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Edited by Marcus E. Raichle, Washington University in St. Louis, Missouri, approved on October 20, 2021 (reviewed on July 30, 2021)

We show a multi-scale phase-contrast X-ray computed tomography (CT) scan of human brain tissue after death. Parallel beam CT can cover large tissue volumes and combine subcellular details to scan selected areas with high magnification. For more individuals, including Alzheimer's disease patients and control groups, this situation has been repeated the same. Optimized phase retrieval, followed by automatic segmentation based on machine learning, and feature recognition and classification based on optimal transmission theory, indicating the path from health to pathological structure without prior assumptions. This research provides a blueprint for studying the cell structure of the human brain and its changes related to neurodegenerative diseases.

We studied the three-dimensional (3D) cell structure of the human hippocampus in neuropathologically healthy and Alzheimer's disease (AD) individuals based on phase-contrast X-ray computed tomography scans of post-mortem human tissue perforation biopsies. In view of recent findings that indicate the nuclear origin of AD, we specifically focused on the nuclear structure of granular cells in the dentate gyrus (DG). Use highly automated measurement and analysis methods to scan and evaluate tissue samples of 20 individuals, combined with multi-scale recording, optimized phase retrieval, machine learning segmentation, structural feature representation in feature space, and classification based on optimal transmission theory. Therefore, we found The prototype transformation between the structure and the pathological state of the representative of healthy granular cells involves the decrease of the nuclear volume of granular cells and the increase of electron density and its spatial heterogeneity. The latter can be explained by the higher ratio of heterochromatin to euchromatin. Similarly, many other structural characteristics can be deduced from the data, reflecting both the natural polydispersity of hippocampal cell structure among different individuals in the physiological environment, and the structural effects related to AD pathology.

The brain mapping of cells and bone marrow structures in larger brain regions after death is needed to promote our quantitative understanding of the human brain. In addition to improving the brain atlas, they are also indispensable for the future integration of in vivo functional observations with high-resolution structural data (1⇓ –3). However, mapping the brain requires additional imaging methods that can visualize and quantify three-dimensional (3D) structures, including data from multiple individuals (2). Recently, the potential of phase-contrast X-ray tomography (also known as phase-contrast computed tomography (PC-CT)) in 3D brain imaging has been demonstrated, whether it is a small animal model (4⇓ ⇓ ⇓ –8) or a human brain (9 ⇓ ⇓ –12). Since the entire 3D architecture at all scales is related to physiological functions and pathological mechanisms, the multi-scale implementation of PC-CT (13) is particularly suitable for brain mapping.

As a supplement to genomics, proteomics, and metabolism, structural data is also needed to unravel the mechanisms of neurodegenerative diseases. Such data must be comprehensive (large patients and controls), quantitative and fully digitized; suitable for advanced analysis, including deep learning; and three-dimensional in nature. Alzheimer's disease (AD) is a good example: MRI can be used to find evidence of morphological changes in the hippocampus with aging and disease in the body. In order to interpret such data based on a reference model, a 3D probability map of the hippocampus is proposed in the reference. 3. Combine autopsy MRI and histology. The authors concluded that, in order to test the different hypotheses of the hippocampus in AD, it is necessary to conduct "more detailed research" on the hippocampus in aging and disease, and therefore requires higher resolution and true 3D data.

To this end, we introduce here the advanced and multi-scale implementation of PC-CT, combined with automatic segmentation and statistical analysis of morphological features. In this way, it provides an urgently needed supplement to traditional 2D histology, avoiding sample sectioning and staining. This signal is generated by the spatial variation of the real part of the X-ray refractive index n=1-δ+iβ, where δ is proportional to the electron density. Importantly, the advantage of PC-CT comes from the fact that the real value decrement is significantly larger than the imaginary number and absorbs the accounting component β; that is, δ/β≈103 in the hard X-ray region. Then through the free space propagation, the image contrast is effectively formed, that is, the self-interference of the coherent light beam behind the object. The fact that this does not require any additional optics between the object and the detector provides benefits for dose efficiency and resolution. Several PC-CT studies have focused on the hippocampal cell structure (7, 14⇓ ⇓ –17) in the AD transgenic mouse model. The typical sign associated with the disease, namely β-amyloid plaque, has shown considerable contrast . In a recent study, we can also demonstrate the potential of PC-CT on paraffin-embedded hippocampal tissues affected by AD, and evaluate its ability to visualize different pathologies, including plaques, neuronal depletion, or microglia Cells may be recruited to the affected area. 12).

In this work, we studied the 3D cell structure of the human hippocampus, which contributes to the formation of declarative long-term memory, that is, remote context or remote semantic memory, but it may also affect recent memory, emotions, and plant functions (18). Pathologically, the hippocampus is one of the first affected areas in AD (19). As we show here, the throughput of PC-CT measurement, reconstruction, segmentation, and analysis is high enough to process data from a larger pool, which consists of paraffin-embedded tissue blocks of several people after death, including AD and control group (CTRL), classified according to the neuropathological assessment of the National Institute of Aging-Alzheimer's Association (NIA-AA)-recommended ABC staging (20, 21). We specialize in the structural changes caused by the dentate gyrus (DG) and AD. As recently shown, the hippocampal neurogenesis and plasticity of the entire hippocampal circuit is related to DG, and it is found to decrease sharply in AD (21). In addition, we deliberately do not pay attention to the plaques and tangles in AD, which have become the target of a lot of research, but pay special attention to the nuclear structure of DG neurons, because recent evidence indicates that the nuclear origin of AD (22) includes chromatin structure (twenty three). In addition, we also include 3D imaging examples of other parts and structures of the hippocampus, and provide corresponding statistical analysis.

