3D virtual histology of human pancreatic tissue by multiscale phase-contrast X-ray tomography

This paper presents propagation-based phase-contrast tomography in two configurations at the beamline endstation GINIX, demonstrated on the application of 1 mm human pancreatic tumor tissue biopsies.

A multiscale three-dimensional (3D) virtual histology approach is presented, based on two configurations of propagation phase-contrast X-ray tomography, which have been implemented in close proximity at the GINIX endstation at the beamline P10/PETRA III (DESY, Hamburg, Germany). This enables the 3D reconstruction of characteristic morphological features of human pancreatic normal and tumor tissue, as obtained from cancer surgery, first in the form of a large-scale overview by parallel-beam illumination, followed by a zoom into a region-of-interest based on zoom tomography using a Kirkpatrick-Baez mirror with additional waveguide optics. To this end 1 mm punch biopsies of the tissue were taken. In the parallel tomography, a volumetric throughput on the order of 0.01 mm 3 s À1 was achieved, while maintaining the ability to segment isolated cells. With a continuous rotation during the scan, a total acquisition time of less than 2 min was required for a full tomographic scan. Using the combination of both setups, islets of Langerhans, a three-dimensional cluster of cells in the endocrine part of the pancreas, could be located. Cells in such an islet were segmented and visualized in 3D. Further, morphological alterations of tumorous

Introduction
The potential of propagation-based X-ray phase-contrast tomography for three-dimensional (3D) virtual histology has been pointed out by a number of recent studies (Saccomano et al., 2018;Tö pperwien et al., 2018;Khimchenko et al., 2016;Albers et al., 2018;Dejea et al., 2019;Ding et al., 2019;De Clercq et al., 2019;Strotton et al., 2018;Mei et al., 2020). Notably, 3D virtual histology by phase-contrast X-ray tomography is able to extend classical histological two-dimensional (2D) approaches, which are based on thin sections and light microscopy, into a full 3D visualization with isotropic resolution and without destructive slicing of the specimen. The interaction of X-rays with the object is described by the continuous complex-valued index of reflection nðrÞ = 1 À ðrÞ þ iðrÞ. The particular advantage of phase contrast for low-absorbing materials such as biological tissue derives from the fact that for X-ray energies of 10 keV to 100 keV the absorptive component is orders of magnitude smaller than ISSN 1600-5775 the refractive component (Nugent, 2010). Contrast is formed by transformation of the phase shifts into measurable intensity variations by self-interference of the exit wave during freespace propagation between sample and detector (Paganin & Nugent, 1998;Cloetens et al., 1999a). By careful optimization of photon energy, illumination function, and phase-retrieval algorithms, the phase sensitivity suffices to probe also the intrinsic electron density variations of unstained tissue, for example tissue embedded in paraffin, ethanol, or even aqueous buffer (Tö pperwien et al., 2019). Compared with other full-field phase-contrast techniques, e.g. based on conventional grating interferometry or analyzer crystals, propagation-based imaging (PBI) can reach a resolution below optical microscopy (Khimchenko et al., 2018).
Apart from non-destructiveness, isotropic resolution, quantitative and label-free contrast mechanisms, PBI has also a particular potential for achieving high volume throughput and for visualizing histological structure on multiple length scales. However, to bring this to reality, particular instrumentation and optical settings are required, as we explore and demonstrate in this work. Generally, synchrotron endstations are used for PBI in only one of two different configurations: (i) parallel-beam tomography, covering a large field of view (FOV), with resolution limited by the detector pixel size, e.g. the endstation ID19 of the European Synchrotron Radiation Facility (ESRF) (Weitkamp et al., 2010) or the endstation TOMCAT of the Swiss Light Source (SLS) (Stampanoni et al., 2007;Marone et al., 2011), and (ii) cone-beam geometry, acquiring high-resolution tomograms with voxel sizes in the range 20 nm to 300 nm (Cloetens et al., 1999a;Mokso et al., 2007;Bartels et al., 2015), based on the geometrical magnification of the pixel size. This regime is typically characterized by small Fresnel numbers F, in the so-called holographic regime, where phase sensitivity is particularly high but phase retrieval can sometimes become a challenge (Lohse et al., 2020). Beamline endstations running in this configuration are for example ID16a at ESRF (Da Silva et al., 2017) or the GINIX endstation at PETRA III. A voxel size below 50 nm can easily be achieved by adjustment of the defocus distance Krenkel et al., 2017;Tö pperwien et al., 2017a). Although both configurations had been run in a multiscale scheme [parallel beam (Dejea et al., 2019) and cone beam ], to our knowledge this is the first time that both configurations have been combined for a multiscale approach.
