  Estimating intra- and extra-axonal microstructure parameters, such as volume
fractions and diffusivities, has been one of the major efforts in brain
microstructure imaging with MRI. The Standard Model (SM) of diffusion in white
matter has unified various modeling approaches based on impermeable narrow
cylinders embedded in locally anisotropic extra-axonal space. However,
estimating the SM parameters from a set of conventional diffusion MRI (dMRI)
measurements is ill-conditioned. Multidimensional dMRI helps resolve the
estimation degeneracies, but there remains a need for clinically feasible
acquisitions that yield robust parameter maps. Here we find optimal
multidimensional protocols by minimizing the mean-squared error of machine
learning-based SM parameter estimates for two 3T scanners with corresponding
gradient strengths of $40$ and $80\,\unit{mT/m}$. We assess intra-scanner and
inter-scanner repeatability for 15-minute optimal protocols by scanning 20
healthy volunteers twice on both scanners. The coefficients of variation all SM
parameters except free water fraction are $\lesssim 10\%$ voxelwise and $1-4
\%$ for their region-averaged values. As the achieved SM reproducibility
outcomes are similar to those of conventional diffusion tensor imaging, our
results enable robust in vivo mapping of white matter microstructure in
neuroscience research and in the clinic.
