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In vivo isotropic 3D diffusion tensor mapping of the rat brain using diffusion-weighted 3D MP-RAGE MRI
Magnetic Resonance Imaging 24 (2006) 287 – 293
In vivo isotropic 3D diffusion tensor mapping of the rat brain using diffusion-weighted 3D MP-RAGE MRI Tomokazu Numanoa,c,4, Kazuhiro Hommaa, Nobuaki Iwasakib, Koji Hyodoa, Naotaka Nittaa, Takeshi Hirosec a
Biomedical Sensing and Imaging Group, National Institute of Advanced Industrial Science and Technology (AIST), Ibaraki 305-8564, Japan b Department of Pediatrics, Ibaraki Prefectural University of Health Sciences, Ibaraki 300-0394, Japan c Department of Precision Machinery Engineering, Graduate School of Science and Technology, Nihon University, Chiba 274-8501, Japan Received 6 June 2005; accepted 11 December 2005
Abstract The purpose of this study was to examine the potential of diffusion-weighted (DW) three-dimensional (3D) MP-RAGE MRI for diffusion-tensor mapping of the rat brain in vivo. A DW-3D-MP-RAGE (3D-DWI) sequence was implemented at 2.0 T using six gradient orientations and a b value of 1000 s/mm2. In this sequence, the preparation sequence with a b908RF-motion proving gradient (MPG): MPG-1808RF–MPG-908RFQ pulse train (DW driven equilibrium Fourier transform) was used to sensitize the magnetization to diffusion. A centric k-space acquisition order was necessary to minimize saturation effects (T1 contamination) from tissues with short relaxation time. The image matrix was 128128128 (interpolated from 646464 acquisitions), which resulted in small isotropic DW image data (voxel size: 0.2730.2730.273 mm3). Moreover, 3D-DWI-derived maps of the fractional anisotropy (FA), relative anisotropy (RA) and main-diffusion direction were completely free of susceptibility-induced signal losses and geometric distortions. Two well-known commissural fibers, the corpus callosum and anterior commissure, were indicated and shown to be in agreement with the locations of these known stereotaxic atlases. The experiment took 45 min, and shorter times should be possible in clinical application. The 3D-DWI sequence allows for in vivo 3D diffusion-tensor mapping of the rat brain without motion artifacts and susceptibility to distortion. D 2006 Elsevier Inc. All rights reserved. Keywords: DWI; Driven equilibrium Fourier transform; Three-dimensional MP-RAGE; Apparent diffusion coefficient (ADC); Diffusion tensor imaging (DTI)
1. Introduction Diffusion-weighted imaging (DWI) is a magnetic resonance technique that provides tissue contrast that is dependent on the motion of water molecules randomly diffusing in the presence of an applied field gradient [1–3]. Diffusion-weighted imaging has become an important clinical modality for early detection of stroke [4,5]. In regions of stroke, the diffusion of tissue water becomes restricted, as manifested by a decrease in its apparent diffusion coefficient (ADC). On another DWI front, the molecular mobility of water in brain tissue exhibits a pronounced directional dependence that mainly originates from the macroscopic, cellular and subcellular structures of white matter. Because diffusion processes are strongly 4 Corresponding author. Tel.: +81 29 861 9488; fax: +81 29 861 7865. E-mail address: [email protected] (T. Numano). 0730-725X/$ – see front matter D 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.mri.2005.12.011
facilitated along the elongated axon, the ADC turns out to be significantly more parallel to the direction of a nerve fiber than perpendicular to it. These anisotropic movements of water molecules are described mathematically by a tensor. A tensor is a matrix of values. In order to map its properties by MRI, it is necessary to record DW images in at least six different motion-proving-gradient (MPG) directions as well as one image without MPG. The resulting data of such a diffusion-tensor-imaging (DTI) study can be utilized effectively for determining the degree of myelination, the separation and extraction of white matter and gray matter [6,7], and the visualization of brain fiber bundle orientations [8–15]. Single-shot (SS) diffusion-weighted (DW) echo-planar imaging (EPI) is the most popular DW-MRI technique because of its snapshot-like (in the range of 100 ms) acquisition and high signal-to-noise ratio (SNR). However, SS-DW-EPI, like all EPI acquisitions in general, has a
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imaging method. Recently, DW 3D acquisition has been performed by 3D first spin-echo (FSE) sequence [16 –19] or 3D gradient-echo sequence [20]. Three-dimensional FSE has the advantage of decreased sensitivity to susceptibility changes and static field inhomogeneities (using spin-echo vs. gradient-echo), and 3D-FSE images demonstrate higher SNRs, owing to the 908 (vs. a8) excitation pulse. However, because the effect of T2 mixes with the DW images as the number of echo trains increases, 3D-FSE imaging has an upper limit to the number of echo trains, and thus a limit to the shortening of the acquisition time. For further shortening of acquisition time, we developed a DW 3D MRI (3D-DWI) sequence using a 3D magnetization-prepared rapid gradientecho (3D-MP-RAGE) method [21]. In this paper, we demonstrate the 3D diffusion-tensor images from the in vivo rat brain with an image acquisition time of 45 min using the 3D-DWI sequence.
