Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

The effect of diffusion gradient direction number on tractography of corticospinal tract in human brain: an along-tract analysis

Nel presente lavoro di tesi ho sviluppato un metodo di analisi di dati di DW-MRI (Diffusion-Weighted Magnetic Resonance Imaging)cerebrale, tramite un algoritmo di trattografia, per la ricostruzione del tratto corticospinale, in un campione di 25 volontari sani. Il diffusion tensor imaging (DTI) sfrutta la capacità del tensore di diffusione D di misurare il processo di diffusione dell’acqua, per stimare quantitativamente l’anisotropia dei tessuti. In particolare, nella sostanza bianca cerebrale la diffusione delle molecole di acqua è direzionata preferenzialmente lungo le fibre, mentre è ostacolata perpendicolarmente ad esse. La trattografia utilizza le informazioni ottenute tramite il DW imaging per fornire una misura della connettività strutturale fra diverse regioni del cervello. Nel lavoro si è concentrata l’attenzione sul fascio corticospinale, che è coinvolto nella motricità volontaria, trasmettendo gli impulsi dalla corteccia motoria ai motoneuroni del midollo spinale. Il lavoro si è articolato in 3 fasi. Nella prima ho sviluppato il pre-processing di immagini DW acquisite con un gradiente di diffusione sia 25 che a 64 direzioni in ognuno dei 25 volontari sani. Si è messo a punto un metodo originale ed innovativo, basato su “Regions of Interest” (ROIs), ottenute attraverso la segmentazione automatizzata della sostanza grigia e ROIs definite manualmente su un template comune a tutti i soggetti in esame. Per ricostruire il fascio si è usato un algoritmo di trattografia probabilistica che stima la direzione più probabile delle fibre e, con un numero elevato di direzioni del gradiente, riesce ad individuare, se presente, più di una direzione dominante (seconda fibra). Nella seconda parte del lavoro, ciascun fascio è stato suddiviso in 100 segmenti (percentili). Sono stati stimati anisotropia frazionaria (FA), diffusività media, probabilità di connettività, volume del fascio e della seconda fibra con un’analisi quantitativa “along-tract”, per ottenere un confronto accurato dei rispettivi percentili dei fasci nei diversi soggetti. Nella terza parte dello studio è stato fatto il confronto dei dati ottenuti a 25 e 64 direzioni del gradiente ed il confronto del fascio fra entrambi i lati. Dall’analisi statistica dei dati inter-subject e intra-subject è emersa un’elevata variabilità tra soggetti, dimostrando l’importanza di parametrizzare il tratto. I risultati ottenuti confermano che il metodo di analisi trattografica del fascio cortico-spinale messo a punto è risultato affidabile e riproducibile. Inoltre, è risultato che un’acquisizione con 25 direzioni di DTI, meglio tollerata dal paziente per la minore durata dello scan, assicura risultati attendibili. La principale applicazione clinica riguarda patologie neurodegenerative con sintomi motori sia acquisite, quali sindromi parkinsoniane sia su base genetica o la valutazione di masse endocraniche, per la definizione del grado di contiguità del fascio. Infine, sono state poste le basi per la standardizzazione dell’analisi quantitativa di altri fasci di interesse in ambito clinico o di studi di ricerca fisiopatogenetica.

Structural analysis of Heschl's gyrus in schizophrenia patients with auditory hallucinations

Heschl's gyrus (HG) is functionally involved in the genesis of auditory verbal hallucinations (AVH). This dysfunction seems to be structurally facilitated. The aim of the study was to analyze macrostructural features of HG in a group of patients reporting AVH who demonstrated white matter diffusion tensor imaging abnormalities reported previously.

Spinal Cord Diffusion-Tensor Imaging and Motor-evoked Potentials in Multiple Sclerosis Patients: Microstructural and Functional Asymmetry

Purpose: To assess possible association between intrinsic structural damage and clinical disability by correlating spinal cord diffusion-tensor (DT) imaging data with electrophysiological parameters in patients with a diagnosis of multiple sclerosis (MS). Materials and Methods: This study was approved by the local ethical committee according to the declaration of Helsinki and written informed consent was obtained. DT images and T1- and T2-weighted images of the spinal cord were acquired in 28 healthy volunteers and 41 MS patients. Fractional anisotropy (FA) and apparent diffusion coefficients were evaluated in normal-appearing white matter (NAWM) at the cervical level and were correlated with motor-evoked potentials (n = 34). Asymmetry index was calculated for FA values with corresponding left and right regions of interest as percentage of the absolute difference between these values relative to the sum of the respective FA values. Statistical analysis included Spearman rank correlations, Mann-Whitney test, and reliability analysis. Results: Healthy volunteers had low asymmetry index (1.5%-2.2%). In MS patients, structural abnormalities were reflected by asymmetric decrease of FA (asymmetry index: 3.6%; P = .15). Frequently asymmetrically affected among MS patients was left and right central motor conduction time (CMCT) to abductor digiti minimi muscle (ADMM) (asymmetry index, 15%-16%) and tibialis anterior muscle (TAM) (asymmetry index, 9.5%-14.1%). Statistically significant correlations of functional (ie, electrophysiological) and structural (ie, DT imaging) asymmetries were found (P = .005 for CMCT to ADMM; P = .007 for CMCT to TAM) for the cervical lateral funiculi, which comprise the crossed pyramidal tract. Interobserver reliability for DT imaging measurements was excellent (78%-87%). Conclusion: DT imaging revealed asymmetric anatomic changes in spinal cord NAWM, which corresponded to asymmetric electrophysiological deficits for both arms and legs, and reflected a specific structure-function relationship in the human spinal cord. © RSNA, 2013.

