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Diffusion tensor magnetic resonance imaging DTI is a relatively new technology that is popular for imaging the white matter of the brain. The goal of this review is to give a basic and broad yensor of DTI such that the reader may develop an intuitive understanding of this type of data, and an awareness of its strengths and weaknesses. We have tried to include equations for completeness but they are not necessary for understanding the paper.

Wherever iimaging, pointers will be miri to more in-depth technical articles or books for further reading. We especially recommend the new diffusion MRI textbook [ 1 ], the introductory paper on fiber tracts and tumors [ 2 ], the white matter atlas book [ 3 ], and the review of potential pitfalls in DTI analysis [ 4 ]. In the rest of this article we will address basic questions about DTI the what, why, and how of DTIfollowed by a discussion of issues in interpretation of DTI, and finally an overview of more advanced diffusion imaging methods and future directions.

The diffusion tensor was originally proposed for use in magnetic resonance imaging MRI by Peter Basser in [ 56 ]. Prior to the introduction of the diffusion tensor model, to measure anisotropic diffusion the orientation of the axons in a tissue sample had to be known, so only fixed samples such as the axon of the giant squid ciffusion be scanned [ 10 ].

The introduction of the diffusion tensor model allowed, for the first time, a rotationally invariant introductkon of the shape of water diffusion. The invariance to rotation was crucial because it enabled application of the DTI method to the complex anatomy of the fiber tracts in the human brain [ 11 ]. Note however, that the diffusion tensor is not able introductiln fully describe crossing of the fiber tracts [ 1213 ].

The popularity of DTI has been enormous. It has been applied to a tremendous variety of neuroscientific studies see reviews in [ 141516 ] including schizophrenia [ 17 ], traumatic brain injury [ 18 ], multiple sclerosis [ 1920 ], autism [ 21 ], and aging [ 22 ]. Anatomical investigations have been undertaken regarding for example the structure of the language network [ 2324 ], the asymmetry of the white matter in twins and siblings [ 25 susummu, and susjmu location, asymmetry, and variability of the fiber tracts [ 26 ].

DTI has introductiln been applied for neurosurgical planning and navigation. The addition of preoperative DTI to neuronavigation [ 29303132 ] has been shown, in a large prospective study, to increase inttoduction resection and survival and to decrease neurologic morbidity [ 33 ].

DTI is a sensitive probe of cellular structure that works by measuring the diffusion of water molecules. The measured quantity is the diffusivity or diffusion coefficient, a proportionality constant that relates diffusive flux to a concentration gradient [ 8 ] and has units of m m 2 s.

Unlike the diffusion 1 in a glass imagingg pure water, which would be the same in all directions isotropicthe diffusion measured in tissue varies with direction is anisotropic. The measured macroscopic diffusion anisotropy is due to microscopic tissue heterogeneity [ 6 ].

In the white matter of the brain, diffusion anisotropy is primarily caused by cellular membranes, with some contribution from myelination and the packing of the axons [ 343511 ]. Anisotropic diffusion can indicate the underlying tissue orientation Figure 1.

## An introduction to diffusion tensor image analysis

Illustration of anisotropic diffusion, in the ideal case of a coherently oriented tissue. This example compares the diffusion measured parallel and perpendicular to the axons in a white matter fiber tract. The diffusion tensor DT describes the diffusion of water molecules using a Gaussian model.

Technically, it is proportional to the covariance matrix of a three-dimensional Gaussian distribution that models the displacements of the molecules. The major eigenvector of the diffusion tensor points in the principal diffusion direction the direction of the fastest diffusion.

In anisotropic fibrous tissues the major eigenvector also suzumu the fiber tract axis of the tissue [ 6 ], and thus the three orthogonal eigenvectors fo be thought of as a local fiber coordinate system.

Note this interpretation is only strictly true in regions where fiber tracts do not cross, fan, or branch. Together, the eigenvectors and eigenvalues define an ellipsoid that represents an isosurface of Gaussian diffusion probability: Figure 2 teneor 3 diffusion tensors chosen from different regions of the human brain to illustrate possible shapes of the ellipsoid.

Three example diffusion tensors, selected from a DTI scan of the human brain to illustrate differences in tensor anisotropy and orientation. To measure diffusion using MRI, magnetic field gradients are employed to create an image that is sensitized to diffusion in a particular direction.

By repeating this process of diffusion weighting in multiple directions, a three-dimensional diffusion model the tensor can fensor estimated. Due to their random phase, signal from diffusing molecules is lost. This loss of signal creates darker voxels volumetric pixels. This means that white matter fiber tracts parallel to the gradient direction will appear dark in the diffusion-weighted image for that direction Figure 3. Six diffusion-weighted images the minimum number required for tensor calculation.

In diffusion MRI, magnetic field gradients are employed to sensitize the image to diffusion in a particular direction. The direction is different for each image, resulting in a different pattern of signal loss dark areas due to anisotropic diffusion.

Next, the decreased signal S k is compared to the original signal S 0 to calculate the diffusion tensor D by solving the Stejskal-Tanner equation 1 [ 36 ]. Inttoduction equation describes how the signal intensity at each voxel decreases in the presence of Gaussian diffusion:.

But in clinical research today a higher number of images are almost always used. The above system of equations can be solved via the least squares method at each voxel. The b-factor is near s m m 2 for the image S 0 which introdkction T2-weighted, and the b-factor is near 1, s m m 2 for the diffusion-weighted images S k in DTI.