2. Materials and methods 2.1. Diffusion tensor determination Fig. 1. Ellipsoidal approximation of directional anisotropy. (A) Coordinate system of MR magnet (O-xyz) and coordinate system of diffusion tensor ellipsoid (O-xVyVzV). (B) The pairs of eigenvectors and eigenvalues; e i and ki (i = 1, 2, 3). (C) The V1 vector is displayed by mixing colors.
notoriously high level of artifacts. The classic EPI artifact is the N/2 (Nyquist) ghost. This arises because of imperfections in the rephasing–dephasing cycle of the rapidly switching bipolar frequency-encode gradient. Another artifact is a consequence of bandwidth. Each frequency-encode lobe is sampled rapidly with a very high gradient amplitude, resulting in a very large signal bandwidth. The phase encode is sampled 64 or 128 times over the whole gradient-echo train. This rather slow sampling rate means that the signal bandwidth in the phase-encode direction may be as little as 10 Hz/pixel. This gives magnetic field differences (air–tissue boundaries) that will result in large image distortions. In addition, most SS-DW-EPI is two-dimensional (2D) multislice imaging. In order to perform multislice imaging, it is necessary to have a few millimeters of slice thickness and slice gap. Multislice imaging by an isotropic voxel in the submillimeter range is difficult. In general, more advanced data analysis strategies that aim at tracking individual brain fiber connections are expected to benefit from more or less isotropic voxel dimensions. An advantage of three-dimensional (3D) acquisition is that you obtain thinner and more slices with better profiles, and a better SNR for an equivalent slice thickness. It has the advantage of very thin slices with no slice gaps (contiguous slices), and it allows acquisition in a small isotropic voxel compared with 2D acquisition. However, 3D acquisition time is greater than 2D acquisition time because the second phase-encode axis is applied by 3D acquisition. Threedimensional acquisition should thus be a high-speed
Let apparent diffusion (perfusion mixing with diffusion) be diffusion for convenience. For anisotropic tissues, the physical orientation (direction) of the tissue in conjunction with the applied motion-proving-gradient (MPG) direction will determine the signal intensity. If these two directions are the same, there is no problem, but usually this is not true. In this most general case, the diffusion properties are described mathematically by a tensor. A tensor is a matrix of values. The diffusion tensor has nine such values, each corresponding to a MPG orientation and a cell orientation. When the diffusion properties are in a Gaussian distribution (normal distribution), the distribution of diffusion becomes a tensor ellipsoid (Fig. 1A). In this case, diffusion tensor D is described as a 33 symmetric matrix (second-rank tensor). 2
Dxx D ¼ 4 Dxy Dxz
Dxy Dyy Dyz
3 Dxz Dyz 5 Dzz
ð1Þ
The first subscript (x,y,z) refers to the bnaturalQ orientation of the cells or tissue, and the second refers to the MPG orientation. The symmetry tensor is potentially diagonalized, and the three diagonal elements k 1 , k 2 , k 3 (k 1 z k 2 z k 3) are called an eigenvalue. 2
Dxx 4 Dxy Dxz
Dxy Dyy Dyz
3 2 Dxz k1 Dyz 5 diagonalization Y 4 0 Dzz 0
0 k2 0
3 0 05 k3 ð2Þ
The coordinate system of the diagonalized tensor is O-xVyVzV, and it agrees with the principal axis of the tensor ellipsoid (Fig. 1B). The vector in this direction of the
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principal axis is called an eigenvector (e1, e2, e3), and each eigenvalue displays the diffusion coefficient in the direction of the principal axis. Several diffusion anisotropy measures were defined by using the eigenvalues, i.e., fractional anisotropy (FA), relative anisotropy (RA), volume ratio and so on [22,23]. The FA value and RA value as calculated by the following formulae are used most frequently for anisotropy measure. rffiffiffi 3 FA ¼ 2
1 RA ¼ pffiffiffi 3
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðk1 kM Þ2 þ ðk2 kM Þ2 þ ðk3 kM Þ2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k21 þ k22 þ k23
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð k1 kM Þ 2 þ ð k2 kM Þ 2 þ ð k3 kM Þ 2 kM
ð3Þ
ð4Þ
where k M is the mean eigenvalue kM ¼
1 1 Dtrace ¼ ðk1 þ k2 þ k3 Þ 3 3
Fig. 3. T1-weighted anatomy (left) and color-coded V1 map (right) of fresh celery. To facilitate the visualization of vascular bundle orientation, only the area where the FA value exceeded 0.27 is displayed. Water molecules inside the vascular bundle were highly directional along the celery branch (arrow).
diffusion. A centric k-space acquisition ordered RAGEloop sequence was necessary to minimize saturation effects from tissues with short relaxation times. For further details, see Ref. [21]. 2.3. MRI experiments
ð5Þ
2.2. Three-dimensional DWI Fig. 2 shows the 3D-DWI sequence. This method combines the DW driven equilibrium Fourier transform (DW-DEFT) preparation with a 3D-MP-RAGE imaging module. In this sequence, the preparation phase with b908RF-MPG–1808RF-MPG–908RFQ pulse train (DW-DEFT) was used to sensitize the magnetization to
Fig. 2. Diagram of the 3D MP-RAGE MRI pulse sequence (3D-DWI) used for 3D diffusion tensor mapping of the rat brain in vivo. The slice phaseencode gradient (Gp1-PEG) happens only once per TRe period, while the phase-encode gradient (Gp2-PEG) changed in each TR period. In order to avoid T1 contamination in the DW image, the phase encoding was centric k-space acquisition ordered.
