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Quantitative Diffusion-Tensor Anisotropy Brain MR Imaging: Normative Human Data and Anatomic Analysis¹

¹ From the Mallinckrodt Institute of Radiology (J.S.S., R.C.M., E.A., J.A.A., A.Z.S., T.S.C.) and Dept of Physics (N.F.L., T.E.C.), Washington University Medical Center, 510 S Kingshighway Blvd, St Louis, MO 63110. Received Jul 20, 1998; revision requested Aug 19; revision received Nov 10; accepted Jan 15, 1999. Supported in part by grants from Major Grants Program of McDonnell Center for Higher Brain Function, National Multiple Sclerosis Society Pilot Research Award, Charles A. Dana Foundation Consortium on Neuroimaging Leadership Training, and PRAXIS III Fellowship from the Portuguese government. J.S.S. supported by RSNA Research and Education Foundation Research Resident Grant. Address reprint requests to J.S.S. (e-mail: shimonyj@npg.wustl.edu).

View larger version (120K): [in a new window]   Figure 1. Characteristic axial single-section MR images (echo time = 106 msec, repetition time > 8,000 msec) obtained from a single acquisition of combined tetrahedral-orthogonal gradient encoding. a-d, Diffusion-weighted MR images encoded along tetrahedral directions one (a), two (b), three (c), and four (d) (26) by using a b value of 1,022 sec/mm2. e-g, Diffusion-weighted MR images encoded along orthogonal directions x (e), y (f), and z (g) by using a b value of 999 sec/mm2. h, One of the seven T2-weighted reference images acquired with very weak diffusion encoding (b = 12 sec/mm2) for each encoding direction. Voxel sizes were 2.11 x 2.11 x 5.00 mm, and the imaging time was approximately 26 seconds per encoding direction (approximately 3 minutes total). All diffusion-weighted images are from a single acquisition and are displayed with the same window width and center, which are one-third the window width and center of h. Note the different WM contrasts in a-g, which encode anisotropic diffusion.

View larger version (119K): [in a new window]   Figure 2. Axial anisotropy (a-c) and anisotropy-weighted (d, e) MR images computed at the level of the basal ganglia by using the data in Figure 1. A (a), Amajor (b), and Aminor (c) images were obtained from a single acquisition of combined tetrahedral-orthogonal encoding. d, AWtet image was obtained from the tetrahedral encodings. e, AWortho image was obtained from the orthogonal encodings. All images have the same window width and center. Note the high sensitivity to WM depiction in a, with delineation of the external capsule, the peripheral occipital WM projections, the thalamic heterogeneity, and the width of the internal capsule. Note also the structural heterogeneity of WM in a (eg, dark bands between the internal capsule, corpus callosum, and adjacent WM) and the heterogeneity in the thalamus, which is not seen on T2-weighted MR images (see Fig 1, h). Visible differences in anisotropy strength exist between WM classes, where the image intensity in a and b can be ranked, from highest to lowest, as follows: commissural WM, projection WM, and association WM. In comparison with a, the anisotropy-weighted component images in d and e show a loss of intensity in the splenium and genu of the corpus callosum, respectively, and there generally is less intensity in e, as compared with that in d.

View larger version (120K): [in a new window]   Figure 3a. ROIs used in data analysis are superimposed on (a) axial T2-weighted reference MR image (echo time = 106 msec, repetition time > 8,000 msec) (same image as Fig 1, h) and (b) axial A MR image (same image as Fig 2, a). 1 = frontal WM, 2 = frontal GM, 3 = head of the caudate nucleus, 4 = genu of the internal capsule, 5 = putamen, 6 = external capsule, 7 = posterior limb of internal capsule, 8 = thalamus, 9 = occipital-temporal GM, 10 = splenium of the corpus callosum, 11 = occipital WM, and 12 = optic radiations. The location of the ROI for occipital-temporal GM varied across subjects. ROI sizes and shapes were kept constant across hemispheres but varied across subjects.

