Maximum-likelihood estimation of scatter components algorithm for x-ray coherent scatter computed tomography of the breast

Fast X-ray diffraction (XRD) tomography for enhanced identification of materials

X-ray computed tomography (CT) is a commercially established modality for imaging large objects like passenger luggage. CT can provide the density and the effective atomic number, which is not always sufficient to identify threats like explosives and narcotics, since they can have a similar composition to benign plastics, glass, or light metals. In these cases, X-ray diffraction (XRD) may be better suited to distinguish the threats. Unfortunately, the diffracted photon flux is typically much weaker than the transmitted one. Measurement of quality XRD data is therefore slower compared to CT, which is an economic challenge for potential customers like airports. In this article we numerically analyze a novel low-cost scanner design which captures CT and XRD signals simultaneously, and uses the least possible collimation to maximize the flux. To simulate a realistic instrument, we propose a forward model that includes the resolution-limiting effects of the polychromatic spectrum, the detector, and all the finite-size geometric factors. We then show how to reconstruct XRD patterns from a large phantom with multiple diffracting objects. We include a reasonable amount of photon counting noise (Poisson statistics), as well as measurement bias (incoherent scattering). Our XRD reconstruction adds material-specific information, albeit at a low resolution, to the already existing CT image, thus improving threat detection. Our theoretical model is implemented in GPU (Graphics Processing Unit) accelerated software which can be used to further optimize scanner designs for applications in security, healthcare, and manufacturing quality control.

Reciprocal-FDK reconstruction for x-ray diffraction computed tomography

Objective. X-ray diffraction (XRD) technology uses x-ray small-angle scattering signal for material analysis, which is highly sensitive to material inter-molecular structure. To meet the high spatial resolution requirement in applications such as medical imaging, XRD computed tomography (XRDCT) has been proposed to provide XRD intensity with improved spatial resolution from point-wise XRD scan. In XRDCT, 2D spatial tomography corresponds to a 3D reconstruction problem with the third dimension being the XRD spectrum dimension, i.e. the momentum transfer dimension. Current works in the field have studied reconstruction methods for either angular-dispersive XRDCT or energy-dispersive XRDCT for small samples. The approximations used are only suitable for regions near the XRDCT iso-center. A new XRDCT reconstruction method is needed for more general imaging applications. Approach. We derive a new FDK-type reconstruction method (Reciprocal-FDK) for XRDCT without limitation on object size. By introducing a set of reciprocal variables, the XRDCT model is transformed into a classical cone-parallel CT model, which is an extension of a circular-trajectory cone-beam CT model, after which the FDK method is applied for XRDCT reconstruction. Main results. Both analytical simulation and Monte Carlo simulation experiments are conducted to validate the XRDCT reconstruction method. The results show that when compared to existing analytical reconstruction methods, there are improvements in the proposed Reciprocal-FDK method with regard to relative structure reconstruction and XRD pattern peak reconstruction. Since cone-parallel CT does not satisfy the data completeness condition, cone-angle effect affects the reconstruction accuracy of XRDCT. The property of cone-angle effect in XRDCT is also analyzed with ablation studies. Significance. We propose a general analytical reconstruction method for XRDCT without constraint on object size. Reciprocal-FDK provides a complete derivation and theoretical support for XRDCT reconstruction by analogy to the well-studied cone-parallel CT model. In addition, the intrinsic problem with the XRDCT data model and the corresponding reconstruction error are discussed for the first time.

Feasibility of estimating volumetric breast density from mammographic x-ray spectra using a cadmium telluride photon-counting detector

PURPOSE

Mammographic density of glandular breast tissue has a masking effect that can reduce lesion detection accuracy and is also a strong risk factor for breast cancer. Therefore, accurate quantitative estimation of breast density is clinically important. In this study, we investigate experimentally the feasibility of quantifying volumetric breast density with spectral mammography using a CdTe-based photon-counting detector.

METHODS

To demonstrate proof-of-principle, this study was carried out using the single pixel Amptek XR-100T-CdTe detector. The total number of x rays recorded by the detector from a single pencil-beam projection through 50%/50% of adipose/glandular mass fraction-equivalent phantoms was measured. Material decomposition assuming two, four, and eight energy bins was then applied to characterize the inspected phantom into adipose and glandular using log-likelihood estimation, taking into account the polychromatic source, the detector response function, and the energy-dependent attenuation.

RESULTS

Measurement tests were carried out for different doses, kVp settings, and different breast sizes. For dose of 1 mGy and above, the percent relative root mean square (RMS) errors of the estimated breast density was measured below 7% for all three phantom studies. It was also observed that some decrease in RMS errors was achieved using eight energy bins. For 3 and 4 cm thick phantoms, performance at 40 and 45 kVp showed similar performance. However, it was observed that 45 kVp showed better performance for a phantom thickness of 6 cm at low dose levels due to increased statistical variation at lower photon count levels with 40 kVp.

CONCLUSION

The results of the current study suggest that photon-counting spectral mammography systems using CdTe detectors have the potential to be used for accurate quantification of volumetric breast density on a pixel-to-pixel basis, with an RMS error of less than 7%.

Non-invasive classification of breast microcalcifications using x-ray coherent scatter computed tomography

We investigate the use of energy dispersive x-ray coherent scatter computed tomography (ED-CSCT) as a non-invasive diagnostic method to differentiate between type I and type II breast calcifications. This approach is sensitive to the differences of composition and internal crystal structure of different types of microcalcifications. The study is carried out by simulating a CSCT system with a scanning pencil beam, considering a polychromatic x-ray source and an energy-resolving photon counting detector. In a first step, the multidimensional angle and energy distributed CSCT data is reduced to the projection-space distributions of only a few components, corresponding to the expected target composition: adipose, glandular tissue, weddellite (calcium oxalate) for type I calcifications, and hydroxyapatite for type II calcifications. The maximum-likelihood estimation of scatter components algorithm used, operating in the projection space, takes into account the polychromatic source, the detector response function and the energy dependent attenuation. In the second step, component images are reconstructed from the corresponding estimated component projections using filtered backprojection. In a preliminary step the coherent scatter differential cross sections for hydroxyapatite and weddellite minerals were determined experimentally. The classification of type I or II calcifications is done using the relative contrasts of their components as the criterion. Simulation tests were carried out for different doses and energy resolutions for multiple realizations. The results were analyzed using relative/receiver operating characteristic methodology and show good discrimination ability at medium and higher doses. The noninvasive CSCT technique shows potential to further improve the breast diagnostic accuracy and reduce the number of breast biopsies.