X-ray phase tomography with near-field speckles for three-dimensional virtual histology

X-ray phase tomography with near-field speckles for three-dimensional virtual histology Marie-Christine Zdora,1,2,3,* Pierre Thibault,1,2 Willy Kuo,4,5 Vincent Fernandez,6 Hans Deyhle,2 Joan Vila-Comamala,7 Margie P. Olbinado,8,9 Alexander Rack,9 Peter M. Lackie,10 Orestis L. Katsamenis,11 Matthew J. Lawson,10 Vartan Kurtcuoglu,4,5,12 Christoph Rau,2 Franz Pfeiffer,13,14 AND Irene Zanette1 School of Physics & Astronomy, University of Southampton, Highfield Campus, Southampton, SO17 1BJ, UK Diamond Light Source, Harwell Science and Innovation Campus, Didcot, OX11 0DE, UK Department of Physics & Astronomy, University College London, Gower Street, London,WC1E 6BT, UK The InterfaceGroup, Institute of Physiology, University of Zurich, 8057 Zurich, Switzerland National Centre of Competence in Research, Kidney.CH, Zurich, Switzerland Imaging and Analysis Centre, Natural HistoryMuseum, London, SW7 5BD, UK Institute for Biomedical Engineering, ETH Zurich, 8092 Zurich, Switzerland Paul Scherrer Institute, 5232 Villigen PSI, Switzerland ESRF—The European Synchrotron, 38000Grenoble, France Clinical and Experimental Sciences, Faculty ofMedicine, University of Southampton, Southampton, SO17 1BJ, UK μ-VIS X-Ray ImagingCentre, Faculty of Engineering and Physical Sciences, University of Southampton, SO17 1BJ, UK Zurich Center for Integrative Human Physiology, University of Zurich, 8057 Zurich, Switzerland Chair of Biomedical Physics, Department of Physics andMunich School of BioEngineering, Technical University ofMunich, 85748Garching, Germany Department of Diagnostic and Interventional Radiology, Klinikum rechts der Isar, Technical University ofMunich, 81675Munich, Germany *Corresponding author: m.zdora@soton.ac.uk


INTRODUCTION
The microscopic visualization of human and animal tissue is a fundamental part of pathological investigations in research and clinical practice. Studying alterations in tissue structure and composition can be key to identify the cause, stage, and progress of treatment of an illness. Revealing the internal organ structure requires imaging methods with high spatial resolution and high contrast for softtissue components, ideally capable of non-invasively providing undistorted three-dimensional (3D) information from hydrated specimens.
Conventional histological examination-using a light microscope to image stained thin slices of a specimen embedded in a hard matrix-has long been the biomedical standard and provides highresolution images of the tissue. Particular components and cell types can be highlighted with different staining agents. However, typically only two-dimensional (2D) information can be extracted. Combining the 2D serial sections into a 3D volume is possible but time-consuming and often hindered by artefacts occurring during tissue preparation and sectioning [1]. Furthermore, the 3D volume generated from the sections does not provide isotropic spatial resolution, which is required for accurate and precise volumetric analysis.
A suitable method to extend and complement conventional histology is the use of x-ray micro computed tomography (microCT) [2], which allows for non-destructive volumetric imaging at isotropic spatial resolution. While x-ray absorption-based microCT is widely applied in a variety of fields, the achievable image contrast is often too low for biomedical applications. Softtissue discrimination requires the use of contrast agents, and the visualization of blood vessels is commonly achieved by corrosion casting with a resin [3][4][5][6][7][8][9]. These approaches, however, bear the risk of altering the tissue structure, are susceptible to incomplete tissue or vessel penetration, and are often incompatible with complementary follow-up imaging techniques including conventional histology. Moreover, corrosion casting is only suitable for vessel imaging, as it dissolves the tissue and is therefore unable to visualize its structure. Alternative x-ray methods based on extracting the x-ray phase shift induced by the sample [10] can provide significantly better contrast for soft biomedical tissue without the need for staining and have recently been identified as a promising approach for virtual histology [9,[11][12][13][14][15]. However, the x-ray phase-contrast imaging methods employed for this purpose to date, such as propagation-based imaging (PBI) [16][17][18] and x-ray grating interferometry (XGI) [19][20][21], have various limitations that have prevented their practical use and wider uptake for virtual histology. These include an elaborate experimental setup with costly, absorbing x-ray optical elements and insufficient spatial resolution for XGI and constraints on the size and nature of the sample and non-quantitative results for PBI.
We here show that phase tomography based on x-ray specklebased imaging (SBI) [22][23][24] has the potential to overcome these limitations and is a promising candidate for virtual histology applications. SBI is a recent x-ray phase-contrast imaging method based on a simple, cost-effective setup that does not require sophisticated optical elements or high-precision instrumentation. Merely a piece of sandpaper is added to the conventional x-ray imaging equipment. SBI, furthermore, does not impose strong restrictions on the properties of the x-ray beam [25][26][27] and the type of sample, making it widely accessible and applicable. Thanks to its high sensitivity, SBI is ideally suited for the investigation of specimens with small density differences.
The first demonstrations of SBI phase tomography were reported a few years ago [26,28]. However, its quantitative character, namely its ability to provide absolute, unbiased density information and enable the accurate measurement of 3D structures, has thus far not been explored. Moreover, while the potential of SBI for applications such as biomedical imaging has been identified in proof-of-principle demonstrations [28,29], sufficient image quality for a quantitative and scientifically relevant analysis has not been reported, to the best of our knowledge. Here, we demonstrate the unexplored potential of SBI x-ray phase tomography for the application of 3D virtual histology on a whole unstained, hydrated kidney of a healthy mouse imaged at a synchrotron radiation facility.

X-RAY SPECKLE-BASED PHASE TOMOGRAPHY
SBI is well suited for visualizing the structure of biomedical tissue on the micrometer scale, providing a phase sensitivity on the order of nanoradians in terms of x-ray refraction angle and a spatial resolution of a few micrometers at a field of view extending to several centimeters. The experimental setup for SBI phase tomography, see Fig. 1(a), is simple. The only addition to the standard x-ray tomography apparatus is a piece of abrasive paper used as a phase modulator, also called a diffuser. Scattering and subsequent interference of the x-rays from the small particles in the diffuser lead to the formation of a near-field speckle pattern [30], see Figs. 1(b) and 1(c), which acts as a wavefront marker. X-ray refraction in the sample results in a displacement of the speckle pattern with respect to its reference without a sample, which can be retrieved computationally and converted to a differential phase signal [22,23,31]. The speckle displacements s x and s y in the horizontal and vertical direction, respectively, obtained by the reconstruction algorithm are directly related to the x-ray refraction angles α x , α y under small-angle approximation and, subsequently, to the differential phase signals ∂ /∂ x, ∂ /∂ y: where λ is the x-ray wavelength, and d 2 is the sample detector distance. The differential phase images in the horizontal and vertical direction, as shown in Fig. S4 in Supplement 1, can be combined together via integration, here a Fourier integration routine [23,32]. The resulting phase shift signal is directly related to the refractive index decrement δ, which is directly proportional to the electron density ρ el , for energies far from the absorption edges [33]. Moreover, a linear relationship between ρ el and the mass density ρ m holds, see Supplement 1. A tomography scan consisting of 2D projections at different viewing angles of the sample delivers a 3D map of these quantities. Among the various ways of performing SBI, we used our recently developed approach, the unified modulated pattern analysis (UMPA) [34]. It allows for multimodal signal retrieval by analyzing the sample-induced modulations of the speckle pattern using a least-squares minimization procedure. UMPA is a robust yet flexible implementation that provides a trade-off between spatial resolution, phase sensitivity, and scan time [35] and does not rely on a motorized stage with nanometer precision required by some other SBI methods [31,36].
We carried out x-ray speckle-based phase tomography measurements at beamline ID19 of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) using an x-ray beam with a narrow energy spectrum with a peak energy of 26.3 keV (see Supplement 1 for a detailed description of the parameters and data acquisition). The sample was mounted on a tomographic stage located d 1 = 72.5 cm downstream of the diffuser. Reference images (without the specimen in the beam) and sample images (with the specimen in the beam) were acquired at N = 20 different transverse positions of the diffuser. The resulting speckle interference patterns were recorded by a detection system placed

A. Virtual Histology of the Murine Kidney
Using the UMPA implementation of SBI, we obtained the phase tomogram of a murine kidney. The virtual slices through the volume in Figs. 2(a) and 2(c)-2(e) contain detailed morphological information. The slice locations within the 3D volume are illustrated in Fig. S5 in Supplement 1. As the phase tomogram can be virtually sectioned along any desired plane, the correlation with slices obtained by conventional histology, which was performed on the same specimen after x-ray imaging (see Supplement 1), is straightforward. The microstructural detail of the hydrated kidney tissue is clearly visualized in the phase volume slices and matches that seen by conventional histology with hemotoxylin and eosin (H&E) stain, see Figs. 2(b) and 2(f )-2(h). For better visualization and comparison, the phase volume images are presented in false colors similar to H&E-stained histology slices. While standard H&E staining for general microstructural overview was used in Fig. 2, histological slices with other common stains are shown in Fig. S6 in Supplement 1.
The four main regions of the kidney, characterized by the presence of different segments of the renal tubules, can be identified: inner medulla (IM), inner stripe of the outer medulla (ISOM), outer stripe of the outer medulla (OSOM), and cortex (COR). Essential microstructural features including small blood vessels, renal tubules, and renal glomeruli can be observed in the enlarged regions of interest (ROIs) in Figs. 2(e) and 2(h). The histological sections in Figs. 2(f )-2(h) show some tissue damage, folding, distortions, and overall shrinkage, here around 20%, which can be encountered in conventional histology due to the sample embedding and physical slicing processes [37].
While conventional histology can achieve superior resolution in 2D, x-ray virtual histology based on SBI delivers the tissue structure in 3D and, in addition, provides absolute quantitative density information.

B. Quantitative Density Information from the Phase Volume
A section through the phase volume of the kidney after conversion to electron density values is shown in Fig. 3(a) and in more detail in Fig. 3(b). The high-density resolution allows for the discrimination of not only the fat, surrounding agar gel, and vessels in the sample, but also of the minute density differences between the four kidney   Table 1. regions. This is illustrated in the histograms of the whole slice [ Fig. 3(c)] and of the kidney tissue only [ Fig. 3(d)]. For the latter, pixels corresponding to fat, the surrounding agar gel, and vessels in the kidney were excluded via semi-automatic segmentation of the slice based on gray-value thresholding and manual refinement. The peak positions [indicated by vertical dashed lines in Fig. 3(d)] were determined by fitting skewed Gaussians to the histograms of the kidney regions. The negative skewness of the distributions, most pronounced for the COR and OSOM, is caused by low-density contributions from the lumen (inner empty space) of the tubules as well as partial volume effects at the interface of the The density values were determined from the peak positions of the skewed Gaussian curves fitted to the histograms in Fig. 3(d). The density-value ranges in the last column correspond to the onestandard-deviation ranges of normal Gaussian fit curves to the right slope of the histograms, see Fig. S3 in Supplement 1.
c Their uncertainties were determined from the co-variance matrices of the fit parameters via error propagation. d The mass density differences between the kidney regions were found to be 8.3 mg/cm 3 for IM-ISOM, 18.3mg/cm 3 for ISOM-OSOM, and 2.0 mg/cm 3 for OSOM-COR, which is consistent with the measurements by Shirai et al. reporting a density difference for OSOM-COR of 1.9 mg/cm 3 for a hydrated formalin-fixed rat kidney [13]. tubule wall and lumen (see Supplement 1). The peak density values and the ranges of the distributions, which were determined from normal Gaussian fits to the right slope, are listed in Table 1.
In our experiment, we obtained a density resolution of better than 1.9 mg/cm 3 for an estimated spatial resolution of approximately 8 µm (see Supplement 1). The latter is determined by the choice of reconstruction parameters in the UMPA analysis routine as well as the setup geometry and the resolution of the detector system. In particular, the spatial resolution in the 2D projections is typically limited by twice the full width at half-maximum (FWHM) of the analysis window in the UMPA reconstruction procedure [34]. While this does not match light microscopy capable of sub-cellular resolution, we can observe features down to the looped structure of the glomerular capillaries, see Fig. 3(b), the diameter of which can be estimated to be comparable to the  diameter of red blood cells [38], i.e., approximately 6-7 µm, just at the spatial resolution limit of our scan.

C. Three-Dimensional Analysis and Segmentation of Complex Networks
As illustrated for a volume of interest (VOI) of the tomogram in Fig. 4(b) and Visualization 1, the high contrast and 3D nature of the data allow for further analysis of the shape, size, and distribution of the functional elements within the organ such as the glomeruli and blood vessels. Retrieving this information reliably from 2D slices, as provided by conventional histology, can be extremely challenging.
As an example, we have measured the average glomerular diameter to be (97 ± 19) µm, based on 20 glomeruli. This is in agreement with the value (99 ± 13) µm (average over different regions) obtained in Ref. [39] by using light microscope images of osmium-stained kidney slices with subsequent alignment and computer-assisted tracing of tubules. Furthermore, as previously observed in the 2D tomogram slices in Fig. 3, the quantitative character of SBI allows for resolving and measuring the minute density differences between the kidney regions in the volume, see Fig. 4(c).
The 3D phase tomogram contains not only information about the internal features, but also the overall shape and volume of the specimen, see Fig. 5(a), which allows for the determination of its total volume, here 163.2 mm 3 . Obtaining this information on hydrated, unstained specimens gives an accurate and precise volume measure without the effects of tissue shrinkage, swelling, or distortions that can be encountered with other methods for tissue visualization that rely on dehydration or staining [7].
The interrelation and connectivity of essential elements of the organ, see Figs. 5(b)-5(e), which are not directly accessible by 2D conventional histology, can give valuable information on its function and health. Using semi-automatic segmentation based on intensity thresholding and region growing with commercially available software, we were able to visualize the blood vessel network of the kidney, see Fig. 5(b) and Visualization 2, simultaneously with the tissue microstructure, see Fig. 5(c) and Fig. S7 in Supplement 1. It should be highlighted that in our measurements, unlike in other x-ray studies on visualizing the renal vascular network [40][41][42][43], neither contrast agent nor blood was present in the vessels, and the segmentation was solely possible because of the high image quality provided by SBI phase tomography.
The vessel network is directly connected to the renal tubules to enable filtration of the blood in the kidney. We were able to visualize the 3D structure of the tubular system down to a single renal nephron, the functional and structural unit of the kidney, as shown in Figs. 5(d) and 5(e). This is an important step towards studying the functional interrelation of the blood vessels, renal tubules, and collecting ducts in the kidney.
A summary of the 3D virtual histology results of the murine kidney is presented in Visualization 3.

DISCUSSION AND CONCLUSION
We have shown that x-ray speckle-based phase tomography is a strong contender for 3D virtual histology applications to complement, extend, and advance conventional histopathological investigations.
While biomedical research and clinical pathology currently make use solely of 2D tissue visualization as provided by conventional histology, the missing 3D information can be critical to obtain a full picture of the tissue morphology, organ volume, and sizes of structural elements in order to identify and quantify changes associated with pathologies. SBI phase tomography is able to provide this volumetric information on unstained, hydrated biomedical samples and has the potential to become a reliable tool for diagnostics and staging of diseases from excised tissue samples, in particular, as it is sensitive to changes in both tissue density and morphology. The absolute density values obtained by SBI provide an objective, quantitative physical measure for this purpose, enabling the unbiased, consistent, and reproducible evaluation of healthy and diseased animal and human tissue. These pathophysiological studies could then be validated and combined with subsequent analyses using complementary techniques including antibody-based and molecular biology-based histopathology.
Moreover, the ability of SBI phase tomography to visualize the tissue microstructure as well as the vascular network of an organ will allow for linking vasculature and organ function, which is an ongoing area of investigation, e.g., for the evaluation of the renal tubular function [44]. We have here performed the first step towards such studies by demonstrating the segmentation of the main renal blood vessel network and a single nephron up to the end of the proximal straight tubule. In the future, the extracted vessel and nephron networks could be the basis for advanced functional studies such as image-based fluid dynamics simulations to assess the overall kidney function and investigate poorly known mechanisms like renal oxygenation [45].
The non-destructive nature of SBI phase tomography makes it compatible with follow-up conventional histology investigations, which can be performed for validation purposes or additional functional information by using histochemical stains. A direct comparison of the virtual SBI phase tomogram slices and conventional histology slices could be performed in the future for a detailed study of tissue alterations induced by the dehydration, embedding, and slicing procedures required for the latter. As SBI can be applied to unstained or stained tissue embedded in hard, soft, or liquid matrices, it is expected to also be compatible with other follow-up imaging techniques, such as electron microscopy or optical tissue clearing.
SBI has the potential to overcome the main limitations of PBI and XGI for virtual histology. While PBI with a single-distance approach benefits from a simple setup, image reconstruction with the most commonly employed phase-retrieval algorithm [18] requires a priori information input based on the assumption of a homogeneous sample, rendering the method non-quantitative for complex specimens. Moreover, PBI is based on the Laplacian of the phase and is as such less sensitive to small density differences than differential phase methods like SBI and XGI, albeit providing a higher spatial resolution. XGI, on the other hand, does deliver quantitative phase information, but uses a more complicated, less robust setup that requires costly specialized absorbing x-ray optical elements, high-precision scanning stages and elaborate alignment procedures. The spatial and density resolution of both SBI and XGI depend on the experimental and setup conditions, the properties of the phase modulator (grating/diffuser), and for UMPA additionally on the reconstruction parameters [24,46,47]. In practice, the spatial resolution of SBI using UMPA is limited by the analysis window size, while for XGI the shear of the first-order diffracted beams created by the phase grating, which is dependent on the grating period, can become the limiting factor if it is larger than the resolution of the detector system. SBI combines the advantages of both XGI and PBI and provides high-sensitivity quantitative phase-contrast images with a simple setup that only requires a piece of sandpaper as an optical element.
The UMPA implementation of SBI has been particularly designed for robustness against potential setup instabilities, flexibility in the experimental arrangement, and data acquisition procedure, as well as the ability to fine-tune the spatial resolution and sensitivity of the phase-contrast images during the reconstruction process [34]. This makes UMPA swiftly adaptable to most existing x-ray imaging setups without additional specialized equipment.
We have here demonstrated the potential of SBI in the field of biomedicine as one of the most promising future applications of the technique. However, SBI is not limited to this area and can be applied to samples with a wide range of compositions and structures on the length scale of micrometers to centimeters. It is hence expected to find uptake in numerous other fields, such as palaeontology, earth sciences, engineering, and materials science.
Importantly, while the data presented here was acquired at a synchrotron source, SBI phase tomography is compatible with laboratory x-ray sources [25][26][27]. Although conventional laboratory sources will not enable the spatial and density resolution of synchrotron data, due to the reduced coherence properties, the shorter propagation distances, and increased blurring by the source, the quality of the results will be sufficiently high for many applications. Moreover, recently developed specialized x-ray sources with submicrometer spot sizes have shown to be a promising instrument for high-resolution x-ray virtual histology [48,49].
Once optimized at conventional x-ray systems, SBI phase tomography will become widely accessible and available for high-throughput applications in research, industry, and clinical pathology.