Evaluation of phase retrieval approaches in magnified X-ray phase nano computerized tomography applied to bone tissue

Phase retrieval in propagation-based X-ray imaging beyond the limits of transport of intensity and contrast transfer function approaches

We derive a phase retrieval formula for propagation-based phase contrast X-ray imaging that does not require weakly attenuating objects or short propagation distances. It is directly applicable to both single- and multiple-distance scenarios. We show the validity conditions and study the error of the underlying mutual intensity approximation, which uses the common assumptions of weak phase shift variations and phase-attenuation duality. The approximation generalizes those behind the transport of intensity (TIE) and contrast transfer function (CTF) models, and it approaches them when their respective additional assumptions are satisfied. When they are not, it clearly outperforms them, which we show both theoretically and practically on synthetic and measured data.

3D quantification of the lacunocanalicular network on human femoral diaphysis through synchrotron radiation-based nanoCT

Osteocytes are the major actors in bone mechanobiology. Within bone matrix, they are trapped close together in a submicrometric interconnected network: the lacunocanalicular network (LCN). The interstitial fluid circulating within the LCN transmits the mechanical information to the osteocytes that convert it into a biochemical signal. Understanding the interstitial fluid dynamics is necessary to better understand the bone mechanobiology. Due to the submicrometric dimensions of the LCN, making it difficult to experimentally investigate fluid dynamics, numerical models appear as a relevant tool for such investigation. To develop such models, there is a need for geometrical and morphological data on the human LCN. This study aims at providing morphological data on the human LCN from measurement of 27 human femoral diaphysis bone samples using synchrotron radiation nano-computed tomography with an isotropic voxel size of 100 nm. Except from the canalicular diameter, the canalicular morphological parameters presented a high variability within one sample. Some differences in terms of both lacunar and canalicular morphology were observed between the male and female populations. But it has to be highlighted that all the canaliculi cannot be detected with a voxel size of 100 nm. Hence, in the current study, only a specific population of large canaliculi that could be characterize. Still, to the authors knowledge, this is the first time such a data set was introduced to the community. Further processing will be achieved in order to provide new insight on the LCN permeability.

3D imaging of SARS-CoV-2 infected hamster lungs by X-ray phase contrast tomography enables drug testing

X-ray Phase Contrast Tomography (XPCT) based on wavefield propagation has been established as a high resolution three-dimensional (3D) imaging modality, suitable to reconstruct the intricate structure of soft tissues, and the corresponding pathological alterations. However, for biomedical research, more is needed than 3D visualisation and rendering of the cytoarchitecture in a few selected cases. First, the throughput needs to be increased to cover a statistically relevant number of samples. Second, the cytoarchitecture has to be quantified in terms of morphometric parameters, independent of visual impression. Third, dimensionality reduction and classification are required for identification of effects and interpretation of results. To address these challenges, we here design and implement a novel integrated and high throughput XPCT imaging and analysis workflow for 3D histology, pathohistology and drug testing. Our approach uses semi-automated data acquisition, reconstruction and statistical quantification. We demonstrate its capability for the example of lung pathohistology in Covid-19. Using a small animal model, different Covid-19 drug candidates are administered after infection and tested in view of restoration of the physiological cytoarchitecture, specifically the alveolar morphology. To this end, we then use morphometric parameter determination followed by a dimensionality reduction and classification based on optimal transport. This approach allows efficient discrimination between physiological and pathological lung structure, thereby providing quantitative insights into the pathological progression and partial recovery due to drug treatment. Finally, we stress that the XPCT image chain implemented here only used synchrotron radiation for validation, while the data used for analysis was recorded with laboratory μ CT radiation, more easily accessible for pre-clinical research.

