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Brain tractography allows estimating in vivo long-range connections between groups of neurons. However, it is well known there is a huge amount of false-positive connections in the estimators that are represented as 3D streamlines. The COMMIT framework allows reducing those false positives, however the required computational time may become very long due to the, usually, huge number of streamlines per brain-volume, and the need to process thousands of brain images to increase the statistical power of current medical studies. In this work, we provide a programming model to parallelize the COMMIT framework on the CUDA language framework. Our results demonstrate that it is possible to reduce the computational burden by one order of magnitude by using this proposal.