Gastric Electrical Impedance Tomography (gEIT) Based on a 3D Jacobian Matrix and Dual-Step Fuzzy Clustering Post-Processing

We propose a gastric electrical impedance tomography ( ${g}$ EIT) scheme that uses a 3D full Jacobian matrix $^\ast \text{J}$ and dual-step fuzzy clustering post-processing to automatically extract the gastric content volume ${V}$ . ${g}$ EIT has two stages: (i) computation of the full 3D Jacobian matrix $^\ast \text{J}$ , including all combinations of the current injection pattern ${I}$ and the impedance measurement ${Z}$ , in order to reconstruct the volumetric abdomen conductivity $\sigma $ ; and (ii) clustering of the gastric composition $^{k} \sigma $ (gastric wall ${k}={1}$ , gastric content ${k}={2}$ ) using dual-step fuzzy clustering post-processing, in order to automatically extract the volumetric gastric conductivity $^{k} \sigma $ . Our ${g}$ EIT scheme is qualitatively evaluated using realistic abdomen phantoms representing three gastric accommodation phases, based on three different values for the gastric content volume filled with liquid meal: (A) ${V}_{A} = {100}$ mL; (B) ${V}_{B} = {300}$ mL; and (C) ${V}_{C} = {600}$ mL, for two abdomen shapes (a normal abdomen ${S}$ and a fatty abdomen ${L}$ ) through both simulation and experimental studies. The results show that ${g}$ EIT automatically estimates ${V}$ with a total mean volume error $\langle \widetilde {V}_{e}\rangle $ that is 65.14% lower than a standard adjacent method. At the same time, ${g}$ EIT detects the gastric conductivity $\sigma $ more effectively, with a total mean conductivity error $\langle \widetilde {\textit {CE}} \rangle $ and total mean root mean square error $\langle \widetilde {\textit {rmse}}\rangle ~33.68$ % and 25.53% lower than a standard adjacent method, respectively.