NeuroImage (Aug 2022)
Improved diffusion parameter estimation by incorporating T2 relaxation properties into the DKI-FWE model
Abstract
The free water elimination (FWE) model and its kurtosis variant (DKI-FWE) can separate tissue and free water signal contributions, thus providing tissue-specific diffusional information. However, a downside of these models is that the associated parameter estimation problem is ill-conditioned, necessitating the use of advanced estimation techniques that can potentially bias the parameter estimates. In this work, we propose the T2-DKI-FWE model that exploits the T2 relaxation properties of both compartments, thereby better conditioning the parameter estimation problem and providing, at the same time, an additional potential biomarker (the T2 of tissue). In our approach, the T2 of tissue is estimated as an unknown parameter, whereas the T2 of free water is assumed known a priori and fixed to a literature value (1573 ms). First, the error propagation of an erroneous assumption on the T2 of free water is studied. Next, the improved conditioning of T2-DKI-FWE compared to DKI-FWE is illustrated using the Cramér-Rao lower bound matrix. Finally, the performance of the T2-DKI-FWE model is compared to that of the DKI-FWE and T2-DKI models on both simulated and real datasets. The error due to a biased approximation of the T2 of free water was found to be relatively small in various diffusion metrics and for a broad range of erroneous assumptions on its underlying ground truth value. Compared to DKI-FWE, using the T2-DKI-FWE model is beneficial for the identifiability of the model parameters. Our results suggest that the T2-DKI-FWE model can achieve precise and accurate diffusion parameter estimates, through effective reduction of free water partial volume effects and by using a standard nonlinear least squares approach. In conclusion, incorporating T2 relaxation properties into the DKI-FWE model improves the conditioning of the model fitting, while only requiring an acquisition scheme with at least two different echo times.
