Integral formulation of the complete electrode model of electrical impedance tomography

Erfang Ma

doi:10.3934/ipi.2020017

Article Contents

2020, Volume 14, Issue 2: 385-398. Doi: 10.3934/ipi.2020017

This issue Previous Article The Linear Sampling Method for Kirchhoff-Love infinite plates Next Article Corrigendum to "Incorporating structural prior information and sparsity into EIT using parallel level sets"

Integral formulation of the complete electrode model of electrical impedance tomography

Erfang Ma

Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Laboratory for Intelligent Computing and Financial Technology, 111 Ren'ai Road, Suzhou Industrial Park, Suzhou, Jiangsu Province, 215123, China

Received: July 31, 2019

Revised: October 31, 2019

Published: February 2020

The author is partially supported by KSF in XJTLU.

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Abstract

We model electrical impedance tomography (EIT) based on the minimum energy principle. It results in a constrained minimization problem in terms of current density. The new formulation is proved to have a unique solution within appropriate function spaces. By characterizing its solution with the Lagrange multiplier method, we relate the new formulation to the so-called shunt model and the complete electrode model (CEM) of EIT. Based on the new formulation, we also propose a new numerical method to solve the forward problem of EIT. The new solver is formulated in terms of current. It was shown to give similar results to that of the traditional finite element method, with simulations on a 2D EIT model.

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Mathematics Subject Classification: Primary: 35F25, 46F20; Secondary: 78A70.

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Figure 1. The layer of contact impedance for the $ i $-th electrode

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Figure 2. A toy 2D EIT model

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Figure 3. An unstructured mesh over the disk

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Figure 4. Potential distributin estimated by the current-based solver (Left) and the traditional potential-based solver (Right)

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Figure 5. Non-uniform conductivity distribution. Black region has conductivity 0.1 S/m. Gray region has conductivity 0.3 S/m. Other parts of the region has conductivity 1 S/m

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Figure 6. Distribution of current densities estimated by the current-based solver (Left) and the traditional potential-based solver (Right)

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Figure 7. The conformal mapping

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