The work presented in this thesis consists of two distinct parts. The first years of my work focused on the development and improvement of a new equipment built to study magnetic and electrical properties, particularly applying microwaves in reflection and transmission conditions. The sample space in conventional cryostats with superconducting magnets is usually smaller than 10-mm-diameter. Our equipment consists of a hollow cylindrical cryostat having a 33-mm-diameter hole all along its vertical axis. These characteristics enable the measurement of large samples and the use of big resonant cavities to get to a wider microwave (MW) range, particularly in transmission measurements. The cryostat has a superconducting magnet made of a solenoid that applies a magnetic field from -5 T to 5 T, and a temperature controller that works in the range 1.8 - 300 K. The system is cooled down with nitrogen and helium and the temperature can be controlled with the precision required by each experiment using a heater and a needle valve. Different probes for a wide range of experiments in our cryostat have been developed in order to be as versatile as possible. Following this idea each one has been divided in two halves that can be combined as it is preferred in each experiment. Each probe is made of a 8-to-10-mm-diameter stainless steel tube that is used to protect and give some stiffness to the measuring device. A coaxial cable and different waveguides are added to these stainless steel jackets, so we end up having nine halves, four upper parts that can be combined with five lower parts. There are three waveguides working in the frequency ranges 33-50 GHz (WR22), 50-75 GHz (WR15) and 75-110 GHz (WR10), and a coaxial cable that maintains the fundamental mode at a frequency of 60 GHz. In the extra lower part a 16-pin Fischer connector is added at the bottom in order to be able to perform more resistance experiments. Once the probes have been built, they have been tested to make sure the system is able to reach high vacuum and to be cooled down. Problems found along the way have been solved and at the end all the probes work properly. Different sample holders have been designed and built according to the needs in each experiment. The system has been tested by reproducing experimental results with Mn12-acetate, as quantum tunneling and magnetic avalanches, and by obtaining new results on microwave transmission in thin TiN films. The second part of the thesis focuses on the measurements of thin TiN films in a dilution refrigerator working with a mixture of 3He and 4He that enables experiments at a few tens of millikelvins. The cryostat also contains a superconductor magnet which can apply a magnetic field up to 5 T. Low-temperature transport properties of nanoperforated superconducting TiN films have been experimentally studied. Resistance measurements have been performed in the critical region of the superconductor-insulator transition (SIT), applying the magnetic field perpendicular to the plane of the structure or the dc current through the sample. SIT is a transition from a superconductor to an insulator state by localizing the Cooper pairs. The evolution of the SIT with temperature, magnetic field and dc current has been investigated in detail. Characteristic parameters have been determined for as-cast thin films using the theory of quantum corrections to conductivity. Disorder-driven and field-induced SITs have been measured. Commensurability effects have been observed down to the lowest experimental temperature, and are emphasized in the more disordered samples. The SIT has been observed for a dc current applied across the sample as changes in the curvature at zero bias current. Experiments prove that electronic transport in the nanoperforated samples is mediated by Andreev conversion. Finally, the existence of the superinsulator state has been experimentally proved. / El treball que es presenta en aquesta tesi consta de dues parts ben diferenciades. La primera pretén el desenvolupament d’un equip experimental concebut per a l’estudi de propietats magnètiques i elèctriques en materials diversos i, en especial, el treball amb radiació de microones en condicions de reflexió i transmissió. La segona s’ha centrat en les mesures de transport d’una capa fina superconductora de nitrur de titani (TiN) de 5 nm de gruix en un criòstat de dilució.

La tomografía de impedancia eléctrica (EIT) permite estimar la conductividad eléctrica interna de un cuerpo. Consiste en aplicar una corriente eléctrica sobre su frontera y medir el potencial eléctrico resultante mediante un arreglo de sensores. Es considerada como una potencial herramienta de diagnóstico médico, caracterizada principalmente por su portabilidad y relativo bajo costo. Si bien se encuentra aún en etapa de desarrollo, está comenzando a ser utilizada en centros de salud para la caracterización del aparato cardio-respiratorio y existe un creciente interés en su aplicación a las neurociencias. Por ejemplo, es posible utilizar la EIT para construir modelos virtuales de la cabeza más precisos mediante la estimación de la conductividad eléctrica de los principales tejidos de la cabeza como un conjunto de parámetros relativamente pequeño, modalidad denominada EIT paramétrico. También se puede utilizar la EIT para generar un mapa de la distribución de conductividad eléctrica interna de un objeto, llamado problema de reconstrucción en EIT. Los cambios de la conductividad eléctrica en la cabeza pueden estar asociados a la actividad neuronal, a focos epilépticos, a accidentes cerebro-vasculares o a tumores. Ambas modalidades de EIT requieren la resolución del problema directo (PD), que consiste en el cálculo de la distribución de potencial eléctrico en el objeto originada por la inyección de corriente sobre su superficie, suponiendo que la conductividad interna es conocida. La estimulación de corriente continua transcraneal (tDCS) es físicamente muy similar a la EIT, pero la corriente eléctrica es aplicada sobre el cuero cabelludo de modo de alterar la tasa de disparos de poblaciones de neuronas en una región de interés. Es una potencial alternativa al empleo de psicofármacos para tratar desórdenes como epilepsia o depresiones. En esta tesis se desarrollan y analizan nuevos métodos para distintos problemas de EIT, centrándose mayormente en aplicaciones a la cabeza humana, y de tDCS. En primer lugar, se describen soluciones analíticas y numéricas para el PD en