  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 ({\it 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. The 2D apparent
conductivity (in terms of EIT data) corresponding to the surface deformation is
anisotropic. Thus, we consider a constrained inverse problem by restricting the
coefficient tensor to the range of the map from pressure to 2D-apparent
conductivity. This paper provides theoretical grounds for the mathematical
model of 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.
