Electrical Impedance Tomography (EIT) is an imaging technique which tries to find conductivity distribution inside a section of body. The EIT deals with an inverse problem in which given the measured voltages on electrodes it estimates the conductivity distribution by using an image reconstruction algorithm. EIT can be used in several applications and, recently, it has been applied for obtainin...

The mathematical problem for Electrical Impedance Tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low...

The assessment of the regional match between alveolar ventilation and perfusion in critically ill patients requires simultaneous measurements of both parameters. Ideally, assessment of lung perfusion should be performed in real-time with an imaging technology that provides, through fast acquisition of sequential images, information about the regional dynamics or regional kinetics of an appropri...

Electrical impedance tomography (EIT) is a non-invasive technique that aims to reconstruct images of internal electrical properties of a domain, based on electrical measurements on the periphery. Improvements in instrumentation and numerical modeling have led to three-dimensional (3D) imaging. The availability of 3D modeling and imaging raises the question of identifying the best possible excit...

Electrical impedance tomography (EIT) uses electrical measurements at electrodes placed around the thorax to image changes in the conductivity distribution within the thorax. This technique is well suited to studying pulmonary function because the movement of air, blood, and extravascular fluid induces significant conductivity changes within the thorax. We conducted three experimental protocols...

The electroporation effect on tissue can be assessed by measurement of electrical properties of the tissue undergoing electroporation. The most prominent techniques for measuring electrical properties of electroporated tissues have been voltage-current measurement of applied pulses and electrical impedance tomography (EIT). However, the electrical conductivity of tissue assessed by means of vol...

In electrical impedance tomography (EIT) two-dimensional models continue to be applied despite their known inability to provide correct reconstruction. In this paper, a reconstruction algorithm that assumes a translationally invariant conductivity distribution is described. A more precise forward solver is obtained by taking off-slice currents into consideration. An appropriate sensitivity matr...

Electrical impedance tomography (EIT) uses body surface electrical stimulation and measurements to create conductivity images; it shows promise as a non-invasive technology to monitor the distribution of lung ventilation. Most applications of EIT have placed electrodes in a 2D ring around the thorax, and thus produced 2D cross-sectional images. These images are unable to distinguish out-of-plan...

These notes represent an extended version of the contents of the third lecture delivered at the AMS Short Course “Radon Transform and Applications to Inverse Problems” in Atlanta in January 2005. They contain a brief description of properties of some generalized Radon transforms arising in inverse problems. Here by generalized Radon transforms we mean transforms that involve integrations over c...

In this paper, we consider the electrical impedance tomography problem in a computational approach. This inverse problem is the recovery of the electrical conductivity σ in a domain from boundary measurements, given in the form of the Neumann-to-Dirichlet map. We formulate the inverse problem as a variational one, with a fitting term and a regularization term. We restrict the minimization with ...