An Introduction to Electrical Impedance Tomography
نویسنده
چکیده
The inverse problem of Electrical Impedance Tomography (EIT) is that of imaging a spatially varying, complex admittivity function γ(x, ω) in a domain Ω ⊂ I R (n = 2 or 3), given measurements of low frequency ω alternating electrical currents and potentials at the boundary ∂Ω. The real and imaginary parts of admittivity γ(x, ω) are the electrical conductivity σ(x) and ω (x), respectively, where (x) is the permittivity (dielectric constant). In mathematical terms, the EIT problem is that of recovering coefficients σ(x) and (x) in a system of elliptic partial differential equations, defined for x ∈ Ω, given knowledge of the Cauchy data, i.e. the Neumann to Dirichlet or Dirichlet to Neumann maps. The EIT problem has important applications in fields such as medical imaging, nondestructive testing, environmental cleaning, geophysics, etc. and, over the last two decades, it has been the topic of many theoretical and numerical studies. In spite of the rich literature on EIT, there are important, outstanding questions that do not have satisfactory answers, so far. Examples of such questions are: improving the stability of imaging algorithms, the resolution and reliability of images of γ(x, ω), increasing the speed of inversion algorithms so γ(x, ω) can be imaged in real time, etc. This set of lectures gives a brief review of theoretical and numerical results available for the EIT problem. A list of topics is: 1. Formulation of the EIT problem. Definition of the Neumann to Dirichlet and Dirichlet to Neumann maps. Variational principles. Regularity of the forward map. 2. Uniqueness of the solution of the EIT problem. Calderon’s proof of injectivity of the linearized map. Sylvester and Uhlmann’s 3D uniqueness proof. 3. Instability of the EIT problem. Regularization. Alessandrini’s stability estimate for regular conductivities. 4. Imaging algorithms. Linearization (Born approximation). Nonlinear, Newton-type imaging algorithms. Variational approaches: equation-error methods and variational constraints on the unknown γ. Layer stripping. Multigrid reconstructions of γ. 5. High contrast imaging. 6. Optimal grids.
منابع مشابه
Applications of Electrical Impedance Tomography in Neurology
Introduction: Electrical impedance tomography (EIT) is a non-invasive technique utilized in various medical applications, including brain imaging and other neurological diseases. Recognizing the physiological and anatomical characteristics of organs based on their electrical properties is one of the main applications of EIT, as each variety of tissue structure has its own electrical characteris...
متن کاملThe Effect of Gold Nanoparticle on Electrical Impedance of Tissue on Low Frequency Ranges
Introduction: Electrical impedance of tissues on low frequencies includes useful information about functional and structural changes in tissues. This property is used in Electrical Impedance Tomography (EIT) imaging modality for the detection of lesions in tissues.Objective: The goal of this article is to study changes in electrical impedance of tissues in the presence of gold nanoparticles.Mat...
متن کاملIntroduction to the numerical solution of inverse problems and shape detection in electrical impedance tomography
متن کامل
Fuzzy Modeling of Electrical Impedance Tomography Images of the Lungs
OBJECTIVES Aiming to improve the anatomical resolution of electrical impedance tomography images, we developed a fuzzy model based on electrical impedance tomography's high temporal resolution and on the functional pulmonary signals of perfusion and ventilation. INTRODUCTION Electrical impedance tomography images carry information about both ventilation and perfusion. However, these images ar...
متن کاملEvaluation of the use of gold nanoparticle as contrast agent in electrical impedance imaging
Introduction: Electrical Impedance Tomography (EIT) is a real time and minimal invasive imaging modality for detection of lesions in tissues even when their structures show no changes. Early detection of lesion with EIT depends on difference between electrical impedance of targeted tissue and its surroundings. Therefore, finding a contrast agent for EIT that increase this diffe...
متن کاملFeasibility Study of MREIT in Clinical Applications
Introduction Several in vitro studies have shown that the electrical impedance of malignant tissues is significantly higher than those of normal and benign tissues. Therefore, impedance imaging has the potential as a diagnostic tool in cancer. Magnetic Resonance Electrical Impedance Tomography (MREIT) is a technique that is used for imaging impedance distribution inside an object noninvasively ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003