Algebraic and analytic reconstruction methods for dynamic tomography.

In this work, we discuss algebraic and analytic approaches for dynamic tomography. We present a framework of dynamic tomography for both algebraic and analytic approaches. We finally present numerical experiments

Extraction of the respiratory signal from cone-beam projections for 4D CT imaging

To be efficient, the treatement of the lung cancers with radiation therapy must take into account the respiratory motion. The knowledge of this motion requires the acquisition of 4D computed tomography (CT) images. The free-breathing thorax 4D CT images currently acquired use gated or respiratory-correlated methods. These methods involve the collection of a respiratory signal during the acquisition of data in order to sort them into different groups. The quality of the 4D CT image thus depends on an accurate description by the signal of the position of the thorax in the respiratory cycle. The signal is generally acquired by independent measurements of densitometric data (spirometer, thermometer, ...). We propose to extract it directly from the sequence of 2D cone-beam (CB) projections acquired around the free-breathing thorax. Our method derives the motion between two consecutive 2D CB projections using a block matching algorithm. Blocks are positioned around points of interest constituting a regular sampling of the 2D CB projections. A unidimensional signal is derived from the trajectory of each block in the sequence after projection. Aggregation of a subset of selected makes it possible to derive the respiratory signal during the acquisition time. Our method is validated quantitatively on simulated data and qualitatively on real data. On simulated data, we obtain a respiratory signal with 97.5 % linear correlation with the reference. On real data, the extracted signal allow to reconstruct 4D CT images for comparison with the blurred 3D CT image obtained without taking into account the respiratory motion.Le traitement des cancers des poumons par radiothérapie doit prendre en compte les mouvements respiratoires pour être efficace. La connaissance de ce mouvement passe par l'obtention d'images tomodensitométriques (TDM) 4D. Les images TDM 4D du thorax en respiration libre acquises actuellement utilisent les méthodes de type gated ou respiration-correlated. Ces méthodes nécessitent un signal respiratoire, recueilli pendant l'acquisition des données, pour trier celles-ci en différents groupes. La qualité de l'image TDM 4D dépend alors d'une description correcte, par le signal respiratoire, de la position du thorax dans le cycle respiratoire au cours de l'acquisition. Ce signal est généralement acquis par une mesure indépendante des données densitométriques (spiromètre, thermomètre,...). Nous proposons de l'extraire directement de la séquence de projections cone-beam (CB) 2D acquises autour du thorax en respiration libre. Notre méthode extrait le mouvement entre deux projections CB 2D consécutives par un algorithme de mise en correspondance de blocs. Ces blocs sont positionnés autour de points d'intérêt constituant un sous-échantillonnage régulier des projections CB 2D. Nous déduisons de la trajectoire de chaque bloc dans la séquence un signal unidimensionnel après projection. Une sélection d'un sous-ensemble de ces signaux nous permet d'obtenir, après agrégation, le signal respiratoire pendant le temps de l'acquisition. Notre méthode est validée quantitativement sur données simulées et qualitativement sur données réelles. Sur données simulées, nous obtenons un signal respiratoire corrélé linéairement à 97,5 % avec la référence. Sur données réelles, le signal extrait nous permet de reconstruire l'image TDM 4D d'un patient que l'on compare à l'image TDM 3D floue, obtenue sans prise en compte du mouvement respiratoire

Registration of phase contrast images in propagation-based X-ray phase tomography

International audienceX-ray phase tomography aims at reconstructing the 3D electron density distribution of an object. It offers enhanced sensitivity compared to attenuation-based X-ray absorption tomography. In propagation-based methods, phase contrast is achieved by letting the beam propagate after interaction with the object. The phase shift is then retrieved at each projection angle, and subsequently used in tomographic reconstruction to obtain the refractive index decrement distribution, which is proportional to the electron density. Accurate phase retrieval is achieved by combining images at different propagation distances. For reconstructions of good quality, the phase-contrast images recorded at different distances need to be accurately aligned. In this work, we characterise the artefacts related to misalignment of the phase-contrast images, and investigate the use of different registration algorithms for aligning in-line phase-contrast images. The characterisation of artefacts is done by a simulation study and comparison with experimental data. Loss in resolution due to vibrations is found to be comparable to attenuation-based computed tomography. Further, it is shown that registration of phase-contrast images is nontrivial due to the difference in contrast between the different images, and the often periodical artefacts present in the phase-contrast images if multilayer X-ray optics are used. To address this, we compared two registration algorithms for aligning phase-contrast images acquired by magnified X-ray nanotomography: one based on cross-correlation and one based on mutual information. We found that the mutual information-based registration algorithm was more robust than a correlation-based method

