Brain Connectivity Exposed by Anisotropic X-ray Dark-field Tomography

To understand the interaction of different parts of the human brain it is essential to know how they are connected. Such connections are predominantly related to the brain’s white matter, which forms the neuronal pathways, the axons. These axons, also referred to as nerve fibers, have a size on the micrometer scale and are therefore too small to be imaged by standard X-ray systems. In this paper, we use a grating interferometer and a method based on Anisotropic X-ray Dark-field Tomography (AXDT) with the goal to generate a three-dimensional tomographic reconstruction of these functional structures. A first preclinical survey shows that we successfully reconstruct the orientations of the brain fibers connectivity with our approach.


Anisotropic X-ray Dark-field CT Imaging
In this paper, we present a method based on grating-based X-ray imaging, namely dark-field imaging 19 , which overcomes the limitations mentioned above. It provides structural information on the brain fiber orientation, but is at the same time capable of being implemented with a large field of view (similar to clinical CT). In Fig. 1A) we illustrate such a grating-based X-ray imaging setup, which consists of a standard X-ray CT setup with three additional gratings, enabling the simultaneous extraction of the additional phase-contrast 20 and dark-field-contrast 19 signals. It has been shown that, in particular, the dark-field signal is correlated to (ultra-) small angle X-ray scattering 21 of the aligned micro-and nano-structures in the sample. For dark-field contrast grating-based setups, the grating bars mainly pick up scattering occurring orthogonally to the grating bars, meaning that the signal is strongest if a microstructure aligns with the grating bars 22,23 . Consequently, for highly structured specimens, the dark-field signal constitutes an anisotropic quantity. This observation lead to the method of X-ray vector radiography 24 . A standard X-ray imaging setup with a source and a detector is augmented with two absorption gratings G0 and G2 and one phase grating G1. Additionally, a Euler cradle is used to rotate the sample in a fully three-dimensional manner. Additionally, the grating orientation t and one X-ray direction l are illustrated. In B) we illustrate the location of the cerebellum within the human brain (left) 32 . In the middle of (B) we show a schematic histology image of the cerebellum with H&E stain. The center region of the histology image shows the fiber tracts located in the white matter of human brain tissue, aligning with it. Finally, on the right side of (C) we sketch the relationship of the fiber tracts, the diffusion MRI and the assumed scattering signal. In (C) we show a slice of conventional attenuation based CT on the left, and on the right an overlay of the additional directional information obtained by the proposed method in this paper.
SCientifiC REPORTs | (2018) 8:14345 | DOI:10.1038/s41598-018-32023-y So far, the concept of dark-field imaging has been successfully used for various applications, including lung imaging 25 , musculoskeletal imaging 26 , materials testing 27 , or imaging of dental samples 28 . Aiming at tomographic reconstruction of this anisotropic signal, we recently proposed a method called Anisotropic X-ray Dark-Field Tomography (AXDT) in 29 , based on the previous work performed by Malecki et al. 30 and Vogel et al. 31 . In order to properly sample this anisotropic signal, the grating-based setup is additionally augmented with a Euler cradle, enabling fully three-dimensional rotation of the sample. AXDT allows the tomographic reconstruction of the scattering profile in each location of the specimen, which in turn enables the imaging of nerve fibers for the very first time.

Scattering and Diffusion in the Human Brain
In order to show the potential of AXDT specifically for brain connectivity applications in a first proof-of-principle feasibility study, we investigated a sample from the region of the cerebellum in a human brain. (Fig. 1B) 32 shows the location of the cerebellum on the left side. In the middle, a schematic illustration of a histology slice of a human cerebellum depicts the gray matter and white matter. To the right, a sketch of the relation of diffusion-MRI (gold), fiber tracts (purple) and scattering on the right side (blue), is shown. While the diffusion process (gold) aligns with the fiber tract (purple), the scattering profile (blue) is supposed to be strongest orthogonal to the aligned structures. The cerebellum can be divided into grey matter and white matter. In Fig. 1B) center we show schematic illustration of a histology slice of a cerebellum with hematoxylin and eosin (H&E) stain leading to a violet/red coloring. The white matter mainly consists of axons, which build a junction between different areas within the central nervous system. Those axons are arranged in long bundles, leading to a mainly aligned/parallel arrangement of the fibers to each other. The grey matter contains multiple different nerve cells, which can be subdivided in three different layers: stratum moleculare, stratum purkinjense, and stratum granulosum, respectively. Parallel fibers represent the axons of the granule cells and build up connections between the different cells within the grey matter.
In Fig. 2 we show an overview of our method. The method basically consists of three parts: First acquisition, second tomographic reconstruction, and third the final fiber orientation extraction.

