Temporal Tracking of Coronaries in Sequences of CT Volumes
Suivi Temporel des Coronaries dans les Séquences de Volumes Scanner
Cardiovascular diseases remain a major worldwide health concern. Although significant advances have been made in heart imaging, much is still expected for improving diagnostic and better assisting interventions. On this way, our work is focused on the planning and the guidance of endovascular therapies such as cardiac resynchronization or revascularization. More precisely, its objective is to find the optimal vascular path to a given target for the insertion of tools like stimulation probes, balloons or stents. The challenge is therefore to track in 3D space and time the structures of interest in order to define the instrument trajectories. This work presents a first attempt toward the temporal tracking of coronary arteries in a sequence of CT volumes.
The beating heart is highly deformed over a cardiac cycle and complex movements are present (contraction, expansion, torsion) with slow, fast and inverted episodes. The coronary arteries, relying on the myocardium, are very difficult to track due to their small diameters diameters (1 to 5 mm while the CT resolution is about 0.4 mm) on one hand and, on the other hand, the CT reconstruction artifacts corresponding to fast motion phases of the heart.
Many motion extraction techniques have been derived over the two last decades and widely applied in the computer vision domain. Optical flow methods , bayesian filtering tracking  and deformable models  are among the most well known. However, few articles have addressed the coronary vessel tracking problem in CT volume sequences. Previous studies dealt with 2D image sequences [4-9] and few of them present an automatic method . To our knowledge, the work of Shechter et al.  based on landmarks (forking points) is the only one really applied to 3D CT sequences.
The present method departs from this approach by only using tracks local intensity patterns and shape features of the vessels. The mean background and vessel intensity distribution are estimated using an EM algorithm. The shape information is recovered by locally modeling the vessel as a cylinder. Its parameters (center, radius and direction) are computed from the geometrical moments computed up to the second order in a spherical neighborhood  (equations 1-4).
The method is divided into three main stages (figure 1) : initialization, temporal tracking and position refinement. At the initialization step, the user picks up a point into one volume Vt of the sequence. Its position is adjusted on the vessel centerline using an iterative process . To get accurately the vessel local features, this process also assesses the size of the spherical neighborhood to be used in the computation of geometrical moments. The overall goal consists to find the position of this point Pt , in each volume of the sequence: (Pt,Pt+1,Pt+2 . . .). We propose an original exploration technique of the volume Vt+i:
- The temporal tracking step researches a point of the vessel into a spherical research space, centered on the position Pt . Its radius is chosen to cover the largest motion expected in the volume sequence. This space is then divided into a set of small spheres which positions and radiuses are adjusted using the same iterative process applied at the initialization step. The spheres are then located on the high intensity regions in the search space and their centers are the candidate points. A similarity criterion between each candidate point and the point Pt is computed to select the best point, let say, ˆPt+i. This measure includes the local histogram, the second order moments and the estimated radius of the vessel (equation 5).
- The last step is aimed at refining the position of the point inside the vessel by performing a local spatial tracking of the vessel around the position ˆPt+i. The displacement is performed along the vessel estimated local direction. The iterative processes, mentioned above, are applied at each step to adjust the position of the point on the vessel centerline. The local sum of squared differences of intensity is then used to select the position of the point Pt+i among the extracted points. Some experiments have been conducted to evaluate the method. They have been first carried out on real data sets submitted to controlled transformations. When translations of growing magnitudes (up to 12 mm for 3 different volumes) are applied, the results (using 20 points located on the main branches of the coronary arteries in each volume) led to an accuracy below 2 mm for 95% of the tests and better than 1 mm for 75% of them. To simulate more realistically the heart movements, we also considered a non rigid B-spline transformation . The transformation parameters were assessed by registering 2 volumes of a sequence. For the 52 points tracked, we obtained 100% success in recovering a point located in the vessel. The mean error was 1.8 mm at the end of the temporal tracking step, and 0.8 mm after the whole process. A second experimental phase has been worked out on real data but, in that case, without knowing the ground truth. 10 points were tracked for each of the 4 available volume sequences. The points were located either on healthy or pathological vessels (figures 4-5). We compared the trajectories of several points of a branch (figure 6) and the same point in the anatomy for several patients (figure 7). The trajectories were consistent between them and also with the physiology (fast motion in systole, diastole containing 3 main motion stages).
To briefly conclude, let us emphasize that the main difficulties come from both the characteristics of the images and the structural complexity of the scene. The images are spatially anisotropic (a linear interpolation between slices needs to be applied), not fully corrected during the reconstruction in term of motion artifacts (figure 5 phase 50%). The scene includes different structures such as myocardium, cavities, venous and arterial trees, which are spatially close and have similar intensities. The vessels are thin and can depict abnormal features (i.e atherosclerosis). The method overcomes most of these problems, except when the data sets are too damaged by strong motion artifacts. The choice to use only local information is well-justified by the objective to process a minimum of information. This two steps strategy was accordingly built on the idea to look for a first vessel point considering only the candidates located at high intensity regions in a limited space, and then, to achieve a local exhaustive search on the vessel centerline. The computation time of the method, around 2s for tracking a new position over the full volume sequence is still too long for a clinical use. However, a code optimization and a sound choice of the number of candidate points will contribute to significantly reduce the computation time. Furthermore, the spatial coherence of the vessel in time could be used to speed up the tracking of an ensemble of points.
Ce travail s’inscrit dans le cadre d’une procédure de planning d’intervention endovasculaire guidée par l’image. L’objectif consiste à déterminer la trajectoire d’accès à un site particulier et implique la capacité de déterminer et caractériser les trajectoires spatiales et temporelles des vaisseaux. L’approche retenue repose sur une technique de mise en correspondance de régions associant des critères de similarité de forme et d’intensité. Une première étape a pour objectif la recherche d’un point correspondant sur le vaisseau d’intérêt dans un espace de recherche de forme sphérique. La seconde étape consiste à améliorer sa localisation en explorant les points de la ligne centrale du vaisseau sur un court segment. Dans un premier temps, la méthode est testée sur des séquences contenant des mouvements simulés linéaires et non linéaires, puis sur des séquences réelles. La méthode permet de faire face à une grande partie des difficultés rencontrées sur ce type de données. Les trajectoires des points suivis sont cohérentes entre elles et avec les autres études présentées dans la littérature.
Tracking, motion, coronaries, 3D, sequences, CT, geometrical moments
Suivi, mouvement, coronaires, 3D, sequences, CT, moments géométriques
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