Marker-based C-arm self-calibration with unknown calibration pattern.

BACKGROUND: Accurate tomographic reconstructions require the knowledge of the actual acquisition geometry. Many mobile C-arm CT scanners have poorly reproducible acquisition geometries and thus need acquisition-specific calibration procedures. Most of geometric self-calibration methods based on projection data either need prior information or are limited to the estimation of a low number of geometric calibration parameters. Other self-calibration methods generally use a calibration pattern with known geometry and are hardly implementable in practice for clinical applications. PURPOSE: We present a three-step marker based self-calibration method which does not require the prior knowledge of the calibration pattern and thus enables the use of calibration patterns with arbitrary markers positions. METHODS: The first step of the method aims at detecting the set of markers of the calibration pattern in each projection of the CT scan and is performed using the YOLO (You Only Look Once) Convolutional Neural Network. The projected marker trajectories are then estimated by a sequential projection-wise marker association scheme based on the Linear Assignment Problem which uses Kalman filters to predict the markers 2D positions in the projections. The acquisition geometry is finally estimated from the marker trajectories using the Bundle-adjustment algorithm. RESULTS: The calibration method has been tested on realistic simulated images of the ICRP (International Commission on Radiological Protection) phantom, using calibration patterns with 10 and 20 markers. The backprojection error was used to evaluate the self-calibration method and exhibited sub-millimeter errors. Real images of two human knees with 10 and 30 markers calibration patterns were then used to perform a qualitative evaluation of the method, which showed a remarkable artifacts reduction and bone structures visibility improvement. CONCLUSIONS: The proposed calibration method gave promising results that pave the way to patient-specific geometric self-calibrations in clinics.

A tomographic reconstruction algorithm for cross-sectional imaging of IMRT beams from six projections.

Objective. Patient-specific Quality Assurance (QA) measurements are of key importance in radiotherapy for safe and efficient treatment delivery and allow early detection of clinically relevant errors. Such QA processes remain challenging to implement for complex Intensity Modulated Radiation Therapy (IMRT) radiotherapy fields delivered using a multileaf collimator (MLC) which often feature small open segments and raise QA issues similar to those encountered in small field dosimetry. Recently, detectors based on long scintillating fibers have been proposed to measure a few parallel projections of the irradiation field with good performance for small field dosimetry. The purpose of this work is to develop and validate a novel approach to reconstruct MLC-shaped small irradiation fields from six projections.Approach. The proposed field reconstruction method uses a limited number of geometric parameters to model the irradiation field. These parameters are iteratively estimated with a steepest descent algorithm. The reconstruction method was first validated on simulated data. Real data were measured with a water-equivalent slab phantom equipped with a detector made of 6 scintillating-fiber ribbons placed at 1 m from the source. A radiochromic film was used to acquire a reference measurement of a first dose distribution in the slab phantom at the same source-to-detector distance and the treatment planning system (TPS) provided the reference for another dose distribution. In addition, simulated errors introduced on the delivered dose, field location and field shape were used to evaluate the ability of the proposed method to efficiently identify a deviation between the planned and delivered treatments.Main results. For a first small IMRT segment, 3%/3 mm, 2%/2 mm and 2%/1 mm gamma analysis conducted between the reconstructed dose distribution and the dose measured with radiochromic film exhibited pass rates of 100%, 99.9% and 95.7%, respectively. For a second and smaller IMRT segment, the same gamma analysis performed between the reconstructed dose distribution and the reference provided by the TPS showed pass rates of 100%, 99.4% and 92.6% for the 3%/3 mm, 2%/2 mm and 2%/1 mm gamma criteria, respectively. Gamma analysis of the simulated treatment delivery errors showed the ability of the reconstruction algorithm to detect a 3% deviation between the planned and delivered doses, as well as shifts lower than 7 mm and 3 mm when considering an individual leaf and a whole field shift, respectively.Significance. The proposed method allows accurate tomographic reconstruction of IMRT segments by processing projections measured with six scintillating-fiber ribbons and is suitable for water-equivalent real-time small IMRT segments QA.

A novel QA phantom based on scintillating fiber ribbons with implementation of 2D dose tomography for small-field radiotherapy.

