This report is a master thesis, written by an engineering physics and electrical engineering student at Luleå University of Technology.The desires of this project was to remove dislocations from wrapped phase maps using sparse reconstructive methods. Dislocations is an error that can appear in phase maps due to improper filtering or inadequate sampling. Dislocations makes it impossible to correctly unwrap the phasemap.The report contains a mathematical description of a sparse reconstructive method. The sparse reconstructive method is based on KSVDbox which was created by R. Rubinstein and is free for download and use. The KSVDbox is a MATLAB implementation of a dictionary learning algorithm called K-SVD with Orthogonal Matching Pursuit and a sparse reconstructive algorithm. A guide for adapting the toolbox for inpainting is included, with a couple of examples on natural images which supports the suggested adaptation. For experimental purposes a set of simulated wrapped phase maps with and without disloca-tions were created. These simulated phase maps are based on work by P. Picart. The MATLAB implementation that was used to generate these test images can be found in the appendix of this report such that they can easily be generated by anyone who has the interest to do so. Finally the report leads to an outline of five different experiments that was designed to test the KSVDbox for the processing of dislocations. Each one of these experiments uses a different dictionary. These experiments are due to inpainting with, 1. A dictionary based on Discrete Cosine Transform. 2. An adaptive dictionary, where the dictionary learning algorithm has been shown what thearea in the phase map that was damaged by dislocations should look like. 3. An adaptive dictionary, where the dictionary learning algorithm has been allowed to trainon the phase map that with damages. This is done such that areas with dislocations areignored. 4. An adaptive dictionary, where training is done on a separate image that has been designedto contain general phase patterns. 5. An adaptive dictionary, that results from concatenating the dictionaries used in experiment 3 and 4. The first three experiments are complimented with experiments done on a natural image for comparison purposes.The results show that sparse reconstructive methods, when using the scheme used in this work, is unsuitable for processing of dislocations in phase maps. This is most likely because the reconstructive method has difficulties in acquiring a high contrast reconstruction and there is nothing in the algorithm that causes the inpainting from any direction to match with the inpainting from other directions.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (leaves 106-122).

[EN] Atrial tachyarrhythmias present a high prevalence in the developed world, and several studies predict that in the coming decades it will be increased. Micro or macro-reentrant mechanisms of the electrical wavefronts that govern the mechanical behavior of the heart are one of the main responsibles for the maintenance of these arrhythmias. Atrial flutter is maintained by a macro-reentry around an anatomical or functional obstacle located in the atria. In the case of atrial fibrillation, the hypothesis which describes high frequency rotors as dominant sources of the fibrillation and responsible for the maintenance of the arrhythmia, has been gaining relevance in the last years. However, the therapies that target high frequency sources have a limited efficacy with current techniques. Radiofrequency ablation allows the destruction of parts of the cardiac tissue resulting in the interruption of the reentrant circuit in case of macro-reentries or the isolation of micro-reentrant circuits. The non-invasive location of reentrant circuits would increment the efficacy of these therapies and would shorten surgery interventions. In parallel, pharmacological therapies modify ionic expressions associated to the excitability and electrical refractoriness of the cardiac tissue with the objective of hindering the maintenance of reentrant behaviors. These therapies require a deep knowledge of the ionic mechanisms underlying the reentrant behavior and its properties in order to be effective. The research in these mechanisms allows the evaluation of new targets for the treatment and thus may improve the efficacy in atrial fibrillation termination. In this thesis, mathematical modeling is used to go forward in the minimization of the limitations associated to these treatments. Body surface potential mapping has been evaluated, both clinically and by means of mathematical simulations for the diagnosis and location of macro-reentrant circuits. The analysis of phase maps obtained from multiple lead electrocardiographic recordings distributed in the whole torso allowed the discrimination between different reentrant circuits. It is the reason why this technique is presented as a tool for the non-invasive location of macro and micro-reentrant circuits. A population of mathematical models designed in this thesis based on the action potentials recordings of atrial cardiomyocites from 149 patients, allowed the evaluation of the ionic mechanisms defining the properties of reentrant behaviors. This study has allowed us defining the blockade of ICaL as a target for the pharmacological treatment. The blockade of this current is associated with the increase of the movement in the core of the rotor which easies the collision of the rotor with other wavefronts or anatomical obstacles promoting the extinction of the reentry. The variability observed between patients modeled in our population has allowed showing and explaining the mechanisms promoting divergent results of a single treatment. This is why the introduction of populations of models will allow the prevention of side effects associated