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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

Procesamiento de señales de tomografía de impedancia eléctrica para el estudio de la actividad cerebral