Imaging Breast Microcalcifications Using Dark-Field Signal in Propagation-Based Phase-Contrast Tomography.

Breast microcalcifications are an important primary radiological indicator of breast cancer. However, microcalcification classification and diagnosis may be still challenging for radiologists due to limitations of the standard 2D mammography technique, including spatial and contrast resolution. In this study, we propose an approach to improve the detection of microcalcifications in propagation-based phase-contrast X-ray computed tomography of breast tissues. Five fresh mastectomies containing microcalcifications were scanned at different X-ray energies and radiation doses using synchrotron radiation. Both bright-field (i.e. conventional phase-retrieved images) and dark-field images were extracted from the same data sets using different image processing methods. A quantitative analysis was performed in terms of visibility and contrast-to-noise ratio of microcalcifications. The results show that while the signal-to-noise and the contrast-to-noise ratios are lower, the visibility of the microcalcifications is more than two times higher in the dark-field images compared to the bright-field images. Dark-field images have also provided more accurate information about the size and shape of the microcalcifications.

Tomographic phase and attenuation extraction for a sample composed of unknown materials using x-ray propagation-based phase-contrast imaging.

Propagation-based phase-contrast x-ray imaging (PB-PCXI) generates image contrast by utilizing sample-imposed phase-shifts. This has proven useful when imaging weakly attenuating samples, as conventional attenuation-based imaging does not always provide adequate contrast. We present a PB-PCXI algorithm capable of extracting the x-ray attenuation  ß and refraction  δ, components of the complex refractive index of distinct materials within an unknown sample. The method involves curve fitting an error-function-based model to a phase-retrieved interface in a PB-PCXI tomographic reconstruction, which is obtained when Paganin-type phase retrieval is applied with incorrect values of δ and ß. The fit parameters can then be used to calculate true δ and ß values for composite materials. This approach requires no a priori sample information, making it broadly applicable. Our PB-PCXI reconstruction is single-distance, requiring only one exposure per tomographic angle, which is important for radiosensitive samples. We apply this approach to a breast-tissue sample, recovering the refraction component  Î´, with 0.6-2.4% accuracy compared with theoretical values.

Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons, Part II: Differential Holographic Tomography.

It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed.

Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons.

The relative roles of multiple electron scattering and in-molecule Fresnel diffraction in atomic-resolution transmission electron microscopy of small molecules are discussed. It is argued that, while multiple scattering tends to have only a moderate effect, the in-molecule Fresnel diffraction can be significant due to the shallow depth of focus in high-resolution electron microscopy. When the depth of focus is smaller than the size of molecule along the trajectory of the electrons, the projection approximation breaks down and pairs of images at orientations of the molecule rotated by 180 degrees are not the same. Put another way, it matters which way the electrons traverse the specimen. In such cases, diffraction tomography based on the first Born or first Rytov approximation represents a more suitable method for the reconstruction of the three-dimensional distribution of the electrostatic potential, compared to conventional computed tomography which intrinsically relies on the validity of the projection approximation. A simplified method for diffraction tomography based on the approximation of Fresnel diffraction by the transport of intensity equation is proposed and tested on numerically simulated examples.

Dark-field signal extraction in propagation-based phase-contrast imaging.

A method for extracting the dark-field signal in propagation-based phase-contrast imaging is proposed. In the case of objects consisting predominantly of a single material, or several different materials with similar ratios of the real decrement to the imaginary part of the complex refractive index, the proposed method requires a single image for extraction of the dark-field signal in two-dimensional projection imaging. In the case of three-dimensional tomographic imaging, the method needs only one image to be collected at each projection angle. Initial examples using simulated and experimental data indicate that this method can improve visualization of small sharp features inside a larger object, e.g. the visualization of microcalcifications in propagation-based x-ray breast cancer imaging. It is suggested that the proposed approach may be useful in other forms of biomedical imaging, where it can help one to obtain additional small-angle scattering information without increasing the radiation dose to the sample.

Propagation-based x-ray phase-contrast tomography of mastectomy samples using synchrotron radiation.