NONLINEAR TUBE-FITTING FOR THE ANALYSIS OF ANATOMICAL AND FUNCTIONAL STRUCTURES

We are concerned with the estimation of the exterior surface of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT)and to a white-matter tract image produced using diffusion tensor `imaging (DTI).

Diffusion tensor imaging of two unrelated Chinese men with hereditary spastic paraplegia associated with thin corpus callosum

Hereditary spastic paraplegia (HSP) associated with thin corpus callosum is a rare autosomal recessive neurodegenerative disorder characterized by an abnormally thin corpus callosum, normal motor development, slowly progressive spastic paraparesis and cognitive deterioration. To investigate and localize abnormalities in the brains of two Chinese patients with HSP-TCC, with mutations in the spatacsin gene. Diffusion tensor imaging (DTI) was used to determine the mean diffusion (MD) and fractional anisotropy (FA) in the brains of the patients in comparison to 20 healthy subjects. Voxel-based analysis (VBA) of both the diffusion and anisotropy values were performed using statistical parametric mapping (SPM). Significant changes with MD increase and FA reduction were found in the already known lesions including the corpus callosum, cerebellum and thalamus. In addition, changes were also found in regions that appear to be normal in conventional MRI, such as the brain stem, internal capsule, cingulum and subcortical white matter including superior longitudinal fascicle and inferior longitudinal fascicle. Neither increase in FA nor reduction in MD was detected in the brain. Our study provides clear in vivo MR imaging evidence of a more widespread brain involvement of HSP-TCC. MD is more sensitive than FA in detecting lesions in thalamus and subcortical white matter, suggesting that MD may be a better marker of the disease progression.

Volumetry and diffusion tensor imaging of hippocampal subregions in schizophrenia

Previous MRI-volumetric studies in schizophrenic psychoses have demonstrated more or less pronounced volume reductions of the hippocampus in patients. Correspondingly, neuropathological examinations on the brains of schizophrenics showed diverse structural changes of the hippocampus. Employing a high-resolution 3D-MPRAGE sequence, we found volume reductions in most hippocampal subregions of schizophrenic patients, which, however, did not reach significant levels. An analysis of co-registered diffusion tensor imaging (DTI) data revealed significant alterations of the inter-voxel coherences in single hippocampal subdivisions of these patients, supporting the assumption of characteristic microstructural tissue changes relevant for the pathogenesis of schizophrenic psychoses. Our results argue for the usage of additional MRI modalities like DTI in order to detect subtle regional alterations of hippocampal structure in schizophrenics.

Deep gray matter atrophy in multiple sclerosis: a tensor based morphometry.

Tensor based morphometry (TBM) was applied to determine the atrophy of deep gray matter (DGM) structures in 88 relapsing multiple sclerosis (MS) patients. For group analysis of atrophy, an unbiased atlas was constructed from 20 normal brains. The MS brain images were co-registered with the unbiased atlas using a symmetric inverse consistent nonlinear registration. These studies demonstrate significant atrophy of thalamus, caudate nucleus, and putamen even at a modest clinical disability, as assessed by the expanded disability status score (EDSS). A significant correlation between atrophy and EDSS was observed for different DGM structures: (thalamus: r=-0.51, p=3.85 x 10(-7); caudate nucleus: r=-0.43, p=2.35 x 10(-5); putamen: r=-0.36, p=6.12 x 10(-6)). Atrophy of these structures also correlated with 1) T2 hyperintense lesion volumes (thalamus: r=-0.56, p=9.96 x 10(-9); caudate nucleus: r=-0.31, p=3.10 x 10(-3); putamen: r=-0.50, p=6.06 x 10(-7)), 2) T1 hypointense lesion volumes (thalamus: r=-0.61, p=2.29 x 10(-10); caudate nucleus: r=-0.35, p=9.51 x 10(-4); putamen: r=-0.43, p=3.51 x 10(-5)), and 3) normalized CSF volume (thalamus: r=-0.66, p=3.55 x 10(-12); caudate nucleus: r=-0.52, p=2.31 x 10(-7), and putamen: r=-0.66, r=2.13 x 10(-12)). More severe atrophy was observed mainly in thalamus at higher EDSS. These studies appear to suggest a link between the white matter damage and DGM atrophy in MS.

Diffusion tensor imaging of cocaine-treated rodents.

