DOI: 10.1148/rg.26si065510
Understanding Diffusion MR Imaging Techniques: From Scalar Diffusion-weighted Imaging to Diffusion Tensor Imaging and Beyond1
Patric Hagmann, MD, PhD,
Lisa Jonasson, PhD,
Philippe Maeder, MD,
Jean-Philippe Thiran, PhD,
Van J. Wedeen, MD and
Reto Meuli, MD, PhD
1 From the Department of Radiology, Lausanne University Hospital (CHUV), Rue du Bugnon, 46, CH-1011 Lausanne, Switzerland (P.H., P.M., R.M.); Signal Processing Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland (P.H., L.J., J.P.T.); and MGH Martinos Center for Biomedical Imaging, Harvard Medical School, Charlestown, Mass (V.J.W.). Recipient of an Excellence in Design award for an education exhibit at the 2005 RSNA Annual Meeting. Received February 28, 2006; revision requested April 21 and received May 25; accepted June 9. All authors have no financial relationships to disclose. Supported by Swiss National Science Foundation 2153-066943.01 and 3235B0-102863, by NIH 1R01-MH64044, and by Yves Paternot.
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Figure 1. Diagram shows the diffusion-driven random trajectory (red line) of a single water molecule during diffusion. The dotted white line (vector r) represents the molecular displacement during the diffusion time interval, between t1 = 0 and t2 =  .
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Figure 3a. Diffusion within a single voxel. (a) Diagram shows the 3D diffusion probability density function in a voxel that contains spherical cells (top left) or randomly oriented tubular structures that intersect, such as axons (bottom left). This 3D displacement distribution, which is roughly bell shaped, results in a symmetric image (center), as there is no preferential direction of diffusion. The distribution is similar to that in unrestricted diffusion but narrower because there are barriers that hinder molecular displacement. The center of the image (origin of the r vector) codes for the proportion of molecules that were not displaced during the diffusion time interval. The color bar (right) shows the spectrum used in color coding to represent probability, from the lowest value, which is indicated by red, to the highest, which is indicated by blue. (b) Diagram shows the diffusion probability density function within a voxel in which all the axons are aligned in the same direction. The displacement distribution is cigar shaped and aligned with the axons. (c) Diagram shows the diffusion probability density function within a voxel that contains two populations of fibers intersecting at an angle of 90°. The molecular displacement distribution produces a cross shape.
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Figure 3b. Diffusion within a single voxel. (a) Diagram shows the 3D diffusion probability density function in a voxel that contains spherical cells (top left) or randomly oriented tubular structures that intersect, such as axons (bottom left). This 3D displacement distribution, which is roughly bell shaped, results in a symmetric image (center), as there is no preferential direction of diffusion. The distribution is similar to that in unrestricted diffusion but narrower because there are barriers that hinder molecular displacement. The center of the image (origin of the r vector) codes for the proportion of molecules that were not displaced during the diffusion time interval. The color bar (right) shows the spectrum used in color coding to represent probability, from the lowest value, which is indicated by red, to the highest, which is indicated by blue. (b) Diagram shows the diffusion probability density function within a voxel in which all the axons are aligned in the same direction. The displacement distribution is cigar shaped and aligned with the axons. (c) Diagram shows the diffusion probability density function within a voxel that contains two populations of fibers intersecting at an angle of 90°. The molecular displacement distribution produces a cross shape.
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Figure 3c. Diffusion within a single voxel. (a) Diagram shows the 3D diffusion probability density function in a voxel that contains spherical cells (top left) or randomly oriented tubular structures that intersect, such as axons (bottom left). This 3D displacement distribution, which is roughly bell shaped, results in a symmetric image (center), as there is no preferential direction of diffusion. The distribution is similar to that in unrestricted diffusion but narrower because there are barriers that hinder molecular displacement. The center of the image (origin of the r vector) codes for the proportion of molecules that were not displaced during the diffusion time interval. The color bar (right) shows the spectrum used in color coding to represent probability, from the lowest value, which is indicated by red, to the highest, which is indicated by blue. (b) Diagram shows the diffusion probability density function within a voxel in which all the axons are aligned in the same direction. The displacement distribution is cigar shaped and aligned with the axons. (c) Diagram shows the diffusion probability density function within a voxel that contains two populations of fibers intersecting at an angle of 90°. The molecular displacement distribution produces a cross shape.
