Abstract: Time difference EIT is useful if the positions of the electrodes are poorly known, as it allows image reconstruction of reasonable quality even when, as is often the case, EIT data from the thorax is reconstructed onto a 2D circular model. However, even though inaccurate models may (and often are) used, there is a significant penalty in terms of reconstructed image accuracy. We focus on developments of the GREIT EIT image reconstruction algorithm. This algorithm represents a novel, optimization based approach to linear EIT reconstruction. So far, results have only been shown for circular thorax geometries, which precludes meaningful definition of conductivity contrast in the models. In this paper, we develop and validate an implementation of the GREIT algorithm for arbitrary thorax shapes. The results are validated on EIT data with simultaneous CT reference data. Results show significant improvements in the anatomical accuracy of reconstructed EIT images, in particular when physiological lung conductivity contrast is taken into account.