Iterative estimation of coherent-scattering profiles from given positions by use of a single-direction beam

Three-dimensional reciprocal space x-ray coherent scattering tomography of two-dimensional object

PURPOSE

X-ray coherent scattering tomography is a powerful tool in discriminating biological tissues and bio-compatible materials. Conventional x-ray scattering tomography framework can only resolve isotropic scattering profile under the assumption that the material is amorphous or in powder form, which is not true especially for biological samples with orientation-dependent structure. Previous tomography schemes based on x-ray coherent scattering failed to preserve the scattering pattern from samples with preferred orientations, or required elaborated data acquisition scheme, which could limit its application in practical settings. Here, we demonstrate a simple imaging modality to preserve the anisotropic scattering signal in three-dimensional reciprocal (momentum transfer) space of a two-dimensional sample layer.

METHODS

By incorporating detector movement along the direction of x-ray beam, combined with a tomographic data acquisition scheme, we match the five dimensions of the measurements with the five dimensions (three in momentum transfer domain, and two in spatial domain) of the object. We employed a collimated pencil beam of a table-top copper-anode x-ray tube, along with a panel detector to investigate the feasibility of our method.

RESULTS

We have demonstrated x-ray coherent scattering tomographic imaging at a spatial resolution ~2 mm and momentum transfer resolution 0.01 Å^-1 for the rotation-invariant scattering direction. For any arbitrary, non-rotation-invariant direction, the same spatial and momentum transfer resolution can be achieved based on the spatial information from the rotation-invariant direction. The reconstructed scattering profile of each pixel from the experiment is consistent with the x-ray diffraction profile of each material. The three-dimensional scattering pattern recovered from the measurement reveals the partially ordered molecular structure of Teflon wrap in our sample.

CONCLUSIONS

We extend the applicability of conventional x-ray coherent scattering tomography to the reconstruction of two-dimensional samples with anisotropic scattering profile by introducing additional degree of freedom on the detector. The presented method has the potential to achieve low-cost, high-specificity material discrimination based on x-ray coherent scattering.

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.

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

Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter cross section of the investigated object revealing structural information of tissue under investigation. In the original CSCT proposals the reconstruction of images from coherently scattered x-rays is done at each scattering angle separately using analytic reconstruction. In this work we develop a maximum likelihood estimation of scatter components algorithm (ML-ESCA) that iteratively reconstructs images using a few material component basis functions from coherent scatter projection data. The proposed algorithm combines the measured scatter data at different angles into one reconstruction equation with only a few component images. Also, it accounts for data acquisition statistics and physics, modeling effects such as polychromatic energy spectrum and detector response function. We test the algorithm with simulated projection data obtained with a pencil beam setup using a new version of MC-GPU code, a Graphical Processing Unit version of PENELOPE Monte Carlo particle transport simulation code, that incorporates an improved model of x-ray coherent scattering using experimentally measured molecular interference functions. The results obtained for breast imaging phantoms using adipose and glandular tissue cross sections show that the new algorithm can separate imaging data into basic adipose and water components at radiation doses comparable with Breast Computed Tomography. Simulation results also show the potential for imaging microcalcifications. Overall, the component images obtained with ML-ESCA algorithm have a less noisy appearance than the images obtained with the conventional filtered back projection algorithm for each individual scattering angle. An optimization study for x-ray energy range selection for breast CSCT is also presented.