Propagation-based X-ray Research Articles

Stability Estimates for Linearized Near-Field Phase Retrieval in X-ray Phase Contrast Imaging

Propagation-based X-ray phase contrast enables nanoscale imaging of biological tissue by probing not only the attenuation but also the real part of the refractive index of the sample. Since only intensities of diffracted waves can be measured, the main mathematical challenge consists in a phase-retrieval problem in the near-field regime. We treat an often used linearized version of this problem known as the contract transfer function model. Surprisingly, this inverse problem turns out to be well-posed assuming only a compact support of the imaged object. Moreover, we establish bounds on the Lipschitz stability constant. In general this constant grows exponentially with the Fresnel number of the imaging setup. However, both for homogeneous objects, characterized by a fixed ratio of the induced refractive phase shifts and attenuation, and in the case of measurements at two distances, a much more favorable algebraic dependence on the Fresnel number can be shown. In some cases we establish order optimality of our estimates.

Amyloid-β plaque deposition measured using propagation-based X-ray phase contrast CT imaging.

Amyloid beta accumulation into insoluble plaques (Aβp) is known to play a significant role in the pathological process in Alzheimer's disease (AD). The presence of Aβp is also one of the neuropathological hallmarks for the disease. AD final diagnosis is generally acknowledged after the evaluation of Aβp deposition in the brain. Insoluble Aβp accumulation may also concur to cause AD as postulated in the so-called amyloid hypothesis. Therefore, the visualization, evaluation and quantification of Aβp are nowadays the keys for a better understanding of the disease, which may point to a possible cure for AD in the near future. Synchrotron-based X-ray phase contrast (XPC) has been demonstrated as the only imaging method that can retrieve the Aβp signal with high spatial resolution (up to 10 µm), high sensitivity and three-dimensional information at the same time. Although at the moment XPC is suitable for exvivo samples only, it may develop into an alternative to positron emission tomography and magnetic resonance imaging in Aβp imaging. In this contribution the possibility of using synchrotron-based X-ray phase propagation computed tomography to visualize and measure Aβp on mouse brains is presented. A careful setup optimization for this application leads to a significant improvement of spatial resolution (∼1 µm), data acquisition speed (five times faster), X-ray dose (five times lower) and setup complexity, without a substantial loss in sensitivity when compared with the classic implementation of grating-based X-ray interferometry.

A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography

Synchrotron source propagation-based X-ray phase contrast computed tomography is increasingly used in pre-clinical imaging. However, it typically requires a large number of projections, and subsequently a large radiation dose, to produce high quality images. To improve the applicability of this imaging technique, reconstruction algorithms that can reduce the radiation dose and acquisition time without degrading image quality are needed. The proposed research focused on using a novel combination of Douglas–Rachford splitting and randomized Kaczmarz algorithms to solve large-scale total variation based optimization in a compressed sensing framework to reconstruct 2D images from a reduced number of projections. Visual assessment and quantitative performance evaluations of a synthetic abdomen phantom and real reconstructed image of an ex-vivo slice of canine prostate tissue demonstrate that the proposed algorithm is competitive in reconstruction process compared with other well-known algorithms. An additional potential benefit of reducing the number of projections would be reduction of time for motion artifact to occur if the sample moves during image acquisition. Use of this reconstruction algorithm to reduce the required number of projections in synchrotron source propagation-based X-ray phase contrast computed tomography is an effective form of dose reduction that may pave the way for imaging of in-vivo samples.

X-ray specks: low dose in vivo imaging of lung structure and function

Respiratory health is directly linked to the structural and mechanical properties of the airways of the lungs. For studying respiratory development and pathology, the ability to quantitatively measure airway dimensions and changes in their size during respiration is highly desirable. Real-time imaging of the terminal airways with sufficient contrast and resolution during respiration is currently not possible. Herein we reveal a simple method for measuring lung airway dimensions in small animals during respiration from a single propagation-based phase contrast x-ray image, thereby requiring minimal radiation. This modality renders the lungs visible as a speckled intensity pattern. In the near-field regime, the size of the speckles is directly correlated with that of the dominant length scale of the airways. We demonstrate that Fourier space quantification of the speckle texture can be used to statistically measure regional airway dimensions at the alveolar scale, with measurement precision finer than the spatial resolution of the imaging system. Using this technique we discovered striking differences in developmental maturity in the lungs of rabbit kittens at birth.

