Super-Resolution in Respiratory Synchronized Positron Emission Tomography

Respiratory motion is a major source of reduced quality in positron emission tomography (PET). In order to minimize its effects, the use of respiratory synchronized acquisitions, leading to gated frames, has been suggested. Such frames, however, are of low signal-to-noise ratio (SNR) as they contain reduced statistics. Super-resolution (SR) techniques make use of the motion in a sequence of images in order to improve their quality. They aim at enhancing a low-resolution image belonging to a sequence of images representing different views of the same scene. In this work, a maximum a posteriori (MAP) super-resolution algorithm has been implemented and applied to respiratory gated PET images for motion compensation. An edge preserving Huber regularization term was used to ensure convergence. Motion fields were recovered using a B-spline based elastic registration algorithm. The performance of the SR algorithm was evaluated through the use of both simulated and clinical datasets by assessing image SNR, as well as the contrast, position and extent of the different lesions. Results were compared to summing the registered synchronized frames on both simulated and clinical datasets. The super-resolution image had higher SNR (by a factor of over 4 on average) and lesion contrast (by a factor of 2) than the single respiratory synchronized frame using the same reconstruction matrix size. In comparison to the motion corrected or the motion free images a similar SNR was obtained, while improvements of up to 20% in the recovered lesion size and contrast were measured. Finally, the recovered lesion locations on the SR images were systematically closer to the true simulated lesion positions. These observations concerning the SNR, lesion contrast and size were confirmed on two clinical datasets included in the study. In conclusion, the use of SR techniques applied to respiratory motion synchronized images lead to motion compensation combined with improved image SNR and contrast, without any increase in the overall acquisition times.

MBIS: Multivariate Bayesian Image Segmentation Tool

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multi-channel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.

Parametric Generation of Planing Hulls with NURBS Surfaces

This article presents a mathematical method for producing hard-chine ship hulls based on a set of numerical parameters that are directly related to the geometric features of the hull and uniquely define a hull form for this type of ship. The term planing hull is used generically to describe the majority of hard-chine boats being built today. This article is focused on unstepped, single-chine hulls. B-spline curves and surfaces were combined with constraints on the significant ship curves to produce the final hull design. The hard-chine hull geometry was modeled by decomposing the surface geometry into boundary curves, which were defined by design constraints or parameters. In planing hull design, these control curves are the center, chine, and sheer lines as well as their geometric features including position, slope, and, in the case of the chine, enclosed area and centroid. These geometric parameters have physical, hydrodynamic, and stability implications from the design point of view. The proposed method uses two-dimensional orthogonal projections of the control curves and then produces three-dimensional (3-D) definitions using B-spline fitting of the 3-D data points. The fitting considers maximum deviation from the curve to the data points and is based on an original selection of the parameterization. A net of B-spline curves (stations) is then created to match the previously defined 3-D boundaries. A final set of lofting surfaces of the previous B-spline curves produces the hull surface.

Regression models with MoPs Bayesian networks

We present a model of Bayesian network for continuous variables, where densities and conditional densities are estimated with B-spline MoPs. We use a novel approach to directly obtain conditional densities estimation using B-spline properties. In particular we implement naive Bayes and wrapper variables selection. Finally we apply our techniques to the problem of predicting neurons morphological variables from electrophysiological ones.

Development of Shape-Optimization Tools for the Aerodynamic Design of Turbomachinery Blades

The aim of this work is to develop an automated tool for the optimization of turbomachinery blades founded on an evolutionary strategy. This optimization scheme will serve to deal with supersonic blades cascades for application to Organic Rankine Cycle (ORC) turbines. The blade geometry is defined using parameterization techniques based on B-Splines curves, that allow to have a local control of the shape. The location in space of the control points of the B-Spline curve define the design variables of the optimization problem. In the present work, the performance of the blade shape is assessed by means of fully-turbulent flow simulations performed with a CFD package, in which a look-up table method is applied to ensure an accurate thermodynamic treatment. The solver is set along with the optimization tool to determine the optimal shape of the blade. As only blade-to-blade effects are of interest in this study, quasi-3D calculations are performed, and a single-objective evolutionary strategy is applied to the optimization. As a result, a non-intrusive tool, with no need for gradients definition, is developed. The computational cost is reduced by the use of surrogate models. A Gaussian interpolation scheme (Kriging model) is applied for the estimated n-dimensional function, and a surrogate-based local optimization strategy is proved to yield an accurate way for optimization. In particular, the present optimization scheme has been applied to the re-design of a supersonic stator cascade of an axial-flow turbine. In this design exercise very strong shock waves are generated in the rear blade suction side and shock-boundary layer interaction mechanisms occur. A significant efficiency improvement as a consequence of a more uniform flow at the blade outlet section of the stator is achieved. This is also expected to provide beneficial effects on the design of a subsequent downstream rotor. The method provides an improvement to gradient-based methods and an optimized blade geometry is easily achieved using the genetic algorithm.

