The voxel grid of an MR image may be compared to a chessboard: selecting a number of adjacent voxels that form a trajectory is like drawing a line on the chessboard (Fig. 8.3). The algorithm used to drawthis trajectory in most fibre tracking techniques involves selecting an initial point (seed point) that is highlighted on the image, and then moving to the next nearest voxel, which in turn is highlighted, along the prevalent aniso-tropic direction, until a condition that halts this process arises (stopping criterion). The differences among these, line propagation, algorithms lie in the way in
which the information contained in the voxels nearest to the one being examined with the algorithm (nearest neighbours approach) is used by the algorithm itself to draw the likeliest trajectories and minimize noise.
Since digital images are represented on discrete fields, the vector will often point to an area straddling at least two adjacent voxels, requiring a choice from one or more possible trajectories. In such cases, the selected tract will be a mere approximation of the information contained in the diffusion data, irrespective of the trajectory that has been selected.
The first researchers to reconstruct a white matter fibre tract successfully [20,21] solved this problem using propagation in a continuous numerical field -where the coordinates can be expressed as decimal values - each time approximating the coordinates of the line to those of the nearest voxel. This simple but fairly rough method can be improved by applying a tract curvature threshold. Assuming that the course of a fibre tract exhibits only reasonably soft curves, whenever two possible trajectories present, the less curved one is selected, while sharp curves (e.g. >60°) are excluded. Line propagation algorithms may require vector interpolation (direction and eigenvalue) at the point of arrival of the previous step, which usually straddles two or more voxels and therefore does not directly correspond to a measured value. Interpolation is a mathematical operation that makes it possible to obtain the value of a point from those of surrounding points. In the simpler algorithms, the vectors corresponding to the neighbouring voxels are interpolated, while the more sophisticated ones directly interpolate the diffusion tensor and calculate a new vector . Interpolation enables more uniform paths to be obtained with respect to the algorithms that do not employ them, and is less sensitive to noise, although the additional calculations considerably increase computation time.
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