Materials and methods

Autopsy, clinical background and tissue preparation
In total we investigated six postmortem lung samples from Covid-19 patients (Menter et al., 2020). A tissue micro-array paraffin block with samples of all six patients and the corresponding HE stain is shown in Figure 1a. Information about age, gender, hospitalization, clinical, radiological and histological characteristics of all patients are shown in Table 2. All patients suffered from hypertension and were treated with RAAS (renin-angiotensin-aldosterone-system) interacting drugs. Heterogeneous ground glass and consolidation were observed in all patients clinical CT scans and the cause of death was also related to respiratory failure in each patient (patient IV cardio-respiratory failure). Additionally, tumor-free lung samples from partial resections of pulmonary carcinomas were analyzed as a reference.
Table 2.  Sample and medical information.
Age and gender, clinical presentation with hospitalization and treatment; NIV: non-invasive ventilation, I: immunosuppression, S: smoker, GGO: ground-glass opacification, C: consolidation, DAD: diffuse alveolar damage.
Sample no.  Age group, gender  Hospitalization, clinical, radiological, and histological characteristics
I  60–70, F  5-10d, GGO, DAD
II  80–90, M  5-10d, C, I, DAD
III  90–100, M  1-4d, GGO, C, DAD
IV  70–80, M  1-4d, NIV, S, GGO, C, DAD
V  60–70, M  5-10d, NIV, S, GGO, C, DAD
VI  70–80, M  1-4d, S, GGO, C, DAD
CTRL  20–30, M  - From each of the six Covid-19 patients, two tissue samples with edge lengths of about 4 mm each were analyzed. To one sample of each patient, a metal containing stain (uranium acetate, UA) was applied, the other samples remained unstained. Separated for their stain, six tissue samples were dehydrated and embedded in the same multi-sample paraffin block. The size of the postmortem tissue samples made available for the study varied between the different patients (I-VI), with maximum cross-section of about 4 mm after dehydration. From all six samples, biopsy punches were taken by either a 8 mm or a 3.5 mm punch, depending on the individual size. The punches were then transferred onto a holder for the parallel-beam local tomography acquisition, followed by a further reduction in size (after measurement of the entire sample) to a 1 mm biopsy punch, for further tomographic recordings. A sketch of the sample preparation is shown in Figure 1b. The control lung sample was first mounted in an Eppendorf tube for parallel beam acquisitions, and a 1 mm biopsy punch was then transferred into a polyimide tube similar to the paraffin-embedded ones, but scanned in fixative buffer solution.

Phase contrast tomography
For Covid-19 lung tissue, the scans were recorded at the GINIX endstation of the PETRA III storage ring (DESY, Hamburg). The projections were acquired at two different photon energies Eph, 8⁢keV and 13.8⁢keV, using the first and third harmonic of the 5 m P10 undulator and a Si(111) channel-cut monochromator, respectively. Data are shown here only for 8⁢keV, which gave highest contrast for the unstained lung tissue. Two tomography configurations were combined to cover a larger range of length scales:

(1–parallel beam)
Recordings with the unfocused quasi-parallel beam illumination and a high resolution microscope detection system, resulting in in a FOV of 1.6 mm sampled at a pixel size of 650 nm.

(2–cone beam)
Holographic recordings with the divergent and coherence filtered beam emanating from a compound focusing system composed of a Kirkpatrick-Baez (KB) mirrors system and an x-ray waveguide, resulting in a FOV of 0.4 mm sampled at a pixel size of about 167 nm (depending on exact geometry).
Both configurations were implemented side-by-side, using the same fully-motorized tomography stage and mounting, as detailed in Frohn et al., 2020. A sketch of both configurations is shown in Figure 1 . First, parallel-beam overview scans were acquired of the entire tissue volume embedded in paraffin. To this end a 3.5 mm biopsy punch was taken from the multi-sample tissue block, and then scanned in a stitching-mode yielding a large overview reconstruction, composed of up to 20 individual tomograms (depending on tissue size). To increase image quality and avoid artifacts related to region-of-interest (ROI) or local tomography, a selected 1 mm punch was then taken from the already scanned larger tissue cylinder, and re-scanned, first in the parallel- and then the cone-beam geometry. Experimental and acquisition parameters used for the data shown are listed in Table 3.
Table 3.  Data acquisition parameters for x-ray phase-contrast tomography measurements.
Cone geometry  Parallel geometry
FOV  0.4 mm × 0.35 mm  1.6 mm × 1.4 mm
Pixel size  167 nm  650 nm
z 01  125 mm  -
z 12  4975 mm  10 mm − 100 mm
Regime  holographic  direct contrast
Rotation  start-stop  continuous
Exposure  2 s  0.035  ⁢ s
Total exposure  ≃ 63  m i n  ≃ 75  s
Volumetric flowrate  1.16 × 10 4   μ m /   3  s  3.75 × 10 7   μ m /   3  s The configuration for (1–parallel beam) is depicted in Figure 1c. The high-resolution microscope detection system (Optique Peter, France) was based on a 50⁢μ⁢m thick LuAG:Ce scintillator imaged with a 10× magnifying microscope objective onto a sCMOS sensor (pco.edge 5.5, PCO, Germany), resulting in an effective pixel size of 0.65⁢μ⁢m. The high photon flux density allowed for image acquisition with continuous motor movement, short acquisition time of 35 ms per frame, and a framerate of 20 fps. Single-distance tomogram recordings with about 1500 projections, and flat images before and after the scan, took less than 2 min. For these scans, the focusing optics (KB-mirrors and waveguide) as well as the fastshutter (Cedrat technologies) were moved out of the beam, and beam size was adjusted by the upstream slit systems. To avoid detector saturation, the beam was attenuated by 4× single crystal silicon wafers.
The configuration for (2–cone beam) is depicted in Figure 1d: The beam was focused by the KB-mirrors to about 300 nm. To further reduce the secondary source size, to increase coherence, and to achieve a smooth wavefront for holographic illumination, an x-ray waveguide formed by 1 mm long lithographic channels in silicon with a cross-section of about 100 nm was positioned in the focal plane of the KB-mirrors, resulting in an exit flux of 1–4⋅109 photon/s (depending on alignment and storage ring), as measured with the single photon counting detector (Pilatus, Dectris). The sample was positioned at variable (defocus) distances behind the focus (waveguide exit), typically z01=125mm for the first distance. The geometrically magnified holograms were recorded by a fibre-coupled sCMOS sensor (Zyla HF 5.5 detector, Andor Technologies) with a customized 15⁢μ⁢m thick Gadox scintillator, and 6.5⁢μ⁢m pixel size. The detector position at about z02=5100mm behind the focus resulted in a magnification of about M=41 (for the first defocus distance), and hence an effective pixel size of 167 nm. 1442 projections were recorded, with a typical exposure time of 2 s per projection.