Figure 1 shows a schematic view of the hippocampus embedded in the left and right temporal lobes of the cerebral cortex as part of the limbic system. In Figure 1A, the hippocampus is depicted in the sagittal plane, where it forms an elongated structure about 4 to 5.2 cm in length (24). In Figure 1B, the front face is shown, where the appearance is usually represented as a snail. Its characteristic functional units are shown in Figure 1C. The most prominent ones include keratinocytes (CA) and DG, the latter being a dense area of ​​granular cells. In the multi-synaptic signaling pathway related to the formation of semantic memory, the input signal from the entorhinal cortex (EC) first reaches the DG, which is composed of oval granular cells with millimeter-long dendrites. Through mossy fiber connections, information is further processed in CA, and its neurons are characterized by their pyramidal bodies. The division of CA and the co-owned sub-areas CA1 to -4 is not fully standardized. The information leaves the hippocampus to reach the inferior temporal cortex, temporal poles and prefrontal cortex, forming gray matter (GM). There are more information processing pathways involving the myelin sheath in the white matter (WM) that connects the hippocampus to other brain regions. The physiological relevance of the hippocampus, regarding several important signal pathways and their key roles in memory function and neurodegenerative diseases, especially in AD, supports the need to study 3D structures with cellular and subcellular resolution .

Overview of the human hippocampus. (A and B) Schematic diagram of the human hippocampus (gold) and its position, (A) sagittal plane and (B) frontal view. (C) A virtual slice of PC-CT data through the overview in the EB configuration. The different neuron layers are outlined: DG; CA differentiation into CA1, CA2, CA3, CA4; WM; general manager; and European Community. Also shown are areas with calcified blood vessels (BV). (D and E) High-resolution PC-CT data from AD patients. (D) Volume rendering of calcified plaques (blue) near DG (gold). (E) Calcified β-amyloid plaques (P) and calcified BV are only observed on one side of the DG, as shown by the maximum intensity projection (16.2 μm thickness). The red arrows indicate the vascular connections between the plaques. (Scale bars: C, 1 mm; E, 30 microns.)

In order to cover the hippocampal cell structure in a larger patient cohort, we increased the sample throughput related to the early work (12) through an optimized recording strategy, thus achieving a large sample pool with high and comparable data quality, and we implemented The multi-scale PC-CT workflow for human brain tissue is based on parallel beam (PB) recording under a high field of view (FOV), combined with a region of interest (ROI) scanned at high magnification based on a cone beam geometry. Then we use machine learning based on the V-net architecture to segment neurons, and then use optimal transmission (OT) theory to unlock pathological changes. Note that OT allows us to identify the "movement" in the patient cohort based on the transmission metric in the structural feature space that we defined in the image segmentation step. OT also provides a significant advantage over standard statistical tools (such as the t-test of a single parameter) because it can compare the entire neuron population by quantifying the index of distribution changes.

The implementation of PC-CT, especially regarding the multi-scale configuration with different zoom levels, is detailed in the materials and methods. Starting from the overview scan of the expanded beam (EB) configuration with a few millimeters FOV in Figure 1 or PB, the sub-regions of the hippocampus are presented at different zoom levels in Result I: Multi-scale tomography of the hippocampus. Then, based on the geometric magnification using divergent and highly coherent beams, with a voxel size of px≈160 nm, and in some cases even px≈50 nm, the structure of the granular cell nucleus in the DG with a volume of 108 to 109 μm3 exits the X-ray waveguide (WG). In high-resolution reconstruction, neurons, especially DG nuclei are segmented. Based on the segmentation mask, a histogram of morphological features is obtained, and each tissue sample contains results of approximately 10,000 neurons. Then compare five choices of 20 individuals (11 subjects with moderate to high AD neuropathological changes according to Reference 20, hereinafter referred to as AD; 7 controls; and 2 diffuse manifestations based on ABC scores) The feature histogram is in Result II: Geometric and Statistical Analysis, using the OT tool. We propose an analysis workflow in a very general way to identify pathways from healthy structures to pathological structures.

Figure 1C shows the PC-CT results with the maximum FOV, 8 mm biopsy perforations covering 2 × 3 × 0.3 -cm3 tissue mass, scanned in EB configuration (SI appendix, Tables S1 and S2, and Figure S1). Supports all the typical structures for further identification of ROI, as described in the introduction, visual inspection based on 3D data is easy to identify and label. Already at this rough level, the granular cell band of DG can be identified. Its border is a blood vessel with a particularly high electron density, indicating calcification. Please note that calcified vasculature in the hippocampus is often observed in the tissues of different subjects (AD and CTRL). In the AD cases shown in Figure 1 D and E, these electrons are so dense that they may even pass through β-amyloid, and then also show a highly elevated electron density (as described in Reference 12). In addition, other areas, such as the pyramidal cell bands of CA, WM, and EC, can be easily located. Given that the 1mm biopsy punch is then used to extract more subvolumes for high-resolution scans, it is important to identify these areas. To prove that these large FOVs can also be scanned with smaller voxel sizes, the complete 8 mm punch was further scanned in the PB configuration (SI Appendix, Table S2). Using the dynamic stitching realized by the NRStitcher (Non-rigid stitching of trillion-pixel volume images) program (25), the 7 × 7 individual scans are combined to cover the entire 8 mm punch with a single large volume again. In this way, the tissue volume of 63 mm3 is covered by the sub-micron voxel size. Figure 2 shows a frontal plane slice of the volume reconstructed by stitching. In Figure 2A, the gray square marks a single tomographic image. Using only some local ring artifacts, it is possible to successfully track the structure of the entire volume, far beyond the boundary of a single scan. Figure 2B illustrates the winding of the DG tape in two different frontal planes throughout the volume. This 3D shape with invagination helps to accommodate enough DG cells. Based on the large FOV even in a single tomography, the PB data is particularly suitable for quantifying the shape and width of the DG band (see Figure 3 and the SI appendix, further analysis summarized in Figure S3, and text details in the SI appendix). In order to image the ROI in a cone beam (CB) configuration with a higher magnification of M≃40 without local tomography artifacts, a 1 mm biopsy punch was used to extract subvolumes from the 8 mm block. Figure 2C shows a slice through this ROI, indicated by a red square in the overview scan. In this configuration, even the substructure of the DG cell nucleus can be uncovered. By further increasing the geometric magnification to M≃130, these details can be resolved even better, such as the slice shown in Figure 2D and the 3D volume rendering of a single nucleus shown in Figure 2E, based on its electron density.

