Abstract: Cardiac magnetic resonance imaging (Cardiac MRI) has become a gold standard diagnostic technique for the assessment of cardiac mechanics, allowing the non-invasive calculation of left ventric- ular long axis longitudinal shortening (LVLS) and absolute myocardial torsion (AMT) between basal and apical left ventricular slices, a movement directly related to the helicoidal anatomic disposition of the myocardial fibers. The aim of this study is to determine AMT and LVLS behaviour and normal values from a group of healthy subjects. A group of 21 healthy volunteers (15 males) (age: 23–55 y.o., mean:30.7 ± 7.5) were prospectively included in an obser- vational study by Cardiac MRI. Left ventricular rotation (degrees) was calculated by custom-made software (Harmonic Phase Flow) in consecutive LV short axis planes tagged cine-MRI sequences. AMT was determined from the difference between basal and apical planes LV rotations. LVLS (%) was determined from the LV longitudinal and horizontal axis cine-MRI images. All the 21 cases studied were interpretable, although in three cases the value of the LV apical rotation could not be determined. The mean rotation of the basal and apical planes at end-systole were -3.71° ± 0.84° and 6.73° ± 1.69° (n:18) respectively, resulting in a LV mean AMT of 10.48° ± 1.63° (n:18). End-systolic mean LVLS was 19.07 ± 2.71%. Cardiac MRI allows for the calculation of AMT and LVLS, fundamental functional components of the ventricular twist mechanics conditioned, in turn, by the anatomical helical layout of the myocardial fibers. These values provide complementary information about systolic ventricular function in relation to the traditional parameters used in daily practice.

Abstract: Crystal unbending, the process that aims to recover a perfect crystal from experimental data, is one of the more important steps in electron crystallography image processing. The unbending process involves three steps: estimation of the unit cell displacements from their ideal positions, extension of the deformation field to the whole image and transformation of the image in order to recover an ideal crystal. In this work, we present a systematic analysis of the second step oriented to address two issues. First, whether the unit cells remain undistorted and only the distance between them should be changed (rigid case) or should be modified with the same deformation suffered by the whole crystal (elastic case). Second, the performance of different extension algorithms (interpolation versus approximation) is explored. Our experiments show that there is no difference between elastic and rigid cases or among the extension algorithms. This implies that the deformation fields are constant over large areas. Furthermore, our results indicate that the main source of error is the transformation of the crystal image.

Abstract: Smoothing of biomedical images should preserve gray-level transitions between adjacent tissues, while restoring contours consistent with anatomical structures. Anisotropic diffusion operators are based on image appearance discontinuities (either local or contextual) and might fail at weak inter-tissue transitions. Meanwhile, the output of block-wise and morphological operations is prone to present a block structure due to the shape and size of the considered pixel neighborhood. In this contribution, we use differential geometry concepts to define a diffusion operator that restricts to image consistent level-sets. In this manner, the final state is a non-uniform intensity image presenting homogeneous inter-tissue transitions along anatomical structures, while smoothing intra-structure texture. Experiments on different types of medical images (magnetic resonance, computerized tomography) illustrate its benefit on a further process (such as segmentation) of images.

Abstract: Any image filtering operator designed for automatic shape restoration should satisfy robustness (whatever the nature and degree of noise is) as well as non-trivial smooth asymptotic behavior. Moreover, a stopping criterion should be determined by characteristics of the evolved image rather than dependent on the number of iterations. Among the several PDE based techniques, curvature flows appear to be highly reliable for strongly noisy images compared to image diffusion processes.
In the present paper, we introduce a regularized curvature flow (RCF) that admits non-trivial steady states. It is based on a measure of the local curve smoothness that takes into account regularity of the curve curvature and serves as stopping term in the mean curvature flow. We prove that this measure decreases over the orbits of RCF, which endows the method with a natural stop criterion in terms of the magnitude of this measure. Further, in its discrete version it produces steady states consisting of piece-wise regular curves. Numerical experiments made on synthetic shapes corrupted with different kinds of noise show the abilities and limitations of each of the current geometric flows and the benefits of RCF. Finally, we present results on real images that illustrate the usefulness of the present approach in practical applications.

Abstract: Tissue biomechanical properties (like strain and stress) are playing an increasing role in diagnosis and long-term treatment of intravascular coronary diseases. Their assessment strongly relies on estimation of vessel wall deformation. Since intravascular ultrasound (IVUS) sequences allow visualizing vessel morphology and reflect its dynamics, this technique represents a useful tool for evaluation of tissue mechanical properties. Image misalignment introduced by vessel-catheter motion is a major artifact for a proper tracking of tissue deformation. In this work, we focus on compensating and assessing IVUS rigid in-plane motion due to heart beating. Motion parameters are computed by considering both the vessel geometry and its appearance in the image. Continuum mechanics laws serve to introduce a novel score measuring motion reduction in in vivo sequences. Synthetic experiments validate the proposed score as measure of motion parameters accuracy; whereas results in in vivo pullbacks show the reliability of the presented methodologies in clinical cases.