X-ray Source Trajectory Research Articles

Pt4: Phantom-4D, an open-source software tool for creating time-evolving 3D phantoms

pt4, an open-source software tool to describe time-evolving phantoms is presented. pt4 allows users to create detailed time-evolving phantoms for testing novel 4D-CT reconstruction algorithms. Ground-truth volumes and simulated X-ray projections can be produced at arbitrary time-points during time-evolution and with customisable pixel dimensions, noise models, and X-ray source trajectories. Phantoms are built up from 3D primitives whose parameters and attenuation can be made arbitrary functions of time. This feature permits both complex continuous and discontinuous time-evolution necessary for thorough testing of 4D-CT reconstruction algorithms. Various phantoms built using pt4 are also presented to demonstrate the versatility of pt4 phantom description. pt4 is written in C++ and is highly parallelised leading to a performant implementation which is feasible to use for up to thousand-of-voxel volume pixel dimensions.

Dedicated cone-beam breast CT: Data acquisition strategies based on projection angle-dependent normalized glandular dose coefficients.

Dedicated cone-beam breast computed tomography (CBBCT) using short-scan acquisition is being actively investigated to potentially reduce the radiation dose to the breast. This would require determining the optimal x-ray source trajectory for such short-scan acquisition. To quantify the projection angle-dependent normalized glandular dose coefficient ( ) in CBBCT, referred to as angular , so that the x-ray ray source trajectory that minimizes the radiation dose to the breast for short-scan acquisition can be determined. A cohort of 75 CBBCT clinical datasets was segmented and used to generate three breast models - (I) patient-specific breast with heterogeneous fibroglandular tissue distribution and real breast shape, (II) patient-specific breast shape with homogeneous tissue distribution and matched fibroglandular weight fraction, and (III) homogeneous semi-ellipsoidal breast with patient-specific breast dimensions and matched fibroglandular weight fraction, which corresponds to the breast model used in current radiation dosimetry protocols. For each clinical dataset, the angular was obtained at 10 discrete angles, spaced 36° apart, for full-scan, circular, x-ray source trajectory from Monte Carlo simulations. Model III is used for validating the Monte Carlo simulation results. Models II and III are used to determine if breast shape contributes to the observed trends in angular . A geometry-based theory in conjunction with center-of-mass ( ) based distribution analysis is used to explain the projection angle-dependent variation in angular . The theoretical model predicted that the angular will follow a sinusoidal pattern and the amplitude of the sinusoid increases when the center-of-mass of fibroglandular tissue ( ) is farther from the center-of-mass of the breast ( ). It also predicted that the angular will be minimized at x-ray source positions complementary to the . The was superior to the in 80% (60/75) of the breasts. From Monte Carlo simulations and for homogeneous breasts (models II and III), the deviation in breast shape from a semi-ellipsoid had minimal effect on angular and showed less than 4% variation. From Monte Carlo simulations and for model I, as predicted by our theory, the angular followed a sinusoidal pattern with maxima and minima at x-ray source positions superior and inferior to the breast, respectively. For model I, the projection angle-dependent variation in angular was 16.4%. The heterogeneous tissue distribution affected the angular more than the breast shape. For model I, the angular was lowest when the x-ray source was inferior to the breast. Hence, for short-scan CBBCT acquisition with aligned with axis-of-rotation, an x-ray source trajectory inferior to the breast is preferable and such an acquisition spanning 205° can potentially reduce the mean glandular dose by up to 52%.

Geometric dependence of image quality in digital tomosynthesis: Simulations of X-ray source trajectories and scan angles

Digital tomosynthesis (DTS) is able to provide the 3-dimensional (3D) images of an object, while reducing radiation dose compared to computed tomography (CT). Despite these benefits, DTS has a geometric sensitivity because only a few dozen projections obtained with limited scan angles are used for DTS imaging. In this study, we evaluated the effects of X-ray source scan trajectories and angles on DTS images for investigating the geometric dependence in DTS. The DTS systems were simulated with linear, rotational and circular scan trajectories, and 54 projections were obtained from each of the four scan angle intervals of ±17, ±27, ±37 and ±47 degrees. The obtained projections were reconstructed by using a model-based filtered back-projection (FBP) technique. The characteristics of reconstructed DTS images were analyzed in terms of quantitative accuracy, noise property, contrast-to-noise ratio (CNR) and spatial resolution. The results showed that the quality of DTS images was highly dependent on the geometric variations, and the characteristics of DTS images differed according to the X-ray source scan trajectories and angles. In conclusion, the DTS geometries should be determined by considering image quality and characteristic in order to optimize their systems and applications.