Multi-scale PC-CT data. (A) A virtual slice of the suture reconstruction volume of the entire 8 mm tissue sample obtained from the 7 × 7 scan in the PB configuration. The label indicates the end of the DG band in this section, as well as the calcified BV. The red dashed box marks the area further detailed in B, located in two different parallel planes, showing how the DG zone passes through the volume. (C, bottom) A detailed view of the DG zone, obtained from a CB scan recorded at M≈40, at the position marked by a solid red square in A. To compare data quality and contrast, C, the corresponding PB data is displayed at the top. (D) The highest zoom of the DG structure, recorded at M≈130. Through the median filter maximum intensity projection exceeding 0.5 μm, the nuclear membrane and heterochromatin can be seen. (E) Full 3D rendering of electron density further highlights individual nuclei. Note that here, darker areas indicate higher density. (Scale bars: A, 1 mm; B, 0.5 mm; C, 100 microns; D, 30 microns.)

Overview of the Director General. The DG band in the section with a thickness of 1.25 mm (interval time axis) shows (A) segmented DG nuclei (gold) and vasculature (red) and (BD) are presented in false colors, representing (B) normalized electron density P nucleus , (C) its variance S, and (D) the local granular cell density.

Importantly, the image quality allows semi-automatic segmentation of granular cell nuclei using Ilastik software (26), followed by volume rendering of the annotated segmentation mask using Avizo Lite (Thermo Fisher Scientific). Figure 3 shows an example of volumetric fluoroscopy, showing the overall curved shape of the DG cell band in Figure 3A (gold), together with the vasculature (red). The holes in the DG band are due to the main blood vessels penetrating the DG. Keeping perspective and applying this DG mask to the PC-CT gray value, we can present a different number of volume renderings: (Figure 3B) normalized electron density P; (Figure 3C) the normalized relative variance of the electron density in the nucleus S=σ2/ρ2, indicating the universality of heterochromatin; and (Figure 3D) local cell density, with an average radius of 50 μm. In this way, the overall distribution and local unevenness can be visualized.

Next, we further illustrate the high-resolution results obtained in the CB configuration, which are used to examine specific areas in the hippocampus, such as CA1, DG, surrounding GM, and WM.

Figure 4 shows exemplary results obtained from the carob 1 (CA1) area, for a 1 mm sample, extracted and scanned as detailed in Table S2 of the SI Appendix. The typical slender cone shape in the CA layer can be well visualized by the maximum intensity projection (MIP) in Figure 4 AC. In every cell, the body, nucleus and nucleolus can all differentiate. For some cells, such as those marked by the arrow at the top (Figure 4A), the contrast between the cell body and the nucleus seems to reflect the position of the nuclear membrane, while for other cells (Figure 4A, arrow at the bottom), the dominant effect is The overall increase in the density of electrons in the nucleus. In addition, the density within the cytoplasm showed some changes. This is also observed for other cell types, as shown in Figure 4B, which depicts the substructure of satellite cells connected to neurons. Consistent with the function of CA neurons for unidirectional signal processing in the entire hippocampus, consistent polarization and direction and characteristic long dendrites are very clearly visible in the entire 3D reconstruction volume. As highlighted in Figure 4C, the contrast is sufficient to track large dendrites of tens of microns. Using Ilastik, the neuron cell body and nucleus are segmented and rendered in 3D, as shown in Figure 4 DF.

CA1 area with pyramidal cells (CB data). (A) When the gray value is subjected to MIP, pyramidal cells with typical uniaxial orientation can be well visualized by their electron density, where the thickness exceeds 13 μm. The contrast is sufficient to distinguish the cell body from the nucleus, either through the visibility of the nuclear membrane (upper arrow) or the overall increased electron density within the nucleus (lower arrow). (B and C) MIP thicker than 8.7 μm. (B) Pyramid cells (arrows) with satellite cells. (C) Pyramidal cells have branches throughout the volume. (D and E) Volume division of the cell body. (F) A three-dimensional rendering of the cell body (gold) and cell nucleus (brown) in the entire reconstructed volume. Contains gray-scale orthodontic slices to support 3D visualization. (G) MIP of gray matter tissue with a thickness of more than 1 μm. (H) The MIP of white matter tissue with a thickness of more than 1.6 μm. (Scale bars: A, D, E, G, and H, 50 μm; B and C, 10 μm.)