Laboratory x-ray microscopy on high brilliance sources equipped with waveguides

We report on the experimental realization of propagation-based x-ray microscopy with laboratory sources equipped with waveguides. We discuss about the experimental setup, the fabrication steps, and the characterization procedures of the waveguide optics. We demonstrate that the system enables high resolution attenuation imaging of poorly absorbing biological specimens. Furthermore, we report the successful realization of propagation-based phase contrast x-ray microscopy, enabling quantitative thickness estimation in homogeneous objects. Advantages and major limitations of the experimental scheme are presented and discussed.

Boundary-enhancement in propagation-based x-ray phase-contrast tomosynthesis improves depth position characterization

Propagation-based x-ray phase-contrast (PB XPC) tomosynthesis combines the concepts of tomosynthesis and XPC imaging to realize the advantages of both for biological imaging applications. Tomosynthesis permits reductions in acquisition times compared with full-view tomography, while XPC imaging provides the opportunity to resolve weakly absorbing structures. In this note, an investigation of the depth resolving properties of PB XPC tomosynthesis is conducted. The results demonstrate that in-plane structures display strong boundary-enhancement while out-of-plane structures do not. This effect can facilitate the identification of in-plane structures in PB XPC tomosynthesis that could normally not be distinguished from out-of-plane structures in absorption-based tomosynthesis.

Effect of the number and position of nozzle holes on in- and near-nozzle dynamic characteristics of diesel injection

Despite the fact that all modern diesel engines use multi-hole injectors, single-hole injectors are frequently used to understand the fundamental properties of high-pressure diesel injections due to their axisymmetric design of the injector nozzles. A multi-hole injector accommodates many holes around the nozzle axis to deliver adequate amount of fuel with small orifices. The off-axis arrangement of the multi-hole injectors significantly alters the inter- and near-nozzle flow patterns compared to those of the single-hole injectors. This study compares the transient needle motion and near-nozzle flow characteristics of the single- and multi-hole (3-hole and 6-hole) diesel injectors to understand how the difference in hole arrangement and number affects the initial flow development of the diesel injectors. A propagation-based X-ray phase-contrast imaging technique was applied to compare the transient needle motion and near-nozzle flow characteristics of the single- and multi-hole injectors. The comparisons were made by dividing the entire injection process by three sub-stages: opening-transient, quasi-steady and closing-transient.

Real-time measurement of alveolar size and population using phase contrast x-ray imaging.

Herein a propagation-based phase contrast x-ray imaging technique for measuring particle size and number is presented. This is achieved with an algorithm that utilizes the Fourier space signature of the speckle pattern associated with the images of particles. We validate this algorithm using soda-lime glass particles, demonstrating its effectiveness on random and non-randomly packed particles. This technique is then applied to characterise lung alveoli, which are difficult to measure dynamically in vivo with current imaging modalities due to inadequate temporal resolution and/or depth of penetration and field-of-view. We obtain an important result in that our algorithm is able to measure changes in alveolar size on the micron scale during ventilation and shows the presence of alveolar recruitment/de-recruitment in newborn rabbit kittens. This technique will be useful for ventilation management and lung diagnostic procedures.