Studies in cocaine-dependent human subjects have shown differences in white matter on diffusion tensor imaging (DTI) compared with non-drug-using controls. It is not known whether the differences in fractional anisotropy (FA) seen on DTI in white matter regions of cocaine-dependent humans result from a pre-existing predilection for drug use or purely from cocaine abuse. To study the effect of cocaine on brain white matter, DTI was performed on 24 rats after continuous infusion of cocaine or saline for 4 weeks, followed by brain histology. Voxel-based morphometry analysis showed an 18% FA decrease in the splenium of the corpus callosum (CC) in cocaine-treated animals relative to saline controls. On histology, significant increase in neurofilament expression (125%) and decrease in myelin basic protein (40%) were observed in the same region in cocaine-treated animals. This study supports the hypothesis that chronic cocaine use alters white matter integrity in human CC. Unlike humans, where the FA in the genu differed between cocaine users and non-users, the splenium was affected in rats. These differences between rodent and human findings could be due to several factors that include differences in the brain structure and function between species and/or the dose, timing, and duration of cocaine administration.

Microstructure and Cerebral Blood Flow within White Matter of the Human Brain: A TBSS Analysis.

BACKGROUND White matter (WM) fibers connect different brain regions and are critical for proper brain function. However, little is known about the cerebral blood flow in WM and its relation to WM microstructure. Recent improvements in measuring cerebral blood flow (CBF) by means of arterial spin labeling (ASL) suggest that the signal in white matter may be detected. Its implications for physiology needs to be extensively explored. For this purpose, CBF and its relation to anisotropic diffusion was analyzed across subjects on a voxel-wise basis with tract-based spatial statistics (TBSS) and also across white matter tracts within subjects. METHODS Diffusion tensor imaging and ASL were acquired in 43 healthy subjects (mean age = 26.3 years). RESULTS CBF in WM was observed to correlate positively with fractional anisotropy across subjects in parts of the splenium of corpus callosum, the right posterior thalamic radiation (including the optic radiation), the forceps major, the right inferior fronto-occipital fasciculus, the right inferior longitudinal fasciculus and the right superior longitudinal fasciculus. Furthermore, radial diffusivity correlated negatively with CBF across subjects in similar regions. Moreover, CBF and FA correlated positively across white matter tracts within subjects. CONCLUSION The currently observed findings on a macroscopic level might reflect the metabolic demand of white matter on a microscopic level involving myelination processes or axonal function. However, the exact underlying physiological mechanism of this relationship needs further evaluation.

The correlation between white-matter microstructure and the complexity of spontaneous brain activity: A difussion tensor imaging-MEG study

The advent of new signal processing methods, such as non-linear analysis techniques, represents a new perspective which adds further value to brain signals' analysis. Particularly, Lempel–Ziv's Complexity (LZC) has proven to be useful in exploring the complexity of the brain electromagnetic activity. However, an important problem is the lack of knowledge about the physiological determinants of these measures. Although acorrelation between complexity and connectivity has been proposed, this hypothesis was never tested in vivo. Thus, the correlation between the microstructure of the anatomic connectivity and the functional complexity of the brain needs to be inspected. In this study we analyzed the correlation between LZC and fractional anisotropy (FA), a scalar quantity derived from diffusion tensors that is particularly useful as an estimate of the functional integrity of myelinated axonal fibers, in a group of sixteen healthy adults (all female, mean age 65.56 ± 6.06 years, intervals 58–82). Our results showed a positive correlation between FA and LZC scores in regions including clusters in the splenium of the corpus callosum, cingulum, parahipocampal regions and the sagittal stratum. This study supports the notion of a positive correlation between the functional complexity of the brain and the microstructure of its anatomical connectivity. Our investigation proved that a combination of neuroanatomical and neurophysiological techniques may shed some light on the underlying physiological determinants of brain's oscillations

Contribution to the analysis and design of reflectarray antennas for reconfigurable beam applications at frequencies above 100 GHz using liquid crystal technology