All MRI experiments were performed on a 2.0-T Biospec 20/30 System with a B-GA20 Gradient System (Bruker, Karlsruhe, Germany) that had a maximum gradient strength of 100 mT/m. The MR data acquisition and reconstruction were performed with the ParaVision (Bruker) software system. A 45-mm-ID saddle coil tuned to 85 MHz for proton resonance was used for all measurements. Three-dimensional DWI sequence parameters were 5000 ms/54.74 ms (effective-TR: TRe/effective-TE: TEe), 8.91 ms/4.7 ms (TR/TE), flip angle of 358, MPG duration (d) of 25.00 ms, MPG separation (D) of 27.37 ms, readout bandwidth of 195 Hz/pixel, matrix of 646464, field of view (FOV) of 353535 mm (acquisition voxel size:
Fig. 4. The 3D rat brain V1 map is displayed by small isotropic voxels (voxel size: 0.2730.2730.273 mm3). The color code was red for right– left (V 1x ), green for dorsal–ventral (V 1y ) and blue for rostral–caudal (V 1z ). Areas where FA values had exceeded 0.3 are displayed.
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body weight) and atropine (0.05 mg/kg body weight). Each anesthetized rat was inserted in an acrylic tube and subjected to scanning. The maintenance of anesthesia was controlled by intraperitoneal injection of ketamine (50 mg/kg per hour) and xylazine (5 mg/kg per hour) from a syringe pump. All studies were performed in accordance with animal protection laws and approved by the Animal Ethical Committee of the National Institute of Advanced Industrial Science and Technology. 2.5. Post-processing for DTI Fig. 5. T2-weighted anatomical image (left) and color-coded V1 map (right) of the rat brain. The anatomical image and V1 map of the corpus callosum location were approximately the same.
0.5470.5470.547 mm3) and 64 phase-encoding steps per RAGE loop. Except during the acquisition of a non-DW image, DTI involved diffusion gradient encoding along six different directions (1,0,1), (1,1,0), (0,1,1), (1,0,1), (1,1,0), (0,1,1) and with two different b values of 0 and 1000 s/mm2 in all cases. The total acquisition time was 45 min 23 s. To allow for anatomic references, T1- or T2-weighted 2D-multislice MRI (T1: spin-echo; T2: fast spin-echo) of fresh celery and a rat brain was performed. T1-weighted spinecho sequence parameters were 500 ms/15 ms (TR/TE), readout bandwidth of 103 Hz/pixel, matrix of 256256, FOV of 70 mm, slice thickness of 2 mm. T2-weighted fast spinecho sequence parameters were 3000 ms/42.33 ms (TR/TEe), readout bandwidth of 326 Hz/pixel, echo train length (ETL) of 10, matrix of 256256, FOV of 70 mm, slice thickness of 2 mm. 2.4. Animal preparation For in vivo studies, three male Crj:Wistar rats (450–470 g, 18 weeks old) were anesthetized by intraperitoneal injection of ketamine (100 mg/kg body weight), xylazine (10 mg/kg
All DW-MRI data were transferred to an offline LINUX PC with a Pentium 4 processor (1.8 GHz) and 1-GB memory. The rat brain diffusion-tensor image processing was performed using a commercial medical image analysis software, Dr. View/LINUX (Asahi Kasei Information Systems, Tokyo, Japan). After linear interpolation of the DW images to twice the matrix size (image voxel size: 0.2730.2730.273 mm3), the DW images were Gaussian filtered with a full width at half-maximum of 1 mm. In all diffusion-tensor images, brain mask processing erased the background noise outside of the brain. To facilitate the visualization of fiber bundle orientations, maps of the main-diffusion direction (principal axes of tensor ellipsoid) were color-coded and superimposed onto corresponding maps of the T2-weighted 3D-DWI (without MPG) image: color-coded V1 map. The main-diffusion-direction vector V1 is shown in Fig. 1C. In explicit form, V1 ¼ k1 e1 ¼ V1x ; V1y ; V1z
ð6Þ
where V 1x , V 1y and V 1z are the x-, y- and z components of V1, respectively. The color code was red for right–left (V 1x ), green for up–down (V 1y ) and blue for front–rear (V 1z ) with mixed colors for intermediate orientations.
Fig. 6. Comparison between the results of the commissural fibers and the rat brain atlas [22] for arbitrary section images: axial, coronal and sagittal 2D slices. CA, Anterior commissure; CC, corpus callosum; CE, external capsule; LV, lateral ventricle.