PI-Line Difference for Alignment and Motion-Correction of Cone-Beam Helical-Trajectory Micro-Tomography Data

In micro-tomography, variants of helical X-ray source trajectories, e.g., double-helix (DH) and space-filling (SF), are attractive alternatives to the conventional circular trajectory, as they satisfy data-sufficiency conditions; this enables exact reconstruction, and large cone-angle (or high flux) imaging. Geometric alignment of micro-tomography experimental data, i.e., radiographs or projection data, to the required micron precision is a difficult problem. In this paper, we consider criteria based on differences in attenuation along opposing rays as a postacquisition software alignment technique. These opposing rays are called PI-lines and lie on lines that intersect two points of the scanning trajectory and pass through the region of support. The PI-line difference method is particularly appealing due to its low computational cost and small set of inherent assumptions, however, previous studies have exposed some limitations in precision. The number and distribution of PI-lines is highly dependent on the trajectory and thus so is the robustness of PI-line difference; here we show that DH and SF trajectories are particularly amenable to this technique. For these trajectories, we observe that the technique is applicable to both static and per-projection alignment estimation. We present results where PI-line difference alignment estimates are of equivalent accuracy as alignment estimates obtained from existing state-of-the-art methods: a tomogram sharpness method for static alignment and a reprojection-alignment method for per-projection alignment. In both cases, the computational expense of PI-line difference alignment estimation is a fraction of the tomogram-based methods.

Imaging of fiber-like structures in digital breast tomosynthesis.

Fiber-like features are an important aspect of breast imaging. Vessels and ducts are present in all breast images, and spiculations radiating from a mass can indicate malignancy. Accordingly, fiber objects are one of the three types of signals used in the American College of Radiology digital mammography (ACR-DM) accreditation phantom. Our work focuses on the image properties of fiber-like structures in digital breast tomosynthesis (DBT) and how image reconstruction can affect their appearance. The impact of DBT image reconstruction algorithm and regularization strength on the conspicuity of fiber-like signals of various orientations is investigated in simulation. A metric is developed to characterize this orientation dependence and allow for quantitative comparison of algorithms and associated parameters in the context of imaging fiber signals. The imaging properties of fibers, characterized in simulation, are then demonstrated in detail with physical DBT data of the ACR-DM phantom. The characterization of imaging of fiber signals is used to explain features of an actual clinical DBT case. For the algorithms investigated, at low regularization setting, the results show a striking variation in conspicuity as a function of orientation in the viewing plane. In particular, the conspicuity of fibers nearly aligned with the plane of the x-ray source trajectory is decreased relative to more obliquely oriented fibers. Increasing regularization strength mitigates this orientation dependence at the cost of increasing depth blur of these structures.

Simulative Assessment of Radiation Exposure for Freely Definable CBCT X-ray Source Trajectories

Article Simulative Assessment of Radiation Exposure for Freely Definable CBCT X-ray Source Trajectories was published on August 24, 2012 in the journal Biomedical Engineering / Biomedizinische Technik (volume 57, issue SI-1-Track-B).

Quality Evaluation of Image Recording Strategies for Limited Angle Tomography

In this paper we propose a new method for evaluating image recording strategies for limited angle tomography. In limited angle tomography exact three-dimensional (3-D) reconstruction is not achievable. With this method a metric for the reachable reconstruction quality by defined X-ray source trajectories is calculated. The result of our method is independent of reconstruction algorithms. Our approach is based on the gradients of the scanned volume and their grade of determinability. Compared to simulated reconstruction accuracy with simultaneous algebraic reconstruction techniques, the method of evaluation shows the same dependencies on X-ray source trajectories. By using the proposed method different source trajectories for a limited angle range are comparable with respect to the reachable reconstruction quality.

