Gaussian decomposition of EIT reconstructions with different inclusion geometries

Abstract Objective Electrical Impedance Tomography (EIT) is a developing medical imaging device. It is a non-invasive modality that operates by injecting a small amount of current into the body and measuring the boundary voltages. An ill-posed inverse problem is solved to determine an estimate of the internal impedance of the body. Due to the ill-posed nature and its associated physics, inclusions with different geometries may appear similar in reconstructed images. This work aims to identify differences between multiple inclusions of varying geometries utilizing a post processing method. It is hypothesized that the spatial variance of the reconstructed inclusion should change proportionately to the central diameter of the inclusion and the peak relative change in impedance should be consistent with the material type of the inclusion. Approach Several inclusions with different vertical geometries were imaged using a validate open-source EIT device at different positions in a saline phantom. The reconstructed images were analysed by considering a 1D slice of the impedance values. This 1D slice was approximated by a Gaussian function. It is proposed that the Gaussian parameters associated with an inclusion should change based on the inclusion geometry and material. Main Results When the 1D slice was coincident with the inclusion the Gaussian function was a good approximation (R2 ≥ 0.93). The Gaussian parameters followed repeatable patterns as the inclusion was moved to different positions. The amplitude was shown to only change with respect to the inclusion’s volume and not the geometry, as the image slice is effectively the average of the electric field solution. The standard deviation was consistent at 10 mm diameter irrespective of the inclusion geometry. Significance This simplified method was unable to distinguish between vertical inclusion geometries compared to the full EIT solution. However, the position and size of the inclusions can be recovered from the 1D slices. Thus, the same information about the inclusion can be determined from a 1D set of impedances as a 2D image.