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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 Cramér-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. |
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