PURPOSE: To develop a novel instrument for real-time quality assurance (QA) procedures in radiotherapy. The system implements a scintillation-based phantom and associated signal acquisition and processing modules and aims to monitor two-dimensional (2D) dose distributions of small fields. MATERIALS AND METHODS: For the proposed phantom, we have designed and realized a prototype implementing six high-resolution tissue-equivalent scintillating fiber ribbons stacked with in-plane 30° rotated orientations from each other. Each ribbon output is coupled to a silicon photodiode linear array (with an element pitch of 400 µm) to detect scintillating signal, which represents the projected irradiation profile perpendicular to the ribbon's orientation. For the system providing six acquired projected dose profiles at different orientations, we have developed a two-step signal processing method to perform 2D dose reconstruction. The first step is to determine irradiation field geometry parameters using a tomographic geometry approach, and the second one is to perform specific penumbra estimation. The QA system prototype has been tested on a Novalis TrueBeam STX with a 6-MV photon beam for small elliptic fields defined by 5- and 10-mm cone collimators and for 10 × 10- and 20 × 10-mm2 rectangular fields defined by the micro-multileaf collimator. Gamma index analysis using EBT3 films as reference has been carried out with tight 2%-dose-difference (DD)/700-µm-distance-to-agreement (DTA) as well as 1%-DD/1-mm-DTA criteria for evaluating the system performances. The testing also includes an evaluation of the proposed two-step field reconstruction method in comparison with two conventional methods: filtered back projection (FBP) and simultaneous iterative reconstruction technique (SIRT). RESULTS: The reconstructed 2D dose distributions have gamma index pass rates higher than 95% for all the tested configurations as compared with EBT3 film measurements with both 2%-DD/700-µm-DTA and 1%-DD/1-mm criteria. 2D global gamma analysis shows that the two-step and FBP radiation field reconstruction methods systematically outperform the SIRT approach. Moreover, higher gamma index success rates are obtained with the two-step method than with FBP in the case of the fields defined with the stereotactic cones. CONCLUSIONS: The proposed small-field QA system makes a use of six water-equivalent scintillating detectors (fiber ribbons) to acquire dose distribution. The developed two-step signal processing method performs tomographic 2D dose reconstruction. A system prototype has been built and tested using hospital facilities with small rectangular and elliptic fields. Testing results show 2D reconstructed dose distributions with high accuracy and resolution. Such a system could potentially be an alternative approach to film dosimetry for small-field QA, which is still widely used as reference in clinical practice.

Fan-Beam Based Virtual Fluoroscopy for Navigated Catheterization in Interventional Radiology.

Personalized medicine implies reducing invasiveness of therapeutic procedures. Although interventional radiology proved a very interesting alternative to surgical procedures, it still raises concerns due to the irradiation dose received by the medical team (and by the patient). We propose a novel concept allowing to reduce very significantly the irradiation dose during the phases where tools inserted in the patient have to be tracked with respect to previously acquired images. This implies inserting a miniaturized X-ray detector in the tip of the tools, and reducing the dose by a "rotating collimator". We demonstrate that real-time processing of the signals allows accurate localization of the tip of the tools, with a dose reduction of at least ten times.

Spline Driven: High Accuracy Projectors for Tomographic Reconstruction From Few Projections.

Tomographic iterative reconstruction methods need a very thorough modeling of data. This point becomes critical when the number of available projections is limited. At the core of this issue is the projector design, i.e., the numerical model relating the representation of the object of interest to the projections on the detector. Voxel driven and ray driven projection models are widely used for their short execution time in spite of their coarse approximations. Distance driven model has an improved accuracy but makes strong approximations to project voxel basis functions. Cubic voxel basis functions are anisotropic, accurately modeling their projection is, therefore, computationally expensive. Both smoother and more isotropic basis functions better represent the continuous functions and provide simpler projectors. These considerations have led to the development of spherically symmetric volume elements, called blobs. Set apart their isotropy, blobs are often considered too computationally expensive in practice. In this paper, we consider using separable B-splines as basis functions to represent the object, and we propose to approximate the projection of these basis functions by a 2D separable model. When the degree of the B-splines increases, their isotropy improves and projections can be computed regardless of their orientation. The degree and the sampling of the B-splines can be chosen according to a tradeoff between approximation quality and computational complexity. We quantitatively measure the good accuracy of our model and compare it with other projectors, such as the distance-driven and the model proposed by Long et al. From the numerical experiments, we demonstrate that our projector with an improved accuracy better preserves the quality of the reconstruction as the number of projections decreases. Our projector with cubic B-splines requires about twice as many operations as a model based on voxel basis functions. Higher accuracy projectors can be used to improve the resolution of the existing systems, or to reduce the number of projections required to reach a given resolution, potentially reducing the dose absorbed by the patient.

Data consistency conditions for truncated fanbeam and parallel projections.

