In Vivo Human Brain

In this section we test our method on anin vivodata set provided by the Human Connectome Project. A detailed description of data properties and preprocess-ing steps can be found in Section 3.3. ODF reconstruction in a part of the

4. A Bayesian Approach for Neighborhood-Informed Tractography

centrum semiovale is depicted in Figure 4.11, along with a corresponding deter-ministic tracking experiment using the proposed algorithm originating from a seed region in the corpus callosum. Parameter settings for both deterministic and probabilistic version of our algorithm (summarized in Section 4.2.5) are as follows: We chose a tract propagation step size of λ = 0.5×voxel-size, forward search with n = 2 steps and step length µ = 1×voxel-size, N = 5 path points for the extrapolation strategy, and regularization parameter β = 0.03. Trac-tography experiments were performed seeding from three different regions: the corpus callosum in the mid-sagittal slice, the pyramidal tracts, and the cingulum bundles. The exact locations are illustrated in the right column of Figure 4.12 as projections onto a sagittal, coronal and transversal slice, respectively. The prior distribution was adapted to the different brain regions with respect to the standard deviation using σ = π/14 for the tracks starting in the corpus callo-sum, σ =π/18 for the pyramidal tracts, and σ=π/2 for the cingulum bundles.

The angle determining the difference from the former tracking direction was set consistently toϕ=π/18, corresponding to approximately 7 candidate directions per cone-shaped region. Tracking starts in left and right direction from the seed region in the corpus callosum of the mid-sagittal slice, in (+/-)-direction of prin-ciple diffusion from the seed region of the pyramidal tracts, and in anterior and posterior direction from the seed region in the cingulum bundles. The tracking algorithm stops when reaching a voxel outside the valid domainW ⊂Ω obtained by combining the white matter mask with GFA and ADC thresholding. In Figure 4.12, results for the deterministic basic tractography Algorithm 2.1 and for our proposed deterministic algorithm are compared. The basic algorithm generates streamlines by following with step sizeλ = 0.5×voxel-size the ODF maximizing direction that lies in a region ofϕ=π/18 around the former stepping direction.

Thus, both algorithms allow for a maximum of 10^◦ difference between successive steps. For each voxel in the seed region, 9 tracks were generated, respectively.

The fibers generated from seeding in the corpus callosum appear similar. Com-pared to the tractogram on the right obtained from our proposed algorithm, the lateral bundles in the tractogram generated by the basic algorithm appear more sparse. Vice versa, the vertical projections are a bit more pronounced for the basic algorithm. Increasing parameter σ, our method approaches the outcome of the basic algorithm. The results for the pyramidal tracts demonstrate the potential of our method to increase lateral projection fibers. The result obtained from the basic method captures merely a vertical course of fibers, whereas us-ing the proposed algorithm the fiber tracks show a broader dispersion towards the cortex. Regarding the outcome for the cingulum bundle, the result from the proposed forward search method appears smoother with less spurious tracks.

Furthermore, the challenging sharp bendings are managed much better as com-pared to the basic algorithm. In Figure 4.13, results for different choices of parameter σ are shown. It can be observed, that a small value for σ promotes smooth tracks, but results in earlier termination of the curvy regions of the

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4.3. Experiments and Results gulum bundle. On the other hand, a larger value forσreduces the reconstruction of lateral connections in the corpus callosum or pyramidal tracts. Results for a first approach to include anatomical information in our tractography algorithm are shown in Figure 4.14. Therefore, the prior probability was in each forward search step multiplied by the sum of WM and GM partial volume map at the re-spective path point. Tracking terminates when GM or CSF partial volume maps are ≥ 0.5 or if the brain region is left. The results show less spurious tracks, but also an earlier termination of tracks. Probabilistic tractography experiments using our proposed algorithm are illustrated in Figure 4.15. Here, 90 tracks were generated from each voxel in the seed region, respectively. Next to the plotted tracks, a GFA map with voxels colored according to the number of track visits is shown for the three regions of interest, respectively. For these probability maps, the number of tracks passing through is summed up along 20 slices whose exact location is highlighted in the S₀ images on the right side.