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3. Results 3.1. Celery experiment Fig. 3 compares a T1-weighted anatomic image of fresh celery with the color-coded V1 map. To facilitate the visualization of vascular bundle orientation, only the area where the FA value exceeded 0.27 is displayed. The ADC value of the water in the vascular bundle of the celery perpendicular and parallel to the vascular bundle direction was measured to be 0.99103 and 1.42103 mm2/s, respectively. The diffusion of the water in the parenchyma looks isotropic, but these water molecules inside the vascular bundle were highly directional along the celery branch (arrow). This result shows that the 3D-DWI sequence can detect the direction of diffusion. 3.2. Rat experiments Fig. 4 illustrates the 3D rat brain V1 map. The color code was red for right–left (V 1x ), green for dorsal–ventral (V 1y ) and blue for rostral–caudal (V 1z ). The area where the FA value had exceeded 0.3 is displayed. A T2-weighted anatomical image is shown in Fig. 5 with the corresponding level in the rat brain V1 axial (arbitrary section: axial image). When the anatomical image and the V1-axial image were compared, the anatomical location of the corpus callosum was approximately the same (arrow). An image resolution of 0.2730.2730.273 mm3 turned out to be sufficient to resolve the main fiber structures of the corpus callosum and anterior commissure as shown in Fig. 6 in accordance with a stereotaxic atlas [24]. However, thinner structures such as the external capsule were not detectable at this resolution. Quantitative data for D trace, FA and RA values are summarized in Table 1. Three regions of interest (ROIs)— lateral ventricle, corpus callosum and cerebral cortex—were selected (Fig. 7). Since tissues restricted the water diffusivity of the corpus callosum and cerebral cortex, the D trace value of the lateral ventricle was larger than that of the corpus callosum and cerebral cortex. Since fibers restricted the water diffusivity of the corpus callosum, the values of FA and RA were larger than those of the cerebral cortex and lateral ventricles. 4. Discussion In this paper, a newly developed DW 3D MRI (3D-DWI) sequence was successfully applied to in vivo rat brain DTI. Table 1 Isotropic ADCs (D trace), FA and RA of lateral ventricle, corpus callosum and cerebral cortex in the rat brain (n = 3) achieved within an acquisition time of 45 min using DW-3D-MP-RAGE (3D-DWI) in vivo
Lateral ventricle Corpus callosum Cerebral cortex
D trace (ADC) (103 mm2/s)
FA
RA
2.292F0.031 1.087F0.016 0.948F0.025
0.268F0.031 0.499F0.017 0.261F0.015
0.076F0.009 0.151F0.006 0.073F0.004
Fig. 7. The FA map (top left), D trace map (top right) and stereotaxic atlas (bottom) of the representative axial section are displayed. ROIs were lateral ventricle, cerebral cortex and corpus callosum.
Comparison of the 3D-tensor data (V1 map) with the rat brain atlas validated the in vivo results. The main advantage of 3D-DT-MRI over 2D-DT-MRI (2D multislice imaging) is the imaging of small isotropic voxels. In other words, 2D multislice imaging has limited imaging resolution in the slice-selection direction, which may inhibit the study of small structures [25]. Although the 3D-DWI sequence was a very promising technique, its limitations should also be addressed. First, although the 3D-DT-MRI by 3D-DWI was shortened compared with other in vivo 3D-DT-MRI methods [17], the acquisition time of 45 min was too long. In principle, DTI requires the collection of six different direction-encoded DW images and a nonencoded DW image (seven times imaging). Furthermore, the 3D-DWI acquisition time was longer than a whole-brain 3D segmented DW spin-echo EPI sequence [25]. Thirty-minute image acquisition time is the maximum realistic value for clinical applications. Use of parallel acquisition techniques, although rather conservative, would shorten the acquisition time. The second limitation of the 3D-DWI sequence was due to inherent limitations in the MP-RAGE sequence. The image contrast of the MP-RAGE sequence is strongly dependent on selecting the k-space acquisition order [26 –30]. An inherent property of the MP-RAGE sequence was that data were acquired during a T1-dependent transient of the longitudinal magnetization. This property arises because the prepared longitudinal magnetization was not in a steady state before the imaging process (RAGE loop). When the prepared longitudinal magnetization was steady state, the image contrast of the RAGE sequence was dominantly interfering with the MP contrast. To detect the effect of DW contrast by MP-RAGE, the 3D-DWI k-space acquisition order was centric. However, since the longitudinal magnetization by the DW-DEFT became steady state as the RAGE-loop proceeded, the high-spatial-frequency views (high-spatial frequency of the k-space) were weak,
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and the image edges and boundaries were blurred compared with the sequential k-space acquisition ordered image. Finally, the 3D-DWI sequence was sensitive to phase errors by subject motion, as is the case for other conventional DW sequences. To remove motion-related phase error, conventional DW sequences incorporate a navigator echo method. This was not done for the 3D-DWI sequence. Misregistration and distortion of the image caused by the effect of the phase error thus occur easily in 3D-DWI. The experimental conditions and imaging sequence were unequal, but the RA value for both corpus callosum and cerebral cortex was in disagreement with literature values. For example, the corpus callosum (RA=0.151F0.006) and cerebral cortex (RA=0.073F0.004) did not correspond to the corpus callosum (RA= 0.80F0.01) and cerebral cortex (0.25F0.01) reported for rats [31]; the RA ratio (corpus callosum/cerebral cortex) of the 3D-DWI and the other report was 2.07 and 3.20, respectively. This finding suggests that the detection ability of diffusion direction by 3D-DWI was poor. Recently, promising 3D-DTI results have been demonstrated with a 3D-FSE sequence [17]. Since the 3D-FSE-DTI image has a higher SNR, the 3D-FSE-DTI resolution was about twice as high as 3D-DWI (0.1090.1560.250 vs. 0.2730.2730.273 mm3). However, 3D-FSE-DTI has an upper limit to the number of echo trains and needs more than twice the acquisition time (2 h vs. 45 min). Nevertheless, the V1 map by 3D-DWI displayed the main fiber structures of the corpus callosum and anterior commissure. In addition, the V1-map results agree approximately with another report [32]. Even if 3D-DWI has a few problems, it can obtain small isotropic DW data and is an effective pulse sequence for in vivo DTI.
5. Conclusions We demonstrated 3D diffusion-tensor imaging of the in vivo rat brain. The use of the DW 3D MP-RAGE MR sequence allowed us to obtain small isotropic diffusiontensor-image data. The resolution of increasing DTI has hidden potential to improve the precision of fiber tractography.
Acknowledgment This work was supported in part by the Japanese Ministry of Economy, Trade and Industry (METI) Grant for Small-Medium-Enterprises (SME) support project and a Grant-in-Aid for Scientific Research (15591084).
