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DIFFUSION IMAGING

DIFFUSION TENSOR BRAIN IMAGING AND TRACTOGRAPHY Ryuta Ito, MD, Susumu Mori, PhD, and Elias R. Melhem, MD

Diffusion-tensor (DT) MR imaging4,5 has been proposed as an attractive noninvasive tool for evaluating structural and physiologic states in biologic tissues by measuring the diffusion process of water molecules. In brain white matter, quantitative maps that indicate the integrity of the tissue, and tractography that identiﬁes macroscopic three-dimensional architecture of ﬁber tracts (e.g., projections to subcortical nuclei and association pathways between cortices), can be obtained with this method. Recently, clinical applications of DT MR imaging for the evaluation of anatomical structures and pathologic processes in white matter have been introduced.* Although it is apparent that this method has potential for the evaluation of white matter, it remains challenging to routinely carry out this procedure in the clinic. In this article, the authors describe how to estimate an effective diffusion tensor (Deff)5 and discuss technical issues that concern data acquisition, data calculation, and map generation. They also present their current experiences, including evaluation of white-matter disease by quantitative maps and tractography, and some of the challenges of characterizing de*References 3, 17, 23, 24, 25, 28, 34, 35, 41, 43, 45, 50, 64, 67, 75, 79, 85, 87, 90, 94, 96, 97, 100, 101, and 106.

velopmental morphologic changes in mouse brain by DT MR imaging.

BASIC CONCEPTS OF DIFFUSION MEASUREMENTS BY DIFFUSION TENSOR MR IMAGING Concepts of Isotropy and Anisotropy Random displacements of water molecules (i.e., diffusion) are modiﬁed by structural and physiologic factors in a medium. In the medium in which diffusion of water molecules is identical in all directions, probable location of water molecules will be within a sphere after a period (Fig. 1A). This kind of diffusion process is termed isotropic diffusion. In contrast, when the process is dependent on direction, it is termed anisotropic diffusion. In such cases, water molecules will be spatially distributed within an ellipsoid after a period (Fig. 1B).

Anisotropic Diffusion in Brain White Matter In brain white matter, diffusivity of water molecules is not the same in all directions of three-dimensional space and is anisotropic at an imaging voxel scale21,61,80 because of its char-

From the Department of Radiology, Shiga University of Medical Science, Otsu, Shiga, Japan (RI); Department of Radiology and Radiological Sciences, The Johns Hopkins University, and F. M. Kirby Research Center for Functional Brain Imaging, Kennedy-Krieger Institute, The Johns Hopkins Medical Institutions, Baltimore, Maryland (SM, ERM) NEUROIMAGING CLINICS OF NORTH AMERICA VOLUME 12 • NUMBER 1 • FEBRUARY 2002

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Figure 1. A, Isotropic diffusion model. Path (tortuous line) of water molecule (black dots) under no spatial constrain (left). The molecule moves randomly by Brownian motion, resulting in a sphere displacement proﬁle (right). This condition is termed isotropic. B, Anisotropic diffusion model. Motion (tortuous arrow) of water molecule (black dots) under ordered structures (rods) (e.g., myelin sheath, axon in white matter) (left). The probable location of the molecule after unit time will be within an ellipsoid (right). This condition is termed anisotropic.

acteristic microscopic and macroscopic features, such as myelin sheath, axon, and ﬁber tract.* The diffusion process in white matter is graphically expressed as an ellipsoid. By estimating properties of the ellipsoid, useful physiologic and structural (i.e., anatomic and histopathologic) information about white matter can be obtained. The shape of an anisotropic diffusion ellipsoid can be characterized by six parameters: three magnitudes of diffusivity along three principal orthogonal coordinate axes of the ellipsoid, and three vectors that describe the orientation of principal coordinates in laboratory coordinate axes (i.e., coordinates of a magnet) (Fig. 2). These parameters can be derived from DT MR imaging.4,5,18,32

How to Measure Diffusion Process The diffusion process can be measured by using a magnetic ﬁeld gradient. In the presence of the magnetic ﬁeld gradient, water mol*References 33, 34, 35, 43, 64, 77, 87, 88, 97, and 102.

Figure 2. Ellipsoid representing diffusion tensor. Diffusion properties can be described by an ellipsoid. The ellipsoid can be characterized by three variables (eigenvalues: 1, 2, 3) to describe the shape and relationship between the principal coordinate axes (x⬘, y⬘, and z⬘) and the laboratory coordinate axes (x, y, and z). Each of the principal axes (x⬘, y⬘, z⬘) are represented by three eigenvectors of the diffusion tensor. The radii (white arrows) of the diffusion ellipsoid along these principal axes are (21)1/2, (22)1/2, and (22)1/2 after unit time. Diagonalization means rotating the laboratory coordinate system and adjusting it to the principal coordinate system of the ellipsoid (curved arrows).

