Which NODDI implementation is nicest for diffusion MRI?

Neurite Orientation Dispersion and Density Imaging (NODDI) is becoming increasingly common as multiband acceleration becomes available for clinical scanning, but fitting the model can be extremely slow. Since the release of the original MATLAB implementation in 2012, three alternatives have become popular: Accelerated Microstructure Imaging via Convex Optimization (AMICO), the Microstructure Diffusion Toolbox (MDT), and the CUDA Diffusion Modelling Toolbox (cuDIMOT). They accelerate fitting through reformulation and/or using GPUs, but the implementation differences raise the question of which approach is best. To our knowledge all previous comparisons lacked knowledge of the true values and used the original implementation as the nominally correct one, with in vivo data. We remedy that using simulations with known NODDI values, in addition to in vivo scans.