Dynamic volumetric (four dimensional- 4D) medical images are typically huge in file size and require a vast amount of resources for storage and transmission purposes. In this paper, we propose an efficient lossless compression method for 4D medical images that is based on a multi-frame motion compensation process employing a 4D search, variable blocksizes and bi-directional prediction. Data redundancies are reduced by recursively applying multi-frame motion compensation in the spatial and temporal dimensions. The proposed method also uses a novel differential coding algorithm to reduce redundancies in motion vectors and a new context-based adaptive binary arithmetic coder (CABAC) for compression of the residual data. Performance evaluations on real medical images of varying modality resulted in lossless