Identifiability of white-matter compartment parameters from diffusion data
In plain words
Models of brain white matter describe the signal using a few water compartments, but different parameter sets fit the same data equally well. It is unclear which measurements make the answer unique.
Precise statement
For the two- or three-compartment model of white matter (intra-axonal sticks with a fibre orientation distribution, an anisotropic extra-axonal compartment, free water), with parameters axonal water fraction f, intra-axonal diffusivity $D_a$, and extra-axonal diffusivities D_e_par and D_e_perp, determine the minimal set of acquisitions (diffusion weightings $b\ \text{up to about}\ 10\,\mathrm{ms}/\text{micron}^2$, b-tensor shapes, echo-time variation) that makes the parameters identifiable at clinical signal-to-noise ratio of 20 to 50, and state the residual estimation variance. An answer is the identifiability condition and the attainable precision.
What would settle it
An analytic or Cramer-Rao analysis of the model with given protocols, confirmed by phantom or in vivo test-retest data with independent ground truth.
Status in the literature
Degeneracy of conventional multi-shell fits is established, and planar or spherical b-tensor encoding and echo-time variation reduce it, but a minimal clinical protocol is not agreed.