EIT, estas últimas basadas en el método de los elementos finitos. Luego, se desarrolla un nuevo procedimiento para resolver el PD con bajo costo computacional basado en la formulación del PD en electroencefalografía (EEG). Se propone un nuevo método para determinar la forma de onda de la fuente de corriente que permite desafectar la actividad propia del cerebro con un bajo número de muestras temporales. En EIT paramétrico, se utiliza la cota de Cramér-Rao (CRB) para determinar pares de electrodos convenientes para la inyección de corriente y para analizar límites teóricos en la estimación de las conductividades del cráneo y del cuero cabelludo, modelizándolos como tejidos isótropos y anisótropos. A su vez, se propone el estimador de máxima verosimilitud (MLE) como herramienta para realizar las estimaciones. El MLE se aplica a mediciones simuladas y reales de EIT mostrando un desempeño muy cercano a los límites teóricos. Para el problema de reconstrucción en EIT se adapta el algoritmo sLORETA, muy utilizado en el problema de localización de fuentes de actividad neuronal en EEG. Además, se lo modifica levemente para incorporar la regularización espacial de Laplace. Por otro lado, se introduce la utilización de filtros espaciales adaptivos para localizar cambios de conductividad de pequeño tamaño y estimar su variación temporal. Los resultados muestran mejoras en sesgo y resolución, en comparación con algoritmos de reconstrucción típicos en EIT. Estas mejoras son potencialmente ventajosas en la detección de accidentes cerebro-vasculares y en la localización indirecta de fuentes de actividad neuronal. En tDCS, se desarrolla un nuevo algoritmo para la determinación de patrones de inyección de corriente basado en el principio de reciprocidad y que considera restricciones de seguridad y de hardware. Los resultados obtenidos a partir de simulaciones muestran que el desempeño de dicho algoritmo es comparable al desempeño de algoritmos de optimización tradicionales cuyas soluciones implicarían un equipamiento comparativamente más complejo y costoso. Los métodos desarrollados en la tesis son comparados con métodos pre-existentes y validados a través de simulaciones numéricas por computadora, mediciones sobre maquetas experimentales (ó fantomas) y, de acuerdo con las posibilidades experimentales y respetando los principios de la bioética, mediciones reales sobre humanos. / Electrical impedance tomography (EIT) is a technique to estimate the electrical conductivity of an object. It consists in the application of an electric current on its boundary and the measurement of the resulting electric potential with a sensor array. In clinical practise, it is considered as a potential diagnostic tool characterized by its portability and relatively low cost. While it is still in a development stage, it is starting to be used in health centers to characterize the cardio-respiratory system. In turn, there is an increasing interest of EIT in neuroscience. For example, EIT can be used to estimate the electrical conductivity of the main tissues of the head as a set of a relatively low number of parameters, which is known as bounded or parametric EIT. This is useful for several medical imaging techniques that require realistic and accurate virtual models of the head. EIT can also be used to generate a map of the internal distribution of the electrical conductivity, known as the reconstruction problem. Tracking conductivity changes inside the head is of great interest as they may be related to neuronal activity, epileptic foci, acute stroke, or tumors. Both modalities of EIT require the solution of the EIT forward problem (FP), i.e., the computation of the electric potential distribution due to current injection on the scalp assuming that the electrical conductivity is known. The transcranial direct current stimulation (tDCS) is another technique which is physically very similar to EIT. It consists in injecting a small electric current in a convenient way such that it stimulates specific neuronal populations, increasing or decreasing their firing rate. It is considered as an alternative to psychoactive drugs in the treatment of brain disorders such as epilepsy or depression. This thesis describes the development and analysis of new methods for EIT FP, parametric EIT, reconstruction in EIT, and tDCS, focusing primarily (although not exclusively) in applications to human head. We first describe analytical and numerical approaches for the EIT FP, where the numerical approach is based on the finite element method. Then, we develop a new procedure to solve the EIT FP based on the electroencephalography (EEG) FP formulation, which results in computational advantages. We propose a new method to determine the waveform of the electric current source such that the neuronal activity of the brain can be neglected with the smallest possible number of time samples. In parametric EIT, we use the Cramér-Rao bound (CRB) to determine convenient electrode pairs for the current injection and theoretical limits in the estimation of the electrical conductivity of the main tissues of the head, which we model as isotropic and anisotropic. We propose the maximum likelihood estimator (MLE) to estimate these conductivities and we test it with simulated and real EIT measurements, showing that the MLE performs close to the CRB. We adapt the sLORETA algorithm to the reconstruction problem in EIT. This algorithm is being widely used in the source localization problem in EEG. We also slightly modify it to include the Laplace smoothing prior in the solution. Likewise, we introduce the use of adaptive spatial filters in the localization of conductivity changes and the estimation of its time courses from EIT measurements. The results show improvements over typical EIT algorithms. These improvements may benefit the early detection of acute strokes and the localization of neuronal activity using EIT. In tDCS, we develop a new algorithm to determine convenient current injection patterns. It is based on the reciprocity principle and considers hardware and safety constraints. Our simulation results show that this method performs similarly to other commonly used algorithms that require more complex and costly equipments. The methods we develop and study in this thesis are compared with pre-existing methods and are validated through numerical simulations, measurements on phantoms and, according to the experimental possibilities and bioethical principles, humans.