Electrode Modelling in Electrical Impedance Tomography

Paulson, Kevin; Breckon, William; Pidcock, Michael

doi:10.1137/0152059

Cited by 95 publications

(71 citation statements)

References 7 publications

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“…A realistic model accounts for the electrodes contact impedance (Paulson et al 1992, Somersalo et al 1992. Other possible boundary conditions for Laplace's equation are the Dirichlet boundary condition u = V on ∂ (6) or a combination of both conditions on different subsets of the boundary.…”

Section: Theorymentioning

confidence: 99%

“…This requires solution for the voltage in the whole domain, which at low frequencies can be modelled using the generalized Laplace's equation together with some boundary conditions (Paulson et al 1992, Somersalo et al 1992. A number of authors have proved uniqueness of the isotropic inverse conductivity problem (Kohn and Vogelius 1984, 1985, Sylvester and Uhlmann 1987.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Validation of a finite-element solution for electrical impedance tomography in an anisotropic medium

et al. 2007

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Electrical impedance tomography is an imaging method, with which volumetric images of conductivity are produced by injecting electrical current and measuring boundary voltages. It has the potential to become a portable non-invasive medical imaging technique. Until now, implementations have neglected anisotropy even though human tissues such as bone, muscle and brain white matter are markedly anisotropic. We present a numerical solution using the finite-element method that has been modified for modelling anisotropic conductive media. It was validated in an anisotropic domain against an analytical solution in an isotropic medium after the isotropic domain was diffeomorphically transformed into an anisotropic one. Convergence of the finite element to the analytical solution was verified by showing that the finiteelement error norm decreased linearly related to the finite-element size, as the mesh density increased, for the simplified case of Laplace's equation in a cubic domain with a Dirichlet boundary condition.

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Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Validation of a finite-element solution for electrical impedance tomography in an anisotropic medium

et al. 2007

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“…This new boundary condition together with (1.3) and (1.4) form the Complete Electrode Model or CEM. For experimental validation of this model see [37], theory [143] and numerical calculations [117,155]. A nonzero contact impedance removes the singularity in the current density, although high current densities still occur at the edges of electrodes (fig 1.1).…”

Section: Measurements and Electrodesmentioning

confidence: 99%

The reconstruction problem

Lionheart¹,

Polydorides²,

Borsic³

2004

Series in Medical Physics and Biomedical Engineering

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“…For studies on comparing different setups, see [11,29,30,31,35]. Optimizing the electrode locations in EIT, however, has been studied only recently in [14].…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

Optimizing Electrode Positions in Electrical Impedance Tomography

Hyvönen¹,

Seppänen²,

Staboulis³

2014

SIAM J. Appl. Math.

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Abstract. Electrical impedance tomography is an imaging modality for recovering information about the conductivity inside a physical body from boundary measurements of current and voltage. In practice, such measurements are performed with a finite number of contact electrodes. This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized) conductivity, i.e., the conditional density of the conductivity given the measurements, is as localized as possible. To make such an approach computationally feasible, the complete electrode forward model of impedance tomography is linearized around the prior expectation of the conductivity, allowing explicit representation for the (approximate) posterior covariance matrix. Two approaches are considered: minimizing the trace or the determinant of the posterior covariance. The introduced optimization algorithm is of the steepest descent type, with the needed gradients computed based on appropriate Fréchet derivatives of the complete electrode model. The functionality of the methodology is demonstrated via two-dimensional numerical experiments.Key words. Electrical impedance tomography, optimal electrode locations, Bayesian inversion, complete electrode model, optimal experiment design AMS subject classifications. 65N21, 35Q60, 62F151. Introduction. Electrical impedance tomography (EIT) is an imaging modality for recovering information about the electrical conductivity inside a physical body from boundary measurements of current and potential. In practice, such measurements are performed with a finite number of contact electrodes. The reconstruction problem of EIT is a highly nonlinear and illposed inverse problem. For more information on the theory and practice of EIT, we refer to the review articles [3,5,36] and the references therein.The research on optimal experiment design in EIT has mostly focused on determining optimal current injection patterns. The most well-known approach to optimizing current injections is based on the distinguishability criterion [17], i.e., maximizing the norm of the difference between the electrode potentials corresponding to the unknown true conductivity and a known reference conductivity distribution. Several variants of the distinguishability approach have been proposed; see, e.g., [24,26] for versions with constraints on the injected currents. The application of the method to planar electrode arrays was considered in [22]. The distinguishability criterion leads to the use of current patterns generated by exciting several electrodes simultaneously. For other studies where the sensitivity of the EIT measurements is controlled by injecting currents through several electrodes at a time, see [32,39]. In geophysical applications of EIT, the data is often collected using four-point measurements; choosing the optimal ones for different electrode settings was studied in [1,10,34,38]...

show abstract

Electrode Modelling in Electrical Impedance Tomography

Cited by 95 publications

References 7 publications

Validation of a finite-element solution for electrical impedance tomography in an anisotropic medium

Validation of a finite-element solution for electrical impedance tomography in an anisotropic medium

The reconstruction problem

Optimizing Electrode Positions in Electrical Impedance Tomography

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