Consistency Conditions for Cone-Beam CT Data Acquired with a Straight-Line Source Trajectory

A consistency condition is developed for computed tomography (CT) projection data acquired from a straight-line X-ray source trajectory. The condition states that integrals of normalized projection data along detector lines parallel to the X-ray path must be equal. The projection data is required to be untruncated only along the detector lines parallel to the X-ray path, a less restrictive requirement compared to Fourier conditions that necessitate completely untruncated data. The condition is implemented numerically on simple image functions, a discretization error bound is estimated, and detection of motion inconsistencies is demonstrated. The results show that the consistency condition may be used to quantitatively compare the quality of projection data sets obtained from different scans of the same image object.

Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization

An iterative algorithm, based on recent work in compressive sensing, is developed for volume image reconstruction from a circular cone-beam scan. The algorithm minimizes the total variation (TV) of the image subject to the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. The constraints are enforced by the use of projection onto convex sets (POCS) and the TV objective is minimized by steepest descent with an adaptive step-size. The algorithm is referred to as adaptive-steepest-descent-POCS (ASD-POCS). It appears to be robust against cone-beam artifacts, and may be particularly useful when the angular range is limited or when the angular sampling rate is low. The ASD-POCS algorithm is tested with the Defrise disk and jaw computerized phantoms. Some comparisons are performed with the POCS and expectation-maximization (EM) algorithms. Although the algorithm is presented in the context of circular cone-beam image reconstruction, it can also be applied to scanning geometries involving other x-ray source trajectories.

A filtered backprojection algorithm for cone beam reconstructionusing rotational filtering under helical source trajectory

With the evolution from multi-detector-row CT to cone beam (CB) volumetric CT, maintaining reconstruction accuracy becomes more challenging. To combat the severe artifacts caused by a large cone angle in CB volumetric CT, three-dimensional reconstruction algorithms have to be utilized. In practice, filtered backprojection (FBP) reconstruction algorithms are more desirable due to their computational structure and image generation efficiency. One of the CB-FBP reconstruction algorithms is the well-known FDK algorithm that was originally derived for a circular x-ray source trajectory by heuristically extending its two-dimensional (2-D) counterpart. Later on, a general CB-FBP reconstruction algorithm was derived for noncircular, such as helical, source trajectories. It has been recognized that a filtering operation in the projection data along the tangential direction of a helical x-ray source trajectory can significantly improve the reconstruction accuracy of helical CB volumetric CT. However, the tangential filtering encounters latitudinal data truncation, resulting in degraded noise characteristics or data manipulation inefficiency. A CB-FBP reconstruction algorithm using one-dimensional rotational filtering across detector rows (namely CB-RFBP) is proposed in this paper. Although the proposed CB-RFBP reconstruction algorithm is approximate, it approaches the reconstruction accuracy that can be achieved by exact helical CB-FBP reconstruction algorithms for moderate cone angles. Unlike most exact CB-FBP reconstruction algorithms in which the redundant data are usually discarded, the proposed CB-RFBP reconstruction algorithm make use of all available projection data, resulting in significantly improved noise characteristics and dose efficiency. Moreover, the rotational filtering across detector rows not only survives the so-called long object problem, but also avoids latitudinal data truncation existing in other helical CB-FBP reconstruction algorithm in which a tangential filtering is carried out, providing better noise characteristics, dose efficiency and data manipulation efficiency.

Investigation of saddle trajectories for cardiac CT imaging in cone-beam geometry

This paper investigates cone-beam tomography for a wide class of x-ray source trajectories called saddles. In particular, a mathematical analysis of the number of intersections between a saddle and an arbitrary plane is given. This analysis demonstrates that axially truncated cone-beam projections acquired along a saddle can be used for exact reconstruction at any point in a large volume. The reconstruction can be achieved either using a new algorithm presented herein or using a formula recently introduced by Katsevich (2003 Int. J. Math. Math. Sci. 21 1305–21). The shape of the reconstructed volume and the properties of saddles make saddles attractive for cardiac imaging. Three examples of saddles are presented with a discussion of implementation on devices similar to modern C-arm systems and multislice CT scanners. Reconstruction with one of these saddles has been tested using computer-simulated data, with and without truncation. The imaged phantom for the truncated data is a FORBILD head phantom (representing the heart) that has been modified and embedded inside the FORBILD thorax phantom. The non-truncated data were generated by excluding the thorax. The reconstructed images demonstrate the accuracy of the mathematical results.