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ELECTRICAL IMPEDANCE TOMOGRAPHY CHAPTER 1: PRINCIPLES OF ELECTRICAL IMPEDANCE Bioimpedance: Principles The concept of electrical impedance is a generalization of the concept of electrical resistance, useful to describe the laws that govern the passage of alternating current through a structure or tissue. Besides the intuitive concept of resistors (essential to describe the behavior of current), it is necessary to grasp the concept of capacitors (structures that act as temporary storage of electrical charge) to understand the behavior of alternating currents. Any structure or biological tissue is a composition of resistors and capacitors. This composition is related to the tissue architecture, which determines the greater or lesser difficulty for the passage of current. For the same intensity of current applied, the greater the difficulty (impedance) to the passage of current, the greater is the voltage gradient through the structure. Numerically, electrical impedance is the difference in voltage between two points of injection, divided by the intensity of the resulting current between these two points. It is expressed by a complex number, the real part of which corresponds to the electrical resistance, and the imaginary part, to the reactance (= inverse of capacitance). All devices that use the principle of electrical impedance - from body fat meters to the impedance tomography - use the measurements of voltages or voltage gradients which result from the injection of low-amplitude alternating currents. During the measurement of body fat, or for the detection of tumors, for example, it may be interesting to estimate the contribution of the impedance components (resistance and reactance) in order to estimate the greater or lesser presence of cells in tissues (the cell membranes act as capacitors). Therefore, for these purposes, a system able to inject current and measure the voltages in a wide range of frequencies (5 to 1000 kHz) is generally used. A sharp fall of total impedance with increasing frequency suggests a higher capacitance and therefore a higher cellular content. TIMPEL: PRINCIPLES OF EIT 1 For applications in respiratory medicine, we usually measure total impedance, without concern for its components, assuming that the entry of the air into the lungs causes mainly a change in the resistance of the lung. Thus, these devices usually work at a pre-determined and fixed frequency, usually around 50-100 kHz. With very high frequencies of the injected current, there is virtually no damage to biological tissues and little interference with the cardiac electrical activity. How EIT works EIT commonly uses the injection of high-frequency (> 10 kHz) and low amplitude (< 12 mAmp) currents applied to the thorax through 8 to 32 electrodes. The electrodes are arranged circumferentially around the chest delimiting a transverse or axial plane that is represented in the image reconstruction of the lungs. The electric currents injected on the thoracic surface follow paths that vary according to the distribution of the tissue inside the thorax as well to the conformation of the chest. In general, multiple points of injection are used simultaneously or sequentially in order to generate multiple perspectives. The most common configuration uses only two electrodes at a time to inject the currents (one electrode for injection and one for current drainage). However, there are devices that inject current through several electrodes simultaneously. The voltages measured in the other (non-injecting) electrodes on the surface of the chest are used to feed an image reconstruction algorithm that solves a mathematical inverse problem, nonlinear and ill-posed. Ill-posedness translates a situation on which the solution (the estimated image) for the distribution of impedances may not be unique, and may be unstable: small errors in voltage measurement can result in significantly different solutions. This problem is compounded by the relatively small number of independent measures on the surface of the chest (usually 104 to 464, depending on the number of electrodes), a number well below the number of pixels in the reconstructed image. The only present limitation to obtain a larger number of independent measures is the technical difficulty to reduce the size of the electrode: the “amount” of currents injected through small electrodes is limited and leads to worse signal-to-noise ratios. With improvements in the technology of the electrodes, it will soon be possible to have a greater number of electrodes, possibly in multiple planes, allowing a greater number of perspectives and image reconstructions with higher spatial resolution. In order to overcome the ill-posed nature of impedance estimation, most EIT imaging algorithms make use of additional assumptions, known as regularizations, such as smoothness of the intrathoracic impedance distribution. These regularizations help the estimation algorithm to decide between competing solutions, producing an image that is a reasonable estimation of the true impedance distribution within the thorax, at the expense of degraded spatial resolution or attenuation of maximum perturbations TIMPEL: PRINCIPLES OF EIT 3