PURPOSE: Propagation-based phase-contrast computed tomography (PB-CT) is a method for three-dimensional x-ray imaging that utilizes refraction, as well as absorption, of x rays in the tissues to increase the signal-to-noise ratio (SNR) in the resultant images, in comparison with equivalent conventional absorption-only x-ray tomography (CT). Importantly, the higher SNR is achieved without sacrificing spatial resolution or increasing the radiation dose delivered to the imaged tissues. The present work has been carried out in the context of the current development of a breast CT imaging facility at the Australian Synchrotron. METHODS: Seven unfixed complete mastectomy samples with and without breast cancer lesions have been imaged using absorption-only CT and PB-CT techniques under controlled experimental conditions. The radiation doses delivered to the mastectomy samples during the scans were comparable to those approved for mammographic screening. Physical characteristics of the reconstructed images, such as spatial resolution and SNR, have been measured and compared with the results of the radiological quality assessment of the complete absorption CT and PB-CT image stacks. RESULTS: Despite the presence of some image artefacts, the PB-CT images have outperformed comparable absorption CT images collected at the same radiation dose, in terms of both the measured objective image characteristics and the radiological image scores. The outcomes of these experiments are shown to be consistent with predictions of the theory of PB-CT imaging and previous reported experimental studies of this imaging modality. CONCLUSIONS: The results presented in this paper demonstrate that PB-CT holds a high potential for improving on the quality and diagnostic value of images obtained using existing medical x-ray technologies, such as mammography and digital breast tomosynthesis (DBT). If implemented at suitable synchrotron imaging facilities, PB-CT can be used to complement existing imaging modalities, leading to more accurate breast cancer diagnosis.

Free propagation phase-contrast breast CT provides higher image quality than cone-beam breast-CT at low radiation doses: a feasibility study on human mastectomies.

In this study we demonstrate the first direct comparison between synchrotron x-ray propagation-based CT (PB-CT) and cone-beam breast-CT (CB-CT) on human mastectomy specimens (N = 12) including different benign and malignant lesions. The image quality and diagnostic power of the obtained data sets were compared and judged by two independent expert radiologists. Two cases are presented in detail in this paper including a comparison with the corresponding histological evaluation. Results indicate that with PB-CT it is possible to increase the level of contrast-to-noise ratio (CNR) keeping the same level of dose used for the CB-CT or achieve the same level of CNR reached by CB-CT at a lower level of dose. In other words, PB-CT can achieve a higher diagnostic potential compared to the commercial breast-CT system while also delivering a considerably lower mean glandular dose. Therefore, we believe that PB-CT technique, if translated to a clinical setting, could have a significant impact in improving breast cancer diagnosis.

Optimization of propagation-based x-ray phase-contrast tomography for breast cancer imaging.

The aim of this study was to optimise the experimental protocol and data analysis for in-vivo breast cancer x-ray imaging. Results are presented of the experiment at the SYRMEP beamline of Elettra Synchrotron using the propagation-based phase-contrast mammographic tomography method, which incorporates not only absorption, but also x-ray phase information. In this study the images of breast tissue samples, of a size corresponding to a full human breast, with radiologically acceptable x-ray doses were obtained, and the degree of improvement of the image quality (from the diagnostic point of view) achievable using propagation-based phase-contrast image acquisition protocols with proper incorporation of x-ray phase retrieval into the reconstruction pipeline was investigated. Parameters such as the x-ray energy, sample-to-detector distance and data processing methods were tested, evaluated and optimized with respect to the estimated diagnostic value using a mastectomy sample with a malignant lesion. The results of quantitative evaluation of images were obtained by means of radiological assessment carried out by 13 experienced specialists. A comparative analysis was performed between the x-ray and the histological images of the specimen. The results of the analysis indicate that, within the investigated range of parameters, both the objective image quality characteristics and the subjective radiological scores of propagation-based phase-contrast images of breast tissues monotonically increase with the strength of phase contrast which in turn is directly proportional to the product of the radiation wavelength and the sample-to-detector distance. The outcomes of this study serve to define the practical imaging conditions and the CT reconstruction procedures appropriate for low-dose phase-contrast mammographic imaging of live patients at specially designed synchrotron beamlines.

Clinical application of low-dose phase contrast breast CT: methods for the optimization of the reconstruction workflow.

Results are presented of a feasibility study of three-dimensional X-ray tomographic mammography utilising in-line phase contrast. Experiments were performed at SYRMEP beamline of Elettra synchrotron. A specially designed plastic phantom and a mastectomy sample containing a malignant lesion were used to study the reconstructed image quality as a function of different image processing operations. Detailed evaluation and optimization of image reconstruction workflows have been carried out using combinations of several advanced computed tomography algorithms with different pre-processing and post-processing steps. Special attention was paid to the effect of phase retrieval on the diagnostic value of the reconstructed images. A number of objective image quality indices have been applied for quantitative evaluation of the results, and these were compared with subjective assessments of the same images by three experienced radiologists and one pathologist. The outcomes of this study provide practical guidelines for the optimization of image processing workflows in synchrotron-based phase-contrast mammo-tomography.

