We present a simple x-ray phase imaging method that utilizes the sample-induced distortion of a high contrast random intensity pattern to quantitatively retrieve the two-dimensional phase map at the exit surface of a coherently illuminated sample. This reference pattern is created by placing a sheet of sandpaper in the x-ray beam, with the sample-induced distortion observed after propagation to the detector, a meter downstream. Correlation analysis comparing a single “sample and sandpaper” image to a reference “sandpaper only” image produces two sensitive differential phase contrast images, giving the sample phase gradient in vertical and horizontal directions. These images are then integrated to recover the projected phase depth of the sample. The simple experimental set-up, retention of flux, and the need for only a single sample image per reconstruction suggest that this method is of value in imaging a range of dynamic processes at both synchrotron and laboratory x-ray sources.

A single-exposure quantitative method of x-ray phase contrast imaging, suitable for animal in vivo observations, is described and shown experimentally both for a known static sample and an ex vivo biological airway. The ability to acquire the desired information within a single exposure is important for dynamic samples, as is sufficient sensitivity to reveal small variations in the composition or thickness of such a sample. This approach satisfies both these needs by analyzing how a reference grid pattern is deformed by the presence of the sample, similar to a Shack-Hartmann sensor. By resolving the shift of the pattern into horizontal and vertical components, a quantitative phase depth map is recovered, sensitive to both sharp edges as well as low phase gradients.

Computed tomography (CT) and spirometry are the mainstays of clinical pulmonary assessment. Spirometry is effort dependent and only provides a single global measure that is insensitive for regional disease, and as such, poor for capturing the early onset of lung disease, especially patchy disease such as cystic fibrosis lung disease. CT sensitively measures change in structure associated with advanced lung disease. However, obstructions in the peripheral airways and early onset of lung stiffening are often difficult to detect. Furthermore, CT imaging poses a radiation risk, particularly for young children, and dose reduction tends to result in reduced resolution. Here, we apply a series of lung tissue motion analyses, to achieve regional pulmonary function assessment in β-ENaC-overexpressing mice, a well-established model of lung disease. The expiratory time constants of regional airflows in the segmented airway tree were quantified as a measure of regional lung function. Our results showed marked heterogeneous lung function in β-ENaC-Tg mice compared to wild-type littermate controls; identified locations of airway obstruction, and quantified regions of bimodal airway resistance demonstrating lung compensation. These results demonstrate the applicability of regional lung function derived from lung motion as an effective alternative respiratory diagnostic tool.

The Fokker–Planck equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity equation. The x-ray Fokker–Planck equation can simultaneously account for both propagation-based phase contrast, and the diffusive effects of sample-induced small-angle x-ray scattering, when forming an x-ray image of a thin sample. Two derivations are given for the Fokker–Planck equation associated with x-ray imaging, together with a Kramers–Moyal generalisation thereof. Both equations are underpinned by the concept of unresolved speckle due to unresolved sample micro-structure. These equations may be applied to the forward problem of modelling image formation in the presence of both coherent and diffusive energy transport. They may also be used to formulate associated inverse problems of retrieving the phase shifts due to a sample placed in an x-ray beam, together with the diffusive properties of the sample. The domain of applicability for the Fokker–Planck and Kramers–Moyal equations for paraxial imaging is at least as broad as that of the transport-of-intensity equation which they generalise, hence the technique is also expected to be useful for paraxial imaging using visible light, electrons and neutrons.