Deep learning to overcome Zernike phase-contrast nanoCT artifacts for automated micro-nano porosity segmentation in bone

Bone material contains a hierarchical network of micro- and nano-cavities and channels, known as the lacuna-canalicular network (LCN), that is thought to play an important role in mechanobiology and turnover. The LCN comprises micrometer-sized lacunae, voids that house osteocytes, and submicrometer-sized canaliculi that connect bone cells. Characterization of this network in three dimensions is crucial for many bone studies. To quantify X-ray Zernike phase-contrast nanotomography data, deep learning is used to isolate and assess porosity in artifact-laden tomographies of zebrafish bones. A technical solution is proposed to overcome the halo and shade-off domains in order to reliably obtain the distribution and morphology of the LCN in the tomographic data. Convolutional neural network (CNN) models are utilized with increasing numbers of images, repeatedly validated by `error loss' and `accuracy' metrics. U-Net and Sensor3D CNN models were trained on data obtained from two different synchrotron Zernike phase-contrast transmission X-ray microscopes, the ANATOMIX beamline at SOLEIL (Paris, France) and the P05 beamline at PETRA III (Hamburg, Germany). The Sensor3D CNN model with a smaller batch size of 32 and a training data size of 70 images showed the best performance (accuracy 0.983 and error loss 0.032). The analysis procedures, validated by comparison with human-identified ground-truth images, correctly identified the voids within the bone matrix. This proposed approach may have further application to classify structures in volumetric images that contain non-linear artifacts that degrade image quality and hinder feature identification.

X-ray Tomography Applied to Electrochemical Devices and Electrocatalysis

X-ray computed tomography (CT) is a nondestructive three-dimensional (3D) imaging technique used for studying morphological properties of porous and nonporous materials. In the field of electrocatalysis, X-ray CT is mainly used to quantify the morphology of electrodes and extract information such as porosity, tortuosity, pore-size distribution, and other relevant properties. For electrochemical systems such as fuel cells, electrolyzers, and redox flow batteries, X-ray CT gives the ability to study evolution of critical features of interest in ex situ, in situ, and operando environments. These include catalyst degradation, interface evolution under real conditions, formation of new phases (water and oxygen), and dynamics of transport processes. These studies enable more efficient device and electrode designs that will ultimately contribute to widespread decarbonization efforts.

Evaluation of imaging setups for quantitative phase contrast nanoCT of mineralized biomaterials

X-ray nano-tomography with phase contrast (nanoCT) using synchrotron radiation is a powerful tool to non-destructively investigate 3D material properties at the nanoscale. In large bone lesions, such as severe bone fractures, bone cancer or other diseases, bone grafts substituting the lost bone might be necessary. Such grafts can be of biological origin or be composed of a synthetic bone substitute. The long-term functioning of artificial bone substitutes depends on many factors. Synchrotron nanoCT imaging has great potential to contribute to further the understanding of integration of implants into bone tissue by imaging the spatial interaction between bone tissue and implant, and by accessing the interface between implant material and bone tissue. With this aim, a methodology for evaluating the image quality is presented for in-line phase contrast nanoCT images of bone scaffold samples. A PMMA-embedded tricalcium phosphate scaffold was used with both a closed and an open porosity structure and bone ingrowths as a representative system of three known materials. Parameters such as spatial resolution and signal-to-noise ratio were extracted and used to explore and quantitatively compare the effects of implementation choices in the imaging setup, such as camera technology and imaging energy, on the resulting image quality. Increasing the X-ray energy from 17.5 keV to 29.6 keV leads to a notable improvement in image quality regardless of the camera technology used, with the two tested camera setups performing at a comparable level when the recorded intensity was kept constant.

Mixed scale dense convolutional networks for x-ray phase contrast imaging

X-ray in-line phase contrast imaging relies on the measurement of Fresnel diffraction intensity patterns due to the phase shift and the attenuation induced by the object. The recovery of phase and attenuation from one or several diffraction patterns is a nonlinear ill-posed inverse problem. In this work, we propose supervised learning approaches using mixed scale dense (MS-D) convolutional neural networks to simultaneously retrieve the phase and the attenuation from x-ray phase contrast images. This network architecture uses dilated convolutions to capture features at different image scales and densely connects all feature maps. The long range information in images becomes quickly available, and greater receptive field size can be obtained without losing resolution. This network architecture seems to account for the effect of the Fresnel operator very efficiently. We train the networks using simulated data of objects consisting of either homogeneous components, characterized by a fixed ratio of the induced refractive phase shifts and attenuation, or heterogeneous components, consisting of various materials. We also train the networks in the image domain by applying a simple initial reconstruction using the adjoint of the Fréchet derivative. We compare the results obtained with the MS-D network to reconstructions using U-Net, another popular network architecture, as well as to reconstructions using the contrast transfer function method, a direct phase and attenuation retrieval method based on linearization of the direct problem. The networks are evaluated using simulated noisy data as well as images acquired at NanoMAX (MAX IV, Lund, Sweden). In all cases, large improvements of the reconstruction errors are obtained on simulated data compared to the linearized method. Moreover, on experimental data, the networks improve the reconstruction quantitatively, improving the low-frequency behavior and the resolution.