PURPOSE: In image reconstruction from projections, data consistency conditions (DCCs) are mathematical relationships that express the overlap of information between ideal projections. DCCs have been incorporated in image reconstruction procedures for positron emission tomography, single photon emission computed tomography, and x-ray computed tomography (CT). Building on published fanbeam DCCs for nontruncated projections along a line, the authors recently announced new DCCs that can be applied to truncated parallel projections in classical (two-dimensional) image reconstruction. These DCCs take the form of polynomial expressions for a weighted backprojection of the projections. The purpose of this work was to present the new DCCs for truncated parallel projections, to extend these conditions to truncated fanbeam projections on a circular trajectory, to verify the conditions with numerical examples, and to present a model of how DCCs could be applied with a toy problem in patient motion estimation with truncated projections. METHODS: A mathematical derivation of the new parallel DCCs was performed by substituting the underlying imaging equation into the mathematical expression for the weighted backprojection and demonstrating the resulting polynomial form. This DCC result was extended to fanbeam projections by a substitution of parallel to fanbeam variables. Ideal fanbeam projections of a simple mathematical phantom were simulated and the DCCs for these projections were evaluated by fitting polynomials to the weighted backprojection. For the motion estimation problem, a parametrized motion was simulated using a dynamic version of the mathematical phantom, and both noiseless and noisy fanbeam projections were simulated for a full circular trajectory. The fanbeam DCCs were applied to extract the motion parameters, which allowed the motion contamination to be removed from the projections. A reconstruction was performed from the corrected projections. RESULTS: The mathematical derivation revealed the anticipated polynomial behavior. The conversion to fanbeam variables led to a straight-forward weighted fanbeam backprojection which yielded the same function and therefore the same polynomial behavior as occurred in the parallel case. Plots of the numerically calculated DCCs showed polynomial behavior visually indistinguishable from the fitted polynomials. For the motion estimation problem, the motion parameters were satisfactorily recovered and ten times more accurately for the noise-free case. The reconstructed images showed that only a faint trace of the motion blur was still visible after correction from the noisy motion-contaminated projections. CONCLUSIONS: New DCCs have been established for fanbeam and parallel projections, and these conditions have been validated using numerical experiments with truncated projections. It has been shown how these DCCs could be applied to extract parameters of unwanted physical effects in tomographic imaging, even with truncated projections.

Full data consistency conditions for cone-beam projections with sources on a plane.

Cone-beam consistency conditions (also known as range conditions) are mathematical relationships between different cone-beam projections, and they therefore describe the redundancy or overlap of information between projections. These redundancies have often been exploited for applications in image reconstruction. In this work we describe new consistency conditions for cone-beam projections whose source positions lie on a plane. A further restriction is that the target object must not intersect this plane. The conditions require that moments of the cone-beam projections be polynomial functions of the source positions, with some additional constraints on the coefficients of the polynomials. A precise description of the consistency conditions is that the four parameters of the cone-beam projections (two for the detector, two for the source position) can be expressed with just three variables, using a certain formulation involving homogeneous polynomials. The main contribution of this work is our demonstration that these conditions are not only necessary, but also sufficient. Thus the consistency conditions completely characterize all redundancies, so no other independent conditions are possible and in this sense the conditions are full. The idea of the proof is to use the known consistency conditions for 3D parallel projections, and to then apply a 1996 theorem of Edholm and Danielsson that links parallel to cone-beam projections. The consistency conditions are illustrated with a simulation example.

Comparison of analytic and algebraic methods for motion-compensated cone-beam CT reconstruction of the thorax.

Respiratory motion is a major concern in cone-beam (CB) computed tomography (CT) of the thorax. It causes artifacts such as blur, streaks, and bands, in particular when using slow-rotating scanners mounted on the gantry of linear accelerators. In this paper, we compare two approaches for motion-compensated CBCT reconstruction of the thorax. The first one is analytic; it is heuristically adapted from the method of Feldkamp, Davis, and Kress (FDK). The second one is algebraic: the system of linear equations is generated using a new algorithm for the projection of deformable volumes and solved using the Simultaneous Algebraic Reconstruction Technique (SART). For both methods, we propose to estimate the motion on patient data using a previously acquired 4-D CT image. The methods were tested on two digital and one mechanical motion-controlled phantoms and on a patient dataset. Our results indicate that the two methods correct most motion artifacts. However, the analytic method does not fully correct streaks and bands even if the motion is perfectly estimated due to the underlying approximation. In contrast, the algebraic method allows us full correction of respiratory-induced artifacts.

Monte Carlo simulations verifying sampling schemes in multislice mode PET.

GATE Monte Carlo simulations are performed to verify sampling schemes in multislice mode PET. Two types of scanner were simulated. The effect of attenuation and scatter were investigated by simulating a realistic phantom. The results are in accordance with the theoretical expectations.

Compensation of some time dependent deformations in tomography.

This work concerns 2D + t dynamic tomography. We show that a much larger class of deformations than the affine transforms can be compensated analytically within filtered back projection algorithms in 2D parallel beam and fan beam dynamic tomography. We present numerical experiments on the Shepp and Logan phantom showing that nonaffine deformations can be compensated. A generalization to 3D cone beam tomography is proposed.

Sampling conditions of 3D parallel and fan-beam x-ray CT with application to helical tomography.