DIFFUSION TENSOR BRAIN IMAGING AND TRACTOGRAPHY

ecules with random displacements (described as incoherent motion) acquire random phase shifts, resulting in an attenuation of the spinecho signal caused by refocusing failure.16,29 Assuming the Gaussian shape of the probability distribution of diffusion displacements, the attenuation is described as: ln(S/S0) ⫽ ⫺bD,

Equation 1

in which S and S0 are signal intensities sampled with and without the magnetic ﬁeld gradient, respectively, and D is the diffusion coefficient.49 Stejskal-Tanner Gradient Pulse For diffusion sensitization, the authors apply a pair of gradient pulses arranged on each side of the 180o radiofrequency (RF) pulse in a spin-echo (SE) sequence (Fig. 3).86 The b-value, which reﬂects the degree of diffusion sensitization, is determined by the gyromagnetic ratio (␥), the strength of the gradients (with an ideal rectangular shape) (G), the duration of each gradient pulse (␦), and the time interval between their onsets (⌬) according to: b⫽␥2G2␦2(⌬⫺␦/3).

Equation 2

In this case, the b factor can be controlled only by parameters of the applied ﬁeld gradients (i.e., diffusion-sensitizing gradients). The SE method with the “Stejskal-Tanner” gradient pulse is commonly used for “diffusionweighted” MR imaging,47,89 although a combination of diffusion-sensitizing gradients with

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stimulated echo imaging also has been reported.56 Apparent Diffusion Coefficient When the attenuation is measured from the series of images with different known magnitudes of b-value (i.e., at least two different b-values), the diffusion coefficient D in each image voxel can be calculated. Because there is a pure Brownian motion of water molecules (diffusion), and also other incoherent motions (e.g., microcirculation of blood in the capillary network) in the image voxel, what can be measured is termed an apparent diffusion coefficient (ADC).47,48 The ADC along the direction of the applied diffusion-sensitizing gradient can be measured. The diffusion sensitization is implemented using one of the gradient devices equipped in x, y, and z directions of a magnet, or by combining them, being applied in any desired direction.4,5 Consequently, ADCs in any desired direction can be measured. Effective Diffusion Tensor To estimate anisotropic water diffusion in white matter, the properties of the diffusion ellipsoid (determined by six parameters) should be characterized. The anisotropic diffusion process in each voxel can be characterized by Deff, which is a 3 ⫻ 3 tensor matrix that consists of nine elements.4,5

Deff ⫽

冤

Deffxx Deffxy Deffxz Deffyx Deffyy Deffyz Deffzx Deffzy Deffzz

冥 Equation 3

Figure 3. Stejskal-Tanner sequence. To measure signal loss by diffusion, a pair of pulsed diffusion sensitizing gradients (shaded rectangles) is arranged on each side of the 180° radiofrequency (RF) pulse in spin-echo sequence. G is the strength of the gradients that can be applied to any direction, ␦ is the duration of each gradient pulse, and ⌬ refers to the tie interval between their onsets.

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Because Deff is symmetric for Gaussian diffusion,4 it is characterized by six scalars: three diagonal elements, Deffxx, Deffyy, and Deffzz, and three off-diagonal elements, Deffxy, Deffxz, and Deffyz. By sampling signal attenuation after applying diffusion-sensitizing gradient in at least six different non-colinear directions, these six elements can be determined.4,7 By diagonalizing Deff, the six parameters to determine the diffusion ellipsoid can be obtained.5,76 This procedure (diagonalization) means rotating the laboratory coordinate system, in which the apparent diffusion coefficients are measured, and aligning it to the principal coordinate system of the ellipsoid. In this calculation process, three eigenvectors (v1, v2, v3) are obtained, which describes the orientation of the principal axes in the laboratory coordinates (orientation of x’, y’, and z’ coordinates in Fig. 2).5,76 The other three parameters obtained after the diagonalization are called eigenvalues (1, 2, 3), which represent diffusivities along three principal coordinate axes of the ellipsoid, thus deﬁning the shape of the ellipsoid. From these six parameters (v1, v2, v3, 1, 2, 3) of the ellipsoid, various quantitative indices that may reﬂect physiologic and structural features of tissues in the voxel can be derived.5,6,62,76,77,95 The trajectories of ﬁber tracts in white matter also can be studied by estimating the relationship between eigenvectors of adjacent voxels.8,19,46,58,73,78,91 Mapping the diffusion process in a voxel by estimating Deff is called DT MR imaging.5

Basics of Spatial Mapping of Diffusion Process For spatial mapping of diffusion process, a total of at least seven images, which include diffusion-weighted MR images with the diffusion-sensitizing gradients applied in six different non-colinear directions, and an image with the same parameters as the diffusion-weighted images but no diffusion sensitization (Fig. 4), must be obtained. From the difference in attenuation of signal intensity between non–diffusion-weighted and diffusion-weighted images, six voxel-byvoxel maps of apparent diffusion coefficient are generated. The Deff in each voxel is constructed from these maps. Once the tensor

