On the origin of visibility contrast in x-ray Talbot interferometry

Simultaneous Maximum-Likelihood Reconstruction of Absorption Coefficient, Refractive Index and Dark-Field Scattering Coefficient in X-Ray Talbot-Lau Tomography

A maximum-likelihood reconstruction technique for X-ray Talbot-Lau tomography is presented. This technique allows the iterative simultaneous reconstruction of discrete distributions of absorption coefficient, refractive index and a dark-field scattering coefficient. This technique avoids prior phase retrieval in the tomographic projection images and thus in principle allows reconstruction from tomographic data with less than three phase steps per projection. A numerical phantom is defined which is used to evaluate convergence of the technique with regard to photon statistics and with regard to the number of projection angles and phase steps used. It is shown that the use of a random phase sampling pattern allows the reconstruction even for the extreme case of only one single phase step per projection. The technique is successfully applied to measured tomographic data of a mouse. In future, this reconstruction technique might also be used to implement enhanced imaging models for X-ray Talbot-Lau tomography. These enhancements might be suited to correct for example beam hardening and dispersion artifacts and improve overall image quality of X-ray Talbot-Lau tomography.

The new neutron grating interferometer at the ANTARES beamline: design, principles and applications

Neutron grating interferometry is an advanced method in neutron imaging that allows the simultaneous recording of the transmission, the differential phase and the dark-field image. The latter in particular has recently been the subject of much interest because of its unique contrast mechanism which marks ultra-small-angle neutron scattering within the sample. Hence, in neutron grating interferometry, an imaging contrast is generated by scattering of neutrons off micrometre-sized inhomogeneities. Although the scatterer cannot be resolved, it leads to a measurable local decoherence of the beam. Here, a report is given on the design considerations, principles and applications of a new neutron grating interferometer which has recently been implemented at the ANTARES beamline at the Heinz Maier-Leibnitz Zentrum. Its highly flexible design allows users to perform experiments such as directional and quantitative dark-field imaging which provide spatially resolved information on the anisotropy and shape of the microstructure of the sample. A comprehensive overview of the neutron grating interferometer principle is given, followed by theoretical considerations to optimize the setup performance for different applications. Furthermore, an extensive characterization of the setup is presented and its abilities are demonstrated using selected case studies: (i) dark-field imaging for material differentiation, (ii) directional dark-field imaging to mark and quantify micrometre anisotropies within the sample, and (iii) quantitative dark-field imaging, providing additional size information on the sample's microstructure by probing its autocorrelation function.

Small angle x-ray scattering with edge-illumination

Sensitivity to sub-pixel sample features has been demonstrated as a valuable capability of phase contrast x-ray imaging. Here, we report on a method to obtain angular-resolved small angle x-ray scattering distributions with edge-illumination- based imaging utilizing incoherent illumination from an x-ray tube. Our approach provides both the three established image modalities (absorption, differential phase and scatter strength), plus a number of additional contrasts related to unresolved sample features. The complementarity of these contrasts is experimentally validated by using different materials in powder form. As a significant application example we show that the extended complementary contrasts could allow the diagnosis of pulmonary emphysema in a murine model. In support of this, we demonstrate that the properties of the retrieved scattering distributions are consistent with the expectation of increased feature sizes related to pulmonary emphysema. Combined with the simplicity of implementation of edge-illumination, these findings suggest a high potential for exploiting extended sub-pixel contrasts in the diagnosis of lung diseases and beyond.

Predicting visibility of interference fringes in X-ray grating interferometry

The interference fringe visibility is a common figure of merit in designs of x-ray grating-based interferometers. Presently one has to resort to laborious computer simulations to predict fringe visibility values of interferometers with polychromatic x-ray sources. Expanding the authors' previous work on Fourier expansion of the intensity fringe pattern, in this work the authors developed a general quantitative theory to predict the intensity fringe pattern in closed-form formulas, which incorporates the effects of partial spatial coherence, spectral average and detector pixel re-binning. These formulas can be used to predict the fringe visibility of a Talbot-Lau interferometer with any geometry configuration and any source spectrum.

Time resolved X-ray Dark-Field Tomography Revealing Water Transport in a Fresh Cement Sample

Grating-based X-ray dark-field tomography is a promising technique for biomedical and materials research. Even if the resolution of conventional X-ray tomography does not suffice to resolve relevant structures, the dark-field signal provides valuable information about the sub-pixel microstructural properties of the sample. Here, we report on the potential of X-ray dark-field imaging to be used for time-resolved three-dimensional studies. By repeating consecutive tomography scans on a fresh cement sample, we were able to study the hardening dynamics of the cement paste in three dimensions over time. The hardening of the cement was accompanied by a strong decrease in the dark-field signal pointing to microstructural changes within the cement paste. Furthermore our results hint at the transport of water from certain limestone grains, which were embedded in the sample, to the cement paste during the process of hardening. This is indicated by an increasing scattering signal which was observed for two of the six tested limestone grains. Electron microscopy images revealed a distinct porous structure only for those two grains which supports the following interpretation of our results. When the water filled pores of the limestone grains empty during the experiment the scattering signal of the grains increases.

