ACEPTACION CATEGORIA I.C.M.S.F METODO DE ANALISIS

Diffusion tensor imaging (DTI) is used to infer the axonal organisation of the brain by measuring the translational displacement of water molecules (LeBihan, 1995). The motion or diffusion of water molecules is much faster along the WM fibres than perpendicular to them (Basser, 1995; Basser et al., 1994; Basser and Pierpaoli, 1996, 1998) because there are fewer obstacles to prevent movement along the fibres (Stejskal, 1965). DTI takes diffusion measurements in multiple directions and using tensor decomposition, extracts the diffusivities parallel and perpendicular to the fibres (also termed principle diffusivities) (Basser, 1995; Basser et al., 1994; Basser and Jones, 2002; Basser and Pierpaoli, 1996, 1998; Pierpaoli et al., 1996). The difference between these two motions (parallel and perpendicular to the fibres), is referred to as diffusion anisotropy and forms the basis of DTI. Details on the MR technique used to acquire DT-MR images are given elsewhere (see Mori and Zhang, 2003).

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Inside cells where water is constrained, the mean diffusion (ADC) is slow. The intensity of each pixel in the ADC map is proportional to the extent of diffusion; water molecules in bright regions diffuse faster than those in dark regions (Figure 3.1, left image). Fractional anisotropy (FA) is the most widely used DTI-based index in brain research for representing the motional anisotropy of water molecules, being sensitive to the presence and integrity of WM fibres (Figure 3.1, centre image). Water motion in CSF is isotropic, meaning that the diffusion is roughly equivalent in all directions (i.e. water diffuses freely). In WM diffusion is anisotropic (highly directional), as axonal membranes and myelin sheaths present barriers to the motion of water molecules in directions not parallel to their own orientation (Jellison et al., 2004).

FA images (also referred to as FA maps) are grey scale, 2D maps representing diffusion anisotropy on a voxel-by-voxel basis with intensity limits between zero and one (Figure 3.1, centre image). FA maps exhibit a high signal (where intensity limits approach 1) in areas of significant anisotropic motion. In contrast, a low signal (where intensity limits would be around 0) is shown in areas of isotropic motion (Pierpaoli et al., 1996). High levels of diffusion in WM (represented by the ADC map) are indicative of poorly developed, immature or structurally compromised WM. High levels of anisotropy (represented in the FA map) are considered a reflection of coherently bundled, myelinated fibres oriented along the axis of the greatest diffusion.

Local values for diffusion or anisotropy can be computed within a small ROI and compared by contrasting values in two or more ROIs. In population studies, differences between two groups of subjects can be calculated by coregistering the images into the same coordinate system and performing individual t-tests at each voxel, producing a map that displays all voxels which the groups differ significantly in anisotropy or diffusion. This latter approach was performed in this thesis, to compare diffusion anisotropy between left- and right-handed groups (see Chapter 6).

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Figure 3.1. Images representing the ADC (left), fractional anisotropy (centre), and colour-coded orientation (right) maps from the diffusion data of a single subject. (Image inspired by Mori and Zhang, 2006).

Pajevic and Pierpaoli (1999) suggested colour-coded schemes to visualise the 3D information in FA maps, in two dimensions (see Figure 3.1, right image). The direction of maximum diffusivity may be mapped using red, green and blue (RGB) colour channels with colour brightness modulated by FA, resulting in a convenient summary map from which the degree of anisotropy and the local fiber direction can be determined. The most basic RGB colour-coded scheme distributes a colour for each orientation of the fibres: fibres crossing left-to-right are visualised in red, fibres crossing anteriorly-posteriorly are visualised in green, and fibres crossing inferiorly-superiorly are visualised in blue. Following voxel-wise comparison of the handedness groups, regions of significant difference are mapped onto the colour-coded orientation maps to determine direction of WM.

Measuring the diffusion tensor

Fibre orientations are estimated from three independent diffusion measurements along the x, y and z axes (Figure 3.2). However these measurements are not enough because fibre orientation is not always along one of these axes. To accurately find the orientation with the largest ADC, diffusion would need to be measured along thousands of axes,

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which is not practical. To simplify this issue, the concept of diffusion tensor was introduced in the early 1990’s (Basser et al., 1994).

