DTI

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Myelin fibers within the brain impose an anisotropy, that is, a direction of diffusion of water flow: tractography allows us to know the direction of this flow

and then to study in vivo the microstructural architecture of the brain even in pathological conditions.

Diffusion can be quantified by the coefficient of apparent

diffusion (ACD) which is greater when the diffusion of water is not hindered, that is, in the ventricles and demyelinated white matter. This diffusion can be represented graphically by an ellipsoid. In MR, by applying different diffusion-sensitive gradients in different directions and then comparing the decay rate of the MR signal with that observed in a reference scan without any diffusion weighting, a set of information on the surface of the ellipsoid can be obtained to define its size, shape and orientation for each voxel.

The mathematical construct used to characterize anisotropic diffusion is the diffusion tensor.

From the diffusion tensor estimated in each voxel, the amplitude and direction of diffusion can be estimated by evaluating the eigenvectors and eigenvalues of the tensor. The eigenvectors of the diffusion tensor identify the three axes of the ellipsoid. The three eigenvalues (λi) represent the diffusivity along each of these three directions. The eigenvector corresponding to the largest eigenvalue (λ1), which represents the longest axis of the ellipsoid, is called the main diffusion direction or axial diffusivity (AD). The mean of the other two eigenvalues corresponds to radial diffusivity (RD).

The mean of the three eigenvalues represents the mean diffusivity (MD), i.e. the average molecular diffusion.

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It is possible to determine the degree to which diffusion is directionally constrained by fractional anisotropy (FA).

FA varies from 0 to 1, where 0 represents a preferred direction, therefore the isotropic diffusion, while 1 represents the unidirectional movement, that is, the anisotropic direction.

The water molecules of the brain's cerebrospinal fluid spread equally in all directions, while in the white matter movement occurs along the stretches of the fibers. Neural axons, in fact, have insulating sheets of myelin that envelop them and facilitate the movement of the molecules contained in the axon in a particular direction, reducing their possibility of escaping from the axonal walls. So DTI tunes in to how randomly scattered water molecules prefer to go in a specific direction, as opposed to all directions in each voxel.

Low AD reflects axon damage in both ischemic and chemically induced lesions, so it is a possible indicator of alterations in axonal integrity.

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High levels of RD, on the other hand, have been associated with incomplete myelination in mice (Song, Sun et al., 2002), drug-induced demyelination, and loss of myelin following axonal damage. It then provides information about

possible alterations in myelin integrity.

FA reflects the density of the fibers within a voxel so a reduced FA reflects the loss of integrity of the fibers.

Finally, high levels of MD have been observed in conditions of reduced membrane density, such as tissue degeneration after injury: it can therefore be a sensitive indicator of overall developmental changes in brain tissue (Pierpaoli et al., 1996).

Through these diffusivity measurements it is possible to characterize the macroscopic anatomy of white matter. Therefore, diffusion anisotropy is considered a marker for white matter integrity, therefore often used for the diagnosis of diseases and studies on the progression, development and aging of normal brain function (Horsfield & Jones, 2002;

Pagani, Filippi et al., 2005).

4.1.1 Analysis of multi-subject diffusion data

Smith and colleagues (2006) proposed a new approach, called Tract-Based Spatial Statistics (TBSS), which performs localized statistical tests of FA and other diffusion-related data. This approach projects each subject's FA data into a common space, in a way that does not depend on the aforementioned non-linear recording. This is achieved by an initial approximate nonlinear recording, followed by projection onto a representation of the alignment invariant

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stroke, called mean_FA_skeleton. No spatial leveling is required in image processing (Smith et al., 2006).

4.1.2 Tractography

Diffusion tensor imaging tractography is a method that allows the in vivo study of white matter fiber pathways, both under clinical and health conditions. It allows to reconstruct bundles of fibers and perform comparisons between FA subjects only for the voxels included in the identified traits. This procedure requires that an operator manually define the regions of interest that will be the starting point for tracing the bundles of faber in the diffusion image of each subject. An average stretch from the average of the images that will be used as a mask is then calculated. Finally, the alignment affine to the standard space will precede the voxelwise statistics inside the mask.

Tractography is based on the accuracy of alignment. Although some researchers have developed more sophisticated methods (Jones, Catani et al., 2006), to compare the variation in FA values along the bundles of fibers derived from tractography, directly between subjects, it is not based on a perfect alignment between subjects. In addition, the problem of user intervention in defining the areas of interest is still unresolved. Therefore, this is a major limitation of this method.

Another limitation is the possibility of evaluating FA only in those traits that have been specifically analyzed, drawing by hand the areas of interest.

Some investigations have tried to solve such problems but, before the advent of TBSS, "it is not safe to assume that recording can align FA data well enough between subjects to allow simple and unambiguous interpretations of voxelwise statistics" (Smith, Jenkinson et al., 2006).

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