In the data in Figure 4 C and E, areas of lower electron density (light gray values) are usually observed around neurons. In order to check whether this observation of lower electron density may ultimately be an artifact of sample preparation, for example, by preparing the dehydration and embedding procedures of formalin-fixed and paraffin-embedded (FFPE) tissue blocks, we changed the preparation Work and scan the tissue in a hydrated state. To this end, a 1 mm sample was taken from the tissue block, first chemically fixed with 10% formalin, and then stored in phosphate buffered saline at 4°C, and checked in its hydrated state, that is, it is neither dehydrated nor dehydrated. Not dehydrated. Paraffin embedding. Interestingly, this indicates that these areas of reduced electron density are also present in the image of the hydrated tissue (SI appendix, Figure S6).

The segmentation of pyramidal neurons was then applied to tissue samples from different subjects in the AD and CTRL groups. Extract samples from the same location in the hippocampus. Please note that pathological changes related to AD are particularly obvious in this area. It is worth noting that the tissue samples from three individuals diagnosed with AD (according to ABC staging; subjects 2, 6, and 21, age 78 ± 11 years) were compared with four controls (subjects 16, 17, 20). And 21, age 66±20 y) and another sample (topic 12). The results are reported in the SI appendix and visualized in the SI appendix, Figure S4.

Figure 4G shows a virtual slice (MIP) through the hippocampal GM tissue. For sample collection, the GM area was determined based on histological analysis (through hematoxylin and eosin and Bielschowsky silver dip staining). Pyramidal cells are also segmented in this area, once again being able to evaluate neuron density, neuron morphology and orientation in full 3D.

Figure 4H shows a cross-section of the WM tissue. Similarly, based on the evaluation of adjacent tissue sections (hematoxylin and eosin staining and Bielschowsky silver impregnation), the location of the FFPE block to extract the sample from the biopsy punch was selected. This tissue segment does not exhibit specific neurons like CA and GM, as expected, but looks quite fibrous, reflecting the myelinated fibers of WM.

DG is a particularly important part of information processing in the hippocampus. Figure 5 shows the reconstruction of the area based on the scanned data in the CB configuration. As shown in Figure 5A, subcellular details can be visualized. The virtual section is on the same plane as Figure 2. In Figure 5B, the volume is cut in a plane parallel to the DG zone, emphasizing its wall-like appearance. Granular cells exhibit a well-structured electron density in their nucleus, which is surrounded by areas of lower electron density (lighter gray value) in the cell body. You can even notice the interconnection between the individual units. The magnification highlights the particularly large changes in the electron density distribution in the nucleus, which may be related to heterochromatin.

Enlarge the DG unit band (CB data). (A) Transverse section through the belt. (B) A slice parallel to the DG zone. The red square marks the enlarged display area, and the gray scale is selected to highlight the structure of the nucleus, that is, the change in the electron density in the nucleus. (C) Volume rendering of DG cell body. (D) Use color to indicate local cell density (see color bar). (Scale bars: A and B, 100 μm; B, inset, 20 μm.)

Then use the interactive learning and segmentation toolkit Ilastik again to identify and segment different features in the DG reconstruction volume. Figure 5C shows the volume rendering segmentation of the DG cell nucleus. Based on the centroid of the nucleus, a 3D cell density map was calculated, as shown in Figure 5D. The density obtained from the high-resolution scan in the CB configuration confirmed the cell density analysis of the large FOV overview recorded in the PB configuration (Figure 3D). The density ranges from 2 to 4.5·105 cells/mm3, which is in good agreement with the literature (27).

In the next step, we quantify the DG cell structure in 3D to understand its inter-subject variability in the context of healthy physiological conditions and AD pathology. To this end, the DG bands in the samples of 20 different subjects were scanned, reconstructed, segmented and analyzed. AD cases are determined based on the ABC score (20). It is worth noting that samples from 11 AD subjects aged 76.6 ±9.3 years old, 7 CTRL subjects aged 76.6 ±7.0 years old, and two other subjects who were not grouped were collected, as shown in Table S1 in the SI Appendix Listed. Similar to the multi-scale workflow described above, a 1 mm sample is taken from each tissue block and imaged first in PB and then in the CB configuration. The following analysis is mainly based on CB data, because the resolution is higher and the nucleic acid structure can be resolved, and the overview scan in the PB configuration helps the correct positioning of the CB scan and the robustness of the analysis. The analysis of the PB configuration data is given in the SI appendix, Figure S3 and the corresponding text section.

Figure 6 illustrates the segmentation of DG neuron nuclei (CB data). In Fig. 6A, the same area is shown before and after the object mask is superimposed. The object mask is segmented and generated by the machine learning workflow, as described in Fig. 6C. For each object in the segmentation output, that is, from each DG cell nucleus, several structural characteristics are evaluated for further analysis: 1) the median value ρ of the electron density (compactness parameter), 2) the normalized variance of the electron density s =σ2/ρ2 as a proxy for spatial variation within the nucleus (heterogeneity parameter), 3) nuclear volume v (size parameter), 4) sphericity φ of the nucleus (shape parameter), and 5) the number of local neighbors nn ( Neuron packaging parameters). Here, the object proximity is defined by the given radius as x¯nn+2·MADx=13.5 μ m, where x¯nn=8.8 μ m represents the median value of the next neighborhood distance distribution of all samples, MADx=3.5 μ mm Absolute deviation of its value. Figure 6D shows the resulting histogram of all five structural features as an example of a subject belonging to the CTRL group. In this particular case, the histogram contains data corresponding to a total of 3,595 segmentation kernels in the reconstruction volume, which meet the following selection criteria applied to the segmentation output: only objects with v> 35 μ m3, 0.6·x¯nn< xnn<x ¯nn+3·MADx, and the 1.5x interquartile range of any one of the five features are considered for statistical evaluation. These criteria were chosen to minimize the deviation of segmentation artifacts.

