Conductivity and Electrode Placement Variability: Evaluating the Cramer-Rao Lower Bound in 2D Electrical Impedance Tomography

TL;DR

This paper analyzes the sensitivity of 2D Electrical Impedance Tomography using the Cramer-Rao Lower Bound, comparing forward models and electrode configurations to improve understanding of resolution limits.

Contribution

It introduces a novel analysis of EIT sensitivity using CRLB with FEM simulations, comparing standard and restricted forward models for the first time.

Findings

Electrode configuration significantly affects sensitivity.

Restricted DtN model offers different sensitivity insights.

CRLB provides a theoretical lower bound on estimator variance.

Abstract

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that has earned significant attention for its potential in real-time monitoring of various physiological parameters. Despite its promise, the sensitivity and resolution of EIT remain areas of active research. This article presents a new way to analyse the sensitivity of EIT systems using the Cramer-Rao Lower Bound (CRLB). This statistical tool provides a theoretical lower bound on the variance of unbiased estimators. To simulate the EIT full cycle, we compared two forward models: standard Dirichlet-to-Neumann (DtN) and restricted DtN. By taking the CRLB over modelled with Finite Elements Method (FEM) 2D circular area with various conductivity patterns, we showed the influence of electrode configuration on each basic FEM element sensitivity. Also, the sensitivity on small perturbations for different conductivity patterns was offered. This article aims to bridge the gap between the research of widely used hardware implementations standard forward DtN model and theoretically approved restricted DtN. We conclude with a discussion on the motivation behind this research and the objectives our work introduces for the inverse restricted DtN model in practice.