Anatomical visualization of airspace-containing organs in intact small animals has been limited by the resolution and contrast available from current imaging methods such as X-ray, micro-computed tomography and magnetic resonance imaging. Determining structural relationships and detailed anatomy has therefore relied on suitable fixation, sectioning and histological processing. More complex and informative analyses such as orthogonal views of an organ and three-dimensional structure visualizations have required different animals and image sets, laboriously processed to gather this complementary structural information. Precise three-dimensional anatomical views have always been difficult to achieve in small animals. Here we report the ability of phase-contrast synchrotron X-ray imaging to provide detailed two-and three-dimensional visualization of airspace organ structures in intact animals. Using sub-micrometre square pixel charge-coupled device array detectors, the structure and anatomy of hard and soft tissues, and of airspaces, is readily available using phase-contrast synchrotron X-ray imaging. Moreover, software-controlled volume-reconstructions of tomographic images not only provide unsurpassed image clarity and detail, but also selectable anatomical views that cannot be obtained with established histological techniques. The morphology and structure of nasal and lung airways and the middle ear are illustrated in intact mice, using two-and three-dimensional representations. The utility of phase-contrast synchrotron X-ray imaging for noninvasively localizing objects implanted within airspaces, and the detection of gas bubbles transiting live airways, are other novel features of this visualization methodology. The coupling of phase-contrast synchrotron X-ray imaging technology with software-based reconstruction techniques holds promise for novel and high-resolution non-invasive examination of airspace anatomy in small animal models.

X-ray imaging has conventionally relied upon attenuation to provide contrast. In recent years, two complementary modalities have been added; (a) phase contrast, which can capture low-density samples that are difficult to see using attenuation, and (b) dark-field x-ray imaging, which reveals the presence of sub-pixel sample structures. These three modalities can be accessed using a crystal analyser, a grating interferometer or by looking at a directly-resolved grid, grating or speckle pattern. Grating and grid-based methods extract a differential phase signal by measuring how far a feature in the illumination has been shifted transversely due to the presence of a sample. The dark-field signal is extracted by measuring how the visibility of the structured illumination is decreased, typically due to the presence of sub-pixel structures in a sample. The strength of the dark-field signal may depend on the grating period, the pixel size and the set-up distances, and additional dark-field signal contributions may be seen as a result of strong phase effects or other factors. In this paper we show that the finite-difference form of the Fokker–Planck equation can be applied to describe the drift (phase signal) and diffusion (dark-field signal) of the periodic or structured illumination used in phase contrast x-ray imaging with gratings, in order to better understand any cross-talk between attenuation, phase and dark-field x-ray signals. In future work, this mathematical description could be used as a basis for new approaches to the inverse problem of recovering both phase and dark-field information.

To determine the efficacy of potential cystic fibrosis (CF) therapies we have developed a novel mucociliary transit (MCT) measurement that uses synchrotron phase contrast X-ray imaging (PCXI) to non-invasively measure the transit rate of individual micron-sized particles deposited into the airways of live mice. The aim of this study was to image changes in MCT produced by a rehydrating treatment based on hypertonic saline (HS), a current CF clinical treatment. Live mice received HS containing a long acting epithelial sodium channel blocker (P308); isotonic saline; or no treatment, using a nebuliser integrated within a small-animal ventilator circuit. Marker particle motion was tracked for 20 minutes using PCXI. There were statistically significant increases in MCT in the isotonic and HS-P308 groups. The ability to quantify in vivo changes in MCT may have utility in pre-clinical research studies designed to bring new genetic and pharmaceutical treatments for respiratory diseases into clinical trials.

Phase contrast x-ray imaging (PCXI) is a promising imaging modality, capable of sensitively differentiating soft tissue structures at high spatial resolution. However, high sensitivity often comes at the cost of a long exposure time or multiple exposures per image, limiting the imaging speed and possibly increasing the radiation dose. Here, we demonstrate a PCXI method that uses a single short exposure to sensitively capture sample phase information, permitting high speed x-ray movies and live animal imaging. The method illuminates a checkerboard phase grid to produce a fine grid-like intensity reference pattern at the detector, then spatially maps sample-induced distortions of this pattern to recover differential phase images of the sample. The use of a phase grid is an improvement on our previous absorption grid work in two ways. There is minimal loss in x-ray flux, permitting faster imaging, and, a very fine pattern is produced for homogenous high spatial resolution. We describe how this pattern permits retrieval of five images from a single exposure; the sample phase gradient images in the horizontal and vertical directions, a projected phase depth image, an edge-enhanced image, and a type of scattering image. Finally, we describe how the reconstruction technique can achieve subpixel distortion retrieval and study the behavior of the technique in regard to analysis technique, Talbot distance, and exposure time.