  Characterizing the properties and orientations of sub-voxel fiber
populations, although essential to study white-matter architecture,
microstructure and connectivity, remains one of the main challenges faced by
the MRI microstructure community. While some progress has been made in
overcoming this challenge using models, signal representations and tractography
algorithms, these approaches are ultimately limited by their key assumptions or
by the lack of specificity of the diffusion signal alone. In order to alleviate
these limitations, we combine diffusion-relaxation MR acquisitions
incorporating tensor-valued diffusion encoding, Monte-Carlo signal inversions
that extract non-parametric intra-voxel distributions of diffusion tensors and
relaxation rates, and density-based clustering techniques. This new approach,
called "Monte-Carlo density-peak clustering" (MC-DPC), first delineates
clusters in the diffusion-orientation subspace of the fiber-like
diffusion-relaxation components output by Monte-Carlo signal inversions and
then draws from the statistical aspect of these inversion algorithms to compute
the median and interquartile range of orientation-resolved means of
diffusivities and relaxation rates. Evaluating MC-DPC on tensor-valued
diffusion-encoded and T2-weighted correlated datasets in silico and in vivo, we
demonstrate its ability to simultaneously capture sub-voxel fiber orientations
and cones of uncertainty, and measure fiber-specific diffusion-relaxation
properties that are consistent with the known anatomy and existing literature.
Straightforwardly translatable to other diffusion-relaxation correlation
experiments probing $T_1$ and $T_2^*$, MC-DPC shows potential in tracking
bundle-specific patient-control group differences and longitudinal
microstructural changes, enabling new tools for microstructure-informed
tractography, and mapping tract-specific myelination states.