View larger version (142K): [in a new window]   Figure 3b. ROIs used in data analysis are superimposed on (a) axial T2-weighted reference MR image (echo time = 106 msec, repetition time > 8,000 msec) (same image as Fig 1, h) and (b) axial A MR image (same image as Fig 2, a). 1 = frontal WM, 2 = frontal GM, 3 = head of the caudate nucleus, 4 = genu of the internal capsule, 5 = putamen, 6 = external capsule, 7 = posterior limb of internal capsule, 8 = thalamus, 9 = occipital-temporal GM, 10 = splenium of the corpus callosum, 11 = occipital WM, and 12 = optic radiations. The location of the ROI for occipital-temporal GM varied across subjects. ROI sizes and shapes were kept constant across hemispheres but varied across subjects.

View larger version (81K): [in a new window]   Figure 4a. Ratio of tetrahedral and orthogonal anisotropy-weighted indexes (AWtet and AWortho) to total anisotropy (A) as a function of and . Three-dimensional displays of the ratios (a) ftet and (b) fortho were computed by using Equations (A7) and (A8) (see Appendix), respectively. These ratios are displayed as the radial distance of a surface in a spherical coordinate system as a function of the directional angles and . (c, d) Graphs that show profiles of the data when (c) is 54.74° and (d) is 90° indicate the orientation of the maxima and minima. The recovery of A generally is higher for the AWtet measurement than for the AWortho measurement. Thus, the majority of the anisotropy information is in the tetrahedral measurements (ie, the majority of anisotropy information is contained in the off-diagonal tensor elements). Note the extent to which the surfaces in a and b approach the ideal case of a sphere (ie, a true A measurement, also indicated by the approach of the solid curves to the dashed lines in c and d). Note also that the surfaces in a and b are complementary, with AWtet insensitive in the orthogonal directions and AWortho insensitive in the tetrahedral directions.

View larger version (71K): [in a new window]   Figure 4b. Ratio of tetrahedral and orthogonal anisotropy-weighted indexes (AWtet and AWortho) to total anisotropy (A) as a function of and . Three-dimensional displays of the ratios (a) ftet and (b) fortho were computed by using Equations (A7) and (A8) (see Appendix), respectively. These ratios are displayed as the radial distance of a surface in a spherical coordinate system as a function of the directional angles and . (c, d) Graphs that show profiles of the data when (c) is 54.74° and (d) is 90° indicate the orientation of the maxima and minima. The recovery of A generally is higher for the AWtet measurement than for the AWortho measurement. Thus, the majority of the anisotropy information is in the tetrahedral measurements (ie, the majority of anisotropy information is contained in the off-diagonal tensor elements). Note the extent to which the surfaces in a and b approach the ideal case of a sphere (ie, a true A measurement, also indicated by the approach of the solid curves to the dashed lines in c and d). Note also that the surfaces in a and b are complementary, with AWtet insensitive in the orthogonal directions and AWortho insensitive in the tetrahedral directions.

View larger version (16K): [in a new window]   Figure 4c. Ratio of tetrahedral and orthogonal anisotropy-weighted indexes (AWtet and AWortho) to total anisotropy (A) as a function of and . Three-dimensional displays of the ratios (a) ftet and (b) fortho were computed by using Equations (A7) and (A8) (see Appendix), respectively. These ratios are displayed as the radial distance of a surface in a spherical coordinate system as a function of the directional angles and . (c, d) Graphs that show profiles of the data when (c) is 54.74° and (d) is 90° indicate the orientation of the maxima and minima. The recovery of A generally is higher for the AWtet measurement than for the AWortho measurement. Thus, the majority of the anisotropy information is in the tetrahedral measurements (ie, the majority of anisotropy information is contained in the off-diagonal tensor elements). Note the extent to which the surfaces in a and b approach the ideal case of a sphere (ie, a true A measurement, also indicated by the approach of the solid curves to the dashed lines in c and d). Note also that the surfaces in a and b are complementary, with AWtet insensitive in the orthogonal directions and AWortho insensitive in the tetrahedral directions.

