Projection-based preprocessing for electrical impedance tomography to reduce the effect of electrode contacts

TL;DR

This paper tackles the vulnerability of electrical impedance tomography (EIT) reconstructions to uncertain electrode contacts. It introduces projection-based preprocessing that removes the influence of contact conductivities (and optionally electrode positions) by projecting data onto the orthogonal complement of the Jacobian ranges, computed from a smoothened complete electrode model. The authors develop two reconstruction pipelines—regularized one-step linearization and total variation with lagged diffusivity iteration—applied to both projected data and forward maps, demonstrating dramatically reduced contact-induced artifacts in simulations and real-water-tank experiments. The results suggest that interior conductivity changes can be recovered without estimating contact parameters, while the projection range shows robustness to background conductivity values, offering potential for clinical monitoring of stroke and other dynamic EIT applications.

Abstract

This work introduces a method for preprocessing measurements of electrical impedance tomography to considerably reduce the effect uncertainties in the electrode contacts have on the reconstruction quality, without a need to explicitly estimate the contacts. The idea is to compute the Jacobian matrix of the forward map with respect to the contact strengths and project the electrode measurements and the forward map onto the orthogonal complement of the range of this Jacobian. Using the smoothened complete electrode model as the forward model, it is demonstrated that inverting the resulting projected equation with respect to only the internal conductivity of the examined body results in good quality reconstructions both when resorting to a single step linearization with a smoothness prior and when combining lagged diffusivity iteration with total variation regularization. The quality of the reconstructions is further improved if the range of the employed projection is also orthogonal to that of the Jacobian with respect to the electrode positions. These results hold even if the projections are formed at internal and contact conductivities that significantly differ from the true ones; it is numerically demonstrated that the orthogonal complement of the range of the contact Jacobian is almost independent of the conductivity parameters at which it is evaluated. In particular, our observations introduce a numerical technique for inferring whether a change in the electrode measurements is caused by a change in the internal conductivity or alterations in the electrode contacts, which has potential applications, e.g., in bedside monitoring of stroke patients. The ideas are tested both on simulated data and on real-world water tank measurements with adjustable contact resistances.

Figures (11)

• Figure 3.1: The finite-element head model used for simulating EIT measurements.
• Figure 4.1: Comparison of $\sigma$-, $\zeta$- and combined signals corresponding to the input current $I^{(3)}$ for a single random draw of the conductivity pair $(\sigma, \zeta)$ in the framework the head model of Section \ref{['sec:head']}. Top left: non-projected signals. Top right: signals projected with $P_\zeta(\sigma_0, \zeta_0)$. Bottom left: signals projected with $P_{\zeta,\phi}(\sigma_0, \zeta_0)$. Bottom right: The original and projected $\sigma$-signals.
• Figure 4.2: Experimental setup described in Section \ref{['sec:experimental']}, with the resistor test case on left and the tape test case on right. Left: the electrodes with adjustable resistors in their cables are marked in white. Right: the taped electrodes are partially white, with a half, one third or two thirds of their respective areas covered by tape. See Table \ref{['tab:resistors_and_tapes']} for more details.
• Figure 4.3: Comparison of experimentally measured $\sigma$-, $\zeta$- and combined signals in the resistor test case; see the left image in Figure \ref{['fig:taped_electrodes']}. Top: non-projected signals. Middle: signals projected with $P_\zeta(\sigma_0, \zeta_0)$. Bottom: signals projected with $P_{\zeta, \phi}(\sigma_0, \zeta_0)$. Left: full signals corresponding to measurements on all electrodes. Right: zoomed in image on a portion of the signals.
• Figure 4.4: Comparison of experimentally measured $\sigma$-, $\zeta$- and combined signals in the tape test case; see the right image in Figure \ref{['fig:taped_electrodes']}. Top: non-projected signals. Middle: signals projected with $P_\zeta(\sigma_0, \zeta_0)$. Bottom: signals projected with $P_{\zeta, \phi}(\sigma_0, \zeta_0)$. Left: full signals corresponding to measurements on all electrodes. Right: zoomed in image on a portion of the signals.

Theorems & Definitions (1)

• Remark 5.1