Experimental comparison of grating- and propagation-based hard X-ray phase tomography of soft tissue

When imaging soft tissues with hard X-rays, phase contrast is often preferred over conventional attenuation contrast due its superior sensitivity. However, it is unclear which of the numerous phase tomography methods yields the optimized results at given experimental conditions. Therefore, we quantitatively compared the three phase tomography methods implemented at the beamline ID19 of the European Synchrotron Radiation Facility: X-ray grating interferometry (XGI), and propagation-based phase tomography, i.e., single-distance phase retrieval (SDPR) and holotomography (HT), using cancerous tissue from a mouse model and an entire heart of a rat. We show that for both specimens, the spatial resolution derived from the characteristic morphological features is about a factor of two better for HT and SDPR compared to XGI, whereas the XGI data generally exhibit much better contrast-to-noise ratios for the anatomical features. Moreover, XGI excels in fidelity of the density measurements, and is also more robust against low-frequency artifacts than HT, but it might suffer from phase-wrapping artifacts. Thus, we can regard the three phase tomography methods discussed as complementary. The application will decide which spatial and density resolutions are desired, for the imaging task and dose requirements, and, in addition, the applicant must choose between the complexity of the experimental setup and the one of data processing.

Quantitative evaluation of a single-distance phase-retrieval method applied on in-line phase-contrast images of a mouse lung.

Propagation-based X-ray phase-contrast computed tomography (PBI) has already proven its potential in a great variety of soft-tissue-related applications including lung imaging. However, the strong edge enhancement, caused by the phase effects, often hampers image segmentation and therefore the quantitative analysis of data sets. Here, the benefits of applying single-distance phase retrieval prior to the three-dimensional reconstruction (PhR) are discussed and quantified compared with three-dimensional reconstructions of conventional PBI data sets in terms of contrast-to-noise ratio (CNR) and preservation of image features. The PhR data sets show more than a tenfold higher CNR and only minor blurring of the edges when compared with PBI in a predominately absorption-based set-up. Accordingly, phase retrieval increases the sensitivity and provides more functionality in computed tomography imaging.

X-ray phase contrast with injected gas for tumor microangiography

We show that the microvasculature of mouse tumors can be visualized using propagation-based phase-contrast x-ray imaging with gas as the contrast agent. The large density difference over the gas–tissue interface provides high contrast, allowing the imaging of small-diameter blood vessels with relatively short exposure times and low dose using a compact liquid-metal-jet x-ray source. The method investigated is applied to tumors (E1A/Ras-transformed mouse embryonic fibroblasts) grown in mouse ears, demonstrating sub-15-µm-diameter imaging of their blood vessels. The exposure time for a 2D projection image is a few seconds and a full tomographic 3D map takes some minutes. The method relies on the strength of the vasculature to withstand the gas pressure. Given that tumor vessels are known to be more fragile than normal vessels, we investigate the tolerance of the vasculature of 12 tumors to gas injection and find that a majority withstand 200 mbar pressures, enough to fill 12-µm-diameter vessels with gas. A comparison of the elasticity of tumorous and non-tumorous vessels supports the assumption of tumor vessels being more fragile. Finally, we conclude that the method has the potential to be extended to the imaging of 15 µm vessels in thick tissue, including mouse imaging, making it of interest for, e.g., angiogenesis research.

Feasibility study of propagation-based phase-contrast X-ray lung imaging on the Imaging and Medical beamline at the Australian Synchrotron

Propagation-based phase-contrast X-ray imaging (PB-PCXI) using synchrotron radiation has achieved high-resolution imaging of the lungs of small animals both in real time and in vivo. Current studies are applying such imaging techniques to lung disease models to aid in diagnosis and treatment development. At the Australian Synchrotron, the Imaging and Medical beamline (IMBL) is well equipped for PB-PCXI, combining high flux and coherence with a beam size sufficient to image large animals, such as sheep, due to a wiggler source and source-to-sample distances of over 137 m. This study aimed to measure the capabilities of PB-PCXI on IMBL for imaging small animal lungs to study lung disease. The feasibility of combining this technique with computed tomography for three-dimensional imaging and X-ray velocimetry for studies of airflow and non-invasive lung function testing was also investigated. Detailed analysis of the role of the effective source size and sample-to-detector distance on lung image contrast was undertaken as well as phase retrieval for sample volume analysis. Results showed that PB-PCXI of lung phantoms and mouse lungs produced high-contrast images, with successful computed tomography and velocimetry also being carried out, suggesting that live animal lung imaging will also be feasible at the IMBL.