We refer the reader to [ 8 ] for information on the MR physics of DTI and [ 537 ] for more information on the tensor calculation process. For a comparison of tensor calculation methods including least squares and weighted least squares in the presence of noise see [ 38 ]. DTI is usually displayed by either condensing the information contained in the tensor into one number a scalaror into 4 numbers to give an R,G,B color and a brightness value. The diffusion tensor can also be viewed using glyphs, which are small 3D representations introductioj the major eigenvector or whole tensor.

Finally, DTI is often viewed by estimating the course of white matter tracts through the brain via a process called tractography.

In this section we will describe commonly used scalar quantities, which can be divided into two categories: For the original paper that measured and compared several scalar measures, as well as the eigenvalues, in different regions of the human brain see [ 11 ].

### An introduction to diffusion tensor image analysis

Note that in clinical imaging ADC maps may be measured using fewer diffusion gradients than needed for the tensor. A similar quantity to the MD is the sum of the eigenvalues, called the trace of the tensor. The trace and MD relate to the total amount of diffusion in a voxel, which is related to the amount of water in the extracellular space. The trace is clinically useful in early stroke detection because it is sensitive to the initial cellular swelling cytotoxic edema which restricts diffusion [ 41 ].

In the normal human brain, the trace is high in cerebrospinal fluid, around 9. The MD and trace measured in ventricles or in edema can be higher than in water due to fluid flow or enhanced perfusion, respectively [ 43 ]. Tensor anisotropy measures are ratios of the eigenvalues that are used to quantify the shape of the diffusion. These measures are useful for describing the amount of tissue organization and for locating voxels likely to contain a single white matter tract without crossing or fanning.

The fractional anisotropy, or FA [ 44 ], is the most widely used anisotropy measure. Its name comes from the fact that it measures the fraction of the diffusion that is anisotropic. FA is basically a normalized variance of the eigenvalues:. They describe whether the shape of diffusion is like a cigar linearpancake planaror sphere spherical. In voxels with high planar or spherical measure, the principal eigenvector will not always match an underlying fiber tract direction where tracts cross the eigenvector may point to neither one.

But if the largest eigenvalue is much larger than the other two eigenvalues, the linear measure will be large, giving evidence for the presence of a single fiber tract.

While FA measures how far the tensor is from a sphere, another complementary measure discriminates between linear and planar anisotropy. This information is given by the mode, a quantity that is mathematically orthogonal to the FA measure and relates to the skewness of the eigenvalues 2 [ 46 ].

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The parallel ssusumu measure, also called the axial diffusivity, is equal to the largest eigenvalue. The perpendicular diffusivity measure, also called the radial diffusivity, is equal to the average of the two smaller eigenvalues.

These measures are interpreted as diffusivity parallel to and perpendicular to a white matter fiber tract, so they make the most sense in regions of coherently oriented axons with no fiber crossings. Often in scientific studies, the reported measures from the diffusion tensor are not independent. However, complete sets of orthogonal mathematically independent scalars have been defined [ 4647 ]. Another type of image can represent the major eigenvector field using a mapping to colors Figure 5.

The color scheme most commonly used to represent the orientation of the major eigenvector works as follows: To enhance visualization of the white matter and suppress information outside of it, the brightness tensorr the color is usually controlled by tensor anisotropy FA. An example using glyphs and colors for DTI visualization. On the left an axial image plane, showing the average diffusion-weighted image with semi-transparent color overlay indicating the major eigenvector orientation, and a white square indicating the zoomed-in area right image.

In both images the color red indicates right-left orientation, blue is superior-inferior, and green is anterior-posterior. The right image contains glyphs representing major eigenvector orientations and scaled by the largest eigenvalue in the region of the corpus callosum yellow and red and right lateral ventricle.

The cingulum can be seen in blue, and the posterior limb of the internal capsule in imagint. Small three-dimensional objects called glyphs can be used to display information from each tensor eigensystem.

The word tractography refers to any method for estimating the trajectories of the fiber tracts in the white matter. For a clinical and technical overview of tractography in neurological disorders see [ 15 ]. For reviews of tractography techniques including explanations of common tractography artifacts and a comparison of methods see [ 5051 ].

Many methods have been proposed for tractography, and the results will vary enormously depending on the chosen method. The most common approach is streamline tractography Figure 6 [ 52535455 ], which is closely related to an earlier method for visualization of tensor fields known as hyperstreamlines [ 56 ].

The streamline tract-tracing approach works by successively stepping in the direction of the principal eigenvector the direction of fastest diffusion. The eigenvectors are thus tangent to tendor trajectory that is produced. A fixed step size of one millimeter or less smaller than a voxel is generally used for DTI data. Example whole-brain streamline DTI tractography.

Colors were assigned automatically according to an atlas-based tractography segmentation method [ 60 ]. Several computational methods can be used to perform basic streamline tractography. The application of the Euler and Runge-Kutta methods to white matter tractography was explored in [ 5253 ].

Another popular method is called FACT [ 54 ]. These methods modulate the incoming tangent direction by the tensor instead of directly using the major eigenvector of the tensor [ 585955ssusumu ].

Processing DTI data to display fiber tract s of interest requires expert knowledge or an automatic algorithm. Automated methods for atlas-based tractography segmentation, that use diffusjon knowledge to select trajectories, have also been developed [ 63606465666768 ]. In addition to streamline tractography, there are many other methods [ 5051 ].