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Current state-of-the-art motion-based dynamic computed tomography reconstruction techniques estimate the deformation by considering motion models in the entire object volume although occasionally the proper change is local. In this article, we address this issue by introducing the region-based Motioncompensated Iterative Reconstruction Technique (rMIRT). It aims to accurately reconstruct the object being locally deformed during the scan, while identifying the deformed regions consistently with the motion models. Moreover, the motion parameters that correspond to the deformation in those areas are also estimated. In order to achieve these goals, we consider a mathematical optimization problem whose objective function depends on the reconstruction, the deformed regions and the motion parameters. The derivatives towards all of them are formulated analytically, which allows for efficient reconstruction using gradient-based optimizers. To the best of our knowledge, this is the first iterative reconstruction method in dynamic CT that exploits the analytical derivative towards the deformed regions.