4.3.6. Spherical Diffusion Phantom

Furthermore, we tested the proposed method on data obtained from the spherical diffusion phantom described in Section 3.2.2. Computation and visualization were performed using the diffusion MRI postprocessing kitpk. The tractography algorithm parameters were chosen as in Section 4.3.2 for the Fiber Cup phantom, that isλ = 0.5 × voxel-size, n = 2, µ= 1 ×voxel-size, σ =π, β = 0.5, N = 6, and ϕ = π/9. The algorithm terminates if FAψ <0.2. For comparison, we also computed results using the DT-based FACT algorithm included inpk. Here, the algorithm stops if the angle between successive directions is larger than 20^◦, and FAD <0.08. We experienced that increasing the FA threshold resulted in early termination of tracks in the crossing regions. Figures 4.16 and 4.17 illustrate the results for seeding in the bundle that crosses both other bundles at 60^◦ and 30^◦ angle, respectively. The exact seeding ROI is located in the mid-coronal slice and highlighted in red in Figure 4.16a. Tractography starts bi-directionally from the points in the center and at the corners of each voxel in the ROI. In Figures 4.16b and 4.16c, the results are shown after the tracks passed through the crossing for the first time. The bundle resulting from the FACT algorithm fans out at the crossing, i.e. some tracks pass the crossing correctly while others make a wrong turn. This is due to the fact that, as described in Section 2.4, the diffusion tensors at the crossings are isotropic. On the other hand, the crossings are passed correctly without deviations by the proposed ODF-based algorithm.

Figure 4.17 shows results where the maximum number of iteration steps of the tracking algorithm is set to 500, but otherwise the parameter setting is the same as above. 500 iteration steps equal approximately 2-3 circles around the sphere.

Now, also the proposed algorithm produces a few tracks that make a wrong turn

4. A Bayesian Approach for Neighborhood-Informed Tractography

ODF-field in a coronal slice Tracking result

Figure 4.11.: ODFs (bottom left) and deterministic tractography using the proposed algorithm (bottom right) in a part of the centrum semiovale. The location and seed region for tractography are highlighted above.

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4.3. Experiments and Results

Basic algorithm Forward search

Figure 4.12.: Deterministic tractography results for basic and the proposed forward search method with extrapolation guiding. First row: seeding in the center sagittal slice of the corpus callosum, second row: seeding in the pyramidal tracts, third row:

seeding in the cingulum bundles. The seed regions are highlighted in the last column, respectively.

4. A Bayesian Approach for Neighborhood-Informed Tractography

σ=π

σ=π/18

Figure 4.13.: Comparison of different choices for parameterσ. Seed regions and the other parameters are equal to those used forforward search in Figure 4.12.

cingulum bundle corpus callosum pyramidal tracts Figure 4.14.: Results for the anatomically-informed deterministic forward search method using the same parameter settings as for the results in Figure 4.12.

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4.3. Experiments and Results

Figure 4.15.: Probabilistic tractography results using the proposed algorithm. First row: seeding in the corpus callosum,second row: seeding in the pyramidal tracts,third row: seeding in the cingulum bundles. The seed regions are the same as in Figure 4.12.

The colored GFA maps in the second column show on a logarithmic scale the number

4. A Bayesian Approach for Neighborhood-Informed Tractography

(a) seedregion (b) DT-based (c) proposed

Figure 4.16.: Tractography results of the crossing region after the first pass through.

(a) DT-based (b) proposed

Figure 4.17.: 3D view of tractography results for maxIter = 500.

at the 30^◦ crossing, which is mainly due to the improperly resolved 30^◦ crossing of the ODF reconstruction discussed in Section 3.2.2.