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Integral formulation of the complete electrode model of electrical impedance tomography

The author is partially supported by KSF in XJTLU.
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  • 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.

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


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

    Figure 2.  A toy 2D EIT model

    Figure 3.  An unstructured mesh over the disk

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

    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

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

    Figure 7.  The conformal mapping

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