Non-Linear Phase Tomography Based on Fréchet Derivative

Phase imaging coupled to micro-tomography acquisition has emerged as a powerful tool to investigate specimens in a non-destructive manner. While the intensity data can be acquired and recorded, the phase information of the signal has to be “retrieved” from the data modulus only. Phase retrieval is an ill-posed non-linear problem and regularization techniques including a priori knowledge are necessary to obtain stable solutions. Several linear phase recovery methods have been proposed and it is expected that some limitations resulting from the linearization of the direct problem will be overcome by taking into account the non-linearity of the phase problem. To achieve this goal, we propose and evaluate a non-linear algorithm for in-line phase micro-tomography based on an iterative Landweber method with an analytic calculation of the Fréchet derivative of the phase-intensity relationship and of its adjoint. The algorithm was applied in the projection space using as initialization the linear mixed solution. The efficacy of the regularization scheme was evaluated on simulated objects with a slowly and a strongly varying phase. Experimental data were also acquired at ESRF using a propagation-based X-ray imaging technique for the given pixel size 0.68 μm. Two regularization scheme were considered: first the initialization was obtained without any prior on the ratio of the real and imaginary parts of the complex refractive index and secondly a constant a priori value was assumed on . The tomographic central slices of the refractive index decrement were compared and numerical evaluation was performed. The non-linear method globally decreases the reconstruction errors compared to the linear algorithm and is achieving better reconstruction results if no prior is introduced in the initialization solution. For in-line phase micro-tomography, this non-linear approach is a new and interesting method in biomedical studies where the exact value of the a priori ratio is not known.

Four-Dimensional Morphological Evolution of an Aluminum Silicon Alloy Using Propagation-Based Phase Contrast X-ray Tomographic Microscopy

Four-dimensional propagation-based phase contrast X-ray tomographic microscopy experiments were performed on an Aluminum29.9mass% Silicon alloy during coarsening. Using propagation-based phase contrast, changes in the three-dimensional morphology of primary silicon particles were captured and the resulting evolution of the microstructure is discussed. While morphologies at earlier times are complex, faceted and highly interconnected, the morphologies at later times are less faceted but remain quite complex.

Comparison of two x-ray phase-contrast imaging methods with a microfocus source

We present a comparison for high-resolution imaging with a laboratory source between grating-based (GBI) and propagation-based (PBI) x-ray phase-contrast imaging. The comparison is done through simulations and experiments using a liquid-metal-jet x-ray microfocus source. Radiation doses required for detection in projection images are simulated as a function of the diameter of a cylindrical sample. Using monochromatic radiation, simulations show a lower dose requirement for PBI for small object features and a lower dose for GBI for larger object features. Using polychromatic radiation, such as that from a laboratory microfocus source, experiments and simulations show a lower dose requirement for PBI for a large range of feature sizes. Tested on a biological sample, GBI shows higher noise levels than PBI, but its advantage of quantitative refractive index reconstruction for multi-material samples becomes apparent.

Measurement of absolute regional lung air volumes from near-field x-ray speckles

Propagation-based phase contrast x-ray (PBX) imaging yields high contrast images of the lung where airways that overlap in projection coherently scatter the x-rays, giving rise to a speckled intensity due to interference effects. Our previous works have shown that total and regional changes in lung air volumes can be accurately measured from two-dimensional (2D) absorption or phase contrast images when the subject is immersed in a water-filled container. In this paper we demonstrate how the phase contrast speckle patterns can be used to directly measure absolute regional lung air volumes from 2D PBX images without the need for a water-filled container. We justify this technique analytically and via simulation using the transport-of-intensity equation and calibrate the technique using our existing methods for measuring lung air volume. Finally, we show the full capabilities of this technique for measuring regional differences in lung aeration.

