Abstract: This manuscript has been withdrawn by bioRxiv due to upload of an incorrect version of the manuscript by the authors. Therefore, this manuscript should not be cited as reference for this project.

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.

Abstract: Medial surfaces are powerful tools for shape description, but their use has been limited due to the sensibility existing methods to branching artifacts. Medial branching artifacts are associated to perturbations of the object boundary rather than to geometric features. Such instability is a main obstacle for a condent application in shape recognition and description. Medial branches correspond to singularities of the medial surface and, thus, they are problematic for existing morphological and energy-based algorithms. In this paper, we use algebraic geometry concepts in an energy-based approach to compute a medial surface presenting a stable branching topology. We also present an ecient GPU-CPU implementation using standard image processing tools. We show the method computational eciency and quality on a custom made synthetic database. Finally, we present some results on a medical imaging application for localization of abdominal pathologies.

Abstract: In order to provide more intuitive and easily interpretable representations of complex shapes/organs, medial manifolds should reach a compromise between simplicity in geometry and capability for restoring the anatomy/shape of the organ/volume. Existing morphological methods show excellent results when applied to 2D objects, but their quality drops across dimensions.
This paper contributes to the computation of medial manifolds in two aspects. First, we provide a standard scheme for the computation of medial manifolds that avoids degenerated medial axis segments. Second, we introduce a continuous operator for accurate and efficient computation of medial structures of arbitrary dimension. We evaluate quantitatively the performance of our method with respect to existing approaches, by applying them to syn- thetic shapes of known medial geometry. We also show its higher performance for medical imaging applications in terms of simplicity of medial structures and capability for reconstructing the anatomical volume.