With the performance of central processing units (CPUs) having effectively reached a limit, parallel processing offers an alternative for applications with high computational demands. Modern graphics processing units (GPUs) are massively parallel processors that can execute simultaneously thousands of light-weight processes. In this study, we propose and implement a parallel GPU-based design of a popular method that is used for the analysis of brain magnetic resonance imaging (MRI). More specifically, we are concerned with a model-based approach for extracting tissue structural information from diffusion-weighted (DW) MRI data. DW-MRI offers, through tractography approaches, the only way to study brain structural connectivity, non-invasively and in-vivo. We parallelise the Bayesian inference framework for the ball & stick model, as it is implemented in the tractography toolbox of the popular FSL software package (University of Oxford). For our implementation, we utilise the Compute Unified Device Architecture (CUDA) programming model. We show that the parameter estimation, performed through Markov Chain Monte Carlo (MCMC), is accelerated by at least two orders of magnitude, when comparing a single GPU with the respective sequential single-core CPU version. We also illustrate similar speed-up factors (up to 120x) when comparing a multi-GPU with a multi-CPU implementation.