is determined, various DT MR imaging– based maps can be generated. Number and Strength of b-values for Each Direction As shown in Figure 4 and Equation 1, at least two b-values (non–diffusion-weighted and diffusion-weighted images) are needed to calculate the D. If there are more than two b-values, the D can be obtained from a linear ﬁtting using Equation 1, which provides higher statistical accuracy. From a standpoint of clinical feasibility, the larger number of b-values leads to longer measurement time. Thus, the number of sampling points for the b-values should be determined from the available scanning time and required signal-to-noise ratio (SNR). An interesting issue is, with the given number of sampling points (e.g., four bvalues), whether the authors should use four different b-values (e.g., b ⫽ 0, 500, 1000, and 2000), or two different b-values with two repeated measurement (e.g., two sets of b ⫽ 0 and 1000). Recent study showed little error when two-point sampling method (b-values of 1 and 1000 second/mm2) is used.13 There is another point in determining the number and strength of b-values because they may affect the diffusivity and anisotropy indices for different anatomic locations.55 An adequate estimation of the principal diffusivities with a large range in brain tissue may require b-value magnitude of 1/i.77 Successful measurement of the apparent diffusion coefficients in gray matter, white matter, and cerebrospinal ﬂuid in human brain is reported using two-point sampling (b-values of 300 and 1550 ⫾ 100 second/mm2, on a 2.0-T magnet equipped with a gradient system with a maximum gradient strength of 36 mT/m).104 Number of Sampling Directions Assuming Gaussian shape of the diffusion tensor, the determination of six apparent diffusion coefficients is sufficient to characterize the 3 ⫻ 3 Deff. To measure six apparent diffusion coefficients, sampling images with the diffusion-sensitizing gradient applied along six non-colinear directions and an image without

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Figure 4. Steps of spatial mapping of diffusion process. First, diffusion-weighted images with various axes of diffusion sensitizing gradient (upper right row) and an image without diffusion sensitization (upper right) are obtained. (Note the diffusion-weighted images at the same location have different contrast that depends on the direction of applied diffusion gradient). From decreases in intensities between “NO-weighted” and “diffusion-weighted” images, apparent diffusion constants at each pixel are calculated (middle). By acquiring at least seven diffusion-weighted images or six apparent diffusion coefficient (ADC) maps, the diffusion ellipsoid at each pixel can be fully characterized, from which various maps that indicate water diffusion process can be calculated (bottom row).

the diffusion sensitizing (a total of seven sampling) are required.7 Although the choice of the six orientations can be anything as long as they are not colinear, the highest accuracy can be obtained if they are uniformly distributed in the three-dimensional space.7,77 If a scanning time is available to acquire more than six diffusion-weighted images, there are two approaches to design the experiment. For example, if there is enough time to acquire 12 diffusion-weighted images, two sets of data with different b-values (e.g., b ⫽ 1000 and 1500) can be obtained. Conversely, images sensitized along 12 different orientations with the same b-value can be acquired. The effect of this kind of experimental design on the SNR still is under active research.42,30,84

Estimation of b-matrix Values Equation 1 can be used when the media is isotropic or diffusion along only one axis is measured in an anisotropic media. For more comprehensive description for an anisotropic media, it has to be rewritten to: ln(S/S0) ⫽

公b– D– 公b– T

Equation 4

= – in which b is a vector for the b-value and D is effective diffusion tensor (i.e., Deff). This equation contains seven unknown parameters, six = – in D and S0. The vector b is deﬁned by the experimental protocols (i.e., combina-

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tions of applied gradients and their strengths), and S is experimental results (image intensities). From seven images (Ss from six diffusionweighted images and one non–diffusionweighted image), this equation can be solved. The result S, however, always contains noise and thus determined seven unknowns are prone to errors. These errors can be reduced by acquiring more than seven images. In this case, Equation 5 is “overdetermined” and the best seven unknown parameters can be found by ﬁtting, which is called weighted multivariate linear regression.5 As mentioned in the previous sections, more than one diffusion weighting – (the magnitude of b ) or more than six different – gradient combinations (the orientation of b ) can be used to improve the SNR. For precise measurement of diffusion coefficients, the interactions (i.e., cross terms) between the diffusion gradients and the imaging gradients should be considered when computing bmatrix values.5,6,53,63 Read-out Sequences for Diffusion Tensor MR Imaging A variety of read-out techniques have been proposed for DT MR imaging. Because diffusion-weighted imaging is sensitive to bulk motions, it requires rapid imaging techniques that reduce artifacts arising from respiration, cerebrovascular and cerebrospinal ﬂuid ﬂow, eye motion, and involuntary head motions. There are two approaches of diffusion-weighted imaging using fast imaging techniques, which are single-shot (“snapshot”) techniques and multishot (“interleaved, segmented”) techniques. An advantage of multishot imaging is higher spatial resolution, whereas the drawback is longer data acquisition time compared with single-shot techniques. In such multishot imaging, even small bulk motions can cause motion artifacts and result in phase encode ghosting because of so-called “phase discontinuity” between the echoes sampled at different timing in k-space. Single-shot imaging sequences can eliminate the discontinuity because the entire set of echoes in k-space is acquired with the same motion-induced error.92 To eliminate deterioration by motions, multishot technique requires cardiac gating and a motion correction scheme using so-called “navi-

gator echo”.2,12,15,57,68 The navigator echo, which is a non–phase encoded read-out gradient echo, provides a measure of motion-induced phase variations between the echoes in each shot, and the data can be subsequently corrected for small amounts of motion.15 Multishot readouts with cardiac gating and a navigator echo technique provide diffusion-weighted images with reduced motion artifact and high spatial resolution that are essential for evaluation of the microstructures of white matter in vivo.15,38 The following sections highlight read-out techniques used currently. Echo-planar Imaging Most of the current applications for diffusion MR imaging implement single-shot echoplanar (EP) read-outs, which effectively freeze physiologic effects.77,92,93 One major disadvantage of single-shot EP read-out relates to severe geometric distortions caused by local magnetic ﬁeld inhomogeneity most pronounced in regions of large magnetic susceptibility differences, such as the base of skull (Fig. 5C). In contrast to single-shot EP imaging, multishot (interleaved) EP read-out is less sensitive to local ﬁeld inhomogeneity (i.e., less distortion) and provides higher spatial resolution.14,15,54 As mentioned previously, however, one drawback of the multishot read-out is its higher sensitivity to subject motions. Instrumental imperfection of gradient units, termed eddy current, is also known to induce image distortion. The amount of this distortion is more severe in the single-shot EP than the multishot. Because the way the images are distorted depends on the strength and orientation of applied gradient, distortion-correcting algorithms often are needed for calculation of accurate diffusion and anisotropy when the single-shot EP is used.31,37,38 Fast Spin-echo Fast spin-echo (FSE) sequences prepared with diffusion-sensitizing gradients have been proposed for diffusion-weighted MR imaging.1,12,57,66 The FSE-based data acquisition’s advantage is that it is less sensitive to ﬁeld inhomogeneity and, thus, the image distortion is minimum. This feature could be more important for high-ﬁeld magnets, in which the ﬁeld inhomogeneity tends to be more severe. The combination of the strong gradients and the FSE, however, has several technical difficulties.57,66,81 The most troublesome difficul-

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Figure 5. Geometric distortion from static ﬁeld inhomogeneity. Axial T1-weighted spin-echo image (A), gradient-and spin-echo (GRASE) (B), and single-shot echo-planar (EP) (C) T2-weighted (b-value ⫽ 0 s/mm2) images are obtained at the level of the temporal lobe base. A thresholded binary image (D) is generated from T1-weighted SE image. Difference images (E and F) are obtained by subtracting the binary maps of GRASE and single-shot EP T2-weighted images from the binary map of the T1-weighted SE image, respectively. Black areas in E and F represent the degree of geometric distortions. The black area of single-shot EP image is greater than the area of GRASE image, which is the result of more severe distortion in the single-shot EP image as demonstrated by thick bands of signal loss (asterisk), and signal hyperintensity (arrows).

ties are phase errors introduced by subject motions or eddy current, which often lead to severe image deterioration in the FSE (socalled “break down of Carr Purcell Meiboom Gill (CPMG) condition”). Unlike EP, these phase error–related problems manifest even for a single-shot FSE and the phase correction based on the navigator echoes is not straightforward because of complex signal phase evolution during the echo train.57 A clever approach that can restore the CPMG condition has been proposed at the expense of a signal loss by a factor of two.1 Gradient- and Spin-echo Read-out Gradient- and spin-echo (GRASE) read-out is a fast imaging technique in which an echo train is formed with RF refocusing pulses and multiple signal read-out gradient reversals.69 Combination of the diffusion weighting and GRASE also has been reported for singleshot39,51 and multishot36 data acquisitions. De-

pending on the number of RF-refocusing pulses and the number of gradient-recalled echoes between the RF refocusing pulses, the GRASE has features similar to FSE or EP. For example, with the arbitrary small number of gradient echoes per refocusing pulse, images obtained from the GRASE have little distortion from static ﬁeld inhomogeneities and diffusion sensitization gradient-induced eddy currents compared with single-shot EP read-outs (Fig. 5).36 GRASE read-out, however, has the same drawback as FSE read-out. To eliminate “break down of CPMG condition,” only half of the original magnetization can be sampled.1 Consequently current diffusion-weighted multishot GRASE sequence needs longer measurement time to sample enough SNR for quality mapping.36 Line-scan Column-selective excitation techniques, socalled “line-scan” techniques, are proposed because of their resistance to physiologic

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motions.26,27,65,98 Line-scan images are composed from multiple self-contained singleshot one-dimensional magnitude proﬁles and do not rely on spatial phase encoding. They are inherently insensitive to mechanisms causing a variation of the MR signal phase. Main disadvantages of this technique are the inherently low SNR because only a single column contributes to the MR signal and longer scan time. Because of their property, which is essentially free from motion artifacts, line-scan techniques may be attractive techniques for DT MR imaging of children.

Correction Techniques In DT MR imaging, misregistration affects the spatial resolution and accuracy of diffusion and anisotropy maps calculated on a pixel-bypixel basis.31,38,77 Main causes of the misregistration originate in geometric distortions of each image and misalignment by small motions between sampled images. The application of correction algorithms is proposed. Geometric Distortion Geometric distortions are the result of the static ﬁeld inhomogeneity caused by imperfect shimming and by differences in magnetic properties of adjacent tissues37 and the result of diffusion sensitization gradient-induced eddy currents.11,31,38 The unwarping algorithm, using inhomogeneity ﬁeld maps, has been proposed for the correction of distortion originating from the static magnetic ﬁeld inhomogeneities (Fig. 6).37 For the correction of diffusion sensitization gradient-induced eddy current distortions, the following two methods have been introduced. The ﬁrst entails the application of least squares straight line ﬁts and cross-correlation functions to the diffusion-weighted image.11,31 The second uses a one-dimensional inhomogeneity ﬁeld map in the read and phase encode directions in each slice and each diffusionsensitizing direction step to correct the distortion.38 Inter-images Misalignment by Bulk Motions Before generating the maps, algorithms such as Automated Image Registration (AIR), http:// bishopw.loni.ucla.edu/AIR3/,103 can be applied for realigning images. In addition to misalignment by the motions, geometric dis-

tortions might be partially corrected by the algorithm. Optionally, to reduce random and systematic errors, applying a nonlinear smoothing technique (PM ﬁlter) to the diffusion-weighted images before calculation of the diffusion tensor is reported.100 Quantitative Indices and Graphical Maps Several indices characterizing the diffusion process in tissues can be calculated based on formulas that incorporate the eigenvalues to generate quantitative brain maps. Furthermore, white-matter ﬁber tract maps are created based on similarities between neighboring voxels in the shape and orientation of the diffusion ellipsoid. Quantitative Indices Quantitative indices derived from DT MR imaging are believed to be able to measure distinct intrinsic features of water diffusion in tissues, which are determined by microstructural (anatomic and histologic) and physiologic states of the tissues, although the determinants of water diffusion in tissues still are not completely understood. These intrinsic measurements allow monitoring brain maturation, changes by disease progression, and changes by interventions. The following are quantitative indices currently proposed. The most fundamental quantitative measures are the three principal diffusivities (eigenvalues, 1, 2, 3) of the Deff, which are the principal diffusion coefficients measured along the three principal coordinates of the ellipsoid in each voxel. The trace of Deff is the basis for the directionally averaged (or isotropic, mean) diffusivity Deffave ⫽ (Deffxx ⫹ Deffyy ⫹ Deffzz). Several indices to measure the degree of diffusion anisotropy in tissues have been proposed. The most intuitive and simplest indices are ratios of the principal diffusivities,5,76 such as the dimensionless anisotropy ratio h/l or 2h/(m⫹l), which measure the relative magnitudes of the diffusivities along the longest axis of the diffusion ellipsoid and other orthogonal axes. Here, the eigenvalues are sorted in order of decreasing magnitude (h⫽ highest diffusivity, m⫽ intermediate diffusivity, and l⫽ lowest diffusivity). Because simulations have revealed that these sorted indices

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Figure 7 C and D.

Figure 10.

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Figure 11.

Figure 12 C.

Figure 13.

DIFFUSION TENSOR BRAIN IMAGING AND TRACTOGRAPHY

are statistically biased by noise contamination,9,52,71,76 other unsorted indices, such as volume ratio (VR),76 relative anisotropy (RA),6,76 and fractional anisotropy (FA)6,76 have been proposed. VR, the ratio of the volume of an ellipsoid to the volume of a sphere whose radius is the averaged diffusivity, is deﬁned as

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RA ⫽ [((1 ⫺ Deffave)2 ⫹ (2 ⫺ Deffave)2 ⫹ (3 ⫺ Deffave)2)]1/2 / 31/2Deffave. Equation 6

VR⫽123/[(1⫹2⫹3)/3]3. Equation 5

For a complete isotropic medium, RA ⫽ 0. FA, the ratio of the anisotropic component of the diffusion tensor to the whole diffusion tensor, is deﬁned as

The magnitude of RV ranges between 0 and 1, in which 0 means highest anisotropy and 1 indicates complete isotropic diffusion. RA, the ratio of the variance of the eigenvalues to their mean, is deﬁned as

FA ⫽ 3/2/2 ((1 ⫺ Deffave)2 ⫹ (2 ⫺ Deffave)2 ⫹ (3 ⫺ Deffave)2)1/2 / (12 ⫹ 22 ⫹ 32)1/2. Equation 7

Figure 6. Sample of correction for geometric distortion in EP image. By unwarping algorithm using inhomogeneity ﬁeld map, distortion in Ep image from the static ﬁeld inhomogeneity can be corrected. Displacement of middle frontal gyrus (black arrows), superior sagittal sinus (white arrows), and postcentral gyrus (arrowheads) caused by distortion in the original EP image (A) is corrected and, in unwarped EP image (B), the structures match their true proﬁles (red lines) derived from the corresponding T1-weighted image. (Courtesy of Xavier Golay, PhD, F.M. Kirby Research Center for Functional Brain Imaging, Kennedy-Krieger Institute, The Johns Hopkins Medical Institutions, Baltimore, Maryland.) Figure 7. Maps derived from diffusion-tensor (DT) MR imaging. By combining A and B, the color-coded map (C) can be created. In this image, brightness represents the degree of anisotropy (same as A) and color represents ﬁber orientation (red: horizontal, green: vertical, blue: perpendicular to the plane). Fiber tracts such as the corpus callosum (cc), superior longitudinal fasciculus (slf), corticospinal tract (cst), and inferior longitudinal fasciculus (ilf) can be identiﬁed by their color representing their orientation. Three-dimensional structures of neural ﬁber pathways in white matter (tractogram) also can be reconstructed (D). Figure 10. A 17-year-old boy with the anterior form of X-linked ALD. Three-dimensional ﬁber tracking of commissural ﬁbers (i.e., the corpus callosum) coregistered onto axial T2-weighted MR images of a healthy volunteer (A) and the patient (B). In the patient, there is signiﬁcant decrease in the white matter tracts crossing the genu of the corpus callosum (arrows) as well as in both frontal lobes compared with the volunteer. Figure 11. Comparison of neural ﬁber pathways for a control (left column) and a patient with spastic cerebral palsy (right column). Neural pathways such as the cingulum (CG), corona radiata (CR), superior longitudinal fasciculus (SLF), inferior longitudinal fasciculus (ILF), and the internal capsule (IC) can be identiﬁed in coronal color maps (red: horizontal, blue: vertical, green: perpendicular to the plane) for a control at the plane including corticospinal tract (A) and at the plane including a body of the corpus callosum (B). Corresponding color maps for the patient reveal decrease in corticospinal ﬁbers (the internal capsule) (arrows) and commissural ﬁbers (the corpus callosum) (arrowhead). Figure 12. A 1-month-old boy with semilobar holoprosencephaly. C, On the color map (blue: horizontal, green: vertical, red: perpendicular to the plane) the corticospinal tract cannot be identiﬁed in the region of the pyramids (arrowheads) despite the normal appearance of the pyramids on the T2-weighted image. The inferior cerebellar peduncles can be identiﬁed (arrows) on the color map. Figure 13. Mouse brain of embryonic stage, day 15.5 (E15.5). A, In a color map, the intensity reﬂects the degree of diffusion anisotropy so that bright regions have high anisotropy, indicating highly ordered ﬁber structures. The different color representation in A means that the structures have different ﬁber directions (red: horizontal, green: vertical, blue: perpendicular to the plane). The map illustrates that high anisotropy is found in regions containing axonal ﬁbers (e.g., white matter tracts), and also in the cortical plate and periventricular zone where axonal ﬁbers are not the preponderant component at this stage. B, The prescence of distinct zones of anisotropy allows their three-dimensional volumetric reconstruction. The shape of the cortical plate at E15.5, which is delineated by pink line A, is three-dimensionally reconstructed. The ventricle is also shown in yellow in B. C, Tractogram reconstructed by tracking procedure, FACT, shows major tracts that are well developed in the E15.5 brain. The internal capsule (ic), ﬁmbria (FI), anterior commisure (ac), stria medullaris (sm), optic tract (ot), fasciculus retroﬂexus (fr), and stria terminalis (st) can be appreciated. Slice-by slice comparison with mouse embryo atlas conﬁrmed that locations of reconstructed tracts are in good agreement. (From Mori S, Itoh R, Zhang J, et al: Diffusion tensor imaging of the developing mouse brain. Magn Reson Med 46:18–23, 2001; Wiley-Liss, a subsidiary of John Wiley & Sons, with permission.)

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For a complete isotropic medium, FA ⫽ 0; for a cylindrically symmetric anisotropic medium (with 1>> 2⫽ 3), FA approaches 1. Simulations have shown a rapid divergence of the diffusivities (eigenvalues) from true values as SNR decreases.10,76,77 Furthermore, lowlevel anisotropic indices strongly suffer from the detrimental effect of low SNR and assign a higher level of anisotropy.36,76,77 Indices that include all the information of the eigenvectors of the diffusion tensor (shape and orientation of the ellipsoid) have been proposed to reduce the noise factor of the measurement. “Lattice” anisotropy index in a particular voxel is determined by correlating with the orientation of the ellipsoids in adjacent voxels.76 Total anisotropy (A),18,82 a diffusion variation based on the second moment (variance) of the diffusion tenser, is deﬁned as A ⫽ [(Dxx ⫺ Deffave)2 ⫹ (Dyy ⫺ Deffave)2 ⫹ (Dzz ⫺ Deffave)2 ⫹ 2(Dxy2 ⫹ Dxz2 ⫹ Dyz2)]1/2 / 61/2Deffave. Equation 8

The magnitude of A ranges between 0 and 1. These unsorted indices can be derived from the tensor without diagonalization and include information about the off-diagonal elements of the effective diffusion. Graphical Maps In white matter, water diffusion is restricted by highly ordered structures, such as neural ﬁber bundles, and is highly anisotropic. Water molecules can move more easily in a direction parallel to the ﬁber bundles than in a direction perpendicular to them. By estimating a magnitude and direction of diffusion process using DT MR imaging, the regional ﬁber structures in white matter can be revealed. Several approaches that picture this directional information of the local ﬁber structures have been reported. These graphical techniques are a color map (Fig. 7C),20,21,70,95 a vector map (see Fig. 7B),34,43 a ellipsoid map,5 and a color-coded ellipsoid map.99 Because of microscopic inhomogeneity of white matter, there may be variations of ﬁber directions within a voxel. By estimating the largest eigenvalue as well as

Figure 7. Maps derived from diffusion-tensor (DT) MR imaging. A, Anisotropy map (fractional anisotropy) in which high anisotropy regions (high density of neuronal ﬁbers) have high intensity. Another parameter that can be derived from the DT MR imaging is the ﬁber direction at each pixel. An example is shown in B, in which small lines indicate the local direction of the ﬁber.

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Figure 8. The principle of ﬁber tracking is ﬁber assignment by continuous tracking (FACT). The long line represents a trace path starting from a seed pixel (black pixel). In this algorithm, the line is propagated from the center of the user-deﬁned seed pixel bidirectionally (forward and backward) by following a direction of the eigenvector with the largest eigenvalue (arrows) of each pixel. The continuous line can be kept by memorizing information on intercept when the tracking line leaves a border of the pixel (asterisks). In this example, in which a regional direction of eigenvectors with the largest eigenvalue is homogeneous (a direction indicated by arrows), the tracking path shown by black and gray pixels can represent precisely the regional ﬁber direction.

second and third eigenvalues, displaying intersection and dispersion of ﬁbers in a voxel also has been attempted.99 The directional property of each voxel may show local information of ﬁber pathways in white matter. The direction of the largest principal axis of the diffusion ellipsoid may suggest local orientation of neural ﬁber pathway so that an entire length of the neural pathway can be reconstructed by connecting the discrete directional information of each voxel. Fiber tracking is implemented by characterizing the orientation of the ellipsoid for each voxel and connecting them to trace neural ﬁber pathways. Several methods that propose how to connect discrete directional properties of each voxel have been reported.8,19,40,58,78 An example of tracking methods termed ﬁber assignment by continuous tracking (FACT)58,105 is shown in Figure 8. This approach is based on line-propagation techniques. In this method, a

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line is propagated from a seed point (voxel) bidirectionally (forward and backward) by following local orientation information (vector) of each voxel to reconstruct neural ﬁber pathway. When a line is propagated from one voxel to the next, the continuous coordinate can be kept by memorizing information of exit point in the voxel (i.e., entrance point for the next voxel) and following orientation information of the voxel. The tracking is terminated when the tracking reaches gray matter, judged by a low anisotropy index (e.g., FA is less than 0.2). Another criterion for termination is transition of angle from one voxel to another. It is preferable to set a threshold that prohibits a sharp turn during the line propagation because it suggests imaging resolution is too low to depict the curvature. The linear propagation approach also is known to accumulate errors when the angle transition is large from one pixel to another.8,52 Diffusion-tensor MR imaging is the only noninvasive in vivo method for mapping neural pathways in white matter. For successful neural ﬁber tracking, however, high quality (i.e., high SNR, isotropic voxel, and high spatial resolution 74 ), three-dimensional, diffusion-weighted MR images should be processed by a robust mathematical framework and a computer-based algorithm that allows the reliable following of the individual white-matter ﬁber tracts. Some technical issues still remain in spite of recent hardware improvements including better stability and homogeneity of the main magnetic ﬁeld, stronger and faster magnetic gradients, and the development of several schemes to reduce commonly encountered artifacts related to motion,2,12,15,57,68,103 eddy currents,11,31,38,72 and ﬁeld inhomogeneity.37 One such issue is the sorting bias issue that is produced by systemic noise when eigenvalues of Deff are ordered according to their magnitudes to determine the direction of the largest principal axis of the diffusion ellipsoid. For reducing sorting bias, there are approaches that attempt to use information of neighboring voxels.8,9,46,52,78 A ﬁber-tracking approach, different from a line-propagation technique like FACT, also is proposed such as using “a spaghetti plate model,”78 ﬁrst marching model,73 and energy minimization based on simulated annealing.91

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Figure 9. A 13-year-old symptomatic boy with X-linked adrenoleukodystrophy (ALD). X-linked ALD is a peroxisomal disorder that involves the central nervous system (CNS), adrenal cortex, and testes. Cerebral form of X-linked ALD is characterized by rapid demyelination with an inﬂammatory component triggered by the presence of very long chain of fatty acids. T2-weighted (A) and diffusion-weighted (b-value ⫽ 600 second/mm2) (B) images obtained at the level of the centrum semiovale demonstrate abnormalities in the deep white matter of both parietal lobes. Corresponding mean ADC (C) and fractional anisotropy (FA) (D) maps show gradation of signal intensity from the periphery to the center of the affected white matter that is shown as a hyperintensity area on a T2-weighted image. The gradation might represent well-established histopathologic zonal changes in white matter lesion of X-linked ALD, which are comprised of three different zones: the outer zone with active myelin destruction and axonal sparing; the intermediate zone characterized by perivascular inﬂammatory cells in addition to myelin destruction; and the central zone with dense mesh of glial ﬁbrils and scattered astrocytes with absence of axons, myelin sheaths, and oligodendroglia.

APPLICATION OF DIFFUSION-TENSOR MR IMAGING Measurement of Quantitative Indices Recently, reports that attempt to apply DT MR imaging to clinical cases are on the increase. By sampling the full diffusion tensor, measures of diffusivity of water molecules and diffusion anisotropy in white matter have been reported from normal and diseased human brain. These measures are revealed as a useful index for monitoring structural changes in brain

development,43,64 aging,67,75,87 and diseases.* Some of the reports show that the anisotropy maps can depict changes beyond the visible abnormalities on conventional T1-weighted or T2-weighted MR images.17,24,25,28,50,67,97 For estimating the effects of treatment in patients, the measures may be useful because of their ability to detect subtle change.28 In patients with demyelinating disease (e.g., multiple sclerosis, cerebral autosomal dominant arteriopathy *References 3, 17, 23, 24, 25, 28, 34, 35, 41, 43, 45, 50, 79, 85, 90, 94, 96, 97, 100, 101, 106.

