H3h

Fig. 3. Schematic of a DW EPI pulse sequence. A spin echo pulse is used to achieve diffusion-weighting from the gradient pulse pairs (colored) as illustrated in Fig. 5. The imaging gradients are shown in black. Diffusion-weighting gradients can be applied in any arbitrary direction using combinations of Gx (red), Gy (green) and Gz (blue)

Fig. 3. Schematic of a DW EPI pulse sequence. A spin echo pulse is used to achieve diffusion-weighting from the gradient pulse pairs (colored) as illustrated in Fig. 5. The imaging gradients are shown in black. Diffusion-weighting gradients can be applied in any arbitrary direction using combinations of Gx (red), Gy (green) and Gz (blue)

to be limited. At 1.5T, it is possible to acquire 2.5 mm isotropic voxels over the entire brain in roughly 15 minutes (Jones et al. 2002b). Smaller voxel dimensions may be achieved using either more sensitive RF coils or by going to higher field strengths. Alternative DW imaging techniques, such as PROPELLER (Pipe et al. 2002) and line scan (Gudbjartsson et al. 1997), are less sensitive to motion, eddy currents and B0 distortions.

In the case of anisotropic diffusion, the direction of the diffusion encoding will influence the amount of attenuation. The cartoon in Fig. 4 illustrates the basis for diffusion anisotropy contrast. For anisotropic tissues like white matter, when the diffusion encoding directions are applied parallel to the white matter tract, the signal is highly attenuated. However, when the encoding direction is applied perpendicular to the tract, the diffusion is significantly hindered and the attenuation is much less than in the parallel case. In more isotropic structure regions (such as gray matter), the signal attenuation is independent of the encoding direction.

A minimum of six non-collinear diffusion encoded measurements are necessary to measure the full diffusion tensor (Shrager and Basser 1998; Papadakis et al. 1999). A wide variety of diffusion-tensor encoding strategies with six or more encoding directions have been proposed (e.g., Basser and Pierpaoli 1998; Jones et al. 1999; Papadakis et al. 1999; Shimony et al. 1999; Hasan et al. 2001b). An example of images with DW encoding in twelve directions

Fig. 4. Illustration of anisotropic signal attenuation with diffusion encoding direction. When the diffusion-weighting (Gd) is applied in the direction parallel (green) to the anisotropic cellular structures (e.g., white matter), the signal (S) is strongly attenuated and the apparent diffusivity (D) is high. Conversely, when the diffusion-weighting is applied in the direction perpendicular to the fibrous tissue, the diffusion is less attenuated and the apparent diffusivity is lower. The signal attenuation and diffusivities are independent of the encoding direction in the anisotropic tissue regions. The difference in the directional diffusivities is the source of anisotropy contrast in DTI. The direction of diffusion encoding is selected using different combinations of the diffusion gradients in Gx, Gy and Gz

Fig. 5. Example images from a DTI study for a single slice in a human brain. The image on the left is without any diffusion-weighting and is T2-weighted. The twelve images on the right were obtained with diffusion weighting (b = 1000 s/mm2) applied in twelve non-collinear directions. Note that the image contrast changes significantly with the diffusion encoding direction

Fig. 5. Example images from a DTI study for a single slice in a human brain. The image on the left is without any diffusion-weighting and is T2-weighted. The twelve images on the right were obtained with diffusion weighting (b = 1000 s/mm2) applied in twelve non-collinear directions. Note that the image contrast changes significantly with the diffusion encoding direction for a single slice is shown in Fig. 5. The observed contrast difference for each of the 12 DW encoded images is the basis for the measurement of diffusion anisotropy, which is described later. The selection of tensor encoding directions is critical for accurate and unbiased assessment of diffusion tensor measures. Hasan et al. (2001b) performed a comprehensive comparison of various heuristic, numerically optimized and natural polyhedra encoding sets. This study demonstrated that encoding sets with uniform angular sampling yield the most accurate diffusion tensor estimates. Several recent studies have provided mounting evidence that more diffusion encoding directions causes the measurement errors to be independent of the tensor orientation (e.g., Batchelor et al. 2003; Jones 2004).

There are a number of considerations that should be made when prescribing a diffusion tensor protocol. This is moderately complicated by the wide spectrum of pulse sequence parameters that must be configured. As discussed above, diffusion-weighted, spin-echo, single-shot EPI is the most common pulse sequence for DTI. The optimum diffusion-weighting (also called b-value) for the brain is roughly between 700 and 1300 s/mm2 with a b-value of 1000 s/mm2 being most common. The selection of the number of encoding directions is dependent upon the availability of encoding direction sets, the desired scan time and the maximum number of images that can be obtained in a series. Measurements of diffusion anisotropy tend to be quite sensitive to image noise, which can also lead to biases in the anisotropy estimates (overestimation of major eigenvalue; underestimation of minor eigenvalue; increase in uncertainty of all eigenvalues) (Pierpaoli and Basser 1996; Chang et al. 2005; Rohde et al. 2005). The accuracy of DTI measures may be improved by either increasing the number of encoding directions or increasing the number of averages. Additional procedures proposed to reduce artifact include the use of peripheral gating to minimize motion related to cardiac pulsitility (Skare and Andersson 2001) and inversion-recovery pulses to minimize partial volume effects from CSF (Bastin 2001; Papadakis et al. 2002; Concha et al. 2005b). Unfortunately, these procedures typically increase the scan time for DTI data collection, and can reduce SNR. The image SNR can also obviously be improved by using larger voxels, although this will increase partial volume averaging of tissues, which can lead to errors in the fits to the diffusion tensor model (Alexander et al. 2001a). The specific parameters for a protocol will depend upon the application. For many routine clinical applications (brain screening, stroke, brain tumors), a fairly coarse spatial resolution can be used with a small number of encoding directions. However, for applications requiring accurate quantification (i.e., quantifying DTI measures in very small white matter tracts, or estimating white matter trajectories with white matter tractography) high spatial resolution is much more important and a large number of diffusion encoding directions or averaging is desirable. High quality DTI data with whole brain coverage, 2.5 mm isotropic resolution and 64 diffusion encoding directions may be obtained in approximately 15 minutes on clinical 1.5T scanners (Jones et al. 2002b). Similar DTI data quality can be achieved in half the time or less at 3.0T, except the image distortions are roughly double.