The tensor matrix of diffusion consists of a 3x3 matrix, which is diagonally symmetric (Dij = Dji). The tensor matrix may be visualised as an ellipsoid (Figure 3.2) whose diameter in any direction estimates the diffusivity in that direction and whose major principle axis is oriented in the direction of maximum diffusivity (note: the ellipsoid represents average diffusion distance in each direction, not ADC) (Basser et al., 1994). The tensor matrix is subjected to a linear algebraic procedure known as diagonalization, resulting in a set of three orientations (V1, V2, and V3) representing the major, medium and minor principle axes of the ellipsoid and the corresponding three eigenvalues (λ1, λ2, λ3) representing the length of the longest, middle and shortest axes (Jellison et al., 2004). The properties of the 3D ellipsoid (used for ADC measurement) can therefore be defined by six parameters.

Using more than six encoding directions will improve the accuracy of the tensor measurement for any arbitrary orientation (Jones et al., 1999; Papadakis et al., 1999). This procedure may be thought of as a rotation of the x, y, and z coordinate system in which the data were acquired (dictated by scanner geometry) to a new coordinate system whose axes are dictated by the directional diffusivity information (Jellison et al., 2004).

Figure 3.2. Fibre orientations are estimated from three independent diffusion measurements along the x, y, and z axis. Fibre orientation is represented by a tensor ellipsoid. The properties of the 3D ellipsoid can be defined by six parameters namely, the length of the longest, middle and shortest axes (eigenvalues λ1, λ2, and λ3) and their respective orientations (eigenvectors V1. V2, and V3).

- 61 - Measuring diffusion anisotropy

Diffusion anisotropy is easily understood as the extent to which the shape of the tensor ellipsoid deviates from that of a sphere; mathematically, this translates as the degree to which the three tensor eigenvalues differ from one another. Any of several anisotropy metrics may be used, one of the commonest being fractional anisotropy (FA) which derives from the standard deviation of the three eigenvalues and ranges from 0 (isotropy) to 1 (maximum anisotropy). For example, the degree of diffusion anisotropy can be measured by using a measurement of difference among the three eigenvalues shown in Equation (3.1):

(3.1)

where λ1, λ2 and λ3 represent the length of the longest, middle and shortest apparent diffusivities respectively. If diffusion is isotropic, (λ1 = λ2 = λ3) this measure becomes 0. Large numbers indicate high diffusion anisotropy. After a diffusion ellipsoid is determined, the information can be reduced to a vector of the longest axis (eigenvector V1) which is assumed to represent the fibre orientation. Because it is very difficult to visualise 3D vectors, this information is generally converted to a colour coded orientation map. By estimating the diffusion tensor in each voxel and subsequently its orientation, it is possible to estimate and display the principal orientation of anisotropic structures in vivo, and several methods have been developed for achieving this (Coremans et al., 1994; Jones et al., 1997; Nakada and Matsuwaza, 1995; Pajevic and Pierpaoli, 1999). One method, called tractography, usually requires seeds from which streamlines are propagated based on V1 orientation (Basser et al., 2000; Conturo et al., 1999; Jones et al., 1999; Mori et al., 1999; Parker et al., 2002; Poupon et al., 2000). The streamlines are terminated when they reach a low anisotropy region where there is no coherent fibre organisation (see Figure 3.3). An example of the streamlines representing perisylvian language fibre tracts can be seen in Figure 3.4.

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Figure 3.3. Three-dimensional tractography streamlines through user defined ROIs (or seedpoints), shown here as two stars. These are virtual representations of WM fibres, and follow a continuous path of greatest diffusivity (i.e. least hindrance to diffusion). (Image taken from Mori and Zhang, 2006).

Figure 3.4. Streamlines representing the three language fibres tracts in the left and right hemisphere of one subject used in this thesis. Red streamlines represent the arcuate fasciculus, blue and green streamlines represent the anterior and posterior indirect language pathways respectively (for further information on these tracts see Catani et al., 2005, 2007). Tracts were created using DTIStudio (http://www.mristudio.org/).

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CHAPTER 4:

PARTICIPANTS, MATERIALS AND METHODOLOGY