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Figure 5. Left part of diagram shows that standard imaging methods provide one value (gray level) for every 3D position p. That value or gray level may code for the linear x-ray attenuation coefficient at CT or for the relative signal intensity at MR imaging. Right part of diagram shows that in diffusion imaging every 3D position p (voxel) is associated not with a gray level but with a 3D image that encodes the molecular displacement distribution in that voxel. The value measured at the coordinates p,r— (p,r)—indicates the proportion of molecules in the voxel that have moved the given distance r.
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Figure 6. Diagram shows two approaches that may be used to simplify the visual representation of 3D diffusion data: replacement of the displacement distribution with an isosurface, and computation of the orientation distribution function (ODF).
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Figure 7. Diagram shows how an orientation distribution function (ODF) is computed and represented. Left: Image of a section through a schematized 3D displacement distribution. The value of the orientation distribution function was computed along two axes (yellow lines). Center: Histograms represent the displacement distribution along the two axes. The value of the orientation distribution function along those axes equals the area under the curve for each axis. In this example, the two areas under the curve are respectively small and large, indicating that there is much less diffusion in the one direction than in the other. Right: The sum of the areas under the curve is represented by a deformed sphere in which the lengths of the two radii (yellow lines) are short and long, corresponding to little diffusion and much diffusion, respectively. To compute the orientation distribution function, the area under the curve is computed for every direction.
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Figure 8. Orientation distribution function map of a coronal brain section. For every brain position p, an orientation distribution function is plotted to characterize the local diffusion probability density function. It is easy to identify the corticospinal tract, in which the dominant color is blue, and the corpus callosum, in which red is predominant. More difficult to see are the cingulum and the arcuate fasciculus, depicted predominantly in green, and the middle cerebellar peduncle, in red.
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Figure 10. Diagram shows the process with which a standard position-encoded MR image is obtained. First, the MR signal that was generated by the application of phase- and frequency-encoding gradients is sampled to fill k-space (a coordinate system used to organize the signal measurements). Next, the raw data (k-space images) are subjected to a mathematical operation known as a Fourier transform to reconstruct an image in the standard position space.
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Figure 11. Diagram shows the process with which a 3D diffusion probability density function is obtained for one voxel (one brain position). In A, a 3D grid that represents q-space, each yellow dot corresponds to an MR signal sampling point. The signal is sampled at each point by varying the direction and strength of the diffusion gradient (q vector) of the pulsed gradient SE sequence. With a single application of the pulsed gradient SE sequence, one point in q-space is sampled for each brain position simultaneously, and the result is one diffusion-weighted image. In B, the left panel shows sections through the MR signal sampled in q-space for a specific brain position (one voxel), and the right panel shows the diffusion probability density function in the same voxel after a 3D Fourier transform of the MR signal in q-space is performed. The cross-shaped appearance of the diffusion probability density function is often seen in voxels in the brainstem, where axons of the corticospinal tract cross with axons of the middle cerebellar peduncle.
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Figure 12. Series of diffusion-weighted MR brain images obtained with variations in the direction and strength of the diffusion gradient in the pulsed gradient SE sequence. Each image shows the signal sampled at one point in q-space (one yellow dot). Every sampling point in q-space corresponds to a specific direction and strength of the diffusion gradient.
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Figure 13. Diffusion-weighted image (right) from signal sampling at a single point in 3D q-space (left). Brain areas where diffusion is intense in the direction of the applied gradient ( ) appear darker because of a decrease in the measured signal that results from dephasing.