Diffusion Tensor Image Processing

Maps of DTI measures (mean diffusivity anisotropy, orientation) are estimated from the raw DW images. As discussed previously, the images may be distorted and misregistered from a combination of eddy currents, subject motion, and magnetic field inhomogeneities. Ideally, these distortions and sources of misregistration should be corrected before calculating any subsequent quantitative diffusion maps. In cases where corrections are not restricted to in-plane errors and distortions, this correction should include recalculation of the diffusion gradient directions or reorienting the tensors (Alexander et al. 2001b; Andersson and Skare 2002; Rohde et al. 2004).

The first step in estimating the diffusion tensor and the associated measures is to calculate the apparent diffusivity maps, Dijapp, for each encoding direction. The signal attenuation for scalar or isotropic diffusion is described in (4). However, this equation has to be adjusted to describe the signal attenuation for anisotropic diffusion with the diffusion tensor:

where S; is the DW signal in the ith encoding direction, g; is the unit vector describing the DW encoding direction, and b is the amount of diffusion weighting in (6). The apparent diffusivity maps are generated by taking the natural log of (6) and solving for Dijapp:

This equation works when measurements are obtained for a single diffusion-weighting (b-value) and an image with very little or no diffusion-weighting (So). The six independent elements of the diffusion tensor (Dxx, Dyy, Dzz, Dxy _ Dyx, Dxz _ Dzx, and Dyz _ Dzy) may be estimated from the apparent diffusivities using least squares methods (Basser et al. 1994; Hasan et al. 2001a). Maps of the diffusion tensor elements for the data in Fig. 5 are shown in Fig. 6.

Diffusion Tensor Image Measures

The display, meaningful measurement, and interpretation of 3D image data with a 3 x 3 diffusion matrix at each voxel is a challenging task without simplification of the data. Consequently, it is desirable to distill the image information into simpler scalar maps, particularly for routine clinical applications. The two most common measures are the trace and anisotropy of the

Fig. 6. Maps of the diffusion tensor elements for the DTI data in Fig. 5. Note that the off-diagonal images are symmetric about the diagonal and that the values are both positive and negative

diffusion tensor. The trace of the tensor (Tr), or sum of the diagonal elements of D, is a measure of the magnitude of diffusion and is rotationally invariant. The mean diffusivity, MD, (also called the apparent diffusion coefficient or ADC) is used in many published studies and is simply the trace divided by three (MD = Tr/3). The degree to which the signal is a function of the DW encoding direction is represented by measures of tensor anisotropy. Many measures of anisotropy have been described (Basser and Pierpaoli 1996; Conturo et al. 1996; Pierpaoli and Basser 1996; Ulug and van Zijl 1999; Westin et al. 2002) Most of these measures are rotationally invariant, but do have differential sensitivity to noise (e.g., Skare et al. 2000). Currently, the most widely used invariant measure of anisotropy is the Fractional Anisotropy (FA) described originally by Basser & Pierpaoli (1996).

A third important measure is the tensor orientation described by the major eigenvector direction. For diffusion tensors with high anisotropy, the major eigenvector direction is generally assumed to be parallel to the direction of white matter tract, which is often represented using an RGB (red-green-blue) color map to indicate the eigenvector orientations (Makris et al. 1997; Pajevic and Pierpaoli 1999). The local eigenvector orientations can be used to identify and parcellate specific WM tracts; thus DT-MRI has an excellent potential for applications that require high anatomical specificity. The ability to identify specific white matter tracts on the eigenvector color maps has proven useful for mapping white matter anatomy relative to lesions for preoperative planning (Witwer et al. 2002) and post-operative follow-up (Field et al. 2004). Recently, statistical methods have been developed for quantifying the distributions of tensor orientation in specific brain regions (Wu et al. 2004). Example maps of the mean diffusivity, fractional anisotropy, and major eigenvector direction are shown in Fig. 7.

Relationship to White Matter Physiology & Pathology

The applications of DTI are rapidly growing, in part because the diffusion tensor is exquisitely sensitive to subtle changes or differences in tissue at the microstructural level. DTI studies have found differences in development (e.g., Barnea-Goraly et al. 2005; Snook et al. 2005) and aging (e.g., Abe et al. 2002; Pfefferbaum et al. 2005; Salat et al. 2005), and across a broad spectrum of diseases and disorders including traumatic brain injury (diffuse ax-onal injury) (Werring et al. 1998; Salmond et al. 2006), epilepsy (Concha et al. 2005a), multiple sclerosis (Cercignani et al. 2000; Rovaris et al. 2002; Assaf et al. 2005), ALS (Ellis et al. 1999; Jacob et al. 2003; Toosy et al. 2003), schizophrenia (Buchsbaum et al. 1998; Lim et al. 1999; Agartz et al. 2001; Jones et al. 2006), bipolar disorder (Adler et al. 2004; Beyer et al. 2005), OCD

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