Feasibility study of a proton CT system based on 4D-tracking and residual energy determination via time-of-flight

For dose calculations in ion beam therapy, it is vital to accurately determine the relative stopping power (RSP) distribution within the treated volume. Currently, RSP values are extrapolated from Hounsfield units (HU), measured with x-ray computed tomography (CT), which entails RSP inaccuracies due to conversion errors. A suitable method to improve the treatment plan accuracy is proton computed tomography (pCT). A typical pCT system consists of a tracking system and a separate residual energy (or range) detector to measure the RSP distribution directly. This paper introduces a novel pCT system based on a single detector technology, namely low gain avalanche detectors (LGADs). LGADs are fast 4D-tracking detectors, which can be used to simultaneously measure the particle position and time with precise timing and spatial resolution. In contrast to standard pCT systems, the residual energy is determined via a time-of-flight (TOF) measurement between different 4D-tracking stations. The design parameters for a realistic proton computed tomography system based on 4D-tracking detectors were studied and optimized using Monte Carlo simulations. The RSP accuracy and RSP resolution were measured inside the inserts of the CTP404 phantom to estimate the performance of the pCT system. After introducing a dedicated calibration procedure for the TOF calorimeter, RSP accuracies < 0.6 % could be achieved. Furthermore, the design parameters with the strongest impact on the RSP resolution were identified and a strategy to improve RSP resolution is proposed.Comment: Preprint submitted to Physics in Medicine and Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Isoscaling in central Sn+Sn collisions at 270 MeV/u

Experimental information on fragment emissions is important in understanding the dynamics of nuclear collisions and in the development of transport model simulating heavy-ion collisions. The composition of complex fragments emitted in the heavy-ion collisions can be explained by statistical models, which assume that thermal equilibrium is achieved at collision energies below 100 MeV/u. Our new experimental data together with theoretical analyses for light particles from Sn+Sn collisions at 270 MeV/u, suggest that the hypothesis of thermal equilibrium breaks down for particles emitted with high transfer momentum. To inspect the system's properties in such limit, the scaling features of the yield ratios of particles from two systems, a neutron-rich system of ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and a nearly symmetric system of ${}^{108}\mathrm{Sn}+{}^{112}\mathrm{Sn}$, are examined in the framework of the statistical multifragmentation model and the antisymmetrized molecular dynamics model. The isoscaling from low energy particles agree with both models. However the observed breakdown of isoscaling for particles with high transverse momentum cannot be explained by the antisymmetrized molecular dynamics model

Prise en compte du mouvement respiratoire pour la reconstruction d'images tomodensitométriques: Obtention d’images TDM 4D en salle de traitement pour la radiothérapie du cancer du poumon

A computed tomography (CT) represents the 3D map of the linear attenuation coefficients of a X-ray beam. If the patient breath and the motion is not taken into account, the CT images of the thorax are disturbed by strong artifacts such as blur, streaks and bands. The objective of this thesis is to propose methods to correct these artifacts and to apply them in the context of the radiotherapy of the lung cancer to sequences of cone-beam projections acquired with a CT scanner mounted on the gantry of a linear accelerator. The first method uses a respiratory signal to select for the reconstruction the projections corresponding to a same phase. To apply it, we proposed a method to extract automatically the respiratory signal from the cone-beam projections. A quantitative analysis was then performed on simulated data to evaluate the impact of the reconstruction algorithm and of the different selection parameters of the cone-beam projections. We obtain thus CT images without blur but with a quality limited due to the small number of projections used. Other approaches modify the reconstruction algorithm to compensate for the respiratory motion using a realistic model, which allows to use all the acquired projections. We proposed two motion compensated reconstruction methods. The first one is analytic and based on a heuristic. The second one solves the problem algebraically from a discrete formulation of the transformations at stake via two new approaches, one forward and the other backward.Une image tomodensitométrique (TDM) représente la carte 3D des coefficients d'atténuation linéaire d'un faisceau de rayons X. Si le patient respire et le mouvement n'est pas pris en compte, les images TDM du thorax sont perturbées par d'importants artefacts, tels que du flou, des traits et des bandes. L'objectif de cette thèse est de proposer des méthodes de correction et de les appliquer dans le cadre de la radiothérapie du cancer du poumon, à partir de séquences de projections acquises par un faisceau à géométrie conique embarqué sur un accélérateur linéaire. La première méthode envisagée s'appuie sur un signal respiratoire permettant de sélectionner pour la reconstruction les projections correspondant à une même phase. Pour l'appliquer, nous avons mis au point une méthode d'extraction automatique du signal respiratoire depuis les projections. Par ailleurs, une étude quantitative a été menée sur données simulées pour évaluer l'impact de l'algorithme de reconstruction et des différents paramètres de sélection des projections. Nous obtenons ainsi des images TDM sans flou mais d'une qualité limitée par l'utilisation d'un faible nombre de projections. D'autres approches modifient l'algorithme de reconstruction pour compenser le mouvement respiratoire à partir d'un modèle réaliste quelconque supposé connu, ce qui permet d'utiliser toutes les projections acquises. Nous avons proposé deux méthodes de reconstruction avec compensation du mouvement. La première est analytique mais basée sur une heuristique. La seconde résout le problème algébriquement à partir d'une modélisation discrète des transformations en jeu via deux nouvelles approches, l'une avant et l'autre arrière