Acquisition
As illustrated in Fig. 1A), a Talbot-Lau interferometer setup is used. In order to sufficiently sample the scattering signal, the sample needs to be rotated in a fully three-dimensional manner. This also implies that a standard tomographic axis as used in standard X-ray CT is not sufficient. In order to sample the specimen more freely, a Euler cradle is added to the setup. This device allows to freely rotate the object in a fully three-dimensional manner (compare Fig. 2A) 32 . Optimal acquisition protocols for this novel imaging modality is an ongoing field of research (c.f 33 ).

Anisotropic X-ray Dark-field Tomography (AXDT)
For tomographic reconstruction of the spherical scattering distribution we use the recently proposed method of AXDT (compare Fig. 2B)). Within this method, the scattering is described as a 3D-field of spherical functions, mapping a specific scattering direction to a scattering strength. As proposed in 29 we use real-valued spherical harmonics in order to express these spherical functions at each location inside the reconstruction volume. Based on this we introduced a forward model for the anisotropic dark-field measurements based on the resulting spherical harmonics coefficients. This enables the tomographic reconstruction of the scattering profile in each location of the specimen with respect to spherical harmonics.

Fiber Tract Extraction
We already illustrated that the effect of scattering is strongest orthogonal to the microstructure/fiber in Fig. 1B). Therefore, we are interested in the direction orthogonal to scattering occurring on plate-like shapes. For this purpose, we 34 recently proposed to utilize the Funk-Radon transform 35 , which transforms spherical functions to the integral values of great circles on the unit sphere. Thus, strong scattering on a plate-like shape will be translated to the accumulated value in orthogonal direction, which is assumed to be the direction of the fiber. Compare Fig. 2B), which shows the relation between the reconstructed scattering profiles, their Funk-Radon and the extracted structure orientations.

Experiments and Results
All methods were performed in accordance with the relevant guidelines and regulations. For our experiments, a piece of a human cerebellum was used. The sample was excised at the Institute of Forensic Medicine (Ludwig Maximilian Universität München, Germany) and is part of the ethics applicant 319/13, which was approved by the ethics commission of the Faculty of Medicine of the Technische Universität München. The review board waived the need for consent as this sample was excised for forensics.
The sample was critical-point-dried prior to any measurements. This allowed for a simplified sample mounting and specimen stability over the rather long measurement times of this proof-of-principle study, but in general no special sample preparation is required for this method. The sample was then measured and reconstructed using AXDT. The exact parameters are discussed in the Supplemental Material. In Fig. 3 we display the three center slices of the reconstructed data. The structure orientations (a vector field) extracted from the AXDT reconstruction are overlaid over a three-dimensional rendering of the corresponding attenuation X-ray CT. The structure orientations have been colored based on their in-plane orientation according to the given color-wheel. Additionally, their length corresponds to the accumulated scattering orthogonal to their orientation, i.e. the value of the Funk-Radon transform in that direction. In Fig. 3D) we additionally visualize the fiber tracts within the white matter, as computed via a streamline method tracking fibers along the vector field of the orientations in 3D.
In the non-white matter regions, we predominantly find less strong and less structured scattering, which fits the circumstance that this region, in addition to axons, contains stellate and basket cells. Within the white matter though, we find the strongest scattering signal and strongly structured orientations. This fits the knowledge from medicine e.g. from histology images such as illustrated in Fig. 1.
Besides the complementary information, with an effective voxel size of 0.5 mm for this study we are already below the resolution of current Diffusion MRI, which is typically in the mm regime. In fact, since we are binning our data by a factor of 4 for computational speed, voxel sizes of 0.125 mm are immediately possible.

Conclusion
In this paper we presented a method for imaging nerve fibers connectivity across macroscopic samples of human brain tissue using AXDT. We presented first preclinical results, which indicate the successful tomographic reconstruction of the directions of nerve fibers in the white matter of the cerebellum. This is particularly interesting, as these fibers are much smaller than the employed detector resolution. Further, as this method poses a complementary imaging method to both attenuation-based X-ray imaging and Diffusion MRI, we are positive that this method will provide additional insight into human anatomy. As any functionality within the human CNS is built upon the connectivity based on nerve fiber tracts, this insight can provide additional insight in the basic functionality, for planning neurosurgeries, and for investigation of CNS related diseases.

Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request. The software code used for the AXDT reconstruction as well as the code used for the fibre extraction and their visualization can be accessed from the corresponding author upon request.