Improved diffusion parameter estimation by incorporating T-2 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 T-2-DKI-FWE model that exploits the T-2 relaxation properties of both compartments, thereby better conditioning the parameter estimation problem and providing, at the same time, an additional potential biomarker (the T-2 of tissue). In our approach, the T-2 of tissue is estimated as an unknown parameter, whereas the T-2 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 T-2 of free water is studied. Next, the improved conditioning of T-2-DKI-FWE compared to DKI-FWE is illustrated using the Cramer-Rao lower bound matrix. Finally, the performance of the T-2-DKI-FWE model is compared to that of the DKI-FWE and T-2-DKI models on both simulated and real datasets. The error due to a biased approximation of the T-2 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 T-2-DKI-FWE model is beneficial for the identifiability of the model parameters. Our results suggest that the T-2-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 T-2 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.