A pressure distribution imaging technique with a conductive membrane using electrical impedance tomography

This paper presents a mathematical framework for a flexible pressure sensor model using electrical impedance tomography (EIT). When pressure is applied to a conductive membrane patch with clamped boundary, the pressure-induced surface deformation results in a change in the conductivity distribution. This change can be detected in the current-voltage data (i.e., EIT data) measured on the boundary of the membrane patch. Hence, the corresponding inverse problem is to reconstruct the pressure distribution from the data. Assuming that the material's conductivity distribution is constant, we derive a two-dimensional (2D) apparent conductivity (in terms of EIT data) corresponding to the surface deformation. Since the 2D apparent conductivity is found to be anisotropic, we consider a constrained inverse problem by restricting the coefficient tensor to the range of the map from pressure to the 2D apparent conductivity. This paper provides theoretical grounds for mathematically modeling the inverse problem. We develop a reconstruction algorithm based on a careful sensitivity analysis. We demonstrate the performance of the reconstruction algorithm through numerical simulations to validate its feasibility for future experimental studies.