On the evolution and relative merits of hard X-ray phase-contrast imaging methods.

This review provides a brief overview, albeit from a somewhat personal perspective, of the evolution and key features of various hard X-ray phase-contrast imaging (PCI) methods of current interest in connection with translation to a wide range of imaging applications. Although such methods have already found wide-ranging applications using synchrotron sources, application to dynamic studies in a laboratory/clinical context, for example for in vivo imaging, has been slow due to the current limitations in the brilliance of compact laboratory sources and the availability of suitable high-performance X-ray detectors. On the theoretical side, promising new PCI methods are evolving which can record both components of the phase gradient in a single exposure and which can accept a relatively large spectral bandpass. In order to help to identify the most promising paths forward, we make some suggestions as to how the various PCI methods might be compared for performance with a particular view to identifying those which are the most efficient, given the fact that source performance is currently a key limiting factor on the improved performance and applicability of PCI systems, especially in the context of dynamic sample studies. The rapid ongoing development of both suitable improved sources and detectors gives strong encouragement to the view that hard X-ray PCI methods are poised for improved performance and an even wider range of applications in the near future.

Quantitative phase retrieval with picosecond X-ray pulses from the ATF Inverse Compton Scattering source.

Quantitative phase retrieval is experimentally demonstrated using the Inverse Compton Scattering X-ray source available at the Accelerator Test Facility (ATF) in the Brookhaven National Laboratory. Phase-contrast images are collected using in-line geometry, with a single X-ray pulse of approximate duration of one picosecond. The projected thickness of homogeneous samples of various polymers is recovered quantitatively from the time-averaged intensity of transmitted X-rays. The data are in good agreement with the expectations showing that ATF Inverse Compton Scattering source is suitable for performing phase-sensitive quantitative X-ray imaging on the picosecond scale. The method shows promise for quantitative imaging of fast dynamic phenomena.

The binary dissector: phase contrast tomography of two- and three-material objects from few projections.

In X-ray computed tomography (CT) increased information requirements (e.g. increased resolution) typically lead to a concurrent increase in the required number of viewing angles, scanning time and delivered dose. We demonstrate that using phase-contrast imaging it is possible to "dissect" two- and three-material objects into their component materials, which in combination with binary tomographic techniques allows us to satisfy increased information requirements without taking the usual images at additional viewing angles. This imaging scheme reduces the scanning time and dose delivered to samples by at least an order of magnitude when compared to conventional X-ray CT. The effects of noise on our reconstruction scheme are investigated for simulated data. Finally, a slice through a glass tube filled with silica and water is reconstructed from 18 projection images taken on an X-ray ultra Microscope (XuM).

Phase-contrast tomography of single-material objects from few projections.

A method is presented for quantitative polychromatic cone-beam phase-contrast tomographic imaging of a single-material object from few projections. This algorithm exploits the natural combination of binary tomography with a phase-retrieval method that makes explicit use of the single-material nature of the sample. Such consistent use of a priori knowledge reduces the number of required projections, implying significantly reduced dose and scanning time when compared to existing phase-contrast tomography methods. Reconstructions from simulated data sets are used to investigate the effects of noise and establish a minimum required number of projections. An experimental demonstration is then given, using data from a point-projection X-ray microscope. Here, the complex distribution of refractive index in a sample containing several nylon fibers with diameters between 100 microm and 420 microm is reconstructed at a spatial resolution of approximately 4 microm from 20 polychromatic phase-contrast projection images with a mean photon energy of 8.4 keV.

On qualitative and quantitative analysis in analyser-based imaging.

Using rigorous wave-optical formalism, a general expression is obtained for the image intensity distribution in combined analyser-based/propagation-based phase-contrast imaging. This expression takes into account partial coherence of the wave incident on the object as well as the finite resolution of the detector system. Using this general expression, two approaches based on the geometrical optics and weak-object approximations are applied to derive simple solutions to the inverse problem of reconstruction of the phase and amplitude of the object wave. With the help of numerical experiments, the two approaches are compared in terms of their validity conditions and are shown to impose certain restrictions on the properties of the object wave. In particular, it is shown that violation of the validity conditions of the geometrical optics or weak-object approximations results in the appearance of strong reconstruction artefacts in the transmitted intensity near the edges of the objects. The effect of the incident wavefront non-uniformity due to imperfections of the imaging set-up on image formation and phase/amplitude reconstruction is also discussed. A solution to this problem is proposed in the form of a multi-image phase/amplitude reconstruction algorithm based on the geometrical optics approximation. This algorithm and an algorithm based on the weak-object approximation are applied to simulated and experimental images of fibres.