El trabajo contenido en esta tesis doctoral está encuadrado en el desarrollo de antenas reconfigurables electrónicamente capaces de proporcionar prestaciones competitivas a las aplicaciones cada vez más comunes que operan a frecuencias superiores a 60 GHz. En concreto, esta tesis se centra en el estudio, diseño, e implementación de las antenas reflectarray, a las que se introduce la tecnología de cristal líquido como elemento característico con el que se consigue reconfigurabilidad de haz de forma electrónica. Desde un punto de vista muy general, se puede describir un cristal líquido como un material cuya permitividad eléctrica es variable y controlada por una excitación externa, que generalmente suele corresponderse con un campo eléctrico quasi-estático (AC). Las antenas reflectarray de cristal líquido se han escogido como objeto de estudio por varias razones. La primera de ellas tiene que ver con las ventajas que los reflectarrays, y en especial aquellos realizados en configuración planar, proporcionan con respecto a otras antenas de alta ganancia como los reflectores o los “phased-arrays”. En los reflectarrays, la alimentación a través de una fuente primaria común (característica de reflectores) y el elevado número de grados de libertad de las celdas que los componen (característica de arrays) hacen que estas antenas puedan proporcionar prestaciones eléctricas iguales o mejores que las anteriores, a un coste más reducido y con estructuras de antena más compactas. La segunda razón radica en la flexibilidad que ofrece el cristal líquido a ser confinado y polarizado en recintos de geometría variada, como consecuencia de su fluidez (propiedad de los líquidos). Por ello, la tecnología de cristal líquido permite que el propio elemento reconfigurable en las celdas de reflectarray se adapte a la configuración planar de manera que en sí mismo, el cristal líquido sea una o varias de las capas características de esta configuración. Esto simplifica de forma drástica la estructura y la fabricación de este tipo de antenas, incluso si se comparan con reflectarrays reconfigurables basados en otras tecnologías como diodos, MEMS, etc. Por tanto, su coste y desarrollo es muy reducido, lo que hace que se puedan fabricar reflectarrays reconfigurables eléctricamente grandes, a bajo coste, y en producción elevada. Un ejemplo claro de una estructura similar, y que ha tenido éxito comercial, son las pantallas de cristal líquido. La tercera razón reside en el hecho de que el cristal líquido es, hasta la fecha, de las pocas tecnologías capaces de ofrecer reconfigurabilidad del haz a frecuencias superiores a 60 GHz. De hecho, el cristal líquido permite reconfigurabilidad en un amplio margen de frecuencias, que va desde DC a frecuencias del espectro visible, incluyendo las microondas y los THz. Otras tecnologías, como los materiales ferroeléctricos, el grafeno o la tecnología CMOS “on chip” permiten también conmutar el haz en estas frecuencias. Sin embargo, la tecnología CMOS tiene un elevado coste y actualmente está limitada a frecuencias inferiores a 150 GHz, y aunque los materiales ferroeléctricos o el grafeno puedan conmutar a frecuencias más altas y en un rango más amplio, tienen serias dificultades que los hacen aún inmaduros. En el caso de los materiales ferroeléctricos, los elevados voltajes para conmutar el material los hacen poco atractivos, mientras que en el caso del grafeno, su modelado aún está en discusión, y todavía no se han arrojado resultados experimentales que validen su idoneidad. Estas tres razones hacen que los reflectarrays basados en cristal líquido sean atractivos para multitud de aplicaciones de haz reconfigurable a frecuencias superiores a 60 GHz. Aplicaciones como radar de escaneo de imágenes de alta resolución, espectroscopia molecular, radiómetros para observación atmosférica, o comunicaciones inalámbricas de alta frecuencia (WiGig) son algunas de ellas. La tesis está estructurada en tres partes. En la primera de ellas se describen las características más comunes de los cristales líquidos, centrándonos en detalle en aquellas propiedades ofrecidas por este material en fase nemática. En concreto, se estudiará la anisotropía dieléctrica (Ae) de los cristales líquidos uniaxiales, que son los que se emplean en esta tesis, definida como la diferencia entre la permitividad paralela (£//) y la perpendicular (e±): Ae = e,, - e±. También se estudiará la variación de este parámetro (Ae) con la frecuencia, y el modelado electromagnético macroscópico más general que, extraído a partir de aquella, permite describir el cristal líquido para cada tensión de polarización en celdas de geometría planar. Este modelo es de suma importancia para garantizar precisión en el desfasaje proporcionado por las diferentes celdas reconfigurables para reflectarrays que se describirán en la siguiente parte de la tesis. La segunda parte de la tesis se centra en el diseño de celdas reflectarray resonantes basadas en cristal líquido. La razón por la que se escogen estos tipos de celdas reside en el hecho de que son las únicas capaces de proporcionar rangos de fase elevados ante la reducida anisotropía dieléctrica que ofrecen los cristales líquidos. El objetivo de esta parte trata, por tanto, de obtener estructuras de celdas reflectarray que sean capaces de proporcionar buenas prestaciones eléctricas a nivel de antena, mejorando sustancialmente las prestaciones de las celdas reportadas en el estado del arte, así como de desarrollar una herramienta de diseño general para aquellas. Para ello, se estudian las prestaciones eléctricas de diferentes tipos de elementos resonantes de cristal líquido que van, desde el más sencillo, que ha limitado el estado de la técnica hasta el desarrollo de esta tesis y que está formado por un sólo resonador, a elementos que constan de varios resonadores (multi-resonantes) y que pueden ser monocapa o multicapa. En un primer paso, el procedimiento de diseño de estas estructuras hace uso de un modelo convencional de cristal líquido que ha venido siendo usado en el estado del arte para este tipo de celdas, y que considera el cristal líquido como un material homogéneo e isótropo cuya permitividad varía entre (e/7) y (e±). Sin embargo, en esta parte de la tesis se demuestra que dicho modelado no es suficiente para describir de forma genérica el comportamiento del cristal líquido en las celdas tipo reflectarray. En la tesis se proponen procedimientos más exactos para el análisis y diseño basados en un modelo más general que define el cristal líquido como un material anisótropo e inhomogeneo en tres dimensiones, y se ha implementado una técnica que permite optimizar celdas multi-resonantes de forma eficiente para conseguir elevadas prestaciones en cuanto a ancho de banda, rango de fase, pérdidas, o sensibilidad al ángulo de incidencia. Los errores cometidos en el uso del modelado convencional a nivel de celda (amplitud y fase) se han analizado para varias geometrías, usando medidas de varios prototipos de antena que usan un cristal líquido real a frecuencias superiores a 100 GHz. Las medidas se han realizado en entorno periódico mediante un banco cuasi-óptico, que ha sido diseñado especialmente para este fin. Uno de estos prototipos se ha optimizado a 100 GHz para conseguir un ancho de banda relativamente elevado (10%), pérdidas reducidas, un rango de fase mayor de 360º, baja sensibilidad al ángulo de incidencia, y baja influencia de la inhomogeneidad transversal del cristal líquido en la celda. Estas prestaciones a nivel de celda superan de forma clara aquellas conseguidas por otros elementos que se han reportado en la literatura, de manera que dicho prototipo se ha usado en la última parte de la tesis para realizar diversas antenas de barrido. Finalmente, en esta parte se presenta una estrategia de caracterización de la anisotropía macroscópica a partir de medidas de los elementos de reflectarray diseñados en banco cuasi-óptico, obteniendo resultados tanto en las frecuencias de interés en RF como en AC, y comparándolas con aquellas obtenidas mediante otros métodos. La tercera parte de la tesis consiste en el estudio, diseño, fabricación y medida de antenas reconfigurables basadas en cristal líquido en configuraciones complejas. En reflectarrays pasivos, el procedimiento de diseño de la antena se limita únicamente al ajuste en cada celda de la antena de las dimensiones de las metalizaciones que se emplean para el control de fase, mediante procesos de optimización bien conocidos. Sin embargo, en el caso de reflectarrays reconfigurables basados en cristal líquido, resulta necesario un paso adicional, que consiste en calcular de forma adecuada las tensiones de control en cada celda del reflectarray para configurar la fase requerida en cada una de ellas, así como diseñar la estructura y los circuitos de control que permitan direccionar a cada elemento su tensión correspondiente. La síntesis de tensiones es por tanto igual o más importante que el diseño de la geometría de las celdas, puesto que éstas son las que están directamente relacionadas con la fase. En el estado del arte, existen varias estrategias de síntesis de tensiones que se basan en la caracterización experimental de la curva de fase respecto al voltaje. Sin embargo, esta caracterización sólo puede hacerse a un solo ángulo de incidencia y para unas determinadas dimensiones de celda, lo que produce que las tensiones sintetizadas sean diferentes de las adecuadas, y en definitiva que se alcancen errores de fase