View larger version (19K): [in a new window]   Figure 4d. Ratio of tetrahedral and orthogonal anisotropy-weighted indexes (AWtet and AWortho) to total anisotropy (A) as a function of and . Three-dimensional displays of the ratios (a) ftet and (b) fortho were computed by using Equations (A7) and (A8) (see Appendix), respectively. These ratios are displayed as the radial distance of a surface in a spherical coordinate system as a function of the directional angles and . (c, d) Graphs that show profiles of the data when (c) is 54.74° and (d) is 90° indicate the orientation of the maxima and minima. The recovery of A generally is higher for the AWtet measurement than for the AWortho measurement. Thus, the majority of the anisotropy information is in the tetrahedral measurements (ie, the majority of anisotropy information is contained in the off-diagonal tensor elements). Note the extent to which the surfaces in a and b approach the ideal case of a sphere (ie, a true A measurement, also indicated by the approach of the solid curves to the dashed lines in c and d). Note also that the surfaces in a and b are complementary, with AWtet insensitive in the orthogonal directions and AWortho insensitive in the tetrahedral directions.

View larger version (131K): [in a new window]   Figure 5a. Axial multisection MR imaging demonstration of A obtained (a) without and (b) with data averaging. Numbers indicate the section numbers. Combined tetrahedral-orthogonal multisection data were acquired with one axial T2-weighted reference MR image obtained with a single sequence (echo time = 97 msec, repetition time = 3,100 msec), with b of 1,003.3 sec/mm2 for tetrahedral data, b of 334.4 sec/mm2 for orthogonal data, and b of 0 sec/mm2 for reference data. In a, only one image was acquired per encoding direction (one shot per image; total acquisition time, 66 seconds), with a voxel size of 1.88 x 1.88 x 5.00 mm. In b, the pulse sequence used in a was repeated a total of 10 times in a different subject (total acquisition time, 16 minutes 40 seconds) but with a section thickness of 3.3 mm. In b, the source image data as depicted in Figure 1 were averaged, followed by computation of the diffusion tensor. In both a and b, A was computed from the estimated diffusion tensor according to Equation (3). Note the sensitive demonstration of WM structures throughout the brain, including subcortical U fibers. In addition to the findings shown in Figure 2, note the detection of other WM structures such as cerebral peduncles (section 18 in a and section 30 in b) and the cerebellar peduncles (sections 38 and 40 in b), as well as heterogeneity in the thalamus, basal ganglia, and occipital WM (eg, in b, note band of anisotropy in the region of the globus pallidus in sections 24 and 26 and ridges of low anisotropy along the optic radiations in sections 20-32). Comparison of a and b indicates that A image quality can be improved by increasing the number of signals acquired and obtaining thinner sections.

View larger version (178K): [in a new window]   Figure 5b. Axial multisection MR imaging demonstration of A obtained (a) without and (b) with data averaging. Numbers indicate the section numbers. Combined tetrahedral-orthogonal multisection data were acquired with one axial T2-weighted reference MR image obtained with a single sequence (echo time = 97 msec, repetition time = 3,100 msec), with b of 1,003.3 sec/mm2 for tetrahedral data, b of 334.4 sec/mm2 for orthogonal data, and b of 0 sec/mm2 for reference data. In a, only one image was acquired per encoding direction (one shot per image; total acquisition time, 66 seconds), with a voxel size of 1.88 x 1.88 x 5.00 mm. In b, the pulse sequence used in a was repeated a total of 10 times in a different subject (total acquisition time, 16 minutes 40 seconds) but with a section thickness of 3.3 mm. In b, the source image data as depicted in Figure 1 were averaged, followed by computation of the diffusion tensor. In both a and b, A was computed from the estimated diffusion tensor according to Equation (3). Note the sensitive demonstration of WM structures throughout the brain, including subcortical U fibers. In addition to the findings shown in Figure 2, note the detection of other WM structures such as cerebral peduncles (section 18 in a and section 30 in b) and the cerebellar peduncles (sections 38 and 40 in b), as well as heterogeneity in the thalamus, basal ganglia, and occipital WM (eg, in b, note band of anisotropy in the region of the globus pallidus in sections 24 and 26 and ridges of low anisotropy along the optic radiations in sections 20-32). Comparison of a and b indicates that A image quality can be improved by increasing the number of signals acquired and obtaining thinner sections.