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In vivo isotropic 3D diffusion tensor mapping of the rat brain using diffusion-weighted 3D MP-RAGE MRI Tomokazu Numanoa,c,4, Kazuhiro Hommaa, Nobuaki Iwasakib, Koji Hyodoa, Naotaka Nittaa, Takeshi Hirosec a
Biomedical Sensing and Imaging Group, National Institute of Advanced Industrial Science and Technology (AIST), Ibaraki 305-8564, Japan b Department of Pediatrics, Ibaraki Prefectural University of Health Sciences, Ibaraki 300-0394, Japan c Department of Precision Machinery Engineering, Graduate School of Science and Technology, Nihon University, Chiba 274-8501, Japan Received 6 June 2005; accepted 11 December 2005
Abstract The purpose of this study was to examine the potential of diffusion-weighted (DW) three-dimensional (3D) MP-RAGE MRI for diffusion-tensor mapping of the rat brain in vivo. A DW-3D-MP-RAGE (3D-DWI) sequence was implemented at 2.0 T using six gradient orientations and a b value of 1000 s/mm2. In this sequence, the preparation sequence with a b908RF-motion proving gradient (MPG): MPG-1808RF–MPG-908RFQ pulse train (DW driven equilibrium Fourier transform) was used to sensitize the magnetization to diffusion. A centric k-space acquisition order was necessary to minimize saturation effects (T1 contamination) from tissues with short relaxation time. The image matrix was 128128128 (interpolated from 646464 acquisitions), which resulted in small isotropic DW image data (voxel size: 0.2730.2730.273 mm3). Moreover, 3D-DWI-derived maps of the fractional anisotropy (FA), relative anisotropy (RA) and main-diffusion direction were completely free of susceptibility-induced signal losses and geometric distortions. Two well-known commissural fibers, the corpus callosum and anterior commissure, were indicated and shown to be in agreement with the locations of these known stereotaxic atlases. The experiment took 45 min, and shorter times should be possible in clinical application. The 3D-DWI sequence allows for in vivo 3D diffusion-tensor mapping of the rat brain without motion artifacts and susceptibility to distortion. D 2006 Elsevier Inc. All rights reserved. Keywords: DWI; Driven equilibrium Fourier transform; Three-dimensional MP-RAGE; Apparent diffusion coefficient (ADC); Diffusion tensor imaging (DTI)
1. Introduction Diffusion-weighted imaging (DWI) is a magnetic resonance technique that provides tissue contrast that is dependent on the motion of water molecules randomly diffusing in the presence of an applied field gradient [1–3]. Diffusion-weighted imaging has become an important clinical modality for early detection of stroke [4,5]. In regions of stroke, the diffusion of tissue water becomes restricted, as manifested by a decrease in its apparent diffusion coefficient (ADC). On another DWI front, the molecular mobility of water in brain tissue exhibits a pronounced directional dependence that mainly originates from the macroscopic, cellular and subcellular structures of white matter. Because diffusion processes are strongly 4 Corresponding author. Tel.: +81 29 861 9488; fax: +81 29 861 7865. E-mail address: [email protected] (T. Numano). 0730-725X/$ – see front matter D 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.mri.2005.12.011
facilitated along the elongated axon, the ADC turns out to be significantly more parallel to the direction of a nerve fiber than perpendicular to it. These anisotropic movements of water molecules are described mathematically by a tensor. A tensor is a matrix of values. In order to map its properties by MRI, it is necessary to record DW images in at least six different motion-proving-gradient (MPG) directions as well as one image without MPG. The resulting data of such a diffusion-tensor-imaging (DTI) study can be utilized effectively for determining the degree of myelination, the separation and extraction of white matter and gray matter [6,7], and the visualization of brain fiber bundle orientations [8–15]. Single-shot (SS) diffusion-weighted (DW) echo-planar imaging (EPI) is the most popular DW-MRI technique because of its snapshot-like (in the range of 100 ms) acquisition and high signal-to-noise ratio (SNR). However, SS-DW-EPI, like all EPI acquisitions in general, has a
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imaging method. Recently, DW 3D acquisition has been performed by 3D first spin-echo (FSE) sequence [16 –19] or 3D gradient-echo sequence [20]. Three-dimensional FSE has the advantage of decreased sensitivity to susceptibility changes and static field inhomogeneities (using spin-echo vs. gradient-echo), and 3D-FSE images demonstrate higher SNRs, owing to the 908 (vs. a8) excitation pulse. However, because the effect of T2 mixes with the DW images as the number of echo trains increases, 3D-FSE imaging has an upper limit to the number of echo trains, and thus a limit to the shortening of the acquisition time. For further shortening of acquisition time, we developed a DW 3D MRI (3D-DWI) sequence using a 3D magnetization-prepared rapid gradientecho (3D-MP-RAGE) method [21]. In this paper, we demonstrate the 3D diffusion-tensor images from the in vivo rat brain with an image acquisition time of 45 min using the 3D-DWI sequence.
2. Materials and methods 2.1. Diffusion tensor determination Fig. 1. Ellipsoidal approximation of directional anisotropy. (A) Coordinate system of MR magnet (O-xyz) and coordinate system of diffusion tensor ellipsoid (O-xVyVzV). (B) The pairs of eigenvectors and eigenvalues; e i and ki (i = 1, 2, 3). (C) The V1 vector is displayed by mixing colors.
notoriously high level of artifacts. The classic EPI artifact is the N/2 (Nyquist) ghost. This arises because of imperfections in the rephasing–dephasing cycle of the rapidly switching bipolar frequency-encode gradient. Another artifact is a consequence of bandwidth. Each frequency-encode lobe is sampled rapidly with a very high gradient amplitude, resulting in a very large signal bandwidth. The phase encode is sampled 64 or 128 times over the whole gradient-echo train. This rather slow sampling rate means that the signal bandwidth in the phase-encode direction may be as little as 10 Hz/pixel. This gives magnetic field differences (air–tissue boundaries) that will result in large image distortions. In addition, most SS-DW-EPI is two-dimensional (2D) multislice imaging. In order to perform multislice imaging, it is necessary to have a few millimeters of slice thickness and slice gap. Multislice imaging by an isotropic voxel in the submillimeter range is difficult. In general, more advanced data analysis strategies that aim at tracking individual brain fiber connections are expected to benefit from more or less isotropic voxel dimensions. An advantage of three-dimensional (3D) acquisition is that you obtain thinner and more slices with better profiles, and a better SNR for an equivalent slice thickness. It has the advantage of very thin slices with no slice gaps (contiguous slices), and it allows acquisition in a small isotropic voxel compared with 2D acquisition. However, 3D acquisition time is greater than 2D acquisition time because the second phase-encode axis is applied by 3D acquisition. Threedimensional acquisition should thus be a high-speed
Let apparent diffusion (perfusion mixing with diffusion) be diffusion for convenience. For anisotropic tissues, the physical orientation (direction) of the tissue in conjunction with the applied motion-proving-gradient (MPG) direction will determine the signal intensity. If these two directions are the same, there is no problem, but usually this is not true. In this most general case, the diffusion properties are described mathematically by a tensor. A tensor is a matrix of values. The diffusion tensor has nine such values, each corresponding to a MPG orientation and a cell orientation. When the diffusion properties are in a Gaussian distribution (normal distribution), the distribution of diffusion becomes a tensor ellipsoid (Fig. 1A). In this case, diffusion tensor D is described as a 33 symmetric matrix (second-rank tensor). 2
Dxx D ¼ 4 Dxy Dxz
Dxy Dyy Dyz
3 Dxz Dyz 5 Dzz
ð1Þ
The first subscript (x,y,z) refers to the bnaturalQ orientation of the cells or tissue, and the second refers to the MPG orientation. The symmetry tensor is potentially diagonalized, and the three diagonal elements k 1 , k 2 , k 3 (k 1 z k 2 z k 3) are called an eigenvalue. 2
Dxx 4 Dxy Dxz
Dxy Dyy Dyz
3 2 Dxz k1 Dyz 5 diagonalization Y 4 0 Dzz 0
0 k2 0
3 0 05 k3 ð2Þ
The coordinate system of the diagonalized tensor is O-xVyVzV, and it agrees with the principal axis of the tensor ellipsoid (Fig. 1B). The vector in this direction of the
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principal axis is called an eigenvector (e1, e2, e3), and each eigenvalue displays the diffusion coefficient in the direction of the principal axis. Several diffusion anisotropy measures were defined by using the eigenvalues, i.e., fractional anisotropy (FA), relative anisotropy (RA), volume ratio and so on [22,23]. The FA value and RA value as calculated by the following formulae are used most frequently for anisotropy measure. rffiffiffi 3 FA ¼ 2
1 RA ¼ pffiffiffi 3
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðk1 kM Þ2 þ ðk2 kM Þ2 þ ðk3 kM Þ2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k21 þ k22 þ k23
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð k1 kM Þ 2 þ ð k2 kM Þ 2 þ ð k3 kM Þ 2 kM
ð3Þ
ð4Þ
where k M is the mean eigenvalue kM ¼
1 1 Dtrace ¼ ðk1 þ k2 þ k3 Þ 3 3
Fig. 3. T1-weighted anatomy (left) and color-coded V1 map (right) of fresh celery. To facilitate the visualization of vascular bundle orientation, only the area where the FA value exceeded 0.27 is displayed. Water molecules inside the vascular bundle were highly directional along the celery branch (arrow).
diffusion. A centric k-space acquisition ordered RAGEloop sequence was necessary to minimize saturation effects from tissues with short relaxation times. For further details, see Ref. [21]. 2.3. MRI experiments
ð5Þ
2.2. Three-dimensional DWI Fig. 2 shows the 3D-DWI sequence. This method combines the DW driven equilibrium Fourier transform (DW-DEFT) preparation with a 3D-MP-RAGE imaging module. In this sequence, the preparation phase with b908RF-MPG–1808RF-MPG–908RFQ pulse train (DW-DEFT) was used to sensitize the magnetization to
Fig. 2. Diagram of the 3D MP-RAGE MRI pulse sequence (3D-DWI) used for 3D diffusion tensor mapping of the rat brain in vivo. The slice phaseencode gradient (Gp1-PEG) happens only once per TRe period, while the phase-encode gradient (Gp2-PEG) changed in each TR period. In order to avoid T1 contamination in the DW image, the phase encoding was centric k-space acquisition ordered.