mayores de 70º. De esta forma, hasta la fecha, las prestaciones a nivel de antena que se han conseguido son reducidas en cuanto a ancho de banda, rango de escaneo o nivel de lóbulos secundarios. En esta última parte de la tesis, se introduce una nueva estrategia de síntesis de tensiones que es capaz de predecir mediante simulaciones, y con alta precisión, las tensiones que deben introducirse en cada celda teniendo en cuenta su ángulo de incidencia, sus dimensiones, la frecuencia, así como la señal de polarización definida por su frecuencia y forma de onda AC. Esta estrategia se basa en modelar cada uno de los estados de permitividad del cristal líquido como un sustrato anisótropo con inhomogeneidad longitudinal (1D), o en ciertos casos, como un tensor equivalente homogéneo. La precisión de ambos modelos electromagnéticos también se discute. Con el objetivo de obtener una herramienta eficiente de cálculo de tensiones, también se ha escrito e implementado una herramienta de análisis basada en el Método de los Momentos en el Dominio Espectral (SD-MoM) para sustratos estratificados anisótropos, que se usa en cada iteración del procedimiento de síntesis para analizar cada una de las celdas de la antena. La síntesis de tensiones se ha diseñado además para reducir al máximo el efecto del rizado de amplitud en el diagrama de radiación, que es característico en los reflectarrays que están formados por celdas con pérdidas elevadas, lo que en sí, supone un avance adicional para la obtención de mejores prestaciones de antena. Para el cálculo de los diagramas de radiación empleados en el procedimiento de síntesis, se asume un análisis elemento a elemento considerando periodicidad local, y se propone el uso de un método capaz de modelar el campo incidente de forma que se elimine la limitación de la periodicidad local en la excitación. Una vez definida la estrategia adecuada de cálculo de las tensiones a aplicar al cristal líquido en cada celda, la estructura de direccionamiento de las mismas en la antena, y diseñados los circuitos de control, se diseñan, fabrican y miden dos prototipos diferentes de antena de barrido electrónico a 100 GHz usando las celdas anteriormente presentadas. El primero de estos prototipos es un reflectarray en configuración “single offset” con capacidad de escaneo en un plano (elevación o azimut). Aunque previamente se realizan diseños de antenas de barrido en 2D a varias frecuencias en el rango de milimétricas y sub-milimétricas, y se proponen ciertas estrategias de direccionamiento que permiten conseguir este objetivo, se desarrolla el prototipo con direccionamiento en una dimensión con el fin de reducir el número de controles y posibles errores de fabricación, y así también validar la herramienta de diseño. Para un tamaño medio de apertura (con un numero de filas y columnas entre 30 y 50 elementos, lo que significa un reflectarray con un número de elementos superior a 900), la configuración “single offset” proporciona rangos de escaneo elevados, y ganancias que pueden oscilar entre los 20 y 30 dBi. En concreto, el prototipo medido proporciona un haz de barrido en un rango angular de 55º, en el que el nivel de lóbulos secundarios (SLL) permanece mejor de -13 dB en un ancho de banda de un 8%. La ganancia máxima es de 19.4 dBi. Estas prestaciones superan de forma clara aquellas conseguidas por otros autores. El segundo prototipo se corresponde con una antena de doble reflector que usa el reflectarray de cristal líquido como sub-reflector para escanear el haz en un plano (elevación o azimut). El objetivo básico de esta geometría es obtener mayores ganancias que en el reflectarray “single offset” con una estructura más compacta, aunque a expensas de reducir el rango de barrido. En concreto, se obtiene una ganancia máxima de 35 dBi, y un rango de barrido de 12º. Los procedimientos de síntesis de tensiones y de diseño de las estructuras de las celdas forman, en su conjunto, una herramienta completa de diseño precisa y eficiente de antenas reflectarray reconfigurables basados en cristales líquidos. Dicha herramienta se ha validado mediante el diseño, la fabricación y la medida de los prototipos anteriormente citados a 100 GHz, que consiguen algo nunca alcanzado anteriormente en la investigación de este tipo de antenas: unas prestaciones competitivas y una predicción excelente de los resultados. El procedimiento es general, y por tanto se puede usar a cualquier frecuencia en la que el cristal líquido ofrezca anisotropía dieléctrica, incluidos los THz. Los prototipos desarrollados en esta tesis doctoral suponen también unas de las primeras antenas de barrido real a frecuencias superiores a 100 GHz. En concreto, la antena de doble reflector para escaneo de haz es la primera antena reconfigurable electrónicamente a frecuencias superiores a 60 GHz que superan los 25 dBi de ganancia, siendo a su vez la primera antena de doble reflector que contiene un reflectarray reconfigurable como sub-reflector. Finalmente, se proponen ciertas mejoras que aún deben se deben realizar para hacer que estas antenas puedan ser un producto completamente desarrollado y competitivo en el mercado. ABSTRACT The work presented in this thesis is focused on the development of electronically reconfigurable antennas that are able to provide competitive electrical performance to the increasingly common applications operating at frequencies above 60 GHz. Specifically, this thesis presents the study, design, and implementation of reflectarray antennas, which incorporate liquid crystal (LC) materials to scan or reconfigure the beam electronically. From a general point of view, a liquid crystal can be defined as a material whose dielectric permittivity is variable and can be controlled with an external excitation, which usually corresponds with a quasi-static electric field (AC). By changing the dielectric permittivity at each cell that makes up the reflectarray, the phase shift on the aperture is controlled, so that a prescribed radiation pattern can be configured. Liquid Crystal-based reflectarrays have been chosen for several reasons. The first has to do with the advantages provided by the reflectarray antenna with respect to other high gain antennas, such as reflectors or phased arrays. The RF feeding in reflectarrays is achieved by using a common primary source (as in reflectors). This arrangement and the large number of degrees of freedom provided by the cells that make up the reflectarray (as in arrays), allow these antennas to provide a similar or even better electrical performance than other low profile antennas (reflectors and arrays), but assuming a more reduced cost and compactness. The second reason is the flexibility of the liquid crystal to be confined in an arbitrary geometry due to its fluidity (property of liquids). Therefore, the liquid crystal is able to adapt to a planar geometry so that it is one or more of the typical layers of this configuration. This simplifies drastically both the structure and manufacture of this type of antenna, even when compared with reconfigurable reflectarrays based on other technologies, such as diodes MEMS, etc. Therefore, the cost of developing this type of antenna is very small, which means that electrically large reconfigurable reflectarrays could be manufactured assuming low cost and greater productions. A paradigmatic example of a similar structure is the liquid crystal panel, which has already been commercialized successfully. The third reason lies in the fact that, at present, the liquid crystal is one of the few technologies capable of providing switching capabilities at frequencies above 60 GHz. In fact, the liquid crystal allows its permittivity to be switched in a wide range of frequencies, which are from DC to the visible spectrum, including microwaves and THz. Other technologies, such as ferroelectric materials, graphene or CMOS "on chip" technology also allow the beam to be switched at these frequencies. However, CMOS technology is expensive and is currently limited to frequencies below 150 GHz, and although ferroelectric materials or graphene can switch at higher frequencies and in a wider range, they have serious difficulties that make them immature. Ferroelectric materials involve the use of very high voltages to switch the material, making them unattractive, whereas the electromagnetic modelling of the graphene is still under discussion, so that the experimental results of devices based on this latter technology have not been reported yet. These three reasons make LC-based reflectarrays attractive for many applications that involve the use of electronically reconfigurable beams at frequencies beyond 60 GHz. Applications such as high resolution imaging radars, molecular spectroscopy, radiometers for atmospheric observation, or high frequency wireless communications (WiGig) are just some of them. This thesis is divided into three parts. In the first part, the most common properties of the liquid crystal materials are described, especially those exhibited in the nematic phase. The study is focused on the dielectric anisotropy (Ac) of uniaxial liquid crystals, which is defined as the difference between the parallel (e/7) and perpendicular (e±) permittivities: Ae = e,, - e±. This parameter allows the permittivity of a LC confined in an arbitrary volume at a certain biasing voltage to be described by solving a variational problem that involves both the electrostatic and elastic energies. Thus, the frequency dependence of (Ae) is also