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Figure 14. Series of diffusion-weighted images obtained for diffusion tensor imaging, in which q-space is sampled in at least six different directions and in which a non–diffusion-weighted reference image is obtained. The direction but not the strength of the diffusion gradient is changed for each sampling.
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Figure 16a. Extraction of scalar values from diffusion tensor imaging. (a) Image shows mean diffusion, which is the trace of the diffusion tensor. An image of ADC averaged over three orthogonal directions would have a similar appearance. (b) Image shows the fractional anisotropy, which is computed from the eigenvalues of the diffusion tensor. (c) Color-coded image shows the orientation of the principal direction of diffusion, with red, blue, and green representing diffusion along x-, y-, and z-axes, respectively. The color intensity is proportional to the fractional anisotropy.
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Figure 16b. Extraction of scalar values from diffusion tensor imaging. (a) Image shows mean diffusion, which is the trace of the diffusion tensor. An image of ADC averaged over three orthogonal directions would have a similar appearance. (b) Image shows the fractional anisotropy, which is computed from the eigenvalues of the diffusion tensor. (c) Color-coded image shows the orientation of the principal direction of diffusion, with red, blue, and green representing diffusion along x-, y-, and z-axes, respectively. The color intensity is proportional to the fractional anisotropy.
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Figure 16c. Extraction of scalar values from diffusion tensor imaging. (a) Image shows mean diffusion, which is the trace of the diffusion tensor. An image of ADC averaged over three orthogonal directions would have a similar appearance. (b) Image shows the fractional anisotropy, which is computed from the eigenvalues of the diffusion tensor. (c) Color-coded image shows the orientation of the principal direction of diffusion, with red, blue, and green representing diffusion along x-, y-, and z-axes, respectively. The color intensity is proportional to the fractional anisotropy.
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Figure 17. Comparison between diffusion tensor and diffusion spectrum imaging in regions that contain fiber crossings. In A, a color-coded coronal diffusion image shows the pons (B) and the centrum semiovale (C), in which diffusion is depicted by both diffusion tensor images (B-DTI, C-DTI) and diffusion spectrum images (B-DSI, C-DSI). In the pons, the middle cerebellar peduncle crosses the corticospinal tract. In the centrum semiovale, the corticospinal tract crosses the corpus callosum and the arcuate fasciculus. In the circled sections (C-DTI, C-DSI), it can be seen that diffusion tensor imaging is not capable of resolving fiber crossings, whereas diffusion spectrum imaging is.
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Figure 18. Diagram shows that in q-ball imaging, points on a shell with a constant b value are acquired in q-space. At least 60 images are necessary to reconstruct an orientation distribution function that is realistic.
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Figure 19. Comparison of fiber tractography based on diffusion tensor imaging (DTI) versus fiber tractography based on diffusion spectrum imaging (DSI) in two healthy volunteers. The diffusion spectrum imaging data were obtained with a 3.0-T imager and a twice-refocused SE pulse (repetition time msec/echo time msec = 3000/154; bmax = 17,000 sec/mm2; voxel size of 3 x 3 x 3 mm); tractography was performed according to the method described in reference 26. The diffusion tensor imaging data were obtained with a 1.5-T imager and a single-shot echo-planar sequence (1000/89; b = 1000 sec/mm2; voxel size of 1.64 x 1.64 x 3 mm); tractography was performed as described in reference 23. Because diffusion spectrum imaging provides higher angular resolution, fiber crossings are better resolved and fibers from different tracts are more clearly separated. The most visible differences between the two axial views (bottom row) are the greater predominance of red, which represents decussating callosal fibers that connect both the parietal and the temporal lobes, and the more uniform distribution of callosal fibers that project into the frontal lobe, on the diffusion spectrum image. These differences reflect typical errors of diffusion tensor imaging tractography in areas where fibers cross.
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Copyright © 2006 by the Radiological Society of North America.
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