Numerical issues in Lagrangian tracking and topological evolution of fluid particles in wallbounded turbulent flows

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.

La aportación de la Península Ibérica a la tecnología naval analizada a través de la interpretación de los documentos y la reproducción de los buques descritos en ellos (1570-1620)

El período de la Historia comprendido entre 1570 y 1620 nos ha dejado un importante conjunto de documentos relacionados con la construcción naval en la Península Ibérica. En una época convulsa en la que los reinos de España y Portugal se aglutinaron bajo una misma Corona, surgen una serie de manuscritos, libros y leyes que reflejan la creciente preocupación de la sociedad por el tema naval. Entre sus páginas encontramos las descripciones del proceso constructivo de los buques que sus autores consideraban más significativos para las demandas que se planteaban en ese momento. Este proceso que combinaba generación de formas y construcción del buque provenía de una secular tradición nacida en el Mediterráneo. Mediante reglas geométricas sencillas, el constructor naval trazaba las secciones centrales y el perfil de la nao, quedando los extremos de la misma (hasta más de la mitad de la eslora) a su buen hacer y experiencia. Las herramientas informáticas de generación de superficies mediante NURBs (Non- Uniform Rational B-spline) permiten reconstruir las formas de los navíos reproduciendo con fiabilidad las carenas de los mismos a partir de los documentos de la época. Mediante un estudio detallado de interpretación de los textos y transcribiendo los procesos, llegamos a obtener con un buen grado de precisión las carenas de los buques descritos en sus páginas. A partir de ahí y mediante el análisis cualitativo y cuantitativo de los parámetros obtenidos es posible valorar si las soluciones representadas por los barcos respondían a las preguntas planteadas por sus autores , la influencia de factores externos a la construcción naval tales como las regulaciones del Estado o identificar su relación con el germen y la expansión de la teoría que ha determinado los efectos de la Ciencia en la Arquitectura Naval. Comenzando por la nao veneciana de 1550, heredera de la secular tradición constructiva mediterránea, hasta llegar a las Reales Ordenanzas promulgadas en 1618, se reproducen hasta nueve carenas a partir de otros tantos documentos, se dibujan sus planos de formas y se exportan para su análisis hidrostático. El trabajo requiere la realización de otros estudios en paralelo necesarios para entender aquellos factores que formaron parte del desarrollo tecnológico naval como son, las unidades de medida en uso en los astilleros, los distintos sistemas de arqueo impuestos por la Corona y la representación de los diferentes instrumentos geométricos de modificación de los parámetros de diseño. A lo largo del trabajo se dan respuesta a interrogantes planteados por la arqueología en relación con el desarrollo de la arquitectura naval poniendo en evidencia que durante este período quedaron establecidos los fundamentos teórico-prácticos de lo que más adelante se convirtió en la ciencia de la ingeniería naval y se plantean nuevos retos para aquellos que deseen continuar la apasionante tarea de la investigación científica de nuestra historia. ABSTRACT The period of the History comprised between 1570 and 1620 has left an important set of shipbuilding documents in the Iberian Peninsula. In a turbulent time in which the kingdoms of Spain and Portugal were ruled under the same Crown, manuscripts, books and laws that reflect the growing concern of society for the naval theme arose. We found among their pages shipbuilding process descriptions of the more relevant vessels that responded to claims that arose at that time. This process brought together hull generation and shipbuilding and came from a secular tradition born in the Mediterranean. By means of simple geometric rules, the shipbuilder traced the central sections and profile of the ship, leaving the ends thereof (almost half of the length) to its good performance and experience. 3D computer modelling software by NURBs (Non-Uniform Rational B-spline) surfaces helps to reconstruct ships hulls from contemporary documents. Through a detailed texts interpretation and transcription processes, we manage to reach with a good degree of accuracy the ship hulls described in its pages. From there and through qualitative and quantitative analysis of the parameters obtained we can assess whether the solutions represented by ships gave response to the questions raised by the authors, the influence of external factors such as shipbuilding state regulations or identify their relationship to the origin and expansion of the theory that has determined the effects of Science in Naval Architecture. From the 1550 Venetian nao, inheritor of the secular Mediterranean building tradition, to the Royal Ordinances enacted in 1618, as nine hulls are reproduced, their line drawings are traced and exported for analysis hydrostatic. Further studies are needed to understand the factors that were part of shipbuilding technology development as the units of measure in use in shipyards, the different official regulations for calculating ship tonnage and the different geometric instruments to amend the design parameters. The work gives response to questions raised by archaeology in relation to the development of naval architecture highlighting that during this period were established the theoretical and practical foundations of what later became the science of naval engineering and raising new challenges for those wishing to continue the exciting task of scientific research of our History.