described and characterised. Note that an appropriate LC modelling is quite important to ensure enough accuracy in the phase shift provided by each cell that makes up the reflectarray, and therefore to achieve a good electrical performance at the antenna level. The second part of the thesis is focused on the design of resonant reflectarray cells based on liquid crystal. The reason why resonant cells have been chosen lies in the fact that they are able to provide enough phase range using the values of the dielectric anisotropy of the liquid crystals, which are typically small. Thus, the aim of this part is to investigate several reflectarray cell architectures capable of providing good electrical performance at the antenna level, which significantly improve the electrical performance of the cells reported in the literature. Similarly, another of the objectives is to develop a general tool to design these cells. To fulfill these objectives, the electrical yields of different types of resonant reflectarray elements are investigated, beginning from the simplest, which is made up of a single resonator and limits the state of the art. To overcome the electrical limitations of the single resonant cell, several elements consisting of multiple resonators are considered, which can be single-layer or multilayer. In a first step, the design procedure of these structures makes use of a conventional electromagnetic model which has been used in the literature, which considers that the liquid crystal behaves as homogeneous and isotropic materials whose permittivity varies between (e/7) y (e±). However, in this part of the thesis it is shown that the conventional modelling is not enough to describe the physical behaviour of the liquid crystal in reflectarray cells accurately. Therefore, a more accurate analysis and design procedure based on a more general model is proposed and developed, which defines the liquid crystal as an anisotropic three-dimensional inhomogeneous material. The design procedure is able to optimize multi-resonant cells efficiently to achieve good electrical performance in terms of bandwidth, phase range, losses, or sensitivity to the angle of incidence. The errors made when the conventional modelling (amplitude and phase) is considered have been also analysed for various cell geometries, by using measured results from several antenna prototypes made up of real liquid crystals at frequencies above 100 GHz. The measurements have been performed in a periodic environment using a quasi-optical bench, which has been designed especially for this purpose. One of these prototypes has been optimized to achieve a relatively large bandwidth (10%) at 100 GHz, low losses, a phase range of more than 360º, a low sensitivity to angle of incidence, and a low influence of the transversal inhomogeneity of the liquid crystal in the cell. The electrical yields of this prototype at the cell level improve those achieved by other elements reported in the literature, so that this prototype has been used in the last part of the thesis to perform several complete antennas for beam scanning applications. Finally, in this second part of the thesis, a novel strategy to characterise the macroscopic anisotropy using reflectarray cells is presented. The results in both RF and AC frequencies are compared with those obtained by other methods. The third part of the thesis consists on the study, design, manufacture and testing of LCbased reflectarray antennas in complex configurations. Note that the design procedure of a passive reflectarray antenna just consists on finding out the dimensions of the metallisations of each cell (which are used for phase control), using well-known optimization processes. However, in the case of reconfigurable reflectarrays based on liquid crystals, an additional step must be taken into account, which consists of accurately calculating the control voltages to be applied to each cell to configure the required phase-shift distribution on the surface of the antenna. Similarly, the structure to address the voltages at each cell and the control circuitry must be also considered. Therefore, the voltage synthesis is even more important than the design of the cell geometries (dimensions), since the voltages are directly related to the phase-shift. Several voltage synthesis procedures have been proposed in the state of the art, which are based on the experimental characterization of the phase/voltage curve. However, this characterization can be only carried out at a single angle of incidence and at certain cell dimensions, so that the synthesized voltages are different from those needed, thus giving rise to phase errors of more than 70°. Thus, the electrical yields of the LCreflectarrays reported in the literature are limited in terms of bandwidth, scanning range or side lobes level. In this last part of the thesis, a new voltage synthesis procedure has been defined and developed, which allows the required voltage to be calculated at each cell using simulations that take into account the particular dimensions of the cells, their angles of incidence, the frequency, and the AC biasing signal (frequency and waveform). The strategy is based on the modelling of each one of the permittivity states of the liquid crystal as an anisotropic substrate with longitudinal inhomogeneity (1D), or in certain cases, as an equivalent homogeneous tensor. The accuracy of both electromagnetic models is also discussed. The phase errors made by using the proposed voltage synthesis are better than 7º. In order to obtain an efficient tool to analyse and design the reflectarray, an electromagnetic analysis tool based on the Method of Moments in the spectral domain (SD-MoM) has also written and developed for anisotropic stratified media, which is used at each iteration of the voltage synthesis procedure. The voltage synthesis is also designed to minimize the effect of amplitude ripple on the radiation pattern, which is typical of reflectarrays made up of cells exhibiting high losses and represents a further advance in achieving a better antenna performance. To calculate the radiation patterns used in the synthesis procedure, an element-by-element analysis is assumed, which considers the local periodicity approach. Under this consideration, the use of a novel method is proposed, which avoids the limitation that the local periodicity imposes on the excitation. Once the appropriate strategy to calculate the voltages to be applied at each cell is developed, and once it is designed and manufactured both the structure to address the voltages to the antenna and the control circuits, two complete LC-based reflectarray antennas that operate at 100 GHz have been designed, manufactured and tested using the previously presented cells. The first prototype consists of a single offset reflectarray with beam scanning capabilities on one plane (elevation and azimuth). Although several LC-reflectarray antennas that provide 2-D scanning capabilities are also designed, and certain strategies to achieve the 2-D addressing of the voltage are proposed, the manufactured prototype addresses the voltages in one dimension in order to reduce the number of controls and manufacturing errors, and thereby validating the design tool. For an average aperture size (with a number of rows and columns of between 30 and 50 elements, which means a reflectarray with more than 900 cells), the single offset configuration provides an antenna gain of between 20 and 30 dBi and a large scanning range. The prototype tested at 100 GHz exhibits an electronically scanned beam in an angular range of 55º and 8% of bandwidth, in which the side lobe level (SLL) remains better than -13 dB. The maximum gain is 19.4 dBi. The electrical performance of the antenna is clearly an improvement on those achieved by other authors in the state of the art. The second prototype corresponds to a dual reflector antenna with a liquid crystal-based reflectarray used as a sub-reflector for beam scanning in one plane (azimuth or elevation). The main objective is to obtain a higher gain than that provided by the single offset configuration, but using a more compact architecture. In this case, a maximum gain of 35 dBi is achieved, although at the expense of reducing the scanning range to 12°, which is inherent in this type of structure. As a general statement, the voltage synthesis and the design procedure of the cells, jointly make up a complete, accurate and efficient design tool of reconfigurable reflectarray antennas based on liquid crystals. The tool has been validated by testing the previously mentioned prototypes at 100 GHz, which achieve something never reached before for this type of antenna: a competitive electrical performance, and an excellent prediction of the results. The design procedure is general and therefore can be used at any frequency for which the liquid crystal exhibits dielectric anisotropy. The two prototypes designed, manufactured and tested in this thesis are also some of the first antennas that currently operate at frequencies above 100 GHz. In fact, the dual reflector antenna is the first electronically scanned dual reflector antenna at frequencies above 60 GHz (the operation frequency is 100 GHz) with a gain greater than 25 dBi, being in turn the first dual-reflector antenna with a real reconfigurable sub-reflectarray. Finally, some improvements that should be still investigated to make these antennas commercially competitive are proposed.