We give the sampling conditions of the 3D fan-beam x-ray transform (3DFBXRT). The motivation of this work lies in the fact that helical tomography with a single detector line is simply a sampling of this transform under the helical constraint. We give a precise description of the geometry of the essential support of the 3DFBXRT Fourier transform and show how to derive efficient sampling schemes. We then give efficient sampling schemes in parallel helical tomography. We present numerical experiments showing that efficient sampling on hexagonal interlaced schemes yields better reconstructions than the standard schemes in both parallel helical tomography (using QDO) and 3DFBXRT. We discuss the practical drawbacks and advantages of these efficient schemes and the possible extension to fan-beam helical CT.

Exact reconstruction in 2D dynamic CT: compensation of time-dependent affine deformations.

This work is dedicated to the reduction of reconstruction artefacts due to motion occurring during the acquisition of computerized tomographic projections. This problem has to be solved when imaging moving organs such as the lungs or the heart. The proposed method belongs to the class of motion compensation algorithms, where the model of motion is included in the reconstruction formula. We address two fundamental questions. First what conditions on the deformation are required for the reconstruction of the object from projections acquired sequentially during the deformation, and second how do we reconstruct the object from those projections. Here we answer these questions in the particular case of 2D general time-dependent affine deformations, assuming the motion parameters are known. We treat the problem of admissibility conditions on the deformation in the parallel-beam and fan-beam cases. Then we propose exact reconstruction methods based on rebinning or sequential FBP formulae for each of these geometries and present reconstructed images obtained with the fan-beam algorithm on simulated data.

Development and validation of an X-ray tomograph for two-phase flow.

This paper describes the development and validation of a high spatial resolution X-ray tomograph designed for the investigation of air-water two-phase flow. The device hardware mainly comprises a 60 keV X-ray source, a detector, and an accurate mechanical bench. Our study concentrated on accurate quantification with emphasis on the reconstruction procedure. As is well known, absorption gradients induce reconstruction artifacts when using standard algorithms based on uniform regularization. In the particular case of two-phase flow in a pipe, this leads to poor measurement accuracy in the vicinity of the walls. To overcome such effects, improved algorithms were developed during this study that involve spatially adaptive regularization methods. Preliminary calibration performed on static phantoms clearly exhibited the benefits of the advanced reconstruction algorithms. A validation procedure was carried out on an air-water bubble column, equipped with an optical probe, which could be translated in order to explore the 80 mm x 80 mm square cross section. Comparisons of local void fraction measurements were performed pixel by pixel. They demonstrate the accuracy improvement induced by the advanced reconstruction algorithms.

Multichannel algorithm for fast 3D reconstruction.

Some recent medical imaging applications such as functional imaging (PET and SPECT) or interventional imaging (CT fluoroscopy) involve increasing amounts of data. In order to reduce the image reconstruction time, we develop a new fast 3D reconstruction algorithm based on a divide and conquer approach. The proposed multichannel algorithm performs an indirect frequential subband decomposition of the image f to be reconstructed (f = sigma fj) through the filtering of the projections Rf. The subband images fj are reconstructed on a downsampled grid without information suppression. In order to reduce the computation time, we do not backproject the null filtered projections and we downsample the number of projections according to the Shannon conditions associated with the subband image. Our algorithm is based on filtering and backprojection operators. Using the same algorithms for these basic operators, our approach is three and a half times faster than a classical FBP algorithm for a 2D image 512 x 512 and six times faster for a 3D image 32 x 512 x 512.

Optimal calibration marker mesh for 2D X-ray sensors in 3D reconstruction.

Image intensifiers suffer from distortions due to magnetic fields. In order to use this X-ray projections images for computer-assisted medical interventions, image intensifiers need to be calibrated. Opaque markers are often used for the correction of the image distortion and the estimation of the acquisition geometry parameters. Information under the markers is then lost. In this work, we consider the calibration of image intensifiers in the framework of 3D reconstruction from several 2D X-ray projections. In this context, new schemes of marker distributions are proposed for 2D X-ray sensor calibration. They are based on efficient sampling conditions of the parallel-beam X-ray transform when the detector and source trajectory is restricted to a circle around the measured object. Efficient sampling are essentially subset of standard sampling in this situation. The idea is simply to exploit the data redundancy of standard sampling and to replace some holes of efficient schemes by markers. Optimal location of markers in the sparse efficient sampling geometry can thus be found. In this case, the markers can stay on the sensor during the measurement with--theoretically--no loss of information (when the signal-to-noise ratio is large). Even if the theory is based on the parallel-beam X-ray transform, numerical experiments on both simulated and real data are shown in the case of weakly divergent beam geometry. We show that the 3D reconstruction from simulated data with interlaced markers is essentially the same as those obtained from data with no marker. We show that efficient Fourier interpolation formulas based on optimal sparse sampling schemes can be used to recover the information hidden by the markers.