A new boundary condition solved with B.I.E.M.

Among the classical operators of mathematical physics the Laplacian plays an important role due to the number of different situations that can be modelled by it. Because of this a great effort has been made by mathematicians as well as by engineers to master its properties till the point that nearly everything has been said about them from a qualitative viewpoint. Quantitative results have also been obtained through the use of the new numerical techniques sustained by the computer. Finite element methods and boundary techniques have been successfully applied to engineering problems as can be seen in the technical literature (for instance [ l ] , [2], [3] . Boundary techniques are especially advantageous in those cases in which the main interest is concentrated on what is happening at the boundary. This situation is very usual in potential problems due to the properties of harmonic functions. In this paper we intend to show how a boundary condition different from the classical, but physically sound, is introduced without any violence in the discretization frame of the Boundary Integral Equation Method. The idea will be developed in the context of heat conduction in axisymmetric problems but it is hoped that its extension to other situations is straightforward. After the presentation of the method several examples will show the capabilities of modelling a physical problem.

SERBA: a B.I.E. program with linear elements for 2-D elastostatics analysis

The great developments that have occurred during the last few years in the finite element method and its applications has kept hidden other options for computation. The boundary integral element method now appears as a valid alternative and, in certain cases, has significant advantages. This method deals only with the boundary of the domain, while the F.E.M. analyses the whole domain. This has the following advantages: the dimensions of the problem to be studied are reduced by one, consequently simplifying the system of equations and preparation of input data. It is also possible to analyse infinite domains without discretization errors. These simplifications have the drawbacks of having to solve a full and non-symmetric matrix and some difficulties are incurred in the imposition of boundary conditions when complicated variations of the function over the boundary are assumed. In this paper a practical treatment of these problems, in particular boundary conditions imposition, has been carried out using the computer program shown below. Program SERBA solves general elastostatics problems in 2-dimensional continua using the boundary integral equation method. The boundary of the domain is discretized by line or elements over which the functions are assumed to vary linearly. Data (stresses and/or displacements) are introduced in the local co-ordinate system (element co-ordinates). Resulting stresses are obtained in local co-ordinates and displacements in a general system. The program has been written in Fortran ASCII and implemented on a 1108 Univac Computer. For 100 elements the core requirements are about 40 Kwords. Also available is a Fortran IV version (3 segments)implemented on a 21 MX Hewlett-Packard computer,using 15 Kwords.

B.I.E.M. in solid mechanics

In solid mechanics the weak formulation produces an integral equation ready for a discretization and with less restrictive requiremets than the standard field equations. Fundamentally the weak formulation is a expresion of a green formula. An alternative is to choose another green formula materializing a reciprocity relationship between the basis unknowns and an auxiliary family of functions. The degree of smoothness requiered to practice the discretization is then translated to the auxiliar functions. The subsequent discretization (constant, linear etc.)produces a set of equations on the boundary of the domain. For linear 3-D problems the BIEM appears then as a powerful alternative to FEM, because of the reduction to 2-D thanks to the features previously described.

B.I.E.M. y estudio de singularidades en problemas de potencial

El objeto del presente artículo es el estudio de singularidades en problemas de Potencial mediante el uso del Método de las Ecuaciones Integrales sobre el contorno del dominio en estudio. Frente a soluciones basadas en la mejora de la discretización, análisis asintótico o introducción de funciones de forma que representen mejor la evolución de la función, una nueva hipótesis es presentada: el término responsable de la singularidad es incluido en la integral sobre el contorno de la función auxiliar. Los resultados obtenidos mejoran los de soluciones anteriores simplificando también el tiempo de cálculo = The subject of this paper is the modelling of singularities in potential problems, using the Boundary Integral Equation Method. As a logical alternative to classical methods (discretization refinement, asymptotic analysis, high order interpolatory functions) a new hypothesis is presented: the singularity responsible term is included in the interpolatory shape function. As shown by several exemples results are splendid and computer time radically shortened.