Numerical study of the influence of changes in electrical conductivity on the solution of the direct problem of electrical impedance tomography

Electrical Impedance Tomography (EIT) uses electrical stimulation and measurement at the body surface to image the electrical properties of internal tissues. It has the advantage of non-invasiveness and high temporal resolution but suffers from poor spatial resolution and sensitivity to electrode movement and contact quality. EIT can be useful to applications where there are conductive contrasts between tissues, fluids or gases, such as imaging of cancerous or ischemic tissue or functional monitoring of breathing, blood flow, gastric motility and neural activity. The work uses a complete electrode model (CEM), which is a practical model in EIT, which most realistically models electrodes. This model can simulate EIT measurements with much greater accuracy than continuum models. The mathematical formulation of the problem is written as follows: 𝜕𝑥 ( σ(𝑥, 𝑦) 𝜕𝑥 ) + 𝜕𝑦 ( σ(𝑥, 𝑦) 𝜕𝑦 ) = 0, (𝑥, 𝑦) ∈ 𝐷; σ 𝜕𝑛 = 0, (𝑥, 𝑦) /∈ ⋃ 𝑙=1 𝐸𝑙; σ 𝜕𝑛 = 1 ⎛ ∫ 𝑢 + ⎞ - 𝑧𝑙 , (𝑥, 𝑦) ∈ 𝐸𝑙, = 1, . . . ,𝐿; Σ 𝑙=1 = 0. In the article [15] shows that in order for the problem to have a unique solution, the following condition must be met: Σ 𝑙=1 = 0. Numerical studies are consistent with the conclusions from the article [14]. Useful information in the EIT is contained mainly on a small part of the boundary, i.e., on the electrodes close to the perturbations of the electrical conductivity. Boundary measurements, which are the input to the inverse conductivity problem, are more sensitive to anomalies near the boundary and to larger anomalies. This study is useful in order to know the critical values of the parameters (size, location) of a low-amplitude perturbation of conductivity, at which the measurements are insensitive and, therefore, inhomogeneities cannot be detected.