DG nucleus segmentation workflow. (A) The slice passes the sample 3D input data (CB configuration), (top) without and (bottom) with mask annotations. (B) The three-dimensional rendering of the mask, in a cubic volume with a side length of 400 μm. (C) A flowchart illustrating the segmentation steps. (D) For each shielded object (DG cell nucleus), it can be attributed to many attributes, resulting in its own histogram. (Scale bar: 100 μm.)

Then, based on the same automated workflow, all individuals (including AD patients and CTRLs) are segmented into granular cell nuclei and the five parameters of each cell are extracted, as described above. For each attribute (parameter) and each individual, a complete histogram containing all segmented particle data can be used. First, compare different attributes independently and one by one. Figure 7 shows the results of the electron density ρ and the heterogeneity parameter s (see the SI appendix, Figure S2 for all other parameters). The violin chart shown in Figure 7A provides a quick overview and illustrates the degree of variation within and between groups of the histogram. Before resolving these differences at the entire histogram level, compare the distribution medians of the two groups (AD and CTRL). The electron density of AD is slightly higher than that of CTRL subjects; that is, ρ¯AD=320.91 nm-3 and ρ¯CTRL=318.77 nm-3, the volume is reduced, namely v¯AD=101.85 μ m3 and v¯CTRL=135.88 μ m3 , Both show a tendency toward more compact cores, with p-values ​​(for ρ and v, Welch’s t-test p≈0.02 and p≈0.07, respectively). At the same time, in the CTRL and AD subjects, the median of the heterogeneity parameter s increased from s¯CTRL=1.07·10-5 to s¯AD=1.45·10-5, indicating that the spatial structure of the research object has A more heterogeneous trend. The nucleus in AD, but p≈0.17, this difference in median is not significant. However, in addition to the comparison of median values, the entire population of particles should also be compared between subjects and groups, which will once again lead us to consider changes in s related to distinguishing between pathological and healthy states (see below). It is important to consider the entire neuron population, because physiological functions may require a certain bandwidth of structural parameters, that is, the dispersion of characteristics related to the functional state of particles. Therefore, it is interesting to consider the entire histogram to compare the differences between and within groups, as quantified by the Wasserstein metric (W). Figure 7B shows the pairwise difference matrix of the ρ distribution ("distance map") evaluated with W. The matrix is ​​divided into four quadrants, showing the differences between individuals within and between groups. Although this display highlights the huge difference in subject level, a slight increase in the difference has been noticed by comparing the two quadrants of the subjects in each group by visual inspection.

Structural characteristics of DG nuclei. (A) The violin plot of electron density ρ and heterogeneity s, reflecting the histogram of the selected characteristics of each individual. The color scheme refers to the ABC score from neuropathological staging. (B) Wasserstein metric W is calculated between any two patients and arranged in a matrix as a measure of the distance between the histograms, shown here as ρ. The gray dashed lines separate the groups. (C) Point cloud in feature space, here defined by two selected features, with two topics (left, AD group; right, CTRL group), (top) s and ρ and (bottom) v and ρ The example is explained. ρ. Each point corresponds to a neuron. The ellipsoid represents the result of PCA with a semi-axis defined main axis or equivalent to 1σ interval when fitting a two-dimensional Gaussian distribution to a point cloud.

In order to cope with the two major challenges of data, namely, the strong inter-discipline variability and the dispersion of neuron structural parameters of any single discipline, we adopted a strategy in which each individual is represented by a point cloud in a five-dimensional space of structural parameters , Denoted as feature space below. The motivation for the following point cloud analysis is that the structural differences between the corresponding classifications of the AD and CTRL groups are expected to be better revealed in higher dimensions. Please note that only for the special and extremely unlikely case where the point cloud distribution can be written as the decomposition (separation) product of the one-dimensional distribution, no information will be lost when each dimension is processed separately. A simple projection of the two-dimensional subspace, as shown in Figure 7C, shows that the point cloud will not separate (decompose) because the structural parameters are weakly correlated.

As described above, the point cloud representing the granular cell population of each subject is further analyzed in the five-dimensional feature space. First, we standardize the point cloud of each dimension (feature) through the mean and standard variation of the population (ie, the union of all sample point clouds). Standardized variables are represented by their respective capital letters (P, S, V, Φ, NN). Then, the point cloud of each subject is approximated by a Gaussian distribution, and the mean and covariance matrix are given by the empirical mean and covariance matrix of the point cloud. This distribution can be conceptualized as an ellipsoid, centered on the average, the direction of the principal axis is given by the eigenbase of the covariance matrix, and their length is given by the square root of the corresponding eigenvalue. By combining the Bures metric (28) on the covariance matrix with the Euclidean distance on the average, the natural metric on the Gaussian distribution set can be obtained. This produces the L2 OT distance between two Gaussian distributions (29), denoted by W, which has recently become more and more popular in data analysis applications (29, 30).

Figure 8 reports the point cloud analysis and the corresponding classification in the feature space. In Figure 8A, the 2D projection of the Gaussian distribution is visualized as an ellipsoid. In Figure 8A, the left is the AD group (orange-red), and the right is the CTRL group (green) in Figure 8A. The distribution in the V/P plane (Figure 8A, top) and S/P plane (Figure 8A, bottom) shows that the AD group has greater diversity than the CTRL group. The visualization of the ellipsoid in 2D is also used to illustrate the optimal transportation cost: for example, the ellipsoids representing patients 15 and 19 are very different, which is reflected in W=0.86 (V/P plane) and W=0.74 (S/P plane) ,respectively. Conversely, patients 15 and 12 were closer, and were assessed as W=0.21 (V/P plane) and W=0.29 (S/P plane), respectively. The distance W between any two individuals is visualized in the matrix shown in Fig. 8B, which can be regarded as a distance map again, now considering the full five dimensions of the feature space. Darker colors indicate higher cost (distance), so the difference between the 5D ellipsoids of the corresponding objects is greater. Two patients are very prominent: Numbers 5 and 8, these are two AD cases in an advanced state (compared to the other subject, the ABC score is "high" and has a significantly high B score).