Imaging, anatomical, and molecular analysis of callosal formation in the developing human fetal brain

A complex set of axonal guidance mechanisms are utilized by axons to locate and innervate their targets. In the developing mouse forebrain, we previously described several midline glial populations as well as various guidance molecules that regulate the formation of the corpus callosum. Since agenesis of the corpus callosum is associated with over 50 different human congenital syndromes, we wanted to investigate whether these same mechanisms also operate during human callosal development. Here we analyze midline glial and commissural development in human fetal brains ranging from 13 to 20 weeks of gestation using both diffusion tensor magnetic resonance imaging and immunohistochemistry. Through our combined radiological and histological studies, we demonstrate the morphological development of multiple forebrain commissures/decussations, including the corpus callosum, anterior commissure, hippocampal commissure, and the optic chiasm. Histological analyses demonstrated that all the midline glial populations previously described in mouse, as well as structures analogous to the subcallosal sling and cingulate pioneering axons, that mediate callosal axon guidance in mouse, are also present during human brain development. Finally, by Northern blot analysis, we have identified that molecules involved in mouse callosal development, including Slit, Robo, Netrin1, DCC, Nfia, Emx1, and GAP-43, are all expressed in human fetal brain. These data suggest that similar mechanisms and molecules required for midline commissure formation operate during both mouse and human brain development. Thus, the mouse is an excellent model system for studying normal and pathological commissural formation in human brain development. (c) 2006 Wiley-Liss, Inc.

