Medical imaging in hospitals requires fast and efficient image compression to support the clinical work flow and to save costs. Least-squares autoregressive pixel prediction methods combined with arithmetic coding constitutes the state of the art in lossless image compression. However, a high computational complexity of both prevents the application of respective CPU implementations in practice. We present a massively parallel compression system for medical volume images which runs on graphics cards. Image blocks are processed independently by separate processing threads. After pixel prediction with specialized border treatment, prediction errors are entropy coded with an adaptive binary arithmetic coder. Both steps are designed to match particular demands of the parallel hardware architecture. Comparisons with current image and video coders show efficiency gains of 3.3-13.6% while compression times can be reduced to a few seconds.