Multi-dimensional analysis, optimal transmission and classification. (A) The ellipsoid representation of the DG cell nucleus in the selected 2D subspace of the full 5D feature space. Shows the ellipsoids of 17 different subjects, (left) subjects with AD and no grouping and (right) CTRL, showing (top) volume V and electron density P and (bottom) electron density variance S and P. (B) Bures cost matrix diagram (distance diagram), each entry refers to the distance between each 5D ellipsoid. For the selected metric, each topic can be located in the topic space constructed by the ellipsoid. (C) The PCA in the appropriate tangent plane of the space produces a dominant component along which the variance between subjects is maximized. The PCA component represents a linear combination of different characteristics. The data points representing different objects are color-coded according to the Thal stage (top left triangle), Braak stage (bottom right triangle), and ABC score (frame), but this information is not used to construct the tangent space. (D) Linear SVM analysis applied to the four most important PCA components reveals a hyperplane separating the two components. (E) It is found that the evolution of the histogram according to the first PCA mode describes the change from a healthy state to a pathological state, indicating a "stereotyped transition" from CTRL (++) to AD (--) tissue. It is found that the histogram obtained by the (left) Gaussian approximation and (right) the complete calculation considering each element of the point cloud is very consistent.

The OT distance W can also be evaluated directly at the point cloud (29) level, making Gaussian approximation an optional intermediate step. For a complete point cloud, a distance map similar to that in Figure 8B can also be obtained. We perform follow-up analysis on the full point cloud and Gaussian approximation. Each topic can now be interpreted as a point in the "topic space" where the distance is measured by W (with or without Gaussian approximation). Although this space is not a linear vector space, it has a Riemannian manifold structure (intuitively, it is a curved hypersurface). The manifold can then be locally approximated by its tangent space at a suitable reference point (usually the Riemannian center of mass of the sample) (31). Therefore, we have obtained the topic embedding into the linear tangent space (where each individual is represented by a point, which in turn represents the point cloud or Gaussian distribution in the feature space), and we can now apply standard data analysis tools in it. Principal component analysis (PCA) can be used to identify the most dominant change mode (direction) in the subject point cloud (in the tangent space). Figure 8C shows the patient's coordinates relative to the two main PCA modes (pca1, pca2). It is important to note that the feature space and its low-dimensional (truncated) tangent space are realized without any prior classification. Instead, the difference in the data itself is used to identify the path of greatest change (pca1 mode). Based on the color code of the data points reflecting the ABC staging, we can already intuitively infer that this pathway also groups patients. In order to further quantify this point, classification is performed by linear support vector machine (SVM), as shown in Figure 8D, using the four main PCA modes, covering 92.4% or 88.7% of the data variance, in Gaussian approximation or point cloud, respectively . The normal vector of the separated hyperplane obtained by SVM can be interpreted as the main direction distinguishing CTRL and AD in the tangent space, which is only 15° different from the direction of the pca1 mode. For Gaussian approximation (Figure 8E, left) and point cloud (Figure 8E, right), Figure 8E shows the offset of the feature histogram corresponding to the direction of pca1, and the color indicates the offset from the CTRL group (green) to AD Group (red), in a continuous manner. The evolution of the histogram (disease progression) is very similar to Gaussian and point cloud analysis, and can be seen as a confirmation of validity and robustness. Therefore, we can now point out typical changes in the histogram of all features, as we move along the main axis, distinguishing pathology and control. These changes are (from physiology to pathology) 1) increase in density, 2) increase in heterogeneity, and 3) decrease in nuclear volume.

The above analysis shows that as the pathology progresses from CTRL to AD, DG cell nuclei become more compact (increased electron density, reduced volume) and exhibit higher heterogeneity (higher variance of electron density). These findings are revealed through a quantitative workflow, which can be summarized as follows: 1) PC-CT of well-controlled areas of the human brain, for a considerable number of individuals; 2) Automatic multi-neuron segmentation based on machine learning and structural feature extraction And classification; 3) create a "feature space" based on the characteristics of single cells and the neuron group of each individual (a point in the feature space corresponds to a cell, and a point cloud corresponds to a patient); and 4) based on the point cloud and its distance Construct the topic space, quantify it by OT theory, and then perform local linearization, PCA and SVM analysis. In the subject space, one point corresponds to one patient, and one point cloud corresponds to one group. The geometric analysis of each subject group shows that the dominant "pattern", which encodes the movement of cells in the feature space, may correspond to the progression from a physiological state to a pathological state. Since the complete OT analysis is numerically complex and relies on recent mathematical work, we also implemented a more conservative Gaussian approximation to the point cloud, which provides a fully established and numerically low-cost alternative to the comprehensive analysis . It is important that the Gaussian approximation is consistent with the point cloud findings, proving that the conclusion is robust to small changes in the point distribution. At the same time, Fig. 8E shows that when estimated on the point cloud, the prototype change of the heterogeneity S histogram tends to be asymmetrically distributed with strong AD. In particular, this distribution showed a higher heterogeneity value, suggesting a subpopulation of DG neurons related to pathology. In the Gaussian framework, this detail cannot be fully captured, but only appears as a widening of the histogram. This is a good example of the more complete description provided by OT on the full point cloud.

