Acquisition C) Visualization

Scattering Funk-Radon Structure orientation Spherical harmonics AXDT model

B) Reconstruction

5mm

Figure 20.2 Illustration of the whole procedure. Firstly, the sample is imaged from various positions using the Euler cradle (A)⁴. The reconstruction (B) uses spherical harmonics to model the scattering in each location, the reconstruction is performed with the AXDT method and finally the orientations are obtained by the Funk-Radon based approach discussed in chapter19. Finally, in (C) a visualization is presented, showing the obtained directions overlaid on-top of the attenuation CT (C). From M.Wieczorek, F. Schaff, C.

Jud, D. Pfeiffer, F. Pfeiffer, and T. Lasser. “Brain connectivity exposed by Anisotropic X-ray Dark-field Tomography”. In:Scientific reports8.1 (2018), p. 14345

DOI:10.1038/s41598-018-32023-y

URL:https://www.nature.com/articles/s41598-018-32023-y.

This image is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).

Figure20.2shows an illustration of the entire procedure. Firstly, the acquisition (A), where the Euler cradle is used to obtain dark-field measurements from various orientations. This step is followed by the reconstruction (B) using the spherical harmonics based AXDT approach, where the scattering is modeled using spherical harmonics. Subsequent to the reconstruction of the scattering profiles the microstructure orientations in each location are extracted by computing the Funk-Radon transform and a maxima detection on the result (compare chapter19). Finally, the attenuation CT result is visualized together with the directions obtained from AXDT (C).

4The brain image is created using the Brainder project with kind permission of A. Winkler [on17]. The data is publicly available under the Creative Commons Attribution-ShareAlike 3.0 License (https://creativecommons.

org/licenses/by-sa/3.0/).

133

20.1 Experiments and Results

The measurements and the reconstructions were performed with the same GBI setup and parameters as given in chapter18and chapter19with few exceptions. Thus, we limit the discussion of the experiments to those parameters that differ from the previous settings.

Firstly, the sample of the human cerebellum was dried with a critical point method. The drying was performed to fix the probe and increase visibility as the sensitivity of the setup is fixed at current⁵.

In total, we have recorded 1404 viewpoints from various orientations providing a well-sampled unit sphere. The measurements took approximately 11 h. The attenuation CT was reconstructed from the original absorption measurements, yielding an effective voxel resolution of isotropic0.127 mm. Due to the additional computational demands for the AXDT reconstruction, the raw dark-field measurements were rebinned by a factor of4prior to any processing. This leads to a voxel resolution of0.508 mmfor the AXDT reconstruction.

The reconstruction was performed on the very same machine and with the same parameters as we have already used in chapters18and19. The AXDT reconstruction took18 minwhile the linear attenuation CT took85 mindue to the higher resolution. While the other parameters remained unchanged, we have used N = 1500directions of a Voronoi tesselation for the directions extraction.

In fig.20.3(A), (B) and (C) we show the results for the three central slices of the volume. The reconstructed fiber orientations extracted from AXDT are overlaid on top of the attenuation reconstruction and colored according to the given color-wheel. The vectors have been scaled by the value of the Funk-Radon transformed scattering function in this direction. Figure20.3 (D) shows a streamline visualization of the fiber tracts of the white matter between three slices parallel to the main planes.

The white matter regions show strong scattering magnitudes as well as directionality. Closer to the border of the sample, less of these effects are observed. The streamline visualization in particular strongly supports the premise that the fiber tracts are aligned within the white matter, which fits the knowledge e.g. from histology (compare the schematic image in fig.20.2 (B)).

20.2 Conclusion

In this chapter, we have summarized the developed methods subsumed under the term Anisotropic X-ray Dark-field Tomography (AXDT). Furthermore, we have presented a first, preclinical application to tomographic imaging of the human CNS.

5Recent advancements by Birnbacheret al.[67] showed that GBI setups are able to reach sensitivity comparable to synchrotrons. However, this requires multiple changes to the setup which at current is not applicable to the setup with the Euler cradle.

5mm 5mm

5mm

A) Top view B) Front view C) Side view

D) Fiber tracts

2x

Figure 20.3 Visualization of the results. (A)-(C) show the three center slices of the results. The attenuation CT is overlaid with the directions obtained from AXDT. (D) shows three slices, each parallel to one of the main planes, and a fiber tract visualization of the directions within the white matter. The streamline visualization was created with the ImFusion Suite [on12]. The yellow lines illustrate the intersections of the slices. The directions are color-coded according to the color-wheel. From M.Wieczorek, F. Schaff, C. Jud, D. Pfeiffer, F. Pfeiffer, and T. Lasser. “Brain connectivity exposed by Anisotropic X-ray Dark-field Tomography”. In:Scientific reports8.1 (2018), p. 14345

DOI:10.1038/s41598-018-32023-y

URL:https://www.nature.com/articles/s41598-018-32023-y.

This image is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).

While due to the lack of a ground truth, the evaluation is limited to interpretation of the visual results, these results strongly indicate the successful reconstruction of fiber tracts orientations using AXDT. This is supported by knowledge from histology as well as D-MRI.

This is particularly interesting as this method is capable of resolving these structures despite being much smaller than the detector resolution. The complementary nature of X-ray imaging to D-MRI imaging supports the assumption that this imaging modality will be capable to provide additional information in the future. While the sample for this experiment was dried, recent advances by Birnbacheret al.[67] render the imaging of raw brain material realistic in the future.

This concludes this thesis and as the chapter itself already summarizes everything developed in this part we will omit another summary.

20.2 Conclusion 135

„

—The Doctor Doctor Who

Part V

Appendix

A