Generalized eikonal of partially coherent beams and its use in quantitative imaging.

The generalized eikonal of a partially coherent paraxial wave is introduced via a differential equation describing the evolution of the time-averaged intensity. The theoretical formalism provides an analytical tool for the study of partially coherent imaging systems. It also makes possible quantitative phase retrieval and compositional mapping of weakly absorbing samples using phase-contrast imaging with broadband polychromatic radiation of known spectral distribution. An experimental demonstration is presented of the quantitative reconstruction of the projected thickness of a sample, given a phase-contrast image obtained using a polychromatic microfocus x-ray source.

X-ray omni microscopy.

The science of wave-field phase retrieval and phase measurement is sufficiently mature to permit the routine reconstruction, over a given plane, of the complex wave-function associated with certain coherent forward-propagating scalar wave-fields. This reconstruction gives total knowledge of the information that has been encoded in the complex wave-field by passage through a sample of interest. Such total knowledge is powerful, because it permits the emulation in software of the subsequent action of an infinite variety of coherent imaging systems. Such 'virtual optics', in which software forms a natural extension of the 'hardware optics' in an imaging system, may be useful in contexts such as quantitative atom and X-ray imaging, in which optical elements such as beam-splitters and lenses can be realized in software rather than optical hardware. Here, we develop the requisite theory to describe such hybrid virtual-physical imaging systems, which we term 'omni optics' because of their infinite flexibility. We then give an experimental demonstration of these ideas by showing that a lensless X-ray point projection microscope can, when equipped with the appropriate software, emulate an infinite variety of optical imaging systems including those which yield interferograms, Zernike phase contrast, Schlieren imaging and diffraction-enhanced imaging.

Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging.

We outline a new approach to X-ray projection microscopy in a scanning electron microscope (SEM), which exploits phase contrast to boost the quality and information content of images. These developments have been made possible by the combination of a high-brightness field-emission gun (FEG)-based SEM, direct detection CCD technology and new phase retrieval algorithms. Using this approach we have been able to obtain spatial resolution of < 0.2 micro m and have demonstrated novel features such as: (i) phase-contrast enhanced visibility of high spatial frequency image features (e.g. edges and boundaries) over a wide energy range; (ii) energy-resolved imaging to simultaneously produce multiple quasi-monochromatic images using broad-band polychromatic illumination; (iii) easy implementation of microtomography; (iv) rapid and robust phase/amplitude-retrieval algorithms to enable new real-time and quantitative modes of microscopic imaging. These algorithms can also be applied successfully to recover object-plane information from intermediate-field images, unlocking the potentially greater contrast and resolution of the intermediate-field regime. Widespread applications are envisaged for fields such as materials science, biological and biomedical research and microelectronics device inspection. Some illustrative examples are presented. The quantitative methods described here are also very relevant to projection microscopy using other sources of radiation, such as visible light and electrons.

Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object.

We demonstrate simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. Subject to the assumptions explicitly stated in the derivation, the algorithm solves the twin-image problem of in-line holography and is capable of analysing data obtained using X-ray microscopy, electron microscopy, neutron microscopy or visible-light microscopy, especially as they relate to defocus and point projection methods. Our simple, robust, non-iterative and computationally efficient method is applied to data obtained using an X-ray phase contrast ultramicroscope.

Quantitative analysis of two-component samples using in-line hard X-ray images.

Methods for rapid quantitative phase-sensitive X-ray imaging of non-crystalline samples consisting of two distinct components are investigated. The transverse spatial distribution of the projected thickness of each component is reconstructed by computer processing of in-line images collected using synchrotron-generated hard X-rays and a position-sensitive detector with submicrometre spatial resolution. Different imaging techniques and associated image-processing algorithms are considered, with relative advantages and difficulties of each approach compared. A possible generalization of the method for the case of n-component samples is briefly discussed.

Quantitative in-line phase-contrast imaging with multienergy X rays.

We present a new method for quantitative nondestructive characterization of objects by x-ray phase-contrast imaging. Spatial distributions of the projected values of the complex refractive index in the sample are reconstructed by processing near-field images collected at a fixed sample-to-detector distance using a polychromatic incident beam and an energy-sensitive area detector, such as a CCD used in the photon-counting spectroscopy mode. The method has the potential advantages of decreased radiation dose and increased accuracy compared to conventional techniques of x-ray imaging.