Phase retrieval, image reconstruction, and segmentation

Phase retrieval and reconstruction
Phase retrieval was performed from dark and empty beam corrected holograms, using both linearised single step CTF-approach (Cloetens et al., 1999; Turner et al., 2004), and non-linear generalizations of the CTF-method based on Tikhonov regularization (NL-CTF), using our code package HoloTomoToolbox as described and deposited (Lohse et al., 2020). Importantly, both CTF and NL-CTF implementations can be augmented by imposing support and range constraints, when needed. When available, projections recorded at several defocus distances were first aligned with sub-pixel accuracy and then used for multi-distance phase retrieval. For these purposes, the HoloTomoToolbox provides auxiliary functions, which also help to refine the Fresnel number or to correct for drift in the illumination function. After phase reconstruction of all projections, the tomographic reconstruction was carried out with the MATLAB implemented iradon-function (Ram-Lak filter) for the parallel geometry and with the FDK-function of the ASTRA toolbox (van Aarle et al., 2015; van Aarle et al., 2016) for the cone beam geometry. Hot pixel and detector sensitivity variations as well as strong phase features in the parallel beam illumination resulting from upstream window materials, which persist after empty beam correction, can all result in ring artifacts in the tomographic reconstruction, in particular as these flaws can increase by phase retrieval. To correct for this, the extra information provided by 360° scans was used to mask out the corresponding pixels and replace them with values of the opposing projection. Stitching of reconstructions from different tomographic scans was performed using (Miettinen et al., 2019). Resolution estimates were obtained by FSC analysis, see Appendix 2.

Image segmentation and quantification
For each patient the stitched overview scans were analyzed with regard to structural characteristics. The 3D-reconstructions were first binned (2 × 2 × 2), and the tissue was then segmented from the surrounding paraffin using the segmentation software Ilastik (Berg et al., 2019), which was then further refined with MATLAB. In order to exclude single macrophages or detached tissue, only voxels connected to the tissue block were considered for the distance map. Further, the areas of the paraffin which represent air compartments were linked to the outside of the tissue block. Individual self-contained areas of paraffin (not connected to air) were excluded from the mask. Based on this segmentation, the distance to the nearest voxel containing oxygen was calculated for each tissue voxel. The tissue volume V is given by the sum of all voxels containing tissue. The surface area SA is defined by all tissue voxels with a distance of 1 pixel to the air. From this information we calculated the specific surface(2) SV=SA/Vwith S⁢A/V surface area volume -ratio. Further a characteristic length(3) Lc=V/SA⋅vxwith v⁢x edge length of a voxel was determined for each sample. Additionally, the mean distance (dO2¯) from all tissue voxels to the closest air compartment and its standard deviation was calculated.
Hyaline membranes and capillary networks were extracted using semi-manual segmentation functions in Avizo (Thermo Fisher Scientific, USA). Beside hyaline membranes and the capillary network, different cell types can be readily identified based on the 3D reconstructions of the electron density. In particular, inflammatory cell subpopulations - that is, macrophages and lymphocytes - can be distinguished. To this end, an automatic and parameter-controlled algorithm denoted as BlobFinder was used (arivis AG, Germany). Based on its segmentation output, the amount and position of the lymphocytes in the 3D-reconstructions from parallel beam scans was calculated. The algorithm is able to identify roundish structures with a given size. For the segmentation of the lymphocytes, we chose a characteristic size of 6.5⁢μ⁢m. The structures identified in this step also include macrophages and parts of the capillary system. For the unbinned datasets, a distinction between lymphocytes and the nuclei of the macrophages was made based on the difference in electron density. In the tomographic reconstructions, the lymphocytes appear denser compared to the nuclei of the macrophages. Further, nuclei from endothelial cells and parts of the capillaries filled with blood residues were excluded based on their elongated shape. Only structures with a sphericity higher than 0.55 were included. Based on the segmentation of lymphocytes, the total number of lymphocytes Nl was obtained and the mean concentration of lymphocytes within the lung tissue cl=Nl/V was estimated.