to inter-subject variability and to go forward in the development of individualized therapies. These works are built through a simulation platform of cardiac electrophysiology based in Graphic Processing Units (GPUs) and developed in this thesis. The platform allows the simulation of cellular models, tissues and organs with a realistic geometry and shows features comparable to that of the platforms used by the most relevant electrophysiology research groups at the moment. / [ES] Las taquiarritmias auriculares tienen una alta prevalencia en el mundo desarrollado, además diversos estudios poblacionales indican que en las próximas décadas ésta se verá incrementada. Los mecanismos de micro o macro-reentrada de los frentes de onda eléctricos que rigen el comportamiento mecánico del corazón, se presentan como una de las principales causas del mantenimiento de estas arritmias. El flutter auricular es mantenido por un macro-reentrada alrededor de un obstáculo anatómico o funcional en las aurículas, mientras que en el caso de la fibrilación auricular la hipótesis que define a los rotores de alta frecuencia como elementos dominantes y responsables del mantenimiento de la arritmia se ha ido imponiendo al resto en los últimos años. Sin embargo, las terapias que tienen como objetivo finalizar o aislar estas reentradas tienen todavía una eficacia limitada. La ablación por radiofrecuencia permite eliminar zonas del tejido cardiaco resultando en la interrupción del circuito de reentrada en el caso de macro-reentradas o el aislamiento de comportamientos micro-reentrantes. La localización no invasiva de los circuitos reentrantes incrementaría la eficacia de estas terapias y reduciría la duración de las intervenciones quirúrgicas. Por otro lado, las terapias farmacológicas alteran las expresiones iónicas asociadas a la excitabilidad y la refractoriedad del tejido con el fin de dificultar el mantenimiento de comportamientos reentrantes. Este tipo de terapias exigen incrementar el conocimiento de los mecanismos subyacentes que explican el proceso de reentrada y sus propiedades, la investigación de estos mecanismos permite definir las dianas terapéuticas que mejoran la eficacia en la extinción de estos comportamientos. En esta tesis el modelado matemático se utiliza para dar un paso importante en la minimización de las limitaciones asociadas a estos tratamientos. La cartografía eléctrica de superficie ha sido testada, clínicamente y con simulaciones matemática,s como técnica de diagnóstico y localización de circuitos macro-reentrantes. El análisis de mapas de fase obtenidos a partir de los registros multicanal de derivaciones electrocardiográficas distribuidas en la superficie del torso permite diferenciar distintos circuitos de reentrada. Es por ello que esta técnica de registro y análisis se presenta como una herramienta para la localización no invasiva de circuitos macro y micro-reentrantes. Una población de modelos matemáticos, diseñada en esta tesis a partir de los registros de los potenciales de acción de 149 pacientes, ha permitido evaluar los mecanismos iónicos que definen las propiedades asociadas a los procesos de reentrada. Esto ha permitido apuntar al bloqueo de la corriente ICaL como diana terapéutica. Ésta se asocia al incremento del movimiento del núcleo que facilita el impacto del rotor con otros frentes de onda u obstáculos extinguiéndose así el comportamiento reentrante. La variabilidad entre pacientes reflejada en la población de modelos ha permitido además mostrar los mecanismos por los cuales un mismo tratamiento puede mostrar efectos divergentes, así el uso de poblaciones de modelos matemáticos permitirá prevenir efectos secundarios asociados a la variabilidad entre pacientes y profundizar en el desarrollo de terapias individualizadas. Estos trabajos se cimientan sobre una plataforma de simulación de electrofisiología cardiaca de basado en Unidades de Procesado Gráfico (GPUs) y desarrollada en esta tesis. La plataforma permite la simulación de modelos celulares cardiacos así como de tejidos u órganos con geometría realista, mostrando unas prestaciones comparables con las de las utilizadas por los grupos de investigación más potentes en el campo de la electrofisiología. / [CA] Les taquiarítmies auriculars tenen una alta prevalença en el món desenvolupat, a més diversos estudis poblacionals indiquen que en les pròximes dècades aquesta es veurà incrementada. Els mecanismes de micro o macro-reentrada dels fronts d'ona elèctrics que regeixen el comportament mecànic del cor, es presenten com una de les principals causes del manteniment d'aquestes arítmies. El flutter auricular és mantingut per una macro-reentrada al voltant d'un obstacle anatòmic o funcional en les aurícules, mentre que en el cas de la fibril·lació auricular la hipòtesi que defineix als rotors d'alta freqüència com a elements dominants i responsables del manteniment de l'arítmia s'ha anat imposant a la resta en els últims anys. No obstant això, les teràpies que tenen com a objectiu finalitzar o aïllar aquestes reentrades tenen encara una eficàcia limitada. L'ablació per radiofreqüència permet eliminar zones del teixit cardíac resultant en la interrupció del circuit de reentrada en el cas de macro-reentrades o l'aïllament de comportaments micro-reentrants. La localització no invasiva dels circuits reentrants incrementaria l'eficàcia d'aquestes teràpies i reduiria la durada de les intervencions quirúrgiques. D'altra banda, les teràpies farmacològiques alteren les expressions iòniques associades a la excitabilitat i la refractaritat del teixit amb la finalitat de dificultar el manteniment de comportaments reentrants. Aquest tipus de teràpies exigeixen incrementar el coneixement dels mecanismes subjacents que expliquen el procés de reentrada i les seues propietats, la recerca d'aquests mecanismes permet