Spatiotemporal Imaging of Extra-/Intracellular Ion Concentrations by Multifrequency Complex Electrical Impedance Tomography (mfc-EIT)

The multifrequency complex electrical impedance tomography (mfc-EIT) has been proposed to image the spatiotemporal extra-/intracellular ion concentrations. In mfc-EIT, four frequency-dependent Jacobian matrices described by the partial derivatives of complex impedance (resistance and reactance) with respect to complex conductivity (conductivity $\sigma $ and relative permittivity $\varepsilon $ ) as a function of radial frequency $\omega $ are newly introduced as a complex Jacobian matrix. The mfc-EIT inversely reconstructs the $\sigma $ and $\varepsilon $ images as a function of frequency from the complex impedance. Based on the electric field simulation, the $\sigma $ and $\varepsilon $ images reconstructed by mfc-EIT and conventional EIT with a general Jacobian matrix are evaluated by spectral stabilities which is an indicator of reasonable spectral trend. The $\sigma $ and $\varepsilon $ images by mfc-EIT have lower ( $\sigma $ : $2.7\times 10^{-9}$ and $\varepsilon $ : $3.0\times 10^{-4}$ ) than those by conventional EIT ( $\sigma $ : $5.5\times 10^{-8}$ and $\varepsilon $ : $5.6\times 10^{-3}$ ), which indicates that mfc-EIT reconstructs the reasonable frequency response. The mfc-EIT is also applied to the imaging of the extra/intrace-cellular ion transfer around cell-spheroids in experiment. According to the reconstructed $\sigma $ and $\varepsilon $ images, the extracellular ion concentration reflected by $\sigma $ at $f=1$ kHz are increased over time, while the intracellular ion concentration reflected by $\sigma $ and $\varepsilon $ at $f=1$ MHz are decreased over time, which is attributed to the ion transfer via the ion channel. Thus, mfc-EIT captures the extra-/intracellular ion concentration changes by ion transfer via ion channels.