A Pressure Distribution Imaging Technique with a Conductive Membrane using Electrical Impedance Tomography

Abstract

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. Introduction.There is a growing demand for cost-effective flexible pressure sensors. These devices have wide potential applicability, including in smart textiles [7,26,27], touch screens [18], artificial skins [35], and wearable health monitoring technologies [25,29]. Electrical measurements have recently been used to monitor the pressure-induced surface deformation of conductive membranes. In particular, electrical impedance tomography (EIT) has been used to develop flexible pressure sensors [31,37,38], because it allows the electromechanical behavior of an electrically conducting film to be monitored. When a pressure-sensitive conductive sheet is exposed to pressure, the deformation of the surface alters the conductivity distribution, which can be detected by an EIT system. However, rigorous studies employing mathematical modeling and reconstruction methods have not yet been conducted. The purpose of this paper is to provide a systematic mathematical framework for an EIT-based flexible pressure sensor.Our rigorous mathematical analysis is based on the consideration of a simple model of an EIT-based pressure sensor using a thin, flexible conductive membrane

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