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[CADASIL], and X-linked adrenoleukodystrophy [ALD] [Fig. 9]), the measures may have a role in monitoring advanced phases of the disease17,25,35,97 and may contribute to distinguish various types of lesions.3,35 A potential for cognitive neuroscience, to which conventional MR imaging has not fully contributed, also is suggested.43,44 The lack of direct comparison between the anisotropy map and histopathology, however, is a common limitation in most of the reports. Although the determinants of water diffusion in tissues still are not completely understood, animal and the human brain studies suggest that density of ﬁber and neuroglial cell packing (e.g., oligodendroglia),34,87 degree of myelination,33,35,43,64,97 axonal integrity35 and orientation (i.e., tortuous or straight),88 and individual ﬁber diameter102 are microstructural features of white matter that are possible contributors to diffu-

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sion anisotropy. MR spectroscopy, which is a powerful tool for testing pathophysiologic state in vivo, reveals strong relationships between fractional anisotropy and Nacetylaspartate (NAA)22 — considered a neuronal marker — predominantly present in axons within white matter. Concerning directionally averaged diffusivity, cellular structure integrity, and increase in free water content may have an inﬂuence on restricted diffusion.64 Still, it is essential to reveal contributors in the tissue to the diffusion process to estimate whether the changes in white matter are reversible or not. Establishing reliable analytic methodologies (i.e., how to analyze the measured indices without bias) is another pressing issue. The normal standard of the indices (region-, age-, and sex-dependent)64,67,75,82,87 also is of critical importance for establishing methodologies. A

Figure 12. A 1-month-old boy with semilobar holoprosencephaly. A, Coronal inversion recovery image demonstrates noncleavage of the deep gray matter nuclei and continuation of subcortical white matter across the midline. Axial T2-weighted image (B) at the level of the medulla.

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regional measurement by manually or semiautomatically placing a region of interest seems labor-intensive and less reliable because of difficulty of eliminating bias in measurement and regional variations of diffusion anisotropy in white matter. Whole-brain estimation using histogram may be one possible solution.67 Another potential analytic method is voxel-byvoxel statistical comparisons of the maps normalized to a standard template (e.g., normalization to Talairach space using statistical parametric mapping [SPM; Welcome Department of Cognitive Neurology, Institute of Neurology, London, UK]).24,44,79 Graphical Maps Diffusion-tensor MR graphic maps provide a new spectacle that shows ﬁber architectures in white matter. Vector maps successfully reveal regional microstructural damage in premature infants with perinatal white-matter injury.34 The maps may be a robust method of estimating cognitive abilities and development. 43,44 Furthermore, visualization of connectivity and continuity of neural pathways in the CNS (i.e., tractogram) may contribute to a wide range of investigations concerned with brain development, normal anatomic connectivity of the brain,19,59,78,105 the functional and anatomic organization of the brain,19 and diseases affecting neural pathway integrity. It also enables estimation of the treatment effects on the diseases. For quantitative assessments, however, normal standards to estimate whitematter ﬁber tract integrity should be established. The method that anatomically normalizes maps to a standard template and estimates statistically on a voxel-by-voxel basis (e.g., using SPM)43,44 may be feasible. The following are three preliminary experiences applying DT MR graphic maps to clinical cases. First, in cerebral form of X-linked ALD, which is a rare genetic disorder characterized by demyelination, the effect of whitematter lesions on commissural tracts (the genu of corpus callosum) is currently being correlated with neuropsychologic function (Fig. 10). Second, in patients with spastic cerebral palsy secondary to periventricular leukomalacia, which is a dominant pattern of anoxic brain injury in the premature, the severity of spastic diplegia also is being correlated with the degree of damage to corticospinal tracts (Fig. 11).

Third, in children with holoprosencephaly (HPE), which is a congenital brain malformation attributed to errors in ventral induction, anomalous white-matter tracts are identiﬁed (Fig. 12). Deﬁning white- and gray-matter anomalies may allow more precise prediction of developmental outcome in HPE. Mouse Experiment In the ﬁeld of brain development research, the manifestation of speciﬁc genes in the development process can be investigated by creating transgenic or knockout mouse strains. MR imaging can easily provide three-dimensional data sets of the entire mouse brain free of artifacts related to brain deformation or missing tissue caused by imperfect sectioning often encountered in histologic procedures. DT MR imaging has great potential for monitoring morphologic changes of developing brain in vivo, and can be an alternative to current labor-intensive histologic procedures in this ﬁeld. The following are potential methods of DT MR imaging for investigating developing mouse brain: (1) a color anisotropy map representing embryonic mouse brain components with ordered structures in different directions (Fig. 13A); (2) segmentation of embryonic mouse brain structures based on differences of FA value and three-dimensional volumetry of anatomic layers, such as cortical plate, periventricular zone, and ventricle (Fig. 13B); and (3) three-dimensional reconstruction of early axonal tracts (Fig. 13C).60 By monitoring FA value and volume of each component, evaluation of brain development can be quantitative and comparable between subjects or different strains. By DT MR imaging, monitoring changes in brain organization is expected to greatly enhance the macroscopic histologic assessment of transgenic and knockout models.

SUMMARY Diffusion-tensor MR imaging is a promising tool to evaluate white-matter integrity by quantitative and graphic maps including neural ﬁber tractogram. Current challenges afoot are to obtain higher quality diffusion-weighted MR images (high SNR, isotropic voxel, and

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high spatial resolution), to create a robust mathematical framework to process the data, to construct a user-friendly computer-based algorithm, to reveal determinants of diffusion process, and to establish analytical methodology. ACKNOWLEDGMENT The authors thank Jiangyang Zhang, PhD and Meiyappan Solaiyappan, PhD, Department of Radiology and Radiological Sciences, The Johns Hopkins University, Baltimore, MD, for help in image preparation and display.

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