100 G/cm) diffusion appears to be a dominant tissue contrast parameter. Since the diffusion coefficient reflects physical status of the tissue, it can be an important physiological contrast parameter in N M R microscopy. The effect of perfusion in high resolution imaging is, however, dependent on the image voxel size and average capillary size; for example, a single capillary flow may be considered as a bulk flow if the voxel size is much less than the capillary size. The ultimate resolution in N M R microscopy is limited by diffusion due to both random phase and the line spread by the diffusion-associated amplitude variation. REFERENCES 1. E. L. HAHN,Phys. Rev. 80, 580 (1950). 2. H. Y. CARRAND E. M. PURCELL,Phys. Rev. 94,630 (1954). 3. G. E. WESBEY,M. A. MOSELEY, AND R. L. EHMAN,Invest. Radiol. 19,491 ( 1984).
4. D. LE BIHAN,E. BRETON,D. LALLEMAND, P.GRENIER,E. A. CABANIS,AND M. LAVAL-JEANTET, Radiology 161,401 (1986). 5. C. B. AHN,S. Y. LEE,0. NALCIOGLU, AND Z. H. CHO,Med. Phys. 13,789 (1986). 6. C. B. AHN,S. Y. LEE,0. NALCIOGLU, AND Z. H. CHO,Med. Phys. 14,43 (1987). 7. D. LE BIHAN,E. BRETON,D. LALLEMAND, M. L. AUBIN,J. VIGNAUD,AND M. LAVAL-JEANTET, Radiology 168, 497 ( 1988). 8. C . B. AHNAND Z. H. CHO,Med. Phys. 16,22 (1989). 9. C. T. W. MOONEN,J. PEKAR,AND P. C. M. VAN ZUL, in “Book of Abstracts, SMRM,” p. 384, 1990. 10. N. FUJITA,K. HARADA, K. SAKURAI, Y. AKAI, K. NAKANISHI, s. W. KIM.,AND T. KOZUKA,in “Book of Abstracts, SMRM,” p. 315, 1990. 11. Z. H. CHOAND C. B. AHN,Med. Phys. 14, 1092 ( 1987). 12. J. B. AGUAYO,S. J. BLACKBAND, J. SCHOWNIGER, M. A. MATTINGLY, AND M. HINTERMANN, Nature 322, 190 (1986). 13. Z. H. CHO,C. B. AHN,S. C. JUH,H. K. LEE,R. E. JACOBS,S. LEE,J. H. Yr, AND J. M. Jo, Med. Phys. 15,815 (1988). 14. R. A. MEYERAND T. R. BROWN,J. Magn. Reson. 76, 393 (1988). 15. C. B. AHN,J. A. ANDERSON, S. C. JUH,I. KIM, W. H. GARNER,AND Z. H. CHO,Invest. Ophthalmol. Vis. Sci. 30, 1612 (1989). 16. Z. H. CHO, C. B. AHN, S. C. JUH, R. M. FRIEDENBERG, R. E. JACOBS,AND S . E. FRASER,J. Visual Commun. Image Represent 1, 56 (1990). 17. P. T. CALLAGHAN AND C. D. ECCLES,J. Magn. Reson. 78, 1 ( 1988).
