Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI

TL;DR

This paper demonstrates that Double Diffusion Encoding (DDE) enhances parameter estimation in biophysical diffusion MRI models by resolving degeneracy issues inherent in Single Diffusion Encoding (SDE), leading to more accurate brain microstructure biomarkers.

Contribution

The study shows that extending from SDE to DDE makes NODDIDA model parameter estimation injective and improves accuracy, solving previous ill-posedness problems.

Findings

DDE provides invariant information not accessible from SDE.

DDE reduces bias and mean square error in parameter estimation.

DDE enables injective estimation of NODDIDA model parameters.

Abstract

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.