Visualization of neonatal lung injury associated with mechanical ventilation using x-ray dark-field radiography

Mechanical ventilation (MV) and supplementation of oxygen-enriched gas, often needed in postnatal resuscitation procedures, are known to be main risk factors for impaired pulmonary development in the preterm and term neonates. Unfortunately, current imaging modalities lack in sensitivity for the detection of early stage lung injury. The present study reports a new imaging approach for diagnosis and staging of early lung injury induced by MV and hyperoxia in neonatal mice. The imaging method is based on the Talbot-Lau x-ray grating interferometry that makes it possible to quantify the x-ray small-angle scattering on the air-tissue interfaces. This so-called dark-field signal revealed increasing loss of x-ray small-angle scattering when comparing images of neonatal mice undergoing hyperoxia and MV-O₂ with animals kept at room air. The changes in the dark field correlated well with histologic findings and provided superior differentiation than conventional x-ray imaging and lung function testing. The results suggest that x-ray dark-field radiography is a sensitive tool for assessing structural changes in the developing lung. In the future, with further technical developments x-ray dark-field imaging could be an important tool for earlier diagnosis and sensitive monitoring of lung injury in neonates requiring postnatal oxygen or ventilator therapy.

2D-Omnidirectional Hard-X-Ray Scattering Sensitivity in a Single Shot

X-ray scattering imaging can provide complementary information to conventional absorption based radiographic imaging about the unresolved microstructures of a sample. The scattering signal can be accessed with various methods based on coherent illumination, which span from self-imaging to speckle scanning. The directional sensitivity of the existing real space imaging methods is limited to a few directions on the imaging plane and requires scanning of the optical components, or the rotation of either the sample or the imaging setup, in order to cover the full range of possible scattering directions. In this Letter the authors propose a new method that allows the simultaneous acquisition of scattering images in all possible directions in a single shot. This is achieved by a specialized phase grating and a detector with sufficient spatial resolution to record the generated interference fringe. The structural length scale sensitivity of the system can be tuned by varying its geometry for a fixed grating design. Taking into account ongoing developments in the field of compact x-ray sources that allow high brightness and sufficient spatial coherence, the applicability of omnidirectional scattering imaging in industrial and medical settings is boosted significantly.

In Vivo Dark-Field Radiography for Early Diagnosis and Staging of Pulmonary Emphysema

OBJECTIVES

The aim of this study was to evaluate the suitability of in vivo x-ray dark-field radiography for early-stage diagnosis of pulmonary emphysema in mice. Furthermore, we aimed to analyze how the dark-field signal correlates with morphological changes of lung architecture at distinct stages of emphysema.

MATERIALS AND METHODS

Female 8- to 10-week-old C57Bl/6N mice were used throughout all experiments. Pulmonary emphysema was induced by orotracheal injection of porcine pancreatic elastase (80-U/kg body weight) (n = 30). Control mice (n = 11) received orotracheal injection of phosphate-buffered saline. To monitor the temporal patterns of emphysema development over time, the mice were imaged 7, 14, or 21 days after the application of elastase or phosphate-buffered saline. X-ray transmission and dark-field images were acquired with a prototype grating-based small-animal scanner. In vivo pulmonary function tests were performed before killing the animals. In addition, lungs were obtained for detailed histopathological analysis, including mean cord length (MCL) quantification as a parameter for the assessment of emphysema. Three blinded readers, all of them experienced radiologists and familiar with dark-field imaging, were asked to grade the severity of emphysema for both dark-field and transmission images.

RESULTS

Histopathology and MCL quantification confirmed the introduction of different stages of emphysema, which could be clearly visualized and differentiated on the dark-field radiograms, whereas early stages were not detected on transmission images. The correlation between MCL and dark-field signal intensities (r = 0.85) was significantly higher than the correlation between MCL and transmission signal intensities (r = 0.37). The readers' visual ratings for dark-field images correlated significantly better with MCL (r = 0.85) than visual ratings for transmission images (r = 0.36). Interreader agreement and the diagnostic accuracy of both quantitative and visual assessment were significantly higher for dark-field imaging than those for conventional transmission images.

CONCLUSIONS

X-ray dark-field radiography can reliably visualize different stages of emphysema in vivo and demonstrates significantly higher diagnostic accuracy for early stages of emphysema than conventional attenuation-based radiography.

Imaging properties of high aspect ratio absorption gratings for use in preclinical x-ray grating interferometry

X-ray grating interferometry is one among various methods that allow extracting the so-called phase and visibility contrasts in addition to the well-known transmission images. Crucial to achieving a high image quality are the absorption gratings employed. Here, we present an in-depth analysis of how the grating type and lamella heights influence the final images. Benchmarking gratings of two different designs, we show that a frequently used proxy for image quality, a grating's so-called visibility, is insufficient to predict contrast-to-noise ratios (CNRs). Presenting scans from an excised rat lung, we demonstrate that the CNRs obtained for transmission and visibility images anti-correlate. This is explained by the stronger attenuation implied by gratings that are engineered to provide high visibilities by means of an increased lamella height. We show that even the visibility contrast can suffer from this effect when the associated reduced photon flux on the detector is not outweighed by a corresponding gain in visibility. Resulting in an inevitable trade-off between the quality of the two contrasts, the question of how an optimal grating should be designed can hence only be answered in terms of Pareto optimality.

Quantification of the sensitivity range in neutron dark-field imaging

In neutron grating interferometry, the dark-field image visualizes the scattering properties of samples in the small-angle and ultra-small-angle scattering range. These angles correspond to correlation lengths from several hundred nanometers up to several tens of micrometers. In this article, we present an experimental study that demonstrates the potential of quantitative neutron dark-field imaging. The dark-field signal for scattering from different particle sizes and concentrations of mono-dispersive polystyrene particles in aqueous solution is compared to theoretical predictions and the good agreement between measurements and calculations underlines the quantitative nature of the measured values and reliability of the technique with neutrons.

