Abstract: Anisotropic differential operators are widely used in image enhancement processes. Recently, their property of smoothly extending functions to the whole image domain has begun to be exploited. Strong ellipticity of differential operators is a requirement that ensures existence of a unique solution. This condition is too restrictive for operators designed to extend image level sets: their own functionality implies that they should restrict to some vector field. The diffusion tensor that defines the diffusion operator links anisotropic processes with Riemmanian manifolds. In this context, degeneracy implies restricting diffusion to the varieties generated by the vector fields of positive eigenvalues, provided that an integrability condition is satisfied. We will use that any smooth vector field fulfills this integrability requirement to design line connection algorithms for contour completion. As application we present a segmenting strategy that assures convergent snakes whatever the geometry of the object to be modelled is.

Abstract: Project-Based Learning (PBL) is an educational strategy to improve student’s learning capability that, in recent years, has had a progressive acceptance in undergraduate studies. This methodology is based on solving a problem or project in a student working group. In this way, PBL focuses on learning the necessary tools to correctly find a solution to given problems. Since the learning initiative is transferred to the student, the PBL method promotes students own abilities. This allows a better assessment of the true workload that carries out the student in the subject. It follows that the methodology conforms to the guidelines of the Bologna document, which quantifies the student workload in a subject by means of the European credit transfer system (ECTS). PBL is currently applied in undergraduate studies needing strong practical training such as medicine, nursing or law sciences. Although this is also the case in engineering studies, amazingly, few experiences have been reported. In this paper we propose to use PBL in the educational organization of the Computer Graphics subjects in the Computer Science degree. Our PBL project focuses in the development of a C++ graphical environment based on the OpenGL libraries for visualization and handling of different graphical objects. The starting point is a basic skeleton that already includes lighting functions, perspective projection with mouse interaction to change the point of view and three predefined objects. Students have to complete this skeleton by adding their own functions to solve the project. A total number of 10 projects have been proposed and successfully solved. The exercises range from human face rendering to articulated objects, such as robot arms or puppets. In the present paper we extensively report the statement and educational objectives for two of the projects: solar system visualization and a chess game. We report our earlier educational experience based on the standard classroom theoretical, problem and practice sessions and the reasons that motivated searching for other learning methods. We have mainly chosen PBL because it improves the student learning initiative. We have applied the PBL educational model since the beginning of the second semester. The student’s feedback increases in his interest for the subject. We present a comparative study of the teachers’ and students’ workload between PBL and the classic teaching approach, which suggests that the workload increase in PBL is not as high as it seems.

Abstract: Deep understanding of myocardial structure linking morphology and func- tion of the heart would unravel crucial knowledge for medical and surgical clinical procedures and studies. Diffusion tensor MRI provides a discrete measurement of the 3D arrangement of myocardial fibres by the observation of local anisotropic
diffusion of water molecules in biological tissues. In this work, we present a multi- scale visualisation technique based on DT-MRI streamlining capable of uncovering additional properties of the architectural organisation of the heart. Methods and Materials: We selected the John Hopkins University (JHU) Canine Heart Dataset, where the long axis cardiac plane is aligned with the scanner’s Z- axis. Their equipment included a 4-element passed array coil emitting a 1.5 T. For DTI acquisition, a 3D-FSE sequence is apply. We used 200 seeds for full-scale tractography, while we applied a MIP mapping technique for simplified tractographic reconstruction. In this case, we reduced each DTI 3D volume dimensions by order- two magnitude before streamlining.
Our simplified tractographic reconstruction method keeps the main geometric features of fibres, allowing for an easier identification of their global morphological disposition, including the ventricular basal ring. Moreover, we noticed a clearly visible helical disposition of the myocardial fibres, in line with the helical myocardial band ventricular structure described by Torrent-Guasp. Finally, our simplified visualisation with single tracts identifies the main segments of the helical ventricular architecture.
DT-MRI makes possible the identification of a continuous helical architecture of the myocardial fibres, which validates Torrent-Guasp’s helical myocardial band ventricular anatomical model.

Abstract: PURPOSE:
Personalized computational simulations of the heart could open up new improved approaches to diagnosis and surgery assistance systems. While it is fully recognized that myocardial fiber orientation is central for the construction of realistic computational models of cardiac electromechanics, the role of its overall architecture and connectivity remains unclear. Morphological studies show that the distribution of cardiac muscular fibers at the basal ring connects epicardium and endocardium. However, computational models simplify their distribution and disregard the basal loop. This work explores the influence in computational simulations of fiber distribution at different short-axis cuts.
METHODS:
We have used a highly parallelized computational solver to test different fiber models of ventricular muscular connectivity. We have considered two rule-based mathematical models and an own-designed method preserving basal connectivity as observed in experimental data. Simulated cardiac functional scores (rotation, torsion and longitudinal shortening) were compared to experimental healthy ranges using generalized models (rotation) and Mahalanobis distances (shortening, torsion).
RESULTS:
The probability of rotation was significantly lower for ruled-based models [95% CI (0.13, 0.20)] in comparison with experimental data [95% CI (0.23, 0.31)]. The Mahalanobis distance for experimental data was in the edge of the region enclosing 99% of the healthy population.
CONCLUSIONS:
Cardiac electromechanical simulations of the heart with fibers extracted from experimental data produce functional scores closer to healthy ranges than rule-based models disregarding architecture connectivity.