Influence of current injection pattern and electric potential measurement strategies in electrical impedance tomography

Abstract

Electrical Impedance Tomography (EIT) is a non-invasive image reconstruction technique, whereby current is injected by electrodes and electric potential is measured by electrodes. In some electronic hardware implementations, only two electrodes inject current simultaneously, and are denominated pair-wise current injection. Several possibilities of pair-wise current injection (electric current patterns) and electric potential measurement (single-ended and differential) have been addressed in the literature. Considering pair-wise current injection, the skip-m current pattern can be defined as a pair-wise injection strategy in which the number of non-current injecting electrodes enclosed between two injection electrodes is m. Single-ended electric potential measurements consist of measurements with a common potential reference. Differential electric potential measurements consist of pair-wise measurements between two electrodes. A theoretical analysis based on control theory is presented to show that some current and measurement pattern strategies convey less information than others. This hypothesis is verified by the analysis of the matrix containing possible measurement vectors, with respect to its rank, condition number and singular values. Additionally, a novel approach is proposed to analyse current and measurement patterns based on uncertainty estimation of difference images by the correlation matrix linearization of the reconstructed impedance matrix. The results show that single-ended potential measurements are usually better when compared to differential electric potential measurements. A conclusion supported by both points of view is that the cross current pattern (diametral) is the least informative for these symmetrical domains.