Lens-term- and edge-effect in X-ray grating interferometry

X-ray grating interferometry requires gratings with periods in the micrometer range and allows the acquisition of the dark-field contrast. The analyzer grating is designed to match the period of the interference pattern in order to translate it into a measurable intensity modulation. In this study, we explore the influence of a sample-induced mismatch between the interference pattern and the analyzer grating on the dark-field contrast. We propose a formula for the calculation of the signal due to a period mismatch and present estimations varying periods and detector pixel size. Furthermore, numerical simulations of the X-ray wave-front demonstrate that the wave-front curvature, described by the lens-term, e.g. behind a parabolic lens or edges of a sample can change the period of the interference pattern. Our results give a concrete explanation for the formation of a dark-field contrast from object edges and thus allow a better understanding of the dark-field signal obtained with a grating interferometer.

Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography

Idiopathic pulmonary fibrosis (IPF) is a chronic and progressive lung disease with a median life expectancy of 4–5 years after initial diagnosis. Early diagnosis and accurate monitoring of IPF are limited by a lack of sensitive imaging techniques that are able to visualize early fibrotic changes at the epithelial-mesenchymal interface. Here, we report a new x-ray imaging approach that directly visualizes the air-tissue interfaces in mice in vivo. This imaging method is based on the detection of small-angle x-ray scattering that occurs at the air-tissue interfaces in the lung. Small-angle scattering is detected with a Talbot-Lau interferometer, which provides the so-called x-ray dark-field signal. Using this imaging modality, we demonstrate-for the first time-the quantification of early pathogenic changes and their correlation with histological changes, as assessed by stereological morphometry. The presented radiography method is significantly more sensitive in detecting morphological changes compared with conventional x-ray imaging, and exhibits a significantly lower radiation dose than conventional x-ray CT. As a result of the improved imaging sensitivity, this new imaging modality could be used in future to reduce the number of animals required for pulmonary research studies.

Computer-aided diagnosis of pulmonary diseases using x-ray darkfield radiography

In this work we develop a computer-aided diagnosis (CAD) scheme for classification of pulmonary disease for grating-based x-ray radiography. In addition to conventional transmission radiography, the grating-based technique provides a dark-field imaging modality, which utilizes the scattering properties of the x-rays. This modality has shown great potential for diagnosing early stage emphysema and fibrosis in mouse lungs in vivo. The CAD scheme is developed to assist radiologists and other medical experts to develop new diagnostic methods when evaluating grating-based images. The scheme consists of three stages: (i) automatic lung segmentation; (ii) feature extraction from lung shape and dark-field image intensities; (iii) classification between healthy, emphysema and fibrosis lungs. A study of 102 mice was conducted with 34 healthy, 52 emphysema and 16 fibrosis subjects. Each image was manually annotated to build an experimental dataset. System performance was assessed by: (i) determining the quality of the segmentations; (ii) validating emphysema and fibrosis recognition by a linear support vector machine using leave-one-out cross-validation. In terms of segmentation quality, we obtained an overlap percentage (Ω) 92.63  ±  3.65%, Dice Similarity Coefficient (DSC) 89.74  ±  8.84% and Jaccard Similarity Coefficient 82.39  ±  12.62%. For classification, the accuracy, sensitivity and specificity of diseased lung recognition was 100%. Classification between emphysema and fibrosis resulted in an accuracy of 93%, whilst the sensitivity was 94% and specificity 88%. In addition to the automatic classification of lungs, deviation maps created by the CAD scheme provide a visual aid for medical experts to further assess the severity of pulmonary disease in the lung, and highlights regions affected.

X-ray Scatter Imaging of Hepatocellular Carcinoma in a Mouse Model Using Nanoparticle Contrast Agents

Hepatocellular carcinoma (HCC) is one of the most common malignant tumors worldwide and is almost uniformly fatal. Current methods of detection include ultrasound examination and imaging by CT scan or MRI; however, these techniques are problematic in terms of sensitivity and specificity, and the detection of early tumors (<1 cm diameter) has proven elusive. Better, more specific, and more sensitive detection methods are therefore urgently needed. Here we discuss the application of a newly developed x-ray imaging technique called Spatial Frequency Heterodyne Imaging (SFHI) for the early detection of HCC. SFHI uses x-rays scattered by an object to form an image and is more sensitive than conventional absorption-based x-radiography. We show that tissues labeled in vivo with gold nanoparticle contrast agents can be detected using SFHI. We also demonstrate that directed targeting and SFHI of HCC tumors in a mouse model is possible through the use of HCC-specific antibodies. The enhanced sensitivity of SFHI relative to currently available techniques enables the x-ray imaging of tumors that are just a few millimeters in diameter and substantially reduces the amount of nanoparticle contrast agent required for intravenous injection relative to absorption-based x-ray imaging.

