Deep learning model fitting for diffusion-relaxometry: a comparative study

Quantitative Magnetic Resonance Imaging (qMRI) signal model fitting is traditionally performed via non-linear least square (NLLS) estimation. NLLS is slow and its performance can be affected by the presence of different local minima in the fitting objective function. Recently, