Characterization of central nervous system structures by magnetic resonance diffusion anisotropy

Transcription

1 Neurochemistry International 45 (2004) Characterization of central nervous system structures by magnetic resonance diffusion anisotropy Hatsuho Mamata, Ferenc A Jolesz, Stephan E Maier Department of Radiology, Brigham and Women s Hospital, Harvard Medical School, 75 Francis Street, Boston, MA 02115, USA Accepted 12 November 2003 Available online 21 January 2004 Abstract Diffusion-weighted magnetic resonance imaging (MRI) provides information about tissue water diffusion. Diffusion anisotropy, which can be measured with diffusion tensor MRI, is a quantitative measure of the directional dependence of the diffusion restriction that is introduced by biological structures such as nerve fibers. Diffusion tensor MRI data was obtained in the brain, brain stem, and cervical spinal cord. For each region, scans were performed in four normal volunteers. Fractional anisotropy (FA), an index of diffusion anisotropy, was measured within regions of interest located in the corpus callosum, capsula interna, thalamus, caudate nucleus, putamen, brain cortex, pyramidal tract of the medulla, accessory olivary nucleus, dorsal olivary nucleus, inferior olivary nucleus, spinal white and gray matter. The highest FA value was measured in the corpus callosum (81±3%). The values of the other areas decreased in the following order: pyramidal tract in the medulla (72 ± 1%), spinal white matter (65 ± 4%), capsula interna (62 ± 3%), accessory olivary nucleus (36 ± 2%), spinal gray matter (34 ± 5%), dorsal olivary nucleus in the medulla (29 ± 2%), thalamus (28 ± 2%), inferior olivary nucleus (15 ± 2%), putamen (13 ± 2%), caudate nucleus (13 ± 2%), and brain cortex (9 ± 1%). Our results indicate that the underlying fiber architecture, fiber density, and uniformity of nerve fiber direction affect anisotropy values of the various structures. Characterization of various central nervous system structures with diffusion anisotropy is possible and may be useful to monitor degenerative diseases in the central nervous system Elsevier Ltd. All rights reserved. Keywords: Diffusion tensor MRI; Fractional anisotropy (FA); Line scan diffusion imaging; Central nervous system; Spinal cord 1. Introduction Diffusion-weighted magnetic resonance imaging (MRI) provides information about tissue water diffusion and is widely used in clinical radiology of brain stroke lesions. Diffusion tensor MRI (Basser et al., 1994) provides information about the preferred diffusion direction and permits non-invasive determination of the course of brain nerve fiber tracts (Moseley et al., 1990; Mori et al., 1999; Mamata et al., 2002). Diffusion anisotropy is a measure of the directional dependence of the diffusion restriction that is introduced by nerve fibers. In the central nervous system (CNS), nerve fibers form various anatomic structures. Each structure presents unique nerve fiber arrangement and density. In this study, we present diffusion tensor MRI data obtained in the normal adult brain, brain stem, and cervical spinal cord. Fractional anisotropy (FA), an index of diffusion anisotropy, was assessed within various anatomical structures. Differ- Corresponding author. Tel.: ; fax: address: hatsuho@bwh.harvard.edu (H. Mamata). ences in the FA values are discussed in terms of the distinct fiber architectures associated with these structures. 2. Experimental procedures 2.1. Subjects Twelve healthy volunteers participated in this study. Diffusion tensor MRI scans were obtained from the brain (N = 4), the brain stem (N = 4), and the spinal cord (N = 4). None of the subjects presented any neurological symptoms or abnormal lesions on the structural MR images. All studies were conducted within the guidelines of the internal review board of our institution Diffusion tensor imaging All studies were performed on a 1.5 T whole-body MR system (Horizon Echospeed LX, General Electric Medical System, Milwaukee, WI) with version software. The scan protocol included T1-weighted spin echo and /$ see front matter 2003 Elsevier Ltd. All rights reserved. doi: /j.neuint

2 554 H. Mamata et al. / Neurochemistry International 45 (2004) T2-weighted fast-spine-echo scans for localization. Line scan diffusion imaging (LSDI) (Gudbjartsson et al., 1996; Maier et al., 1998) was applied to collect diffusion tensor data. LSDI is relatively insensitive to bulk motion and exhibits only minimal chemical shift, magnetic field susceptibility, and eddy current related artifacts. The insensitivity to chemical shift and susceptibility variations is particularly important when images of spinal cord and brain stem are obtained. Scans of brain and brain stem were performed with the standard quadrature head coil. At the level of the basal ganglia, image data were acquired in two axial sections and at the level of the inferior olivary nucleus in one axial section. Axial scans of the spinal cord were performed with a phased-array coil at the level of the cervical enlargement (C5 C7). Images were obtained with diffusion weightings (b-factor) of 5 and 1000 s/mm 2 in brain and brain stem, and 5 and 750 s/mm 2 in the spinal cord. For the high b-factor, diffusion weighting was applied along six non-collinear and non-coplanar directions [(1, 1, 0), (0, 1, 1), (1, 0, 1), (0, 1, 1), (1, 1, 0), ( 1, 0, 1), where (x, y, z) indicates which diffusion-sensitive gradients and their polarities are being applied during a particular scan]. For the low b-factor, diffusion weighting was only applied along two directions [(1, 1, 0), (0, 1, 1)]; collection of all gradient configurations at low diffusion weighting is not necessary, since the directionally-dependent, diffusion-related signal attenuation is minimal. To obtain data free of gradient cross-term effects, diffusion gradient polarity was alternated between excitations (Neeman et al., 1991). The LSDI scan parameters for brain scans were set as follows: repetition time (TR), 2640 ms; echo time (TE), 65 ms; rectangular field of view (FOV), 220 mm 165 mm; slice thickness, 4 mm with a 1 mm gap; matrix size, (frequency column); receiver bandwidth, ±3.91 khz; number of excitations (NEX), 20. The scan time was 1 min per slice and excitation. For brain stem and spinal cord scans, the parameters were the same, except that a slightly smaller and narrower FOV (160 mm 80 mm) and matrix (128 64) was used. The narrower FOV reduced the TR to about 1800 ms. For two brain stem scans, NEX = 10 was used, otherwise, NEX = Postprocessing Diffusion tensor MRI permits the quantitative assessment of the directional dependence of restricted diffusion. The term tensor originates from the physics and engineering field, where it was introduced to describe tension forces in solid bodies with an array of three-dimensional vectors. The particular tensors used to describe diffusion can be conceptualized and visualized as ellipsoids (Fig. 1) (Westin et al., 2002). The directions of the orthogonal ellipsoid main axes represent the diffusion tensor eigenvectors and their length the diffusion tensor eigenvalues λ 1, λ 2, and λ 3. The arithmetic average of the three diffusion eigenvalues is a rotationally invariant measure of diffusion. If the magni- Fig. 1. Ellipsoid representation of the diffusion tensor with the eigenvalues λ 1, λ 2, and λ 3. Three situations of diffusion are shown. If the size of the three axes is equal (A), then the diffusion is said to be isotropic and the diffusion tensor can be visualized as a sphere. This type of diffusion is characteristic for CSF. If the size of the three axes is not equal, then the diffusion is said to be anisotropic (B, C). Nerve fibers show this type of diffusion. The axis with the highest diffusion (i.e., the axis associated with eigenvalue λ 1 ) coincides with the long axis of the nerve fiber. tude of the three axes or eigenvalues is equal, then the diffusion is said to be isotropic and the diffusion tensor can be visualized as a sphere (Fig. 1A). For example, in cerebrospinal fluid, the diffusion tensor is best characterized by spherical, or isotropic, diffusion. If the magnitude of the three eigenvalues is not equal, then the diffusion is said to be anisotropic (Fig. 1B and C). For example, in white matter nerve fibers, diffusion is anisotropic and the preferred diffusion direction, which is represented by the longest axis of the diffusion ellipsoid (i.e., λ 1 ), coincides with the nerve fiber s longitudinal direction. (Hsu et al., 1998; Scollan et al., 1998; Lin et al., 2001). Various formulas have been proposed that derive rotationally invariant measures of diffusion anisotropy from the three eigenvalues. The most widely used diffusion anisotropy measure is the fractional anisotropy index (Papadakis et al., 1999). Fractional anisotropy values range from 0 (isotropic diffusion) to 100% (totally restricted diffusion). Anisotropy measures are very sensitive to a low signal-to-noise ratio (SNR) of the MR image (Bastin et al., 1998). In general, in areas of diffusion with no or little variance of directional dependence, i.e., isotropic diffusion or diffusion with low anisotropy, low SNR leads to an overestimation of diffusion anisotropy. In areas of highly restricted diffusion, however, low SNR may result in an underestimation of diffusion anisotropy. Single-shot MR diffusion imaging sequences, which are preferred because of their minimal motion artifacts, unlike multi-shot sequences, yield image data with rather poor SNR.

3 H. Mamata et al. / Neurochemistry International 45 (2004) The diffusion tensor MRI data was processed off-line. For each diffusion encoding direction, the apparent diffusion coefficient (ADC) was determined using the Stejskal/Tanner equation (Stejskal and Tanner, 1965), where the signal attenuation, S(b) = S(0) exp( b ADC), is determined by the b-factor. This computation was followed by the calculation of the diffusion eigenvalues and eigenvectors. For each slice, a T2-weighted image (average of the two images obtained at low diffusion weighting), a geometric-average diffusion-weighted map, a arithmetic-average ADC map, and a FA map were reconstructed. In addition, maps overlaid with the first eigenvector direction (i.e., λ 1 ) were generated. Fractional anisotropy values were determined within regions of interest (ROI) of the following areas: corpus callosum, capsula interna, thalamus, caudate nucleus, putamen, brain cortex, pyramidal tract of medulla, accessory olivary nucleus, dorsal olivary nucleus, inferior olivary nucleus, as well as the white and central gray matter of the spinal cord. To study the effect of image SNR on the anisotropy measures, data subsets with 1, 2, 4, 8, and if available, up to 16 excitations (NEX) were generated. Data sets with more than one excitation were magnitude signal averaged. For each data subset, FA maps were computed and anisotropy was quantified for the same, previously defined, ROIs. Statistical analysis of FA values was performed with a two sided t-test. A P-value of less than 0.05 was considered significant. Finally, SNR was assessed for each scanned region, i.e., brain, brain stem, and spinal cord. To obtain this measure, the ratio between signal in a tissue ROI and the signal in a void area outside skull was determined and averaged for the six tensor diffusion-weighting directions of a single excitation data subset. In brain, the tissue signal was determined within the putamen, i.e., an area with relatively low diffusion anisotropy. For medulla and spinal cord, the tissue signal was determined over the entire cross-section of the nerve tissue. 3. Results Brain diffusion MRI data obtained in a healthy subject with LSDI is illustrated in Fig. 2. Cerebrospinal fluid (CSF)-filled spaces appear dark on the diffusion-weighted image (Fig. 2B) and exhibit a high ADC value on the ADC map (Fig. 2C). Brain tissue structures show a very uniform ADC value on the ADC map (Fig. 2C). In contrast, the FA map (Fig. 2D) reveals distinct differences between white and gray matter; FA is high for all white matter fiber tracts. In cortical and deep gray matter structures, FA is much lower. The thalamic deep gray matter, however, exhibits a FA that is distinctly higher than the FA of the other gray matter structures, i.e., cortex, putamen, or caudate nucleus. Fig. 2E demonstrates the appearance of the FA map without signal averaging, i.e., NEX = 1. The same anatomic section overlaid with lines and dots that indicate the first eigenvector direction is depicted in Fig. 3. Different anatomic nerve structures can well be discerned based on the direction of the eigenvector. A highly organized pattern of the first eigenvector direction is also revealed in the thalamic gray matter. Fractional anisotropy maps of brain stem and spinal cord are shown in Fig. 4. Nuclei in the medulla, central gray matter in the spinal cord, and main white matter tracts can readily be distinguished by their different anisotropy. In each section, in white and gray matter structures, the first eigenvector was found to point in the cranio-caudal direction. A plot of FA of various brain structures measured as a function of NEX is shown in Fig. 5. The noise-related overestimation in areas of low anisotropy for low NEX is clearly demonstrated. The SNR for the single-excitation brain scan was 10.3, for the brain stem scan 5.5, and for the spinal-cord scan 2.4. A chart with FA values of all structures measured is shown in Fig. 6. White matter structures, such as corpus callosum, capsula interna, pyramidal tract, and spinal-cord white matter, exhibit FA values that are six to eight times higher than the FA value measured in the brain cortex. In other gray matter structures, such as the caudate nucleus, putamen, and inferior olivary nucleus, the FA is only slightly higher than in cortex gray matter. Thalamus, dorsal olivary nucleus, accessory olivary nucleus, and spine gray matter are characterized by FA values which lie between the FA values of white matter tracts and typical gray matter structures. 4. Discussion This is a comprehensive study of MR diffusion anisotropy in different CNS structures. It is the first human in vivo study that reports separate anisotropy values for spine white and gray matter. Brain stem and spinal cord are areas notoriously difficult to scan with the commonly used single-shot diffusion-weighted echo-planar imaging techniques. LSDI, as documented in this study and other studies (Maier et al., 1998; Kubicki et al., in press), unlike single-shot echo-planar methods, yields diffusion-weighted images that are free of severe distortion artifacts. Thus, apart from issues of limited SNR, anisotropy measures obtained with LSDI in these regions, may be considered more reliable. Our findings of FA values in an axial section through the lateral ventricles are similar to previously reported anisotropy values (Pierpaoli et al., 1996). Pierpaoli et al., however, used a different anisotropy index, which precludes a direct comparison of nerve tissue structure specific anisotropy values. The corpus callosum and the capsula interna are the brain structures with the highest anisotropy. They are composed of myelinated nerve fibers, which share the same direction (Carpenter, 1991). The difference in anisotropy between the corpus callosum and the capsula interna was statistically significant (P <0.005) and may be due to differences in axon density of the nerve fiber bundles. Indeed, Takahashi et al. (2002) found that in lamprey spinal cord, diffusion perpendicular to the axonal direction varies inversely with

4 556 H. Mamata et al. / Neurochemistry International 45 (2004) Fig. 2. Axial brain diffusion MRI data obtained with line scan diffusion imaging (LSDI) (numbers of excitation [NEX] = 20). (A) T2-weighted MR image. (B) Geometric-average Diffusion-weighted image. (C) Arithmetic-average apparent diffusion coefficient (ADC) map. White corresponds to an ADC value of 3.6 m 2 /ms. (D) Fractional anisotropy (FA) map. White corresponds to a FA value of 90%. (E) Fractional anisotropy map reconstructed from a single excitation (NEX = 1) data subset. Overestimation of FA in areas of low anisotropy, such as cortex, thalamus, and putamen is evident. the number of axons. In agreement with the presence of dense myelinated fibers, medullary pyramidal tract and spinal cord white matters also exhibited high FA values. Fractional anisotropy of thalamus, accessory olivary and dorsal olivary nucleus in the medulla, and spinal gray matter was distinctly lower than the FA of pure white matter tracts and at the same time distinctly higher than the FA of areas with only gray matter. Unlike the corpus callosum, capsula interna, spinal white matter, and medullary pyramidal tract, these structures are composed of both nuclei and numerous thin interconnecting nerve fibers, which are less uniformly arranged than white matter fibers. These structural characteristics may explain the intermediate anisotropy values. Less uniform fiber arrangement alone may result in intermediate anisotropy values, as demonstrated by Pierpaoli et al. for nucleus-free structures, such as optic radiation, centrum semi ovale, and U-fibers. Finally, putamen, caudate nucleus, brain cortex, and inferior olivary nucleus are mostly composed of nuclei and contain only few interconnecting nerve fibers, which is consistent with their low anisotropy. Spinal-cord diffusion anisotropy has been reported previously in animal (Inglis et al., 1997; Pattany et al., 1997; Fenyes and Narayana, 1999) and human (Clark et al., 1999; Ries et al., 2000; Bammer et al., 2000; Murphy et al., 2001) studies. In these previously published human studies, the anisotropy value was measured in sagittal sections of the

5 H. Mamata et al. / Neurochemistry International 45 (2004) Fig. 3. Axial T2-weighted image at the level of the basal ganglia with an overlay showing the first eigenvector direction. The in-plane component of the eigenvector is represented by blue lines and the out-of-plane component by yellow discs of different sizes. For improved visualization of white matter tracts, only eigenvectors with FA of 15% or higher are displayed. Corpus callosum (black arrow, genu; white arrow, splenium) and capsula interna (black and white arrow heads) are the largest nerve bundles visualized by the first eigenvector. The anterior limb of the capsula interna (black arrow head) runs in-plane, whereas the posterior limb (white arrow head) runs through-plane. The thalamic deep gray matter (adjacent to the posterior limb of the capsula interna) also exhibits remarkably organized fiber directions. cervical spinal cord, whereas in the present study, anisotropy was measured in an axial section. Due to better coverage of the tissue of interest, sagittal slice orientation is preferred for clinical spinal cord scans. However, the anisotropy measured in a sagittal section is likely to include both white and gray matter. The spinal-cord diffusion-imaging study by Wheeler-Kingshott et al. (2002) was performed in axial sections. Fractional anisotropy values, however, were averaged over the entire cross-section and no attempts were made to separate spinal-cord gray and white matter. According to our findings, FA values in spinal-cord gray and white matter are statistically significantly different (P <0.005). Hence, one would expect that measurements in sagittal sections underestimate spinal-cord white matter anisotropy and overestimate spinal-cord gray matter anisotropy. There are several factors that influence the accuracy of the FA measurements. First, for very small regions of interest, such as spinal-cord gray matter and the olivary nuclei in the medulla, the definition of the ROI is difficult. The inclusion of surrounding white matter may result in an overestimation of anisotropy. The brain cortex layer is slightly thicker than the in-plane pixel dimension (1.7 mm) and slightly thinner than the slice thickness (4 mm) employed in this study. Therefore, partial volume errors due to the highly anisotropic white matter and the isotropic CSF are likely. Similarly, the anisotropy of small peripheral white matter tracts may be underestimated due to partial volume effects. Another factor that strongly determines the accuracy of the anisotropy measurements is the low SNR of single-shot diffusion-weighted scans. For structures with low

6 558 H. Mamata et al. / Neurochemistry International 45 (2004) Fig. 4. Fractional anisotropy map (20 20 mm subimage) of 4 mm axial cross-sections in the medulla (A) and spinal cord (B). White corresponds to a FA value of 90%. (A) Dark areas of low anisotropy are recognized and correspond to the dorsal olivary nucleus (black arrow heads), the inferior olivary nucleus (white arrow heads) and the accessory olivary nucleus (circles). The particularly bright ventral area of high FA corresponds to the pyramidal tract. (B) Spinal-cord white matter is characterized by high FA. Spinal-cord central gray matter appears as a butterfly-shaped dark area inside the white matter area, with relatively low anisotropy. anisotropy, the low SNR of scans without signal averaging resulted in a twofold overestimation of FA values. For structures with very high anisotropy, SNR had a negligible effect on the estimation of the FA. Bastin et al. (1998) recommend a SNR of at least 20:1. Evidently, without signal averaging, none of the scan protocols employed in this study reached this threshold. The brain scan protocol resulted in the highest SNR. The SNR for the higher resolution scan in the brain stem was 1.9 times lower. As expected, this ra- tio equals the ratio of the pixel volumes of the two protocols. The SNR for the spinal-cord scans was considerably lower than the SNR of the brain stem scans. This difference is largely explained by the depth-dependent sensitivity of the surface coil that was used for the spinal-cord scans. When data with such low SNR is magnitude averaged, the background noise follows a Rician (Gudbjartsson and Patz, 1995), rather than a Gaussian distribution and is likely to introduce errors in the FA estimation that can not be removed Fig. 5. Average FA of different brain structures in four healthy subjects measured as a function of the number of excitations (NEX). For structures with low diffusion anisotropy, FA decreases with increasing NEX (i.e., increasing signal-to-noise ratio) until it reaches a stable value after four to eight excitations. In the corpus callosum, an area of very high anisotropy, increasing the NEX has relatively little effect on the FA value (N.S., P = 0.3).

7 H. Mamata et al. / Neurochemistry International 45 (2004) Fig. 6. Different brain structures sorted according their average multiple-excitation FA value in four healthy subjects. The FA value of spine gray matter was measured in the ventral portion. In all structures, except corpus callosum, multiple excitation data (NEX = 20, except for two brain stem scans with NEX = 10) resulted in a lower FA value than single excitation data. The overestimation of FA with NEX = 1 is more striking in brain stem and spinal cord structures. This is readily explained by the lower overall signal-to-noise ratio (SNR) of the brain stem and spinal cord scans. with signal averaging. No attempts were made to correct the data by estimation and subtraction of background noise. In general, however, LSDI, when compared with the commonly used single-shot echo-planar diffusion-weighted sequences, yields a relatively high SNR. In a comparative study (Kubicki et al., in press), we found that more than four signal averages were required for the single-shot echo-planar sequences to match the SNR of LSDI without signal averaging. Moreover, as was found in the same study, FA maps that are obtained with single-shot echo-planar methods tend to contain additional errors that stem from chemical shift, magnetic field susceptibility variations, and eddy currents. Signal averaging would not eliminate such errors. In summary, diffusion tensor MRI yields anisotropy measures (such as FA) that permit characterization of various CNS structures. A direct correlation between FA value and microscopic findings in terms of fiber density, average fiber diameter, and degree of fiber myelination has not yet been established. However, the relative differences in FA between different neurological structures is certainly consistent with the extent of ordered anisotropic microstructure within the tissue. Normal values of the various structures may be useful to evaluate pathologies in the CNS based on their FA characteristics. Particularly for low FA values, which may indeed result from a destructive disease process, sufficient SNR is required in order to prevent overestimating tissue anisotropy and thereby underestimating the progress of disease. References Bammer, R., Fazekas, F., Augustin, M., Simbrunner, J., Strasser-Fuchs, S., Seifert, T., Stollberger, R., Hartung, H-P., Diffusion-weighted MR imaging of the spinal cord. Am. J. Neuroradiol. 21, Basser, P.J., Mattiello, J., LeBihan, D., MR diffusion tensor spectroscopy and imaging. Biophys. J. 66 (1), Bastin, M.E., Armitage, P.A., Marshall, I., A theoretical study of the effect of experimental noise on the measurement of anisotropy in diffusion imaging. Magn. Reson. Imaging 16 (7), Carpenter, M.B., Gross anatomy of the brain. In: Core Text of Neuroanatomy, fourth ed. William & Wilkins, Baltimore, MD, pp Clark, C.A., Barker, G.J., Tofts, P.S., Magnetic resonance diffusion imaging of the human cervical spinal cord in vivo. Magn. Reson. Med. 41 (6), Fenyes, D.A., Narayana, P.A., In vivo diffusion tensor imaging of rat spinal cord with echo planar imaging. Magn. Reson. Med. 42 (2), Gudbjartsson, H., Maier, S.E., Mulkern, R.V., Morocz, I.A., Patz, S., Jolesz, F.A., Line scan diffusion imaging. Magn. Reson. Med. 36 (4), Gudbjartsson, H., Patz, S., The Rician distribution of noisy MRI data. Magn. Reson. Med. 34 (6), Erratum in: Magn. Reson. Med. 36(2), 332, August Hsu, E.W., Muzikant, A.L., Matulevicius, S.A., Penland, R.C., Henriquez, C.S., Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation. Am. J. Phys. 274 (5 Pt 2), H Inglis, B.A., Yang, L., Wirth 3rd, E.D., Plant, D., Mareci, T.H., Diffusion anisotropy in excised normal rat spinal cord measured by NMR microscopy. Magn. Reson. Imaging 15 (4), Kubicki, M., Maier, S.E., Westin, C.-F., Mamata, H., Ersner-Hershfield, H., Estepar, R., Kikinis, R., Jolesz, F.A., McCarley, R.W., Shenton,