Actionable pattern analysis in computing and business intelligence systems

With advances in science and technology, computing and business intelligence (BI) systems are steadily becoming more complex with an increasing variety of heterogeneous software and hardware components. They are thus becoming progressively more difficult to monitor, manage and maintain. Traditional approaches to system management have largely relied on domain experts through a knowledge acquisition process that translates domain knowledge into operating rules and policies. It is widely acknowledged as a cumbersome, labor intensive, and error prone process, besides being difficult to keep up with the rapidly changing environments. In addition, many traditional business systems deliver primarily pre-defined historic metrics for a long-term strategic or mid-term tactical analysis, and lack the necessary flexibility to support evolving metrics or data collection for real-time operational analysis. There is thus a pressing need for automatic and efficient approaches to monitor and manage complex computing and BI systems. To realize the goal of autonomic management and enable self-management capabilities, we propose to mine system historical log data generated by computing and BI systems, and automatically extract actionable patterns from this data. This dissertation focuses on the development of different data mining techniques to extract actionable patterns from various types of log data in computing and BI systems. Four key problems—Log data categorization and event summarization, Leading indicator identification , Pattern prioritization by exploring the link structures , and Tensor model for three-way log data are studied. Case studies and comprehensive experiments on real application scenarios and datasets are conducted to show the effectiveness of our proposed approaches.