Next, we propose to explain these findings in the context of brain aging and AD. We must specifically address the increasing compactness and heterogeneity of the DG nucleus, and analyze it to determine it as the main marker of AD progression. Please note that OT can also detect changes in structural features, such as nuclear volume v, density ρ, or heterogeneity s, when the average parameter (ie, the average value of the patient's neuron population) does not change significantly between groups, such as Pass the at test test. This is because OT provides a measure of changes in the entire neuron population and therefore also takes into account changes in distribution, such as the widening observed in Figure 8E. The observed heterogeneity changes can be explained based on Figures 2D and E, where we can identify the typical structural pattern of heterochromatin as the main contribution to the electron density variance, which is the heterogeneity S. This identification is reasonable, because before quantizing P and S, the noise contribution of S is minimized by median filtering. s The attribution of heterochromatin patterns is also consistent with the study of chromosome conformation by soft X-ray absorption tomography (32). Therefore, it is reasonable to conclude that the heterogeneity is increased, that is, the ratio of heterochromatin to euchromatin is increased or more generally chromatin conformation changes. In fact, the percentage of DNA in the euchromatic state in AD is lower than in healthy tissues, as can be seen from the fractionation of DNA extracted from the brain after death (33). With PC-CT, subnuclear structures can be assessed at the single neuron level in a larger volume of human brain tissue without slicing or staining. At present, since chromatin organization is related to aging and dysregulation of genomic structure in AD brain tissue, the topic of nuclear structure and AD has attracted much attention (23). In addition, the nuclear origin of AD and the dominant role of nuclear tau and lamin have been pointed out (34). The specific contribution of the increased level of heterogeneity we observe here may also be due to the formation of different heterochromatic structures, called aging-associated heterochromatic foci (SAHF). SAHF was first reported to be used in senescent human fibroblasts (35) and was described as a subnuclear heterochromatin compartment, which may silence genes that promote cell cycle progression (36). Recently, the formation and aging of SAHF have also been discussed in neurons and glial cells to have a putative role in AD (37). Another factor of the observed heterogeneity may be that the nucleoplasmic reticulum interrupts the smooth nuclear surface through the tubular invagination of the nuclear membrane. It has been reported that significant expansion occurs in AD brain tissue (38), which is caused by neurodegeneration. Caused by lamina disease.

In view of the possible role in AD, after discussing the structure of nucleic acids, in view of the average structural parameters and their inter-subject variability, as well as the general situation in physiological conditions, we briefly introduce the DG and hippocampal structure. To this end, we evaluated the average neuron density ρ¯n, the local density fluctuation ζn as indicators of possible local defects, the average width of the DG band dDG, and the next neighbor distance dNN. Please note that dNN is quantified based on the reciprocal of the structural factor peak position, which is calculated based on the nuclear centroid position (SI appendix, method, short-range order of DG granular cells). The results are summarized in Table 1. Two observations are worth noting: First, compared with the nuclear structure, the overall spatial distribution of DG neurons in terms of density, density fluctuations and accumulation has no difference between the groups (AD and CTRL), but it is found that there are differences between subjects Significant differences. As a result of this research, we can now give an accurate number of human DG structure, especially its width dDG=32.8 μm, neuron density ρ¯n=2.32·105 1/mm3, and adjacent distance dNN = 14.29μm. In addition, we can quantify the inter-subject differences in these numbers. Define the structural polydispersity of the structural parameter p as P=Δp/p, we find that the width of the DG band has a surprisingly large value P=26%, and for the neuron density and adjacent distance, we have P=16% And P=7%, respectively.

Structural parameters of DG cell band: mean and standard deviation (All, AD, CTRL)

Finally, we briefly introduced the accessibility, scalability and possible translation of PC-CT. The capabilities of PC-CT have now been significantly enhanced in the quantity and quality of almost all synchrotron radiation (SR) sources in the world. The upgrade of the electronic storage ring and X-ray optics, combined with a dedicated beam line designed for fully automatic sample processing and automatic reconstruction, will significantly improve resolution, image quality and sample throughput. In addition, the current pandemic is promoting mailing and remote transmission time operations. At the same time, ongoing instrumental advancements have made the method at least partially converted from SR to compact laboratory μ-CT, compatible with clinical use, for example, in the neuropathology unit of the University Medical Center. Both of these developments require or at least significantly benefit from optimized PC-CT reconstruction, machine learning-based segmentation, and OT-based data analysis, as shown here.

With the approval of the ethics committee of the University of Göttingen Medical Center, human hippocampal tissue was extracted during routine autopsy. According to the routine clinical pathology protocol, autopsy anatomical blocks from 23 subjects were fixed with 10% paraformaldehyde, dehydrated and paraffin embedded (FFPE). The size of an FFPE block is approximately 2×3×0.3 cm3. Reference below. 20. Then we classify the subjects according to the ABC score, explain (A) β-amyloid plaque according to Thal stage (39), and according to Braak stage (19, 40) and (C) neuron of neuritis plaque Fibrous tangles are scored according to CERAD (Consortium that established the Alzheimer's Disease Registry) (41). Follow the reference again. 20. Subjects with "medium" or "high" probability of AD based on the composite ABC score are classified as AD (11/20 subjects; 2/11 subjects data set is excluded from the CB analysis, See the SI appendix, sample collection and preparation for details). Subjects with "no" or "low" probability of AD were classified as controls (7/20 subjects; 1/7 data sets were excluded from the CB analysis for the same reasons as above). For each subject analyzed in Outcome II: Geometric and Statistical Analysis, the neuropathological results are listed in Table S1 in the SI Appendix. Note that due to the scattered performance of the A, B, and C scores (subjects 12 and 13), 2/20 subjects were not assigned to any group. For PC-CT analysis, a 1 or 8 mm biopsy punch is then used to extract a cylindrical sample from the FFPE block and insert it into a polyimide tube.