Effect of beam hardening on a visibility-contrast image obtained by X-ray grating interferometry

X-ray grating interferometry has been highlighted in the last decade as a multi-modal X-ray phase-imaging technique for providing absorption, differential phase, and visibility-contrast images. It has been mainly reported that the visibility contrast in the visibility-contrast image originates from unresolvable random microstructures. In this paper, we show that the visibility contrast is even reduced by a uniform sample with flat surfaces due to the so-called "beam-hardening effect", which has to be taken into account when X-rays with a continuous spectrum is used. We drive a criterion for determining whether the beam-hardening effect occurs or not, and propose a method for correcting the effect of beam hardening on a visibility-contrast image.

Enhancing Tabletop X-Ray Phase Contrast Imaging with Nano-Fabrication

X-ray phase-contrast imaging is a promising approach for improving soft-tissue contrast and lowering radiation dose in biomedical applications. While current tabletop imaging systems adapt to common x-ray tubes and large-area detectors by employing absorptive elements such as absorption gratings or monolithic crystals to filter the beam, we developed nanometric phase gratings which enable tabletop x-ray far-field interferometry with only phase-shifting elements, leading to a substantial enhancement in the performance of phase contrast imaging. In a general sense the method transfers the demands on the spatial coherence of the x-ray source and the detector resolution to the feature size of x-ray phase masks. We demonstrate its capabilities in hard x-ray imaging experiments at a fraction of clinical dose levels and present comparisons with the existing Talbot-Lau interferometer and with conventional digital radiography.

Grating-based X-ray Dark-field Computed Tomography of Living Mice

Changes in x-ray attenuating tissue caused by lung disorders like emphysema or fibrosis are subtle and thus only resolved by high-resolution computed tomography (CT). The structural reorganization, however, is of strong influence for lung function. Dark-field CT (DFCT), based on small-angle scattering of x-rays, reveals such structural changes even at resolutions coarser than the pulmonary network and thus provides access to their anatomical distribution. In this proof-of-concept study we present x-ray in vivo DFCTs of lungs of a healthy, an emphysematous and a fibrotic mouse. The tomographies show excellent depiction of the distribution of structural – and thus indirectly functional – changes in lung parenchyma, on single-modality slices in dark field as well as on multimodal fusion images. Therefore, we anticipate numerous applications of DFCT in diagnostic lung imaging. We introduce a scatter-based Hounsfield Unit (sHU) scale to facilitate comparability of scans. In this newly defined sHU scale, the pathophysiological changes by emphysema and fibrosis cause a shift towards lower numbers, compared to healthy lung tissue.

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We present so far unreported x-ray scatter dark-field CT scans of living mice performed with a Talbot–Lau interferometer.

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Dark field gives access to structural information not provided by attenuation CT at scales below the detector pixel size.

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Changes of lung alveoli structure are clearly visualized by dark-field CT for emphysema and fibrosis.

Lung diseases pose one of the leading causes of death worldwide. They are often difficult to diagnose at an early stage due to low sensitivity of conventional medical imaging systems towards structural changes of the lung tissue. With dark-field imaging based on scattering of x-rays such structural changes can be visualized even at imaging system resolutions coarser than the lung alveoli, as opposed to conventional x-ray imaging based on attenuation. By overcoming experimental scan time and dose issues, we report the first dark-field computed tomography scans on living mice, demonstrating excellent depiction of the anatomical distribution of pathological lung changes.

A general theory of interference fringes in x-ray phase grating imaging

PURPOSE

The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need.

METHODS

In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance.

RESULTS

The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints.

CONCLUSIONS

In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers.

Ex Vivo Perfusion-Simulation Measurements of Microbubbles as a Scattering Contrast Agent for Grating-Based X-Ray Dark-Field Imaging

The investigation of dedicated contrast agents for x-ray dark-field imaging, which exploits small-angle scattering at microstructures for contrast generation, is of strong interest in analogy to the common clinical use of high-atomic number contrast media in conventional attenuation-based imaging, since dark-field imaging has proven to provide complementary information. Therefore, agents consisting of gas bubbles, as used in ultrasound imaging for example, are of particular interest. In this work, we investigate an experimental contrast agent based on microbubbles consisting of a polyvinyl-alcohol shell with an iron oxide coating, which was originally developed for multimodal imaging and drug delivery. Its performance as a possible contrast medium for small-animal angiography was examined using a mouse carcass to realistically consider attenuating and scattering background signal. Subtraction images of dark field, phase contrast and attenuation were acquired for a concentration series of 100%, 10% and 1.3% to mimic different stages of dilution in the contrast agent in the blood vessel system. The images were compared to the gold-standard iodine-based contrast agent Solutrast, showing a good contrast improvement by microbubbles in dark-field imaging. This study proves the feasibility of microbubble-based dark-field contrast-enhancement in presence of scattering and attenuating mouse body structures like bone and fur. Therefore, it suggests a strong potential of the use of polymer-based microbubbles for small-animal dark-field angiography.

X-ray Moiré deflectometry using synthetic reference images

Moiré fringe deflectometry with grating interferometers is a technique that enables refraction-based x-ray imaging using a single exposure of an object. To obtain the refraction image, the method requires a reference fringe pattern (without the object). Our study shows that, in order to avoid artifacts, the reference pattern must be exactly matched in phase with the object fringe pattern. In experiments, however, it is difficult to produce a perfectly matched reference pattern due to unavoidable interferometer drifts. We present a simple method to obtain matched reference patterns using a phase-scan procedure to generate synthetic Moiré images. The method will enable deflectometric diagnostics of transient phenomena such as laser-produced plasmas and could improve the sensitivity and accuracy of medical phase-contrast imaging.

Achromatic approach to phase-based multi-modal imaging with conventional X-ray sources

Compatibility with polychromatic radiation is an important requirement for an imaging system using conventional rotating anode X-ray sources. With a commercially available energy-resolving single-photon-counting detector we investigated how broadband radiation affects the performance of a multi-modal edge-illumination phase-contrast imaging system. The effect of X-ray energy on phase retrieval is presented, and the achromaticity of the method is experimentally demonstrated. Comparison with simulated measurements integrating over the energy spectrum shows that there is no significant loss of image quality due to the use of polychromatic radiation. This means that, to a good approximation, the imaging system exploits radiation in the same way at all energies typically used in hard-X-ray imaging.

Statistical iterative reconstruction algorithm for X-ray phase-contrast CT

Grating-based phase-contrast computed tomography (PCCT) is a promising imaging tool on the horizon for pre-clinical and clinical applications. Until now PCCT has been plagued by strong artifacts when dense materials like bones are present. In this paper, we present a new statistical iterative reconstruction algorithm which overcomes this limitation. It makes use of the fact that an X-ray interferometer provides a conventional absorption as well as a dark-field signal in addition to the phase-contrast signal. The method is based on a statistical iterative reconstruction algorithm utilizing maximum-a-posteriori principles and integrating the statistical properties of the raw data as well as information of dense objects gained from the absorption signal. Reconstruction of a pre-clinical mouse scan illustrates that artifacts caused by bones are significantly reduced and image quality is improved when employing our approach. Especially small structures, which are usually lost because of streaks, are recovered in our results. In comparison with the current state-of-the-art algorithms our approach provides significantly improved image quality with respect to quantitative and qualitative results. In summary, we expect that our new statistical iterative reconstruction method to increase the general usability of PCCT imaging for medical diagnosis apart from applications focused solely on soft tissue visualization.

Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study

Objectives

Conventional X-ray attenuation-based contrast is inherently low for the soft-tissue components of the female breast. To overcome this limitation, we investigate the diagnostic merits arising from dark-field mammography by means of certain tumour structures enclosed within freshly dissected mastectomy samples.

Methods

We performed grating-based absorption, absolute phase and dark-field mammography of three freshly dissected mastectomy samples containing bi- and multifocal carcinoma using a compact, laboratory Talbot-Lau interferometer. Preoperative in vivo imaging (digital mammography, ultrasound, MRI), postoperative histopathological analysis and ex vivo digital mammograms of all samples were acquired for the diagnostic verification of our results.

Results

In the diagnosis of multifocal tumour growth, dark-field mammography seems superior to standard breast imaging modalities, providing a better resolution of small, calcified tumour nodules, demarcation of tumour boundaries with desmoplastic stromal response and spiculated soft-tissue strands extending from an invasive ductal breast cancer.

Conclusions

On the basis of selected cases, we demonstrate that dark-field mammography is capable of outperforming conventional mammographic imaging of tumour features in both calcified and non-calcified tumours. Presuming dose optimization, our results encourage further studies on larger patient cohorts to identify those patients that will benefit the most from this promising additional imaging modality.

Key Points

• X-ray dark-field mammography provides significantly improved visualization of tumour features

• X-ray dark-field mammography is capable of outperforming conventional mammographic imaging

• X-ray dark-field mammography provides imaging sensitivity towards highly dispersed calcium grains

Non-invasive differentiation of kidney stone types using X-ray dark-field radiography

Treatment of renal calculi is highly dependent on the chemical composition of the stone in question, which is difficult to determine using standard imaging techniques. The objective of this study is to evaluate the potential of scatter-sensitive X-ray dark-field radiography to differentiate between the most common types of kidney stones in clinical practice. Here, we examine the absorption-to-scattering ratio of 118 extracted kidney stones with a laboratory Talbot-Lau Interferometer. Depending on their chemical composition, microscopic growth structure and morphology the various types of kidney stones show strongly varying, partially opposite contrasts in absorption and dark-field imaging. By assessing the microscopic calculi morphology with high resolution micro-computed tomography measurements, we illustrate the dependence of dark-field signal strength on the respective stone type. Finally, we utilize X-ray dark-field radiography as a non-invasive, highly sensitive (100%) and specific (97%) tool for the differentiation of calcium oxalate, uric acid and mixed types of stones, while additionally improving the detectability of radio-lucent calculi. We prove clinical feasibility of the here proposed method by accurately classifying renal stones, embedded within a fresh pig kidney, using dose-compatible measurements and a quick and simple visual inspection.

Effects of unresolvable edges in grating-based X-ray differential phase imaging

We investigated effects of unresolvable sharp edges on images obtained in a grating-based X-ray differential phase imaging technique. Results of numerical calculations for monochromatic X-rays show that an unresolvable sharp edge generates not only differential-phase contrast but also visibility contrast. The latter shows that the visibility contrast has another major origin other than ultra-small-angle X-ray scattering (USAXS) from randomly distributed unresolvable microstructures, which has been considered the main origin for the contrast. The effects were experimentally confirmed using a synchrotron X-ray source.

Single-shot Z(eff) dense plasma diagnostic through simultaneous refraction and attenuation measurements with a Talbot-Lau x-ray moiré deflectometer

The Talbot-Lau x-ray moiré deflectometer is a powerful plasma diagnostic capable of delivering simultaneous refraction and attenuation information through the accurate detection of x-ray phase shift and intensity. The diagnostic can provide the index of refraction n=1-δ+iβ of an object (dense plasma, for example) placed in the x-ray beam by independently measuring both δ and β, which are directly related to the electron density n(e) and the attenuation coefficient μ, respectively. Since δ and β depend on the effective atomic number Z(eff), a map can be obtained from the ratio between phase and absorption images acquired in a single shot. The Talbot-Lau x-ray moiré deflectometer and its corresponding data acquisition and processing are briefly described to illustrate how the above is achieved; Z(eff) values of test objects within the 4-12 range were obtained experimentally through simultaneous refraction and attenuation measurements. We show that Z(eff) mapping of objects does not require previous knowledge of sample length or shape. The determination of Z(eff) from refraction and attenuation measurements with moiré deflectometry could be of high interest to various domains of high energy density research, such as shocked materials and inertial confinement fusion experiments, as well as material science and nondestructive testing.

A highly sensitive x-ray imaging modality for hepatocellular carcinoma detection in vitro

Innovations that improve sensitivity and reduce cost are of paramount importance in diagnostic imaging. The novel x-ray imaging modality called spatial frequency heterodyne imaging (SFHI) is based on a linear arrangement of x-ray source, tissue, and x-ray detector, much like that of a conventional x-ray imaging apparatus. However, SFHI rests on a complete paradigm reversal compared to conventional x-ray absorption-based radiology: while scattered x-rays are carefully rejected in absorption-based x-ray radiology to enhance the image contrast, SFHI forms images exclusively from x-rays scattered by the tissue. In this study we use numerical processing to produce x-ray scatter images of hepatocellular carcinoma labeled with a nanoparticle contrast agent. We subsequently compare the sensitivity of SFHI in this application to that of both conventional x-ray imaging and magnetic resonance imaging (MRI). Although SFHI is still in the early stages of its development, our results show that the sensitivity of SFHI is an order of magnitude greater than that of absorption-based x-ray imaging and approximately equal to that of MRI. As x-ray imaging modalities typically have lower installation and service costs compared to MRI, SFHI could become a cost effective alternative to MRI, particularly in areas of the world with inadequate availability of MRI facilities.

General solution for quantitative dark-field contrast imaging with grating interferometers

Grating interferometer based imaging with X-rays and neutrons has proven to hold huge potential for applications in key research fields conveying biology and medicine as well as engineering and magnetism, respectively. The thereby amenable dark-field imaging modality implied the promise to access structural information beyond reach of direct spatial resolution. However, only here a yet missing approach is reported that finally allows exploiting this outstanding potential for non-destructive materials characterizations. It enables to obtain quantitative structural small angle scattering information combined with up to 3-dimensional spatial image resolution even at lab based x-ray or at neutron sources. The implied two orders of magnitude efficiency gain as compared to currently available techniques in this regime paves the way for unprecedented structural investigations of complex sample systems of interest for material science in a vast range of fields.

Large-angle x-ray scatter in Talbot-Lau interferometry for breast imaging

Monte Carlo simulations were used to investigate large-angle x-ray scatter at design energy of 25 keV during small field of view (9.6 cm × 5 cm) differential phase contrast imaging of the breast using Talbot-Lau interferometry. Homogenous, adipose and fibroglandular breasts of uniform thickness ranging from 2 to 8 cm encompassing the field of view were modeled. Theoretically determined transmission efficiencies of the gratings were used to validate the Monte Carlo simulations, followed by simulations to determine the x-ray scatter reaching the detector. The recorded x-ray scatter was classified into x-ray photons that underwent at least one Compton interaction (incoherent scatter) and Rayleigh interaction alone (coherent scatter) for further analysis. Monte Carlo based estimates of transmission efficiencies showed good correspondence [Formula: see text] with theoretical estimates. Scatter-to-primary ratio increased with increasing breast thickness, ranging from 0.11 to 0.22 for 2-8 cm thick adipose breasts and from 0.12 to 0.28 for 2-8 cm thick fibroglandular breasts. The analyzer grating reduced incoherent scatter by ~18% for 2 cm thick adipose breast and by ~35% for 8 cm thick fibroglandular breast. Coherent scatter was the dominant contributor to the total scatter. Coherent-to-incoherent scatter ratio ranged from 2.2 to 3.1 for 2-8 cm thick adipose breasts and from 2.7 to 3.4 for 2-8 cm thick fibroglandular breasts.

Signal decomposition for X-ray dark-field imaging

Grating-based X-ray dark-field imaging is a new imaging modality. It allows the visualization of structures at micrometer scale due to small-angle scattering of the X-ray beam. However, reading darkfield images is challenging as absorption and edge-diffraction effects also contribute to the dark-field signal, without adding diagnostic value. In this paper, we present a novel--and to our knowledge the first--algorithm for isolating small-angle scattering in dark-field images, which greatly improves their interpretability. To this end, our algorithm utilizes the information available from the absorption and differential phase images to identify clinically irrelevant contributions to the dark-field image. Experimental results on phantom and ex-vivo breast data promise a greatly enhanced diagnostic value of dark-field images.

Complex dark-field contrast and its retrieval in x-ray phase contrast imaging implemented with Talbot interferometry

PURPOSE

Under the existing theoretical framework of x-ray phase contrast imaging methods implemented with Talbot interferometry, the dark-field contrast refers to the reduction in interference fringe visibility due to small-angle x-ray scattering of the subpixel microstructures of an object to be imaged. This study investigates how an object's subpixel microstructures can also affect the phase of the intensity oscillations.

METHODS

Instead of assuming that the object's subpixel microstructures distribute in space randomly, the authors' theoretical derivation starts by assuming that an object's attenuation projection and phase shift vary at a characteristic size that is not smaller than the period of analyzer grating G₂ and a characteristic length dc. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the zeroth- and first-order Fourier coefficients of the x-ray irradiance recorded at each detector cell are derived. Then the concept of complex dark-field contrast is introduced to quantify the influence of the object's microstructures on both the interference fringe visibility and the phase of intensity oscillations. A method based on the phase-attenuation duality that holds for soft tissues and high x-ray energies is proposed to retrieve the imaginary part of the complex dark-field contrast for imaging. Through computer simulation study with a specially designed numerical phantom, they evaluate and validate the derived analytic formulae and the proposed retrieval method.

RESULTS

Both theoretical analysis and computer simulation study show that the effect of an object's subpixel microstructures on x-ray phase contrast imaging method implemented with Talbot interferometry can be fully characterized by a complex dark-field contrast. The imaginary part of complex dark-field contrast quantifies the influence of the object's subpixel microstructures on the phase of intensity oscillations. Furthermore, at relatively high energies, for soft tissues it can be retrieved for imaging with a method based on the phase-attenuation duality.

CONCLUSIONS

The analytic formulae derived in this work to characterize the complex dark-field contrast in x-ray phase contrast imaging method implemented with Talbot interferometry are of significance, which may initiate more activities in the research and development of x-ray differential phase contrast imaging for extensive biomedical applications.

Energy weighted x-ray dark-field imaging

The dark-field image obtained in grating-based x-ray phase-contrast imaging can provide information about the objects' microstructures on a scale smaller than the pixel size even with low geometric magnification. In this publication we demonstrate that the dark-field image quality can be enhanced with an energy-resolving pixel detector. Energy-resolved x-ray dark-field images were acquired with a 16-energy-channel photon-counting pixel detector with a 1 mm thick CdTe sensor in a Talbot-Lau x-ray interferometer. A method for contrast-noise-ratio (CNR) enhancement is proposed and validated experimentally. In measurements, a CNR improvement by a factor of 1.14 was obtained. This is equivalent to a possible radiation dose reduction of 23%.

Correlation of X-ray dark-field radiography to mechanical sample properties

The directional dark-field signal obtained with X-ray grating interferometry yields direction-dependent information about the X-ray scattering taking place inside the examined sample. It allows examination of its morphology without the requirement of resolving the micrometer size structures directly causing the scattering. The local morphology in turn gives rise to macroscopic mechanical properties of the investigated specimen. In this study, we investigate the relation between the biomechanical elasticity (Young's modulus) and the measured directional dark-field parameters of a well-defined sample made of wood. In our proof-of-principle experiment, we found a correlation between Young's modulus, the average dark-field signal, and the average dark-field anisotropy. Hence, we are able to show that directional dark-field imaging is a new method to predict mechanical sample properties. As grating interferometry provides absorption, phase-contrast, and dark-field data at the same time, this technique appears promising to combine imaging and mechanical testing in a single testing stage. Therefore, we believe that directional dark-field imaging will have a large impact in the materials science world.

Reconstruction of scalar and vectorial components in X-ray dark-field tomography

Grating-based X-ray dark-field imaging is a novel technique for obtaining image contrast for object structures at size scales below setup resolution. Such an approach appears particularly beneficial for medical imaging and nondestructive testing. It has already been shown that the dark-field signal depends on the direction of observation. However, up to now, algorithms for fully recovering the orientation dependence in a tomographic volume are still unexplored. In this publication, we propose a reconstruction method for grating-based X-ray dark-field tomography, which models the orientation-dependent signal as an additional observable from a standard tomographic scan. In detail, we extend the tomographic volume to a tensorial set of voxel data, containing the local orientation and contributions to dark-field scattering. In our experiments, we present the first results of several test specimens exhibiting a heterogeneous composition in microstructure, which demonstrates the diagnostic potential of the method.

Multiple scattering tomography

Multiple scattering represents a challenge for numerous modern tomographic imaging techniques. In this Letter, we derive an appropriate line integral that allows for the tomographic reconstruction of angular resolved scattering distributions, even in the presence of multiple scattering. The line integral is applicable to a wide range of imaging techniques utilizing various kinds of probes. Here, we use x-ray grating interferometry to experimentally validate the framework and to demonstrate additional structural sensitivity, which exemplifies the impact of multiple scattering tomography.

Moiré deflectometry using the Talbot-Lau interferometer as refraction diagnostic for high energy density plasmas at energies below 10 keV

The highly localized density gradients expected in High Energy Density (HED) plasma experiments can be characterized by x-ray phase-contrast imaging in addition to conventional attenuation radiography. Moiré deflectometry using the Talbot-Lau grating interferometer setup is an attractive HED diagnostic due to its high sensitivity to refraction induced phase shifts. We report on the adaptation of such a system for operation in the sub-10 keV range by using a combination of free standing and ultrathin Talbot gratings. This new x-ray energy explored matches well the current x-ray backlighters used for HED experiments, while also enhancing phase effects at lower electron densities. We studied the performance of the high magnification, low energy Talbot-Lau interferometer, for single image phase retrieval using Moiré fringe deflectometry. Our laboratory and simulation studies indicate that such a device is able to retrieve object electron densities from phase shift measurements. Using laboratory x-ray sources from 7 to 15 μm size we obtained accurate simultaneous measurements of refraction and attenuation for both sharp and mild electron density gradients.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

Sensitivity of a non-interferometric grating-based x-ray imaging system

Grating-based x-ray imaging systems are of two categories: interferometric and non-interferometric. This work focuses on the angular sensitivity of the phase-stepping-based non-interferometric setup. First, a numerical model of the system is developed and verified with experimental results. Then, an existing system is optimized and verified by comparison with biological sample experiments. The results are also compared with those of a Talbot-Lau interferometer. Finally, an analytical formula of the system sensitivity is derived and limitations of the setup are discussed.