The goal of the present work is threefold: First, we want to demonstrate how PBI can be carried out on the same instrument in parallel-and cone-beam setting, in such a way that different scales of the same sample can be investigated in close temporal and spatial proximity during the same beam time. Second, we want to demonstrate high volumetric flow rate (volume throughput) on the order of 0.01 mm 3 s À1 with submicrometre pixel size and maintaining the ability to segment single cells. Third, we want to apply 3D virtual histology to human biopsies taken from surgery with the goal of extending conventional histopathology to full 3D and quantitative image analyis.
A full 3D imaging and automated digital pathology could provide new insights into patho-mechanisms and etiology of diseases. It may also serve for improved diagnosis, e.g. for subclassification of tumors thereby supporting clinical decisions. Even if future pathology applications might preferably be based on advanced laboratory micro-computed tomography (m-CT) instrumentation for reasons of accessibility, one would probably still need synchrotron PBI for comparison and verification.
In this spirit, our group has previously shown that post mortem analysis of human tissue autopsies can be carried out at a liquid-anode m-CT instrument, but required ground truth verification of segmentation parameters by synchrotron radiation (Tö pperwien et al., 2018).
As proof-of-concept for this multiscale histology approach, we choose tissue biopsies of human pancreatic cancer tissue (Kamisawa et al., 2016). Pancreatic cancer is the fourth leading cause of cancer death and has the lowest five-year relative survival rate of all cancer types, for example (9%) in the USA (Siegel et al., 2019). The most common pancreatic tumor, pancreatic ductal adenocarcinoma (PDAC), accounts for about 90% of the cases and is characterized by an invasive mucin-producing neoplasm of epthelial origin that causes an intense stromal desmoplastic reaction (Hruban, 2010). Morphologic criteria such as irregular arrangement of tubular glands, embedded in desmoplastic stroma, and signs of inflammation are characteristic features identified by conventional histology thereby helping to diagnose PDAC (Haeberle & Esposito, 2019). Since conventional histology requires slicing of the sample with several micrometre thickness, the 3D resolution perpendicular to the slice direction is limited by the slice thickness. 3D virtual histology can overcome this limitation and can hence probe the morphology more completely and at higher resolution Khimchenko et al., 2016Khimchenko et al., , 2018. Finally, automated image segmentation and analysis enable to interrogate and to classify the 3D reconstructed volume.
Below, we first detail the instrumentation and optics of the cone-and parallel-beam configuration in Sections 2 and 3. Details on sample preparation and experimental workflow are given in Section 4. Section 5 presents the multiscale tomography results, before the paper closes with conclusions and outlook in Section 6.

GINIX -setups
Experiments were carried out at the holotomography endstation GINIX, installed at the P10 beamline at PETRA III located at DESY . By tuning the 5 m undulator, the instrument can be operated in an X-ray energy range between 6 keV (first harmonic) and 15 keV (third harmonic). The beam is monochromated by either a channel-cut or a double-crystal monochromator [both Si(111)]. Here, two tomography configurations were combined to extend the range of length scales covered, one based on cone-beam the other on parallel-beam illumination. They were implemented in a side-by-side fashion, using the same research papers tomographic stage and mounting. Experimental parameters used in this work are listed in Table 1 for both configurations. Here we used 13.8 keV in the cone-beam configuration, and 8 keV in the parallel-beam configuration for samples with a thickness (d 1 mm). In both cases, the channel-cut monochromator was used to achieve high pointing stability.
Nanoscale tomography in cone-beam geometry, which is the standard use of the endstation, was carried out with a maximum FOV of 0.4 mm (h) Â 0.35 mm (v) and an effective pixel size of 167 nm. The acquisition time for a single projection was 1 s. A single distance recording of 1500 projections including 100 empty beam images and 20 dark images took 42 min. The parallel beam configuration covered a 16 times larger FOV (1.6 mm Â 1.4 mm) with an effective pixel size of 650 nm. The acquisition time for a single image was 35 ms. Both configurations and the corresponding empty beam images are shown in Fig. 1.
The configuration for the cone-beam geometry is detailed in Fig. 1(a, top): A pair of Kirkpatrick-Baez (KB) mirrors was used to focus the beam down to about 300 nm Â 300 nm. To increase the spatial coherence and to filter the wavefront, an X-ray waveguide was placed in the focal plane of the KB mirrors. Between the KB mirrors and the waveguide, a 1 mm aperture in tungsten was used to block the remaining nonreflected primary beam as well as the single reflected beams. For 13.8 keV, a germanium waveguide was used with 200 mm optical depth and a channel diameter of 100 nm. Images were acquired with a Zyla HF 5.5 detector (Andor, USA) with a customized 15 mm-thick Gadox scintillator on a fiber optic plate coupled to a sCMOS chip with a 1:1 coupling and a pixel size of 6.5 mm. A detector point spread function of $ 2.0 pixels was determined at 10% of the detector modulation transfer function, measured at an inhouse setup. The detector was placed at a distance of x 02 = 5100 mm behind the waveguide exit. Tomograms were acquired at several distances (Zabler et al., 2005), starting with waveguide-tosample distance x 01 = 125 mm, corresponding to a magnification factor M = ðx 01 þ x 12 Þ=x 01 = 40.8, and an effective pixel size of 167 nm. A typical waveguide empty beam image is shown in Fig. 1(b). It exhibits a smooth far-field diffraction pattern with only a few contributing modes, and a particularly high photon flux of 5 Â 10 9 photon s À1 .
The parallel-beam configuration is depicted in Fig. 1(a, bottom). Here, the high beam intensity in the sample plane enables fast tomographic scans with continuous motor movement. For this purpose, the sCMOS camera pco.edge 5.5 was used, which is able to acquire with maximum frame rate of 100 Hz for rolling shutter and fast scan mode. The camera was mounted on an Optique Peter system with a 50 mm-thick LuAG:Ce scintillator and a 10Â magnifying microscope objective, resulting in an effective pixel size of 0.65 mm. Since the fastshutter (Cedrat technologies) movement was still too slow for the short acquisition time of 35 ms, it was removed together with the focusing elements, i.e. KB mirrors and waveguide, by moving these components out of the beam. To maximize the beam size for a larger FOV the upstream slits were opened to a size of 2 mm Â 2 mm. To prevent scintillator damages due to the beam intensity, even if only minor changes in the sensitivity, the beam was attenuated   by 100 mm (4 times 25 mm) single-crystal silicon attenuator foils for 8 keV and 600 mm (24 times 25 mm) silicon attenuator foils for 13.8 keV. An example flat-feld image with 35 ms exposure time for 13.8 keV is shown in Fig. 1(c). When changing between both geometries, the tomographic stage was adjusted accordingly (lookup table), since the KB mirrors reflect the X-ray beam at an angle of 8 mrad in the y-and z-direction.

Data acquisition parallel beam setup
Parallel-beam illumination with undulator radiation allows for short exposure times on the order of a few milliseconds. A step-wise rotation scan with acceleration, movement, deceleration, and settle times would result in an overhead of up to one order of magnitude in 'wasted' time. To adapt actual scanning speed to the true exposure time, a continuously rotating setup with burst-mode acquisitions [i.e. acquisitions to the solid-state drive (SSD) of the camera PC] by the detector was therefore implemented. In a first configuration, full tomograms consisting of 1500 projections within 180 were measured in less than two minutes (including setup time, residual motor overhead, and rotating back). In addition to the scan, empty beam and dark field acquisitions were recorded after the scan (500 flat images and 500 dark images). Although the pco.edge camera is capable of 100 Hz acquisition rate, we limited the rate to 20 Hz, corresponding to an exposure period of 35 ms and a read-out time of 15 ms. The camera was operated in external trigger mode. Tests showed that at this rate the read-out is reliable. The control and trigger system is sketched in Fig. 2(a).
Since the highly brilliant PETRA III parallel beam easily saturates the detector in less than 1 ms, attenuator foils needed to be deployed in order to achieve exposure times of 35 ms. Hence, significant further progress can be expected by detectors with internal frame-buffering and multi-kHz framerates. This can already routinely be reached by hybrid pixel detectors such as EIGER X 4M (Dectris, Baden-Daettwil, Switzerland) or Lambda (Pennicard et al., 2012), but not by detectors with small pixel sizes, as required for parallel-beam tomography. For an accurate timing, the external trigger mode of the pco.edge was connected to an arbitrary function generator (TG4001 by Aim TTi, Huntingdon, UK), which provided 1500 TTL pulses of 35 ms duration at a rate of 50 ms, i.e. 20 Hz. Both incoming pulses and the frame clock of the detector were monitored by an oscilloscope (RTB 2004 by Rohde & Schwarz, Munich, Germany). Crucial for the success of a continuous tomography is a precise movement of the rotational axis. Within this work, the accurate position (i.e. absolute angle) is not of interest, but the spacing given by the angular velocity and frame rate has to be constant. Therefore, the analog encoder output signals of the Micos UPR 160-AIR (PI miCos, Eschbach, Germany) stage, which is controlled by a Micos Taurus unit, were fed into the oscilloscope as well. The UPR uses an incremental rotary encoder 'RIK' (Numerik Jena, Jena, Germany; miCos alias: 'AE-051'), with 9000 steps per revolution, and delivers a 1/V pp sin/cos signal to the Taurus controller. One encoder step corresponds to a rotation by 0.04 ; hence, one projection of the tomograms corresponds to three full encoder steps. Note that the sin/cos signal allows for an interpolation by a factor of 100; in fact, the measurement accuracy is stated to be 0.0004 , which coincides with the manufacturer specifications. Typical encoder signals including the trigger signal are shown in Fig. 2(b), here for a run of 1500 projections separated by 0.12 at 20 Hz. From the sin/cos encoder values, the current angular position can be obtained by taking the arctangent and unwrapping the data; Fig. 2(c) shows the values for one continuous tomogram; the shaded area highlights the actual measurement range.
Before conducting the tomographic scans, the angular movements of the UPR were measured for different velocities, and the linearity (constant rotational speed) was quantified. The data show that the acceleration phase was usually shorter than 1 s; with a safety margin of 100%, the trigger train to the   pco.edge started 2 s after the movement of the rotation stage (UPR) was initiated. Note that the stage was commanded to perform a rotation of 210 , although the tomograms consist only of 180 within 30 s. In this way, the angular acceleration and deceleration phase was separated from the phase with linear rotation speed, where data were recorded. For the rotation back to 0 , the velocity was increased to about 210 / 2.1 s. Comparison of encoder positions and nominal positions yielded a linearity of 2 Â 10 À5 (deviation of the slope when fitting measured versus nominal angle between). During rotation, the encoder values showed a sawtooth-like ripple of less than 0.006 at a frequency of about 60 Hz; see the inset in Fig. 2(c). Since this is not visible in the steady-state, we attributed this to the stage's closed-loop operation; since the amplitude is smaller than 1/20 of the per-frame movement, it is of no concern for the data shown here.

Sample preparation and workflow
The sample preparation and the workflow for the 3D virtual histology of two human PDAC tissues by X-ray phase-contrast tomography was divided into the following steps, illustrated in Fig. 3(a). (i) Surgery: the tumorous pancreatic tissue of two different patients was removed by pancreatic cancer surgeries. (ii) Sectioning: a small piece with a size of a few millimetres was sectioned from both removed tissues (Ethics statement: Nr. 5/10/17 UMG Goettingen). (iii) Fixation and staining: one sample (Sample A) was fixated in 4% Formalin without additional staining, while the other sample (Sample B) was fixated and stained in a phosphotungstic acid (PTA) staining solution as described before by Missbach-Guentner et al. (2018). Note that one of the technical goals in this study was to investigate how staining affects image quality and contrast and whether it is required in order to detect the morphological features. (iv) Paraffin embedding: the tissue samples were dehydrated in an ethanol series and then embedded in paraffin. (v) Inhouse m-CT: tomograms of the tissue samples within the paraffin blocks were acquired at our home-built X-ray laboratory phase-contrast m-CT instrument to obtain a 3D volume of the entire tissue pieces before further destructive preparation steps. The instrument was equipped with a liquid-metal anode (JXS D2, Excillum, Sweden), a tomographic sample tower (SmarAct, Germany) and a flatpanel detector (1512 CMOS Detector, PerkinElmer, USA) (Tö pperwien et al., 2017b). Based on the geometrical magnification in a cone-beam geometry the effective pixel size was adjusted to 5.3 mm. The shape of the entire PTA stained sample (Sample B) is illustrated in Fig. 3(b) as a volume rendering. A virtual slice through the reconstructed volume indicated by the black dashed square is shown in Fig. 3   stained with H&E (hematoxylin and eosin). Notable morphological features of the tumor were defined. An image of the histology slice corresponding to the virtual slice from the inhouse m-CT is shown in Fig. 3(d). Both images represented the tissue morphology with comparable quality. (vii) Punch biopsies: to fit into the detector FOV at the synchrotron setup and to decrease the X-ray absorption of the sample, 1 mm punch biopsies were taken from the samples by using a needle of 1 mm diameter (biopsy punch, Integra Miltex, Germany). The choice of the punch biopsies (red circle) was made based on the histology slice in Fig. 3(d), aiming for specific structures of pathologically relevance. The punch biopsies were inserted into a polyimide tube of 1 mm diameter and mounted on respective brass pins. (viii) Synchrotron CT: tomograms of both punch biopsies were recorded at the synchrotron endstation GINIX. Results and findings are discussed in the next section in detail. (ix) Validation by 2D histology: to confirm morphological structures visible in the synchrotron tomograms, tissue sections of 2.5 mm thickness were taken at controlled height positions of the punch biopsies, after recording the tomograms.