definir les dianes terapèutiques que milloren l'eficàcia en l'extinció d'aquests comportaments. En aquesta tesi el modelatge matemàtic s'utilitza per a fer un pas important en la minimització de les limitacions associades a aquests tractaments. La cartografia elèctrica de superfície ha sigut testada, clínicament i amb simulacions matemàtiques com a tècnica de diagnòstic i localització de circuits macro-reentrants. L'anàlisi de mapes de fase obtinguts a partir dels registres multicanal de derivacions electrocardiogràfiques distribuïdes en la superfície del tors permet diferenciar diferents circuits de reentrada. És per açò que aquesta tècnica de registre i anàlisi es presenta com una eina per a la localització no invasiva de circuits macro i micro-reentrants. Una població de models matemàtics, dissenyada en aquesta tesi a partir dels registres dels potencials d'acció de 149 pacients, ha permès avaluar els mecanismes iònics que defineixen les propietats associades als processos de reentrada. Açò ha permès apuntar al bloqueig del corrent ICaL com a diana terapèutica. Aquesta s'associa a l'increment del moviment del nucli que facilita l'impacte del rotor amb altres fronts d'ona o obstacles extingint-se així el comportament reentrant. La variabilitat entre pacients reflectida en la població de models ha permès a més mostrar els mecanismes pels quals un mateix tractament pot mostrar efectes divergents, així l'ús de poblacions de models matemàtics permetrà prevenir efectes secundaris associats a la variabilitat entre pacients i aprofundir en el desenvolupament de teràpies individualitzades. Aquests treballs es fonamenten sobre una plataforma de simulació de electrofisiologia cardíaca basat en Unitats de Processament Gràfic (GPUs) i desenvolupada en aquesta tesi. La plataforma permet la simulació de models cel·lulars cardíacs així com de teixits o òrgans amb geometria realista, mostrant unes prestacions comparables amb les de les utilitzades per els grups de recerca més importants en aquesta área. / Liberos Mascarell, A. (2016). Mathematical modeling approaches for the diagnosis and treatment of reentrant atrial tachyarrhythmias [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/62166

Non-destructive testing (NDT) of glass-fibre reinforced polyester (GRP) composite materials has been becoming increasingly important due to their wide applications in engineering components and structures. Electronic Speckle Pattern Interferometry (ESPI) has promising potential in this context because it is a non-contact, whole-field and real-time measurement system. This potential has never been fully exploited and there is only limited knowledge and understanding available in this area. This reality constrains the wide popularity and acceptance of ESPI as a novel NDT technique. Therefore it is of considerable importance to develop an understanding of the capability of ESPI with respect to damage evaluation in GRP composite materials. The research described in this thesis is concerned with an investigation into the applicability of ESPI in the NDT of GRP composite materials. Firstly, a study was carried out to determine excitation techniques in terms of practicality and effectiveness in the ESPI system. Three categories of defects were artificially introduced in GRP composite materials, namely holes, cracks and delaminations each with different geometrical features. ESPI was then employed to evaluate the three kinds of defects individually. It has been found that cracks and holes on back surfaces can be defined when the technique is used in conjunction with thermal excitation. Internal Temperature Differential (ITD) induced fringe patterns were more efficient than External Thermal Source (ETS) induced fringe patterns with regard to detecting the presence of holes and cracks. In the case of delamination, ESPI was found to be capable of detecting the damage when used in combination with mechanical excitation originating from a force transducer hammer. The geometrical features and magnitudes of delaminations were also established as being quantifiable. The validation of ESPI as an NDT technique was carried out in an attempt to establish a better understanding of its suitability and have more confidence in its applications. Four damaged specimens were Subjected to ESPI examination in conjunction with visual inspection, ultrasonic C-scan and sectioning techniques. The geometrical features and magnitudes of damage evaluated using ESPI showed a good correlation with those evaluated by conventional techniques. Poor visibility and readability is an inherent problem associated with ESP! due to an overlapping between the noise and signal frequencies. An improvement of image quality is expected in an attempt to achieve a wide acceptance of ESPI as a novel NDT technique. It has also been demonstrated that this problem can be tackled using optical phase stepping techniques in which optical phase data can be extracted from the intensity fringes. A three-frame optical phase stepping technique was employed to produce the "wrapped" and "unwrapped" phase maps which are capable of indicating internal damage with high visibility and clarity. Finally ESPI was practically employed to evaluate damage in GRP composites introduced by quasi-static and dynamic mechanical loading. It was found that ESP! was capable of monitoring the progressive damage development of specimens subjected to incremental flexural loading. The initial elastic response, damage initiation, propagation and ultimate failure of specimens were clearly characterised by the abnormal fringe pattern variations. In a similar manner, ESPI was employed to evaluate the low velocity falling weight impact induced damage. A correlation was established between the magnitude of damage and the impact event parameters as well as the residual flexural properties.