Electrical impedance tomography meets reduced order modelling: a framework for faster and more reliable electrical conductivity estimations

<i>Objective.</i>Inclusion of individualised electrical conductivities of head tissues is crucial for the accuracy of electrical source imaging techniques based on electro/magnetoencephalography and the efficacy of transcranial electrical stimulation. Parametric electrical impedance tomography (pEIT) is a method to cheaply and non-invasively estimate them using electrode arrays on the scalp to apply currents and measure the resulting potential distribution. Conductivities are then estimated by iteratively fitting a forward model to the measurements, incurring a prohibitive computational cost that is generally lowered at the expense of accuracy. Reducing the computational cost associated with the forward solutions would improve the accessibility of this method and unlock new capabilities.<i>Approach.</i>We introduce reduced order modelling (ROM) to massively speed up the calculations of these solutions for arbitrary conductivity values.<i>Main results.</i>We demonstrate this new ROM-pEIT framework using a realistic head model with six tissue compartments, with minimal errors in both the approximated numerical solutions and conductivity estimations. We show that the computational complexity required to reach a multi-parameter estimation with a negligible relative error is reduced by more than an order of magnitude when using this framework. Furthermore, we illustrate the benefits of this new framework in a number of practical cases, including its application to real pEIT data from three subjects.<i>Significance.</i>Results suggest that this framework can transform the use of pEIT for seeking personalised head conductivities, making it a valuable tool for researchers and clinicians.