View larger version (25K): [in a new window]   Figure 6a. Graphs show results of simulation of the effect of noise on the accuracy and precision of A measurements for (a) isotropic tissues and (b) axisymmetric anisotropic tissues. (a) Bias and random noise in the observed A are graphed on linear (inset) and log-log scales versus the input SNR on the T2-weighted reference image. The bias and random noise are calculated as the mean and SD (std. dev.) of multiple experimental simulations as described in Materials and Methods. The simulation in a is for an ideal isotropic GM tissue that has the averaged diffusivity value of the putamen ( = 0.72 x 10-3 mm2/sec). The mean and SD in A are fit to the expression y = AxB, where A is the value at an SNR of 1 and B is the power of the dependence on SNR. (b) Bias and random noise in the observed A are graphed as a function of A at different reference image (I0) SNR levels for an ideal axisymmetric WM tissue that has the same averaged diffusivity value as in a, similar to the averaged diffusivity value of the splenium of the corpus callosum. The simulations are for an A value that ranges from 0.0 to 0.5, to represent the range for tissues shown in Table 1. Three reference SNR levels indicative of a range of MR imaging hardware are simulated, and the results are offset on the vertical axis for clarity. The SNR for the data acquired for Table 1 was approximately 40-60.

View larger version (28K): [in a new window]   Figure 6b. Graphs show results of simulation of the effect of noise on the accuracy and precision of A measurements for (a) isotropic tissues and (b) axisymmetric anisotropic tissues. (a) Bias and random noise in the observed A are graphed on linear (inset) and log-log scales versus the input SNR on the T2-weighted reference image. The bias and random noise are calculated as the mean and SD (std. dev.) of multiple experimental simulations as described in Materials and Methods. The simulation in a is for an ideal isotropic GM tissue that has the averaged diffusivity value of the putamen ( = 0.72 x 10-3 mm2/sec). The mean and SD in A are fit to the expression y = AxB, where A is the value at an SNR of 1 and B is the power of the dependence on SNR. (b) Bias and random noise in the observed A are graphed as a function of A at different reference image (I0) SNR levels for an ideal axisymmetric WM tissue that has the same averaged diffusivity value as in a, similar to the averaged diffusivity value of the splenium of the corpus callosum. The simulations are for an A value that ranges from 0.0 to 0.5, to represent the range for tissues shown in Table 1. Three reference SNR levels indicative of a range of MR imaging hardware are simulated, and the results are offset on the vertical axis for clarity. The SNR for the data acquired for Table 1 was approximately 40-60.

View larger version (16K): [in a new window]   Figure 7a. Graphs shows the results of simulation of partial volume effects on measurement of A for (a) intravoxel averaging of GM and WM and (b) averaging of two WM tissues with unaligned fiber orientations. (a) Ideal GM and WM were modeled after the putamen and splenium of the corpus callosum ( = 0.72 x 10-3 mm2/sec for GM and WM, A = 0 for GM, A = 0.5 and Aminor = 0 for WM, and arbitrary settings of = 20° and = 30° for WM). Note the nearly exact linear partial volume effect of GM on WM measurements. (b) Two WM tissues, each with the same WM averaged diffusivity () and A values as in a and with fibers lying in the transverse imaging plane ( = 0°), were averaged at different in-plane angular separations (). Note that angular separations of 90° result in a decrease of more than 50% in the observed A. Dashed line = ideal measurement with no partial volume effect.

View larger version (14K): [in a new window]   Figure 7b. Graphs shows the results of simulation of partial volume effects on measurement of A for (a) intravoxel averaging of GM and WM and (b) averaging of two WM tissues with unaligned fiber orientations. (a) Ideal GM and WM were modeled after the putamen and splenium of the corpus callosum ( = 0.72 x 10-3 mm2/sec for GM and WM, A = 0 for GM, A = 0.5 and Aminor = 0 for WM, and arbitrary settings of = 20° and = 30° for WM). Note the nearly exact linear partial volume effect of GM on WM measurements. (b) Two WM tissues, each with the same WM averaged diffusivity () and A values as in a and with fibers lying in the transverse imaging plane ( = 0°), were averaged at different in-plane angular separations (). Note that angular separations of 90° result in a decrease of more than 50% in the observed A. Dashed line = ideal measurement with no partial volume effect.