Propagation-based phase-contrast X-ray microtomography of a cerebral protection device retrieved after carotid artery stenting

Phase-contrast synchrotron X-ray microtomography (pcSyncX) based on the highly coherent X-ray beam has previously been used to visualize the microstructures of biologic specimens, but it has never been used to evaluate embolic debris adherent on a cerebral protection device (CPD). The purpose of this study was to demonstrate the feasibility of pcSyncX for evaluating embolic debris during carotid artery stenting (CAS). Five patients (four males, age range 67-77 years) with severe carotid artery stenosis underwent CAS. The retrieved CPD was exposed to synchrotron radiation and 1000 pcSyncX projection images were obtained by rotating the CPD through 180°. An X-ray shadow of a CPD was converted into a visual image by the scintillator. After microtomographic reconstruction, the three-dimensionally reconstructed images were further segmented into the embolic debris and CPD. The total volume of emboli was calculated by summing the volume at each scanning level. The number of membrane pores covered by emboli as seen from the outer surface was counted and the percentage of covered area was calculated. Embolic debris was clearly demonstrated not only on the inner surface and within pores but also on the outer surface of the CPD. The mean total volume of embolic debris was 0.538 × 10(-6) mm(3) (range 0.225-0.965 × 10(-6) mm(3)). Most (61.5%) of the debris was located at the apical one-third of the CPD and 20.8% of the pore area was covered by debris.

X-ray phase-contrast imaging: the quantum perspective

Time-resolved phase-contrast imaging using ultrafast x-ray sources is an emerging method to investigate ultrafast dynamical processes in matter. Schemes to generate attosecond x-ray pulses have been proposed, bringing electronic timescales into reach and emphasizing the demand for a quantum description. In this paper, we present a method to describe propagation-based x-ray phase-contrast imaging in nonrelativistic quantum electrodynamics. We explain why the standard scattering treatment via Fermi’s golden rule cannot be applied. Instead, the quantum electrodynamical treatment of phase-contrast imaging must be based on a different approach. It turns out that it is essential to select a suitable observable. Here, we choose the quantum-mechanical Poynting operator. We determine the expectation value of our observable and demonstrate that the leading order term describes phase-contrast imaging. It recovers the classical expression of phase-contrast imaging. Thus, it makes the instantaneous electron density of non-stationary electronic states accessible to time-resolved imaging. Interestingly, inelastic (Compton) scattering does automatically not contribute in leading order, explaining the success of the semiclassical description.

Near-field ptychography: phase retrieval for inline holography using a structured illumination

Inline holography is a common phase-contrast imaging method which uses free-space propagation to encode the phase signal into measured intensities. However, quantitative retrieval of the sample's image remains challenging, imposing constraints on the nature of the sample or on the propagation distance. Here, we present a way of simultaneously retrieving the sample's complex-valued transmission function and the incident illumination function from near-field diffraction patterns. The procedure relies on the measurement diversity created by lateral translations of the sample with respect to a structured illumination. The reconstruction approach, in essence identical to that employed in ptychography, is applied to hard X-ray synchrotron measurements and to simulations. Compared to other inline holography techniques, we expect near-field ptychography to reduce reconstruction artefacts by factoring out wavefront imperfections and relaxing constraints on the sample's scattering properties, thus ultimately improving the robustness of propagation-based X-ray phase tomography.

Characterization of speckle in lung images acquired with a benchtop in-line x-ray phase-contrast system

We investigate the manifestation of speckle in propagation-based x-ray phase-contrast imaging of mouse lungs in situ by use of a benchtop imager. The key contributions of the work are the demonstration that lung speckle can be observed by use of a benchtop imaging system employing a polychromatic tube-source and a systematic experimental investigation of how the texture of the speckle pattern depends on the parameters of the imaging system. Our analyses consists of image texture characterization based on the statistical properties of pixel intensity values.