The data provided in this work was recorded at the GINIX holographic imaging terminal station of the P10 undulator beamline, Petra III, DESY, Hamburg, Germany (42), with a photon energy of 8.0 or 13.8 keV, and the Si (111) selects the channel cutting unit Color device. In order to cover the cell structure in a wide range of length scales, from the entire hippocampus structure in the frontal plane to the ROI in the dentate gyrus with subcellular resolution, the multi-scale capabilities of this instrument (13), including three different optics Configuration. First, a large FOV up to about 8 mm is scanned in a beam focused by a Kirkpatrick-Bez (KB) mirror system, and then expanded by its divergence. This is represented as EB configuration. Secondly, after moving the mirror out of the beam path, scan the middle FOV up to about 1.5 mm in the PB configuration. Finally, composite optics using KB mirrors and X-ray WG (CB configuration) scanned small FOVs up to approximately 0.4 mm (10, 43) at the highest resolution. By adjusting the distance z 01 between the WG and the sample, two different voxel sizes px≃160 nm and px≃50 nm were selected in this configuration to provide further scaling. The SI appendix, the method further details the different configurations and parameters.

The projection is first corrected for empty beams and dark images, and recorded before and after tomography. The phase retrieval is performed by the linearized contrast transfer function (CTF) scheme or the nonlinear Tikhonov (NLT) algorithm (44). Both are very suitable for the holographic scheme of image formation corresponding to the small Fresnel number F=px2zeffλ≪1, the wavelength is λ, and the effective propagation distance zeff=z12/M. After phase retrieval of the projections, tomographic reconstruction is performed by filtered back projection (FBP) or cone beam (FDK; Feldkamp-Davis-Kress) algorithms, both of which are implemented in the ASTRA toolbox (45). After applying a 7-pixel Kaiser-Bessel window and half-position threshold, Fourier Shell Correlation (FSC) is used to determine the spatial resolution. Based on the image quality index, the 2/11 AD and 1/7 control CB datasets were excluded from the analysis to keep the segmentation quality of all datasets at a similar level. More detailed information is given in the SI Appendix, Methods.

For PB data, the Blobfinder tool of the segmentation and visualization package Arivis (Arivis AG) was used to segment the DG nuclei. The CB data was segmented using the interactive software package Ilastik (26), and further manual optimization was performed based on image filters and object removal based on visual control. These segmentations are used as the real input of machine learning based on Convolutional Neural Networks (CNN), implemented by deep learning V-net, which is a three-dimensional summary of U-net design (46), as detailed in the appendix, method, DG cell nucleus in SI Segmentation.

For the segmented DG cell nuclei, five features were selected for further analysis and calculation according to the segmentation mask of each individual: the median value of nuclear electron density ρ (on the DG neuron), and the normalized nuclear electron density variance s=σ2 /ρ¯ 2 (heterogeneity parameter), nuclear volume v, nuclear sphericity φ (shape parameter) and the number of neighbors nn with a radius of 13.5 μm, in the first and second coordination shells of the correlation function g(r) Choose a value between (10). The pairwise similarity (or equivalent distance) between the one-dimensional histograms (single foreach feature, Figure 7) is calculated using the Wasserstein metric W of order p = 2, as implemented in the reference. 47.

In the Gaussian approximation, each individual is represented by a normal distribution N(Σ, μ) with a covariance matrix Σ and a mean μ. The Bures measure between two covariance matrices is used in the reference. 28 Construct the best transmission graph between the multidimensional normal distributions fitted to the point cloud data. In addition to this Gaussian approximation, the optimal point cloud transmission plan is calculated using entropy regularization and Sinkhorn algorithm. The local linearization of the best transmission metric is performed as described in the reference. 31, including the approximate extraction of the best transmission map from the best transmission plan between two point clouds. In the Gaussian approximation, the best transmission centroid ("center of gravity") is used as a reference for linearization, which can be efficiently calculated using ref's fixed-point algorithm. 48 It also serves as the basis for sampling 104 points from the Gaussian distribution for point cloud analysis. Use ref's implementation for linear SVM classification. 49. The SI Appendix, Methods, Analysis Based on Optimal Transport gives complete details.

The CT reconstruction data has been stored in Zenodo DOI: 10.5281/zenodo.5658994 (50). All research data can be provided upon request.

We thank Michael Sprung, Markus Osterhoff and Bastian Hartmann for their support at GINIX and Thomas Jentschke and Jakob Frost for their help with segmentation. The German Research Foundation (DFG) (German Research Foundation) is grateful for the German Excellence Strategy-EXC 2067/1-390729940 Multiscale Bioimaging-and the support provided by the German Federal Ministry of Education and Research through Grant 05K19MG2 NeuroTomo. JF and CS recognize the funding of DFG (TRR274-1) and related clinician-scientist programs.

Author contribution: ME, CS and TS design research; ME, FvdM, JF and TS research; BS, OH and CS contributed new reagents/analysis tools; ME, BS and TS analysis data; ME and TS wrote Thesis; BS contributed expertise in optical transmission (OT) and designed OT analysis workflow; CS provided and supervised neuropathological evaluation and interpretation; and TS supervised X-ray imaging and data analysis.

The author declares no competing interests.

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