Mapping brain anatomical connectivity using white matter tractography

Abstract

Integration of the neural processes in the human brain is realized through interconnections that exist between different neural centers. These interconnections take place through white matter pathways. White matter tractography is currently the only available technique for the reconstruction of the anatomical connectivity in the human brain noninvasively and in vivo. The trajectory and terminations of white matter pathways are estimated from local orientations of nerve bundles. These orientations are obtained using measurements of water diffusion in the brain. In this article, the techniques for estimating fiber directions from diffusion measurements in the human brain are reviewed. Methods of white matter tractography are described, together with the current limitations of the technique, including sensitivity to image noise and partial voluming. The applications of white matter tractography to the topographical characterization of the white matter connections and the segmentation of specific white matter pathways, and corresponding functional units of gray matter, are discussed. In this context, the potential impact of white matter tractography in mapping the functional systems and subsystems in the human brain, and their interrelations, is described. Finally, the applications of white matter tractography to the study of brain disorders, including fiber tract localization in brains affected by tumors and the identification of impaired connectivity routes in neurologic and neuropsychiatric diseases, are discussed.

Figure 1

(a) The diffusion tensor may be visualized using the diffusion ellipsoid, which has the direction of its main axis (the direction of the fastest diffusivity, λ₁) given by the DT major eigenvector, e₁. The two other eigenvectors, e₂ and e₃, give the orientation of the ellipsoid’s medium and minor axes. Their corresponding eigenvalues, λ₂ and λ₃, relate to the ellipsoid magnitude along these axes. The relative magnitudes of the three eigenvalues determine the ellipsoidal shape which varies for brain voxels from prolate to spherical (b), with the oblate and spherical shapes being assumed to characterize crossing fiber regions (see also Fig. 2). For tractography applications, the diffusion tensor (c) and major eigenvector (d) are calculated at each brain voxel.

Figure 2

(a) ODF reconstructions of two and three simulated fibers crossing at large angle (top two rows) and of fibers crossing at 30 degrees (bottom row) using DK-ODF, Q-ball, and DT methods (from left to right). The original fiber directions are indicated by lines. Note that the ODF methods are able to resolve the fibers, with better accuracy for large angle crossings. (b) DT and (c) DK-ODF maps of the intersection between posterior corona radiata, superior longitudinal fasciculus, and short association fibers. The position of the mapped area is shown in (d). Several of the voxels with apparent crossing fibers are detailed in (e), using both DK-ODF and the diffusion ellipsoid. Fiber estimates (given by the ODF and diffusion ellipsoid peaks) are indicated by lines. Adapted by permission from Lazar et al (31).

Figure 3

(a) and (b): Fiber trajectories are obtained by following fiber direction estimates from voxel to voxel; the trajectory is initiated in both forward and backwards vector field directions starting at a “seed” point (indicated by a dot) ; (c)–(e) Several strategies may be used to step along the trajectory including a constant step size with the propagation direction estimated at the beginning of the step (Euler, (c)) or along the step (Runge-Kutta, (d)), or a variable step size (FACT, (e)); (f) Tractography reconstruction of the corpus callosum obtained from seeds situated in the mid-sagittal region of the tract.

Figure 4

(a) Intersection of a callosal (red) and a short association (green) fiber bundle with the projection fibers of the corona radiata (blue). Fiber directionality was estimated using the DK-ODF method; (b) Detailed view of the crossing region highlighted in (a).

Figure 5

Image noise and tensor field characteristics affect the accuracy and precision of the tractography methods; consequently reconstructed pathways may deviate from the true trajectory. (a) An example of fiber tract dispersion due to noise in a linear tensor field. (b) Tract error was characterized using the standard deviations of the two-dimensional distribution of fibers in planes perpendicular to the true trajectory at different distances from the seed point and the displacement of the mean trajectory position relative to the true trajectory position. The tractography error increases with the distance from the seed point (c), decreasing SNR (d) and increased tensor field convergence (e). The error decreases in regions of field convergence (e). Reproduced with permission from Lazar and Alexander (12).