In-vivo dark-field and phase-contrast x-ray imaging

Novel radiography approaches based on the wave nature of x-rays when propagating through matter have a great potential for improved future x-ray diagnostics in the clinics. Here, we present a significant milestone in this imaging method: in-vivo multi-contrast x-ray imaging of a mouse using a compact scanner. Of particular interest is the enhanced contrast in regions related to the respiratory system, indicating a possible application in diagnosis of lung diseases (e.g. emphysema).

Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures

Over the recent years X-ray differential phase-contrast imaging was developed for the hard X-ray regime as produced from laboratory X-ray sources. The technique uses a grating-based Talbot-Lau interferometer and was shown to yield image contrast gain, which makes it very interesting to the fields of medical imaging and non-destructive testing, respectively. In addition to X-ray attenuation contrast, the differential phase-contrast and dark-field images provide different structural information about a specimen. For the dark-field even at length scales much smaller than the spatial resolution of the imaging system. Physical interpretation of the dark-field information as present in radiographic and tomographic (CT) images requires a detailed look onto the geometric orientation between specimen and the setup. During phase-stepping the drop in intensity modulation, due to local scattering effects within the specimen is reproduced in the dark-field signal. This signal shows strong dependencies on micro-porosity and micro-fibers if these are numerous enough in the object. Since a grating-interferometer using a common unidirectional line grating is sensitive to X-ray scattering in one plane only, the dark-field image is influenced by the fiber orientations with respect to the grating bars, which can be exploited to obtain anisotropic structural information. With this contribution, we attempt to extend existing models for 2D projections to 3D data by analyzing dark-field contrast tomography of anisotropically structured materials such as carbon fiber reinforced carbon (CFRC).

A three-image algorithm for hard x-ray grating interferometry

A three-image method to extract absorption, refraction and scattering information for hard x-ray grating interferometry is presented. The method comprises a post-processing approach alternative to the conventional phase stepping procedure and is inspired by a similar three-image technique developed for analyzer-based x-ray imaging. Results obtained with this algorithm are quantitatively comparable with phase-stepping. This method can be further extended to samples with negligible scattering, where only two images are needed to separate absorption and refraction signal. Thanks to the limited number of images required, this technique is a viable route to bio-compatible imaging with x-ray grating interferometer. In addition our method elucidates and strengthens the formal and practical analogies between grating interferometry and the (non-interferometric) diffraction enhanced imaging technique.

Coherent superposition in grating-based directional dark-field imaging

X-ray dark-field scatter imaging allows to gain information on the average local direction and anisotropy of micro-structural features in a sample well below the actual detector resolution. For thin samples the morphological interpretation of the signal is straight forward, provided that only one average orientation of sub-pixel features is present in the specimen. For thick samples, however, where the x-ray beam may pass structures of many different orientations and dimensions, this simple assumption in general does not hold and a quantitative description of the resulting directional dark-field signal is required to draw deductions on the morphology. Here we present a description of the signal formation for thick samples with many overlying structures and show its validity in experiment. In contrast to existing experimental work this description follows from theoretical predictions of a numerical study using a Fourier optics approach. One can easily extend this description and perform a quantitative structural analysis of clinical or materials science samples with directional dark-field imaging or even direction-dependent dark-field CT.

On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography

We show that a distribution of micrometer-sized calcifications in the human breast which are not visible in clinical x-ray mammography at diagnostic dose levels can produce a significant dark-field signal in a grating-based x-ray phase-contrast imaging setup with a tungsten anode x-ray tube operated at 40 kVp. A breast specimen with invasive ductal carcinoma was investigated immediately after surgery by Talbot-Lau x-ray interferometry with a design energy of 25 keV. The sample contained two tumors which were visible in ultrasound and contrast-agent enhanced MRI but invisible in clinical x-ray mammography, in specimen radiography and in the attenuation images obtained with the Talbot-Lau interferometer. One of the tumors produced significant dark-field contrast with an exposure of 0.85 mGy air-kerma. Staining of histological slices revealed sparsely distributed grains of calcium phosphate with sizes varying between 1 and 40 μm in the region of this tumor. By combining the histological investigations with an x-ray wave-field simulation we demonstrate that a corresponding distribution of grains of calcium phosphate in the form of hydroxylapatite has the ability to produce a dark-field signal which would-to a substantial degree-explain the measured dark-field image. Thus we have found the appearance of new information (compared to attenuation and differential phase images) in the dark-field image. The second tumor in the same sample did not contain a significant fraction of these very fine calcification grains and was invisible in the dark-field image. We conclude that some tumors which are invisible in x-ray absorption mammography might be detected in the x-ray dark-field image at tolerable dose levels.