8 560 H. Mamata et al. / Neurochemistry International 45 (2004) M.E., in press. Comparison of single-shot echo planar and line scan protocols for diffusion tensor imaging. Invest. Radiol. Lin, C.P., Tseng, W.Y., Cheng, H.C., Chen, J.H., Validation of diffusion tensor magnetic resonance axonal fiber imaging with registered manganese-enhanced optic tracts. Neuroimage 14 (5), Maier, S.E., Gudbjartsson, H., Patz, S., Hsu, L., Lovblad, K.O., Edelman, R.R., Warach, S., Jolesz, F.A., Line scan diffusion imaging: characterization in healthy subjects and stroke patients. Am. J. Roentgenol. 171 (1), Mamata, H., Mamata, Y., Westin, C.F., Shenton, M.E., Kikinis, R., Jolesz, F.A., Maier, S.E., High-resolution line scan diffusion tensor MR imaging of white matter fiber tract anatomy. Am. J. Neuroradiol. 23, Mori, S., Crain, B.J., Chacko, V.P., van Zijl, P.C., Three dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann. Neurol. 45, Moseley, M.E., Cohen, Y., Kucharczyk, J., Mintorovitch, J., Asgari, H.S., Wendland, M.F., Tsuruda, J., Norman, D., Diffusion-weighted MR imaging of anisotropic water diffusion in cat central nervous system. Radiology 176, Murphy, B.P., Zientara, G.P., Huppi, P.S., Maier, S.E., Barnes, P.D., Jolesz, F.A., Volpe, J.J., Line scan diffusion tensor MRI of the cervical spinal cord in preterm infants. J. Magn. Reson. Imaging 13, Neeman, M., Freyer, J.P., Sillerud, L.O., A simple method for obtaining cross-term-free images for diffusion anisotropy studies in NMR microimaging. Magn. Reson. Med. 21 (1), Papadakis, N.G., Xing, D., Houston, G.C., Smith, J.M., Smith, M.I., James, M.F., Parsons, A.A., Huang, C.S., Hall, L.D., Carpenter, T.A., A study of rotationally invariant and symmetric indices of diffusion anisotropy. Magn. Reson. Imaging 17 (6), Pierpaoli, C., Jezzard, P., Basser, P.J., Barnett, A., Di Chiro, G., Diffusion tensor MR imaging of the human brain. Radiology 201 (3), Pattany, P.M., Puckett, W.R., Klose, K.J., Quencer, R.M., Bunge, R.P., Kasuboski, L., Weaver, R.G., High-resolution diffusion-weighted MR of fresh and fixed cat spinal cords: evaluation of diffusion coefficients and anisotropy. Am. J. Neuroradiol. 18 (6), Ries, M., Jones, R.A., Dousset, V., Moonen, C.T.W., Diffusion tensor MRI of the spinal cord. Magn. Reson. Med. 44, Scollan, D.F., Holmes, A., Winslow, R., Forder, J., Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am. J. Physiol. 275 (6 Pt 2), H Stejskal, E.O., Tanner, J.E., Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Phys. 42, Takahashi, M., Hackney, D.B., Zhang, G., Wehrli, S.L., Wright, A.C., O Brien, W.T., Uematsu, H., Wehrli, F.W., Selzer, M.E., Magnetic resonance microimaging of intraaxonal water diffusion in live excised lamprey spinal cord. Proc. Natl. Acad. Sci. U.S.A. 99 (25), Westin, C.F., Maier, S.E., Mamata, H., Nabavi, A., Jolesz, F.A., Kikinis, R., Processing and visualization for diffusion tensor MRI. Med. Image Anal. 6 (2), Wheeler-Kingshott, C.A.M., Hickman, S.J., Parker, G.J.M., Ciccarelli, O., Symms, M.R., Miller, D.H., Barker, G.J., Investigating cervical spinal cord structure using axial diffusion tensor imaging. NeuroImage 16 (1),