Phase-contrast formation and retrieval
For propagation-based phasecontrast, interference effects and hence contrast is governed by the unitless Fresnel number F = p 2 eff =ðx eff Þ, where denotes wavelength, p eff the effective pixel size, and x eff the effective propagation distance. The two setup configurations cover different regimes, as illustrated in Fig. 4. The parallel-beam configuration yields data in the so-called direct-contact regime (F ' 1). Here, the phase-contrast is visible in the recorded images in the form of edge enhancement. This effect intensifies with increasing propagation distances, visualized in Fig. 4(a). The cone-beam geometry at high geometric magnification yields data in the holographic regime (F ( 1), visible in the form of multiple overlaying interference fringes. An empty-beam corrected image is shown in Fig. 4(b). The power spectral densities (PSDs) for the five propagation distances (four parallel + one cone) are plotted in Fig. 4(c). Larger propagation distances led to more oscillations in the PSD. The shape is well described by the sin-weighted phase term of the contrast transfer function (CTF) (Cloetens et al., 1999b;Zabler et al., 2005) For this reason, phase retrieval was performed with the singlestep CTF approach (Turner et al., 2004), The reconstructed phase of the holographic projection Fig. 4(b) is shown in Fig. 4(d). Phase retrieval was performed for all projections based on H olotomotoolbox (Lohse et al., 2020). After the phase retrieval for the entire set of projections, the tomographic reconstruction was performed 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., 2015Aarle et al., , 2016 for the conebeam geometry. Tomograms were reconstructed from 1500 projections over 180 for both cone and parallel beam. Ring artifact correction according to the method of Ketcham (2006) was performed on every tomogram.

Virtual histology
Two samples of human pancreatic cancer tissue, originating from different patients, were investigated. Sample A repre-   sents an unstained 1 mm punch biopsy taken from putative healthy tissue. Heavy metal staining often increases the image contrast in conventional X-ray imaging based on absorption.
To check the image contrast of a stained sample in the context of the present phase-contrast tomography, Sample B was a PTA stained 1 mm punch biopsy, consisting mainly of tumor tissue. Four different tomograms were acquired, including one tomogram in the parallel-beam configuration and one in the cone-beam configuration for both samples, respectively. The image quality was evaluated and morphological features were assessed, and compared with conventional 2D histology, illustrated in Fig. 5. An example slice in the xy-plane for virtual histology of Sample A, obtained using the parallel-beam configuration with 10 mm propagation distance, is shown in Fig. 5(a). The pancreatic tumor tissue is surrounded by the polyimide tube (black) and did not fill the entire tube, since there was an air-filled gap between tissue and tube in the bottom right. Contrast of the reconstruction was sufficient to investigate the morphology of the tissue. Here, we focused on a cluster of specific cells within the normal pancreatic tissue, the islet of Langerhans, which is a distinct shaped accumulation of endocrine cells, located within the exocrine pancreatic parenchyma, responsible for the endocrine function of the pancreas. The most common islet cell, the beta cell, produces insulin, the primary hormone regulating glucose metabolism. A representative islet of Langerhans is located in the red marked area in Fig. 5(a). Figure 5(b) shows approximately the same slice (adjusted by hand), presented as an image of an H&E stained section obtained by routine histology after the tomographic acquisition. The image corresponds to the blue marked area in Fig. 5(a). Comparative inspection, as illustrated in Fig. 5(c), revealed that both slices show the same morphology. Slight differences of shapes of the structures, i.e. the bright duct at the middle of the right side, and of the image contrast, i.e. the dark surrounding at the top left of the X-ray image, were visible. Minor shape differences can be explained by the fact that both slices are only approximately identical, as well as by deformations induced during sectioning and staining. Contrast differences could result from the structure specific H&E staining in the histological image compared with the unstained sample in the X-ray image. The H&E staining confirmed that the cluster of cells in the central [ Fig. 5(a), marked red area] is an islet of Langerhans. Figure 5(d) visualizes the entire 3D dataset of Sample A as a volume rendering. The dataset covers a volume of 3.888 mm 3 in total. The virtual slice of Fig. 5(a) is included, and the volume of the high-resolution scan is indicated by the red cube with a volume of 0.035 mm 3 . Note, however, that the drawing is intended to illustrate a comparison of reconstruction volume size -the positions of the high-resolution slices shown in the following below may not coincide. The cylindrical shape of the punch biopsy is clearly visible. The polyimide tube was masked out for the purpose of visualization. It was difficult to distinguish specific structures in the 3D rendered volume, due the homogeneous morphological structure of the sample. The paraffin-filled areas stand out from the surrounding as brighter blobs in this large-scale rendering, visible for example in the top region.
Next, the image quality of paralleland cone-beam setups was assessed by comparing the reconstructed slices of the same area of an islet of Langerhans for Sample A and Sample B, respectively, as illustrated in Fig. 6. A reconstructed slice of Sample A in the xyplane obtained from the parallel beam geometry is shown in Fig. 6(a). The image contrast is sufficient to identify the islet of Langerhans, which is marked by the dashed red line. The image of the same islet of Langerhans, obtained in the cone-beam geometry, is shown in Fig. 6(b). As expected, the resolution is higher (pixel size 167 nm) compared with the parallel beam reconstruction (pixel size 650 nm). Finer structures such as small collagen fibers from surrounding connective tissue at the top edge of the islet of Langerhans are visible in the cone-beam reconstruction.  In both images, the contrast is high enough to locate nuclei in some cells.
In order to increase the image contrast, we also recorded tomograms of the PTA stained punch biopsy (Sample B). The parallel-beam reconstruction is shown in Fig. 6(c). The entire islet of Langerhans as well as single-cell bodies were visualized with higher contrast compared with the unstained Sample A. Figure 6(d) shows the same slice (approximately, adjusted by hand) as Fig. 6(c), obtained with the cone-beam configuration. The difference in the resolution is highlighted by the insets. The resolution of the cone-beam reconstruction [ Fig. 6(d)] was sufficient to resolve single-cell nuclei, which were not visible in the parallel-beam reconstruction.
To quantify the resolution, the Fourier shell correlation (FSC) ( Van Heel & Schatz, 2005) was computed for the parallel-beam volumes, indicating a half period resolution of 0.90 mm for Sample A and 0.82 mm for Sample B.

3D properties of an islet of Langerhans
Next, we used the 3D dataset of Sample B, obtained in parallel-beam geometry, to analyze the shape of the islet of Langerhans in more detail, shown in Fig. 7. Since the resolution of the parallel-beam data was sufficient for segmentation of cells, and higher resolution with sub-cellular features can even be a source of complication for cell segmentation, we chose the parallelbeam dataset for this task.
The segmentation was performed using the software ilastik (Berg et al., 2019). Cells located inside the islet, shown in the reconstructed slice in Fig. 7(a), were segmented by interactively marking a few cells, followed by an automatic completion of the entire volume based on machine-learning algorithms. Figure 7(b) shows the same xy-slice of the segmented volume. Segmentation comprises three tissue classes: 1 = high gray-value stroma, 2 = low gray-value stroma, 3 = cells. The segmentation step was completed by a masking step, to exclude false positive cells outside the islet. Figure 7(c) shows a 3D rendering of all segmented cells located inside the islet.
The segmented volume was then further analyzed with Matlab. Cells were identified using the Matlab function bwconncomp(), which detects connected components in a binary image/volume. With an input parameter 'Connectivity' of 6, which takes the 6 nearest voxel into account, 1309 single cells were counted inside the islet of Langerhans without any corrections. Visual inspection shows that some segmentation components include more than one cell, due to a connection in the segmentation. To filter the connected cells out for the subsequent histograms, we introduced a volume threshold. Based on an estimated maximum cell size of 20 pixels (= 13 mm), all cells with a larger size in one of the x-, y-, z-directions were subjected to a veto, as illustrated in Fig. 7(d). The squares represent the boundary boxes of each segmented component in 3D. Green squares contain connected binary components below 20 pixel width and red squares comprise larger connected components within the volume. In this way, 139 objects were found to be too large. In order to count the connected cells inside the larger objects (consisting of seemingly connected cells), we divided the corresponding volume of all segmented objects above threshold (224 865 voxel) by the median volume of a single cell (271 voxel), obtained from the distribution of properly segmented cells (below threshold), as shown in Fig. 7(e). This led in this example to a total number of 2000 cells located within the islet of Langerhans, which is in good agreement with the literature (Welsch & Kummer, 2018).   Volume, surface area and boundary boxes of each component were determined by using the Matlab function regionprops3(). As a further morphological measure, the sphericity of each cell was computed and calculated by the following definition (Wadell, 1932), with the cell volume V cell and the cell surface area A cell . The sphericity distribution is shown in Fig. 7( f ).

Anisotropy parameter
Since the tumorous pancreatic tissue is characterized by an abundance of collagen fibers known as typical desmoplastic reaction (intratumoral fibrosis), the 3D tissue structure shows a pronounced fiber orientation. Based on this one specific property of the tumorous tissue, our goal was to introduce a parameter, quantifying the tumor-induced fibrotic morphology, i.e. the degree to which the tissue is affected.
