2.2 Data acquisition and analysis
The MRI protocol was based on routine clinical imaging, extended with diffusion imaging. Sedation was used only in subjects undergoing clinical imaging if necessary to prevent significant motion The imaging protocol included a T1w MPRAGE, and a T2w TSE, with diffusion imaging (16
) acquired in the axial plane, utilizing 30 images with b=1000 s/mm2
and 5 b=0 images (22 cm FOV, slice thickness=2.0mm, TE=88 ms, TR=10s, 128×128 matrix, 1 NEX, iPAT=2, modified as necessary to facilitate completion of the scan if the subject was unable to remain perfectly still).
A segmentation of the intracranial cavity was created from the structural MRI (17
). Compensation for residual distortion and patient motion was achieved by aligning the diffusion images to the T1w MPRAGE scan, with appropriate reorientation of the gradient directions (19
). Tensors were estimated using robust least squares, and were displayed via color-coding (20
We used a stochastic streamline tractography algorithm that combines the speed and efficacy of deterministic decision making at each voxel, with probabilistic sampling from the space of all streamlines. Potential streamlines are stochastically initialized and evaluated, starting from a seeding region of interest, such as all the white matter in the brain. Streamlines are initialized at stochastically sampled locations inside the seeding region-of-interest, and are constructed by stepping with sub-voxel resolution through the tensor field. For each potential streamline, we avoid loss of connectivity due to local aberrations by incorporating a low pass filter along the estimated pathway for conventional stopping criteria, including streamline curvature and fractional anisotropy criteria. The range of potential streamlines examined is broad in comparison to conventional deterministic streamline tracing, and is formed by log-Euclidean tensor interpolation (21
) at each location, with stepping direction determined by a linear combination of tensor deflection (22
) and primary eigenvector orientation, with stopping based on fractional anisotropy and angle criteria.
Specifically, from each stochastically selected subvoxel location pk
, a new point along the streamline is identified by stepping, with a fixed stepsize s, in the direction vk
, determined by the primary eigenvector of the tensor estimate at pk
The new point pk+1
is tested to ensure it is inside the image boundary and inside the region to be considered for tractography. A mask can be used to ensure tractography does not step through regions with no white matter. Streamline generation is terminated if points are not validated. Streamline termination criteria related to the fractional anisotropy and angle changes are then checked. The trajectory fractional anisotropy is assessed as a linear combination of the fractional anisotropy of the tensor estimate and the previous trajectory fractional anisotropy:
) is the FA of the tensor Dk+1
. The primary eigenvector of the tensor is computed, providing ek+1
. The angle criterion is assessed by accumulating the cosine of trajectory angle changes,θ:
The new direction of the streamline is calculated using a combination of the primary eigenvector and tensor deflection, while accounting for the previous direction of the streamline:
Propagation of each streamline was terminated if the trajectory fractional anisotropy fell below 0.15, or if the tract trajectory angle exceeded 30 degrees. The trajectories were obtained using the step size parameter s=0.33mm, α=0.5, β=0.5, γ=0.5, δ=0.5, and tensor deflection power ε=2.
Furthermore, as proposed by (23
), regions-of-interest may be specified to ensure potential streamlines meet requirements of known anatomy, by requiring streamlines to pass through certain regions-of-interest (selection ROIs), or requiring that they do not pass through certain regions-of-interest (exclusion ROIs). This process of stochastically sampling potential streamlines from the seeding region-of-interest enables us to identify the streamlines that are most consistent with the diffusion tensor image, even in the presence of abnormal anatomy. Stochastic sampling is continued until a predetermined number of streamlines has been examined, and each streamline meeting all criteria is stored. A streamline density image is then constructed by counting the number of times each streamline entered a voxel and dividing by the total number of streamlines.
The streamlines identified by stochastic tractography can be used to delineate a region of interest, in which the assessment of parameters of white matter microstructural integrity may be carried out. However, such an assessment can be confounded by partial volume effects (PVE), as described by (24
). When voxels associated with a fiber tract are identified, the proportion of the voxel associated with the fiber tract is important. A common strategy to select a tract-based region of interest has been to threshold the streamline density to identify voxels associated with a particular white matter (25
). Average parameters, such as FA or MD, characteristic of the region are then assessed by computing the mean value of the parameter by summing the parameter over all the voxels above the threshold and dividing by the number of voxels in the region (25
). Vos et al. (24
) demonstrate that the interaction between the geometry and curvature of a white matter fascicle, and the voxel grid creates a partial volume effect that confounds the analysis. We propose to avoid the confounding due to the partial volume effect by avoiding the thresholding. Instead, we utilize the streamline density directly to enable an appropriate weighted average of diffusion tensor parameters. In our analysis, the diffusion tensor parameters of a region are calculated based on equal weighting of each of the trajectories, rather than equal weighting of each voxel. Given a streamline density image, d, and an image of a tensor scalar parameter, p, on the same discrete image lattice with voxels indexed by i, the streamline density weighted mean, m, and variance, v, of the parameter are given by :
The corpus callosum region-of-interest was located by inspection of the structural MRI scans and a color coded image of local tensor orientation, and delineated interactively () using previously established criteria (23
). The stochastic tractography was utilized to identify streamlines consistent with the projections of the corpus callosum, and are illustrated in . Scalar measures called Fractional Anisotropy (FA), Mean Diffusivity (MD), Axial Diffusivity (AD) and Radial Diffusivity (RD) were derived from each tensor. These measures reflect properties of the underlying white matter, but do not have high specificity for particular microstructural white matter changes (27
). The streamlines passing through the corpus callosum ROI were used to construct a streamline density image, constructed by counting the number of times each trajectory entered a voxel and dividing by the total number of trajectories created, as illustrated (). In order to characterize the microstructural properties of the white matter of these trajectories, streamline density weighted averages of these scalar parameter values were calculated.
Figure 1 (A) T1-weighted image, superimposed color coded representation of tensors, intensity proportional to the fractional anisotropy. Red for left-right, blue for superior-inferior, green for anterior-posterior. A manually drawn two-dimensional ROI delineates (more ...)
This provided four scalar variables characterizing the projections of the corpus callosum in each subject, the average FA (AFA), average MD (AMD), average AD (AAD) and average RD (ARD). The weighted average and variance of the fractional anisotropy (and similarly for the other scalar parameters) in the projections of the corpus callosum were computed as shown:
where i is the index of each voxel, di
is the streamline density at voxel i, and FAi
is the fractional anisotropy.
Callosal volume was estimated by thresholding the streamline density image at 5% (28
), counting the number of voxels and multiplying by the size of each voxel.