  Purpose: Biophysical tissue models are increasingly used in the
interpretation of diffusion MRI (dMRI) data, with the potential to provide
specific biomarkers of brain microstructural changes. However, the general
Standard Model has recently shown that model parameter estimation from dMRI
data is ill-posed unless very strong magnetic gradients are used. We analyse
this issue for the Neurite Orientation Dispersion and Density Imaging with
Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from
Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the
ill-posedness and increases the accuracy of the parameter estimation. Methods:
We analyse theoretically the cumulant expansion up to fourth order in b of SDE
and DDE signals. Additionally, we perform in silico experiments to compare SDE
and DDE capabilities under similar noise conditions. Results: We prove
analytically that DDE provides invariant information non-accessible from SDE,
which makes the NODDIDA parameter estimation injective. The in silico
experiments show that DDE reduces the bias and mean square error of the
estimation along the whole feasible region of 5D model parameter space.
Conclusions: DDE adds additional information for estimating the model
parameters, unexplored by SDE, which is enough to solve the degeneracy in the
NODDIDA model parameter estimation.