To this end, the anisotropy parameter was used, defined as a scalar field. describes the local degree of orientation for a chosen subvolume Ã k centered around the voxel in question. Its value is based on the three eigenvalues i of the structure tensor ST as in Reichardt et al. (2019). By shifting the subvolumes voxelwise, every voxel of the tomographic volume can be allocated with an -value. The structure tensor can be defined as the sum (or average) over the subvolume Ã k of the multiplication of the intensity gradient components of each voxel, from which the Eigenvalues i are calculated by The anisotropy parameter can then be defined as evaluates to 0 for an isotropic structure ( 1 ' 2 ' 3 ), while for a highly anisotropic structure ( 1 ' 2 ) 3 ) converges to 1. For the following results Ã k was chosen with a subvolume size of 40 pixel 3 . Subvolume Ã kþ1 was shifted by 10 pixel with respect to Ã k , leading to a binning of the volume by a factor of ten.
The concept of the measure was demonstrated on three volumes with different collagen abundance: Volume (1) -containing mostly healthy tissue, consisting of glandular tissue (blue); Volume (2) -containing in part intratumoral fibrosis tissue (yellow); Volume (3) -containing large areas of intratumoral fibrosis tissue (red).
Due to the morphology of both samples, Volumes (1) and (2) were selected from the parallel-beam reconstruction of Sample A, while Volume (3) was selected from the parallelbeam reconstruction of Sample B. Figure 8(a) shows the virtual slice from the parallel beam reconstruction (top), and the corresponding anisotropy map (bottom). The position within the biopsy for the volumes is shown in Fig. 8  The three volumes are compared by their -histograms in Fig. 8(c). The histogram of the healthy tissue Volume (1) is Gaussian distributed with a mean value of " healthy = 0.38 and a standard deviation of healthy = 0.104. Volume (2) still contains healthy tissue, but the presence of collagen fibers increases as shown in the virtual slice, and the distribution of the histogram is broadened and shifted towards higher -values ( " partial = 0.43 and partial = 0.132). In the histogram of Volume (3), which contained mostly tumorous tissue, the -values of the histogram are further shifted to higher ( " full = 0.68 and full = 0.118). These three examples indicate that the tissue volumes can be classified based on their histograms into different stages of affected tissue. The -values increased with the increased presence of fiber, as expected, and the average value " of a biopsy might therefore serve as a suitable biomarker to classify the tumor. To this end, future work should extend this analysis to a representative number of cases, and a validation based on the correlative imaging technique.

Conclusion and outlook
In this work we have performed multiscale 3D virtual histology of human pancreatic biopsies combining two configurations of X-ray propagation imaging with synchrotron radiation. Since cancer surgery is often confronted with removal of substantial tissue volumes, 3D patho-histology automatically faces a multiscale challenge.
Here we have met this challenge by first scanning a large tissue block by inhouse m-CT to obtain a large-scale overview. In addition to the morphological assessment by m-CT, the paraffin-embedded tissue block was cut by a microtome, H&E stained, and morphologically notable regions of the tumor were defined. This pre-characterization allowed a precise selection of tissue regions, which were then targeted by punch  Results of the anisotropy parameter for three example volumes of pancreatic tumor tissue. (a) Virtual slices (top) obtained from the parallel-beam configuration and corresponding anisotropy maps (bottom) for Volume (1), containing mostly healthy, glandular tissue (blue); Volume (2), containing partially tumorous tissue (yellow); and Volume (3), containing mostly tumorous tissue with intratumoral fibrosis (red). Note that the blue and yellow marked slices were chosen from the 3D reconstruction of Sample A, while the red marked slice was chosen from the 3D reconstruction of Sample B. biopsies, i.e. cylindrical volumes of 1 mm diameter were selected for subsequent high-resolution analysis at the synchrotron endstation GINIX. Here, the punch biopsies were first scanned by parallel-beam tomography, followed by further zooms into regions-of-interest by cone-beam holotomography.
Approaches of 3D multiscale phase-contrast X-ray tomography with synchrotron radiation have been realized before, e.g. by Dejea et al. (2019) at the TOMCAT beamline with an effective pixel size of 5.8 mm for low and 0.65 mm for highresolution tomograms, respectively. Massimi et al. (2019) used two different beamline endstations for scans with a pixel size of 1.62 mm at TOMCAT and 50 nm at ID16A-ESRF. Contrarily, here both modalities were integrated side-by-side and hence available in close spatial and temporal proximity during a single beam time.