All MRI experiments were performed on a 2.0-T Biospec 20/30 System with a B-GA20 Gradient System (Bruker, Karlsruhe, Germany) that had a maximum gradient strength of 100 mT/m. The MR data acquisition and reconstruction were performed with the ParaVision (Bruker) software system. A 45-mm-ID saddle coil tuned to 85 MHz for proton resonance was used for all measurements. Three-dimensional DWI sequence parameters were 5000 ms/54.74 ms (effective-TR: TRe/effective-TE: TEe), 8.91 ms/4.7 ms (TR/TE), flip angle of 358, MPG duration (d) of 25.00 ms, MPG separation (D) of 27.37 ms, readout bandwidth of 195 Hz/pixel, matrix of 646464, field of view (FOV) of 353535 mm (acquisition voxel size:
Fig. 4. The 3D rat brain V1 map is displayed by small isotropic voxels (voxel size: 0.2730.2730.273 mm3). The color code was red for right– left (V 1x ), green for dorsal–ventral (V 1y ) and blue for rostral–caudal (V 1z ). Areas where FA values had exceeded 0.3 are displayed.
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body weight) and atropine (0.05 mg/kg body weight). Each anesthetized rat was inserted in an acrylic tube and subjected to scanning. The maintenance of anesthesia was controlled by intraperitoneal injection of ketamine (50 mg/kg per hour) and xylazine (5 mg/kg per hour) from a syringe pump. All studies were performed in accordance with animal protection laws and approved by the Animal Ethical Committee of the National Institute of Advanced Industrial Science and Technology. 2.5. Post-processing for DTI Fig. 5. T2-weighted anatomical image (left) and color-coded V1 map (right) of the rat brain. The anatomical image and V1 map of the corpus callosum location were approximately the same.
0.5470.5470.547 mm3) and 64 phase-encoding steps per RAGE loop. Except during the acquisition of a non-DW image, DTI involved diffusion gradient encoding along six different directions (1,0,1), (1,1,0), (0,1,1), (1,0,1), (1,1,0), (0,1,1) and with two different b values of 0 and 1000 s/mm2 in all cases. The total acquisition time was 45 min 23 s. To allow for anatomic references, T1- or T2-weighted 2D-multislice MRI (T1: spin-echo; T2: fast spin-echo) of fresh celery and a rat brain was performed. T1-weighted spinecho sequence parameters were 500 ms/15 ms (TR/TE), readout bandwidth of 103 Hz/pixel, matrix of 256256, FOV of 70 mm, slice thickness of 2 mm. T2-weighted fast spinecho sequence parameters were 3000 ms/42.33 ms (TR/TEe), readout bandwidth of 326 Hz/pixel, echo train length (ETL) of 10, matrix of 256256, FOV of 70 mm, slice thickness of 2 mm. 2.4. Animal preparation For in vivo studies, three male Crj:Wistar rats (450–470 g, 18 weeks old) were anesthetized by intraperitoneal injection of ketamine (100 mg/kg body weight), xylazine (10 mg/kg
All DW-MRI data were transferred to an offline LINUX PC with a Pentium 4 processor (1.8 GHz) and 1-GB memory. The rat brain diffusion-tensor image processing was performed using a commercial medical image analysis software, Dr. View/LINUX (Asahi Kasei Information Systems, Tokyo, Japan). After linear interpolation of the DW images to twice the matrix size (image voxel size: 0.2730.2730.273 mm3), the DW images were Gaussian filtered with a full width at half-maximum of 1 mm. In all diffusion-tensor images, brain mask processing erased the background noise outside of the brain. To facilitate the visualization of fiber bundle orientations, maps of the main-diffusion direction (principal axes of tensor ellipsoid) were color-coded and superimposed onto corresponding maps of the T2-weighted 3D-DWI (without MPG) image: color-coded V1 map. The main-diffusion-direction vector V1 is shown in Fig. 1C. In explicit form, V1 ¼ k1 e1 ¼ V1x ; V1y ; V1z
ð6Þ
where V 1x , V 1y and V 1z are the x-, y- and z components of V1, respectively. The color code was red for right–left (V 1x ), green for up–down (V 1y ) and blue for front–rear (V 1z ) with mixed colors for intermediate orientations.
Fig. 6. Comparison between the results of the commissural fibers and the rat brain atlas [22] for arbitrary section images: axial, coronal and sagittal 2D slices. CA, Anterior commissure; CC, corpus callosum; CE, external capsule; LV, lateral ventricle.
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3. Results 3.1. Celery experiment Fig. 3 compares a T1-weighted anatomic image of fresh celery with the color-coded V1 map. To facilitate the visualization of vascular bundle orientation, only the area where the FA value exceeded 0.27 is displayed. The ADC value of the water in the vascular bundle of the celery perpendicular and parallel to the vascular bundle direction was measured to be 0.99103 and 1.42103 mm2/s, respectively. The diffusion of the water in the parenchyma looks isotropic, but these water molecules inside the vascular bundle were highly directional along the celery branch (arrow). This result shows that the 3D-DWI sequence can detect the direction of diffusion. 3.2. Rat experiments Fig. 4 illustrates the 3D rat brain V1 map. The color code was red for right–left (V 1x ), green for dorsal–ventral (V 1y ) and blue for rostral–caudal (V 1z ). The area where the FA value had exceeded 0.3 is displayed. A T2-weighted anatomical image is shown in Fig. 5 with the corresponding level in the rat brain V1 axial (arbitrary section: axial image). When the anatomical image and the V1-axial image were compared, the anatomical location of the corpus callosum was approximately the same (arrow). An image resolution of 0.2730.2730.273 mm3 turned out to be sufficient to resolve the main fiber structures of the corpus callosum and anterior commissure as shown in Fig. 6 in accordance with a stereotaxic atlas [24]. However, thinner structures such as the external capsule were not detectable at this resolution. Quantitative data for D trace, FA and RA values are summarized in Table 1. Three regions of interest (ROIs)— lateral ventricle, corpus callosum and cerebral cortex—were selected (Fig. 7). Since tissues restricted the water diffusivity of the corpus callosum and cerebral cortex, the D trace value of the lateral ventricle was larger than that of the corpus callosum and cerebral cortex. Since fibers restricted the water diffusivity of the corpus callosum, the values of FA and RA were larger than those of the cerebral cortex and lateral ventricles. 4. Discussion In this paper, a newly developed DW 3D MRI (3D-DWI) sequence was successfully applied to in vivo rat brain DTI. Table 1 Isotropic ADCs (D trace), FA and RA of lateral ventricle, corpus callosum and cerebral cortex in the rat brain (n = 3) achieved within an acquisition time of 45 min using DW-3D-MP-RAGE (3D-DWI) in vivo
Lateral ventricle Corpus callosum Cerebral cortex
D trace (ADC) (103 mm2/s)
FA
RA
2.292F0.031 1.087F0.016 0.948F0.025
0.268F0.031 0.499F0.017 0.261F0.015
0.076F0.009 0.151F0.006 0.073F0.004
Fig. 7. The FA map (top left), D trace map (top right) and stereotaxic atlas (bottom) of the representative axial section are displayed. ROIs were lateral ventricle, cerebral cortex and corpus callosum.
Comparison of the 3D-tensor data (V1 map) with the rat brain atlas validated the in vivo results. The main advantage of 3D-DT-MRI over 2D-DT-MRI (2D multislice imaging) is the imaging of small isotropic voxels. In other words, 2D multislice imaging has limited imaging resolution in the slice-selection direction, which may inhibit the study of small structures [25]. Although the 3D-DWI sequence was a very promising technique, its limitations should also be addressed. First, although the 3D-DT-MRI by 3D-DWI was shortened compared with other in vivo 3D-DT-MRI methods [17], the acquisition time of 45 min was too long. In principle, DTI requires the collection of six different direction-encoded DW images and a nonencoded DW image (seven times imaging). Furthermore, the 3D-DWI acquisition time was longer than a whole-brain 3D segmented DW spin-echo EPI sequence [25]. Thirty-minute image acquisition time is the maximum realistic value for clinical applications. Use of parallel acquisition techniques, although rather conservative, would shorten the acquisition time. The second limitation of the 3D-DWI sequence was due to inherent limitations in the MP-RAGE sequence. The image contrast of the MP-RAGE sequence is strongly dependent on selecting the k-space acquisition order [26 –30]. An inherent property of the MP-RAGE sequence was that data were acquired during a T1-dependent transient of the longitudinal magnetization. This property arises because the prepared longitudinal magnetization was not in a steady state before the imaging process (RAGE loop). When the prepared longitudinal magnetization was steady state, the image contrast of the RAGE sequence was dominantly interfering with the MP contrast. To detect the effect of DW contrast by MP-RAGE, the 3D-DWI k-space acquisition order was centric. However, since the longitudinal magnetization by the DW-DEFT became steady state as the RAGE-loop proceeded, the high-spatial-frequency views (high-spatial frequency of the k-space) were weak,
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and the image edges and boundaries were blurred compared with the sequential k-space acquisition ordered image. Finally, the 3D-DWI sequence was sensitive to phase errors by subject motion, as is the case for other conventional DW sequences. To remove motion-related phase error, conventional DW sequences incorporate a navigator echo method. This was not done for the 3D-DWI sequence. Misregistration and distortion of the image caused by the effect of the phase error thus occur easily in 3D-DWI. The experimental conditions and imaging sequence were unequal, but the RA value for both corpus callosum and cerebral cortex was in disagreement with literature values. For example, the corpus callosum (RA=0.151F0.006) and cerebral cortex (RA=0.073F0.004) did not correspond to the corpus callosum (RA= 0.80F0.01) and cerebral cortex (0.25F0.01) reported for rats [31]; the RA ratio (corpus callosum/cerebral cortex) of the 3D-DWI and the other report was 2.07 and 3.20, respectively. This finding suggests that the detection ability of diffusion direction by 3D-DWI was poor. Recently, promising 3D-DTI results have been demonstrated with a 3D-FSE sequence [17]. Since the 3D-FSE-DTI image has a higher SNR, the 3D-FSE-DTI resolution was about twice as high as 3D-DWI (0.1090.1560.250 vs. 0.2730.2730.273 mm3). However, 3D-FSE-DTI has an upper limit to the number of echo trains and needs more than twice the acquisition time (2 h vs. 45 min). Nevertheless, the V1 map by 3D-DWI displayed the main fiber structures of the corpus callosum and anterior commissure. In addition, the V1-map results agree approximately with another report [32]. Even if 3D-DWI has a few problems, it can obtain small isotropic DW data and is an effective pulse sequence for in vivo DTI.
5. Conclusions We demonstrated 3D diffusion-tensor imaging of the in vivo rat brain. The use of the DW 3D MP-RAGE MR sequence allowed us to obtain small isotropic diffusiontensor-image data. The resolution of increasing DTI has hidden potential to improve the precision of fiber tractography.
Acknowledgment This work was supported in part by the Japanese Ministry of Economy, Trade and Industry (METI) Grant for Small-Medium-Enterprises (SME) support project and a Grant-in-Aid for Scientific Research (15591084).
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