White matter tractography using diffusion tensor deflection

Abstract

Diffusion tensor MRI provides unique directional diffusion information that can be used to estimate the patterns of white matter connectivity in the human brain. In this study, the behavior of an algorithm for white matter tractography is examined. The algorithm, called TEND, uses the entire diffusion tensor to deflect the estimated fiber trajectory. Simulations and imaging experiments on in vivo human brains were performed to investigate the behavior of the tractography algorithm. The simulations show that the deflection term is less sensitive than the major eigenvector to image noise. In the human brain imaging experiments, estimated tracts were generated in corpus callosum, corticospinal tract, internal capsule, corona radiata, superior longitudinal fasciculus, inferior longitudinal fasciculus, fronto-occipital fasciculus, and uncinate fasciculus. This approach is promising for mapping the organizational patterns of white matter in the human brain as well as mapping the relationship between major fiber trajectories and the location and extent of brain lesions.

Figure 1

a: Illustration of tensor deflection (TEND) for a cylindrically symmetric diffusion tensor. Incoming vector: blue; deflected vector: dark red; major eigenvector: dashed red. b: Illustration of TEND as function of the tensor shape. For more anisotropic tensor (left) the incoming vector is deflected toward the major eigenvector. The amount of deflection decreases with decreasing anisotropy (from left to right). c: Illustration of four cases where TEND will not cause any vector deviation. These cases include the incoming vector being either parallel or perpendicular to the major eigenvector of a cylindrically symmetric tensor ellipsoid, in the plane of a oblate tensor ellipsoid, or in any orientation for a spherical ellipsoid.

Figure 2

a: The deflected angle, acos(v _in · v _out), as a function of the angle between the incoming vector and tensor major eigenvector direction, acos(v _in · e ₁), for five FA levels (0.10, black; 0.36, blue; 0.55, green; 0.70, red; 0.91, magenta). The tensor is assumed to be cylindrically symmetric. The deflection angle decreases with lower anisotropy and is zero for both the parallel and perpendicular orientations. TEND: dashed line; STT: solid line. b: Angular dispersion for STT (solid lines) and TEND (dashed lines) for a signal‐to‐noise ratio of 50 for the same FA levels as described in a. c: Same as b with a smaller horizontal axis range to highlight differences in the TEND plots.

Figure 3

Fibers of corpus callosum (Subject 1, top row; Subject 3, bottom row). The pathways were seeded on the midline of the corpus callosum in the sagittal plane. The fiber trajectories were terminated if they reached regions with FA lower than 0.15 or if the angle between two consecutive steps was larger than 45 degrees. The voxels intersected by estimated fiber trajectories were labeled and the resulting volume was rendered. Different tract reconstructions were obtained using a: STT, b: TEND, c: tensorlines (Equation (4) w/ f = 0, g = 0.3). c: illustrates that a combination of deflection and incoming vector resulted in fibers that connect more lateral regions of the two hemispheres.

Figure 4

STT vs. TEND for fibers of the internal capsule (Subject 1). a: seeding region (light blue) overlaid over FA map; b: STT, for an threshold angle of 45 degrees, average tract length 76.1 mm; c: STT, for an threshold angle of 36 degrees, average tract length 66.4 mm; d: TEND, for an threshold angle of 45 degrees, average tract length 117.7 mm. The average tract length when using TEND, for a threshold angle of 36 degrees remains 117.7 mm (image similar to d).

Figure 5

Fibers of corticospinal tract. a: Subject 1. b: Subject 3. TEND trajectories were generated from white matter regions situated in motor and sensory cortex. The fibers reaching the basis pedunculi were retained. The coloring corresponds to the anisotropy (yellow = high vs. red = low anisotropy).

Figure 6

Projection fibers (corona radiata) reconstruction (Subject 1). The fibers were parsed and color‐coded according to their anterior‐posterior position in the internal capsule. a,b: Two rendered views of the parsed pathways. c: Axial and sagittal cross‐sectional images. Although similar, there are slight bilateral variations due to imperfections in the region selection (by hand) and asymmetries in the brain. The color encoding enables the simultaneous visualization of different fibers groups. Most of the fibers project upwards into the corona radiata and reach different regions of the cortex. In the inferior direction, the fibers propagate toward brainstem where a large number reach the cerebellum and others propagate towards the spine. Note that when fibers from more than one group cross the same voxel, only the last path painted will appear, resulting in a painting artifact.

Figure 7

Association pathways: Superior longitudinal fasciculus (blue), fronto‐occipital fasciculus and uncinate fasciculus (orange), inferior longitudinal fasciculus (green‐yellow). a–c: Subject 2, right and left hemispheres. d: Subject 3. All the pathways were obtained using the TEND algorithm and are similar to those obtained using STT by Mori et al. [2002].

Figure 8

Superior longitudinal fasciculus tracking in a patient with a left frontal oligodendroglioma (Subject 4). The estimated tracts are superimposed over ADC maps. a: Side view. b: Partial top view. Similar appearance to the SLF in normal subjects is observed on the contralateral side. On the ipsilateral side, the SLF pathways appear to terminate at the tumor periphery. Close examination of the anisotropy and eigenvector images show some preserved directional anisotropy within the tumor although it is below the anisotropy stopping threshold for the tracking algorithm.

Figure 9

The deflected angle, acos(v _in · v _out), for second order TEND, as a function of the angle between the incoming vector and tensor major eigenvector direction, acos(v _in · e ₁), for the same FA levels as in Figure 2. TEND, dashed line; STT, solid line.