As a proof-of-concept of this multiscale 3D virtual histology approach, we chose pancreatic tumor samples obtained from pancreas cancer surgery, a tumor type exhibiting morphological alterations with very heterogeneous features. As a result, we could show that the degree of intratumoral fibrosis could be quantified in regions containing pancreatic tumors consisting of tumor cells and areas of desmoplastic reaction. To this end, we used an order parameter for tissue anisotropy, designed to measure the fibrous structure based on the structure tensor. As a further result, we noted that the islets of Langerhans, a cluster of endocrine cells located within pancreatic tissue, are clearly detected in tomograms, even in unstained paraffin-embedded tissue and the parallel-beam configuration. In the case of PTA staining, the contrast of the islet is increased. Much finer structures, e.g. cell nuclei, can be resolved in the zoom tomogram of the islets by holotomography. Comparison with classical histology on selected slices, sectioned after the synchrotron beam time, confirmed the identification of the islets. Importantly, tomography allows for enhanced quantification of the 3D structure. For the present example of a representative islet of Langerhans, 2000 endocrine cells were counted by semi-automatic segmentation with a median volume size of 74 mm 3 and a median cell sphericity of 0.87. In future, similar analysis might be very helpful to obtain more insights into the histopathology of type 1 diabetes by analysing the islets of Langerhans in 3D within the pancreas tissue of these patients. Furthermore, specific features identified by tomography in large tissue volumes can be subsequently studied by well controlled histological sections, taking advantage of the possibility to characterize the morphological structures of interest by further immunohistochemical analysis. Note that coverage of comparably large volumes with micrometre-or sub-micrometre resolution is nearly impossible by parallel sections, or at least extremely tedious.
Since previous virtual histology applications at synchrotron as well as at laboratory setups were largely limited to smallanimal models Busse et al., 2018;Dejea et al., 2019)  Katsamenis et al., 2019) is now particular timely. Beyond research of tumor patho-physiology, the technique may even be applied in future in a clinical context with potential impact on the diagnosis of and on clinical treatment decisions. By identifying novel patho-histological features in 3D, tumors might be characterized in more detail, enabling to classify tumors more precisely in subgroups to allocate patients to the best treatment option. The novel information from phasecontrast X-ray tomography includes volumetric and shape measurements, not accessible by classical patho-histology. Since 3D virtual histology offers the advantage of large volume throughput, high resolution, as well as compatibility with systematic and automated analysis, we believe that this virtual histology could be integrated into biomedical workflows.
In contrast to standard 2D imaging of selected histological sections, which sample the tissue structures only in an exemplary manner, the tissue can be probed in its full dimensionality and without gaps. At the same time, this calls for a multiscale high-throughput approach, which we have demonstrated here at the GINIX endstation of the coherence beamline P10/PETRA III. A parallel-beam configuration for overview tomograms has been implemented with high volume throughput on the order of 0.01 mm 3 s À1 and sufficient image quality for single cell segmentation. This was then complemented by cone-beam configuration with high geometrical magnification for high-resolution scans of selected regionsof-interest (42 min for a single-distance tomogram).
For the immediate future, straightforward technical improvements can be envisioned. With novel waveguide design, exposure times of 350 ms per projection are possible, which makes it reasonable to also implement continuous rotation for the tomography scans in cone-beam geometry. A reduction in scan time by a factor of 3-5 is realistic. Further, different staining and embedding protocols can be implemented and validated to find the best compromise between image contrast and structure alterations by the sample preparation. Moreover, characteristic morphological structures of the normal and tumorous pancreatic tissue can be analyzed in more detail and segmented including blood vessels or intact pancreatic acini and glandular ducts as well as areas of tumor cells and of immunological response.
Beyond these obvious extensions, more important steps are studies with a high number of tumorous samples to obtain convincing parameters and thresholds for the structural metrics with respect to tumor classification. Given successful foundation work and clinical trials as an important next step, 3D virtual histology of cancer biopsies could become effective for more precise diagnosis followed by the optimal selection of treatment in two possible scenarios. In the first scenario, the synchrotron work would be translated to laboratory m-CT (see the supporting information for a comparison of present image quality), for which it could provide ground truth calibration (for selected samples when needed), while the compact instruments would be used in a clinical environment, possibly even in the form of fast tomography to characterize tissues during surgical procedures. In a second scenario, fully dedi-cated endstations with automated measurement, evaluation and reporting would operate with biopsy express delivery, so that results can be presented to the clinicians within a time frame of 2-3 days, similar to other laboratory tests. Both scenarios will require further demonstrations of possible insights and diagnostic benefits. The technical and instrumental requirements for this research have now been provided.

Related literature
The following references, not cited in the main body of the paper, have been cited in the supporting information: De Witte et al.