Improving spatial resolution with an edge-enhancement model for low-dose propagation-based X-ray phase-contrast computed tomography

Propagation-based X-ray phase-contrast computed tomography (PB-PCCT) has been increasingly popular for distinguishing low contrast tissues. Phase retrieval is an important step to quantitatively obtain the phase information before the tomographic reconstructions, while typical phase retrieval methods in PB-PCCT, such as homogenous transport of intensity equation (TIE-Hom), are essentially low-pass filters and thus improve the signal to noise ratio at the expense of the reduced spatial resolution of the reconstructed image. To improve the reconstructed spatial resolution, measured phase contrast projections with high edge enhancement and the phase projections retrieved by TIE-Hom were weighted summed and fed into an iterative tomographic algorithm within the framework of the adaptive steepest descent projections onto convex sets (ASD-POCS), which was employed for suppressing the image noise in low dose reconstructions because of the sparse-view scanning strategy or low exposure time for single phase contrast projection. The merging strategy decreases the accuracy of the linear model of PB-PCCT and would finally lead to the reconstruction failure in iterative reconstructions. Therefore, the additive median root prior is also introduced in the algorithm to partly increase the model accuracy. The reconstructed spatial resolution and noise performance can be flexibly balanced by a pair of antagonistic hyper-parameters. Validations were performed by the established phase-contrast Feldkamp-Davis-Kress, phase-retrieved Feldkamp-Davis-Kress, conventional ASD-POCS and the proposed enhanced ASD-POCS with a numerical phantom dataset and experimental biomaterial dataset. Simulation results show that the proposed algorithm outperforms the conventional ASD-POCS in spatial evaluation assessments such as root mean square error (a ratio of 9.78%), contrast to noise ratio (CNR) (a ratio of 7.46%), and also frequency evaluation assessments such as modulation transfer function (a ratio of 66.48% of MTF_50% (50% MTF value)), noise power spectrum (a ratio of 35.25% of f_50% (50% value of the Nyquist frequency)) and noise equivalent quanta (1-2 orders of magnitude at high frequencies). Experimental results again confirm the superiority of proposed strategy relative to the conventional one in terms of edge sharpness and CNR (an average increase of 67.35%).

PyPhase - a Python package for X-ray phase imaging

X-ray propagation-based imaging techniques are well established at synchrotron radiation and laboratory sources. However, most reconstruction algorithms for such image modalities, also known as phase-retrieval algorithms, have been developed specifically for one instrument by and for experts, making the development and diffusion of such techniques difficult. Here, PyPhase, a free and open-source package for propagation-based near-field phase reconstructions, which is distributed under the CeCILL license, is presented. PyPhase implements some of the most popular phase-retrieval algorithms in a highly modular framework supporting its deployment on large-scale computing facilities. This makes the integration, the development of new phase-retrieval algorithms, and the deployment on different computing infrastructures straightforward. Its capabilities and simplicity are presented by application to data acquired at the synchrotron source MAX IV (Lund, Sweden).

Material Decomposition Using Spectral Propagation-Based Phase-Contrast X-Ray Imaging

Material decomposition in X-ray imaging uses the energy-dependence of attenuation to digitally decompose an object into specific constituent materials, generally at the cost of enhanced image noise. Propagation-based X-ray phase-contrast imaging is a developing technique that can be used to reduce image noise, in particular from weakly attenuating objects. In this paper, we combine spectral phase-contrast imaging with material decomposition to both better visualize weakly attenuating features and separate them from overlying objects in radiography. We derive an algorithm that performs both tasks simultaneously and verify it against numerical simulations and experimental measurements of ideal two-component samples composed of pure aluminum and poly(methyl methacrylate). Additionally, we showcase first imaging results of a rabbit kitten's lung. The attenuation signal of a thorax, in particular, is dominated by the strongly attenuating bones of the ribcage. Combined with the weak soft tissue signal, this makes it difficult to visualize the fine anatomical structures across the whole lung. In all cases, clean material decomposition was achieved, without residual phase-contrast effects, from which we generate an un-obstructed image of the lung, free of bones. Spectral propagation-based phase-contrast imaging has the potential to be a valuable tool, not only in future lung research, but also in other systems for which phase-contrast imaging in combination with material decomposition proves to be advantageous.

Dense neuronal reconstruction through X-ray holographic nano-tomography

Imaging neuronal networks provides a foundation for understanding the nervous system, but resolving dense nanometer-scale structures over large volumes remains challenging for light microscopy (LM) and electron microscopy (EM). Here we show that X-ray holographic nano-tomography (XNH) can image millimeter-scale volumes with sub-100-nm resolution, enabling reconstruction of dense wiring in Drosophila melanogaster and mouse nervous tissue. We performed correlative XNH and EM to reconstruct hundreds of cortical pyramidal cells and show that more superficial cells receive stronger synaptic inhibition on their apical dendrites. By combining multiple XNH scans, we imaged an adult Drosophila leg with sufficient resolution to comprehensively catalog mechanosensory neurons and trace individual motor axons from muscles to the central nervous system. To accelerate neuronal reconstructions, we trained a convolutional neural network to automatically segment neurons from XNH volumes. Thus, XNH bridges a key gap between LM and EM, providing a new avenue for neural circuit discovery.

Quantification of the bone lacunocanalicular network from 3D X-ray phase nanotomography images

There is a growing interest in developing 3D microscopy for the exploration of thick biological tissues. Recently, 3D X-ray nanocomputerised tomography has proven to be a suitable technique for imaging the bone lacunocanalicular network. This interconnected structure is hosting the osteocytes which play a major role in maintaining bone quality through remodelling processes. 3D images have the potential to reveal the architecture of cellular networks, but their quantitative analysis remains a challenge due to the density and complexity of nanometre sized structures and the need to handle and process large datasets, for example, 2048³ voxels corresponding to 32 GB per individual image in our case. In this work, we propose an efficient image processing approach for the segmentation of the network and the extraction of characteristic parameters describing the 3D structure. These parameters include the density of lacunae, the porosity of lacunae and canaliculi, and morphological features of lacunae (volume, surface area, lengths, anisotropy etc.). We also introduce additional parameters describing the local environment of each lacuna and its canaliculi. The method is applied to analyse eight human femoral cortical bone samples imaged by magnified X-ray phase nanotomography with a voxel size of 120 nm, which was found to be a good compromise to resolve canaliculi while keeping a sufficiently large field of view of 246 μm in 3D. The analysis was performed on a total of 2077 lacunae showing an average length, width and depth of 17.1 μm × 9.2 μm × 4.4 μm, with an average number of 58.2 canaliculi per lacuna and a total lacuno-canalicular porosity of 1.12%. The reported descriptive parameters provide information on the 3D organisation of the lacuno-canalicular network in human bones.

Two-photon X-ray ghost microscope

This article presents a non-classical imaging mechanism that produces a diffraction-limited and magnified ghost image of the internal structure of an object through the measurement of intensity fluctuation correlation formed by two-photon interference. In principle, the lensless X-ray ghost imaging mechanism may achieve a spatial resolution determined by the wavelength and the angular diameter of the X-ray source, ∼λ/Δθ_s, with possible reduction caused by additional optics. In addition, it has the ability to image select "slices" deep within an object, which can be used for constructing 3D view of its internal structure.

Experimental optimization of X-ray propagation-based phase contrast imaging geometry

Propagation-based phase contrast imaging (PB-PCI) with an X-ray lab source is a powerful technique to study low absorption samples, e.g. soft tissue or plastics, on the micrometer scale but is often limited by the low flux and coherence of the source. The setup geometry is essential for the performance since there is a trade-off where a short source distance yields a high contrast-to-noise ratio (CNR) but a low relative fringe contrast. While theoretical optimization strategies based on Fresnel propagation have been reported, there is a need for experimental testing of these models. Here, we systematically investigate this trade-off experimentally using two different setups with high-resolution detectors: a custom-built system with a Cu X-ray source and a commercial system (Zeiss Xradia) with a W source. The fringe contrast, CNR and fringe separation for a low-absorption test sample were measured for 130 different combinations of magnification and overall distances. We find that these figures-of-merit are sensitive to the magnification and that an optimum can be found that is independent of the overall source-detector distance. In general, we find that the theoretical models show excellent agreement with the measurements. However, this requires the complicated X-ray spectrum to be considered, in particular for the broadband W source.

Vascular Casting of Adult and Early Postnatal Mouse Lungs for Micro-CT Imaging

Blood vessels form intricate networks in 3-dimensional space. Consequently, it is difficult to visually appreciate how vascular networks interact and behave by observing the surface of a tissue. This method provides a means to visualize the complex 3-dimensional vascular architecture of the lung. To accomplish this, a catheter is inserted into the pulmonary artery and the vasculature is simultaneously flushed of blood and chemically dilated to limit resistance. Lungs are then inflated through the trachea at a standard pressure and the polymer compound is infused into the vascular bed at a standard flow rate. Once the entire arterial network is filled and allowed to cure, the lung vasculature may be visualized directly or imaged on a micro-CT (µCT) scanner. When performed successfully, one can appreciate the pulmonary arterial network in mice ranging from early postnatal ages to adults. Additionally, while demonstrated in the pulmonary arterial bed, this method can be applied to any vascular bed with optimized catheter placement and endpoints.

Assessment of the human bone lacuno-canalicular network at the nanoscale and impact of spatial resolution

Recently, increasing attention has been given to the study of osteocytes, the cells that are thought to play an important role in bone remodeling and in the mechanisms of bone fragility. The interconnected osteocyte system is deeply embedded inside the mineralized bone matrix and lies within a closely fitted porosity known as the lacuno-canalicular network. However, quantitative data on human samples remain scarce, mostly measured in 2D, and there are gaps to be filled in terms of spatial resolution. In this work, we present data on femoral samples from female donors imaged with isotropic 3D spatial resolution by magnified X-ray phase nano computerized-tomography. We report quantitative results on the 3D structure of canaliculi in human femoral bone imaged with a voxel size of 30 nm. We found that the lacuno-canalicular porosity occupies on average 1.45% of the total tissue volume, the ratio of the canalicular versus lacunar porosity is about 37.7%, and the primary number of canaliculi stemming from each lacuna is 79 on average. The examination of this number at different distances from the surface of the lacunae demonstrates branching in the canaliculi network. We analyzed the impact of spatial resolution on quantification by comparing parameters extracted from the same samples imaged with 120 nm and 30 nm voxel sizes. To avoid any bias related to the analysis region, the volumes at 120 nm and 30 nm were registered and cropped to the same field of view. Our results show that the measurements at 120 and 30 nm are strongly correlated in our data set but that the highest spatial resolution provides more accurate information on the canaliculi network and its branching properties.

Diamond refractive micro-lenses for full-field X-ray imaging and microscopy produced with ion beam lithography

We demonstrate that ion-beam lithography can be applied to the fabrication of rotationally parabolic refractive diamond X-ray micro-lenses that are of interest to the field of high-resolution X-ray focusing and microscopy. Three single half-lenses with curvature radii of 4.8 µm were produced and stacked to form a compound refractive lens, which provided diffraction-limited focusing of X-ray radiation at the P14 beamline of PETRA-III (DESY). As shown with SEM, the lenses are free of expressed low- and high-frequency shape modulations with a figure error of < 200 nm and surface roughness of 30 nm. Precise micro-manipulation and stacking of individual lenses are demonstrated, which opens up new opportunities for compact X-ray microscopy with nanometer resolution.