An intuitive 2D model of circular electrical impedance tomography (EIT) sensor with small size electrodes is established based on the theory of analytic functions. The validation of the model is proved using the result from the solution of Laplace equation. Suggestions on to electrode optimization and explanation to the ill-condition property of the sensitivity matrix are provided based on the model, which takes electrode distance into account and can be generalized to the sensor with any simple connected region through a conformal transformation. Image reconstruction algorithms based on the model are implemented to show feasibility of the model using experimental data collected from the EIT system developed in Tianjin University. In the simulation with a human chest-like configuration, electrical conductivity distributions are reconstructed using equi-potential back-projection (EBP) and Tikhonov regularization (TR) based on a conformal transformation of the model. The algorithms based on the model are suitable for online image reconstruction and the reconstructed results are good both in size and position.