Improving iterative 4D CBCT through the use of motion information

International audienceIn Image-Guided RadioTherapy (IGRT) of lung tumors, patients undergo a 4D CT, on the basis of which their treatment is planned. It is implicitely assumed that their breathing motion will not change much throughout the treatment, and remain close to what it was during the 4D CT acquisition. During the treatment, several cone beam CT acquisitions are performed, and used to re-position the patient. Obtaining a 4D reconstruction from this cone beam data would allow the therapists to check whether the breathing motion of the day still matches that of the planning CT, and if not, take appropriate corrective actions. Unfortunately, most tomography methods currently available are inadequate for such a task: static 3D reconstructions are pointless for motion assessment, respirationcorrelated reconstructions are affected by streak artifacts, and regularization techniques only bring limited improvement. Recently, regularized 4D methods have been proposed, in which the whole respiratory cycle is reconstructed at once. As these methods allow to explicitely enforce similarity between consecutive frames, they considerably improve image quality. In the case of IGRT, the motion information extracted from the 4D planning CT can be used to further improve the 4D reconstruction results. We describe a recent 4D reconstruction method (ROOSTER), propose its motion-compensated counterpart (MC-ROOSTER), and compare their results

Cone-beam projection of a deformable volume for motion compensated algebraic reconstruction

International audienceThe cone-beam tomographic projection and the deformation of a discrete volume are problems that have generally been studied separately. They are combined in someapplications such as motion compensated algebraic reconstruction. In this paper, we propose two methods to compute the cone-beam projections of a volume deformed with a known motion. The first method is based on an inverse mapping between the reference 3D volume and the 2D cone-beam projection and the second method on a forward mapping. Both methods were evaluated on a dynamic digital phantom andconfronted to another method. The quality of the cone-beam projections was increased by 70% with both methods compared to the projection obtained without including the motion model. The proposed methods yield accurate linear equations, the first step before tomographic reconstruction of the deformable volume with algebraic methods

Consistency-based auto-calibration of the spectral model in dual-energy CT

International audienceWe propose a consistency-based material decomposition algorithm. The method is free from any calibration procedure. The inverse spectral mixing model is approximated by a polynomial whose indeterminates are the raw-data values and whose coefficients are estimated by minimizing a consistency-based cost function. The consistency is in both the material sinograms and their mono-energetic combination. A small a priori on the object is incorporated in the minimization problem as a constraint. The method was evaluated on dual-energy simulations of a numerical phantom made of water and bone

Equal parallel and cone-beam projections: a curious property of D-symmetric object functions

International audienceIn tomographic image reconstruction, the object density function is the unknown quantity whose projections are measured by the scanner. In the three-dimensional (3D) case, we define the D-reflection of such a density function as the object obtained by a particular weighted reflection about the plane z = D, and a D-symmetric function as one whose D-reflection is equal to itself. D-symmetric object functions have the curious property that their parallel projection onto the detector plane z = D is equal to their cone-beam projection onto the same detector with x-ray source location at the origin. Much more remarkable is the additional fact that for any fixed D-symmetric object, every oblique parallel projection onto this same detector plane equals the cone-beam projection for a corresponding source location. The mathematical proof is straight forward but not particularly enlightening, and we also provide here an alternative physical demonstration that explains the various weighting terms in the context of classical tomosynthesis. Furthermore, we clarify the distinction between the new formulation presented here, and the original formulation of Edholm and co-workers who obtained similar properties but for a pair of objects whose divergent and parallel projections matched, but with no D-symmetry. We do not claim any immediate imaging application or useful physics from these notions, but we briefly comment on consequences for methods that apply data consistency conditions in image reconstruction