Abstract: Image registration has been for many years the gold standard method to bring two images into correspondence. It has been used extensively in the eld of medical imaging in order to put images of dierent patients into a common overlapping spatial position. However, medical image registration is a slow, iterative optimization process, where many variables and prone to fall into the pit traps local minima.
A coordinate system parameterizing the interior of organs is a powerful tool for a systematic localization of injured tissue. If the same coordinate values are assigned to specic anatomical sites, parameterizations ensure integration of data across different medical image modalities. Harmonic mappings have been used to produce parametric meshes over the surface of anatomical shapes, given their ability to set values at specic locations through boundary conditions. However, most of the existing implementations in medical imaging restrict to either anatomical surfaces, or the depth coordinate with boundary conditions is given at discrete sites of limited geometric diversity.
The medial surface of the shape can be used to provide a continuous basis for the denition of a depth coordinate. However, given that dierent methods for generation of medial surfaces generate dierent manifolds, not all of them are equally suited to be the basis of radial coordinate for a parameterization. It would be desirable that the medial surface will be smooth, and robust to surface shape noise, with low number of spurious branches or surfaces.
In this thesis we present methods for computation of smooth medial manifolds and apply them to the generation of for anatomical volumetric parameterization that extends current harmonic parameterizations to the interior anatomy using information provided by the volume medial surface. This reference system sets a solid base for creating anatomical models of the anatomical shapes, and allows comparing several patients in a common framework of reference.

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: The operational model of agonism assumes that the maximum effect a particular receptor system can achieve (the Em parameter) is fixed. Em estimates are above but close to the asymptotic maximum effects of endogenous agonists. The concept of Em is contradicted by superagonists and those positive allosteric modulators that significantly increase the maximum effect of endogenous agonists. An extension of the operational model is proposed that assumes that the Em parameter does not necessarily have a single value for a receptor system but has multiple values associated to multiple active receptor conformations. The model provides a mechanistic link between active receptor conformation and agonist efficacy, which can be useful for the analysis of agonist response under different receptor scenarios.

Abstract: Two-state and operational models of both agonism and allosterism are compared to identify and characterize common pharmacological parameters. To account for the receptor-dependent basal response, constitutive receptor activity is considered in the operational models. By arranging two-state models as the fraction of active receptors and operational models as the fractional response relative to the maximum effect of the system, a one-by-one correspondence between parameters is found. The comparative analysis allows a better understanding of complex allosteric interactions. In particular, the inclusion of constitutive receptor activity in the operational model of allosterism allows the characterization of modulators able to lower the basal response of the system; that is, allosteric modulators with negative intrinsic efficacy. Theoretical simulations and overall goodness of fit of the models to simulated data suggest that it is feasible to apply the models to experimental data and constitute one step forward in receptor theory formalism.

Abstract: Confident use of medial surfaces in medical decision support systems requires evaluating their quality for detecting pathological deformations and describing anatomical volumes. Validation in the medical imaging field is a challenging task mainly due to the difficulties for getting consensual ground truth. In this paper we propose a validation benchmark for assessing medial surfaces in the context of medical applications. Our benchmark includes a home-made database of synthetic medial surfaces and volumes and specific scores for evaluating surface accuracy, its stability against volume deformations and its capabilities for accurate reconstruction of anatomical volumes.