Figure 6

(a) RAVE method involves the DT transformation in its reference frame, the perturbation of the major eigenvector, and the rotation of the perturbed eigenvector back into the laboratory frame. (b) and (c): Fiber trajectories obtained for the same seed point using deterministic streamline(b) and RAVE(c) algorithms. Three-dimensional renderings of the fiber density for the trajectories depicted in (c) are shown in (d) and (e) using a sagittal and coronal view, respectively.

Figure 7

(a) Bootstrap tractography for a seed point situated near the corpus callosum’s midline (yellow arrow). In this example, one thousand trajectories were generated to construct the bootstrap fiber distribution for the seed. Other bootstrap parameters included a pool size of eight independent measurements (N_s=8). (b) Corresponding density maps shown for two different slices (top, full slice, and bottom magnified ROI) demonstrate increased fiber dispersion as the distance from the seed point increases. Reproduced with permission from Lazar and Alexander (39).

Figure 8

White matter tractography may be used to label brain voxels according to the white matter structure they are part of. (a) Image tractograms of the projection (green), association (red), and callosal (blue) fibers are mapped into the brain space indicating their position with respect to other brain regions. (b) A similar procedure has been used to label various white matter tracts including the corpus callosum (purple), superior longitudinal fasciculus (yellow), cingullum (green), uncinate fasciculus (dark red), inferior occipito-frontal fasciculus (orange), inferior longitudinal fasciculus (brown), cortico-bulbar tract (light blue), cortico-spinal tract (white), fornix and stria terminalis (light yellow). Tract positions are shown in several sagittal and axial slices. Adapted by permission from Wakana et al. (51).

Figure 9

(a)–(d) Segmentation of the thalamus based on its cortical connectivity; each thalamic voxel is labeled according to its predominant cortical projection (e.g., blue-prefrontal, red-occipital, etc.). (e)–(f) Segmentation of the pre-SMA and SMA based on their connectivity patterns is obtained by first constructing a connectivity matrix (g) from the tractography data of the entire pre-motor region (e); this matrix is then reordered (h) to segregate voxels with different connectivity. The voxels separated using the connectivity matrices are then mapped back into the space brain (f) to reveal two contiguous and distinct regions. (a–d) Reproduced with permission from Behrens et al (82). (e–f) Reproduced with permission from Johansen-Berg et al. (82). Copyright (2004) National Academy of Sciences, U.S.A.

Figure 10

Whole brain tractography was used to generate connections between the different cortical regions obtained by parcellating the cortex into1000 regions of interest. The cortical regions and resulting connectivity graph are shown for one subject in (a). The connectivity backbone, indicating regions highly connected and highly central, is shown in (b) for one subject and in (c) averaged across five subjects. The edges and nodes of the network are labeled according to their connection weight and strength. The connection weight of an edge is given by the number of trajectories connecting its end nodes, normalized by the connection length and total surface area of the connected cortical regions. The node strength gives a measure of the extent to which a node is connected to the rest of the network. Adapted from Hagmann et al. (27).

Figure 11

Cingulum displacement due to tumor-mass effect in a patient with a grade III astrocytoma situated in the superior medial region of the left frontal lobe. The tractograms were generated from a set of seeds placed in the anterior region of the tract. The relative positions of the ipsilateral (red) and contralateral (purple) bundles are labeled onto axial, sagittal, and coronal fractional anisotropy maps. Adapted by permission from Lazar et al. (91).

Figure 12

Tractograms of the cortico-spinal tracts superimposed onto preoperative (left) and postoperative (right) fractional anisotropy maps in a patient with a ganglioglioma involving left cerebral peduncle and deviating in a splaying fashion the fibers of the right cortico-spinal tract anteromedially and posterolaterally. Postoperatively, the ipsilateral tract appears preserved after the surgery and positioned closer to normal anatomical position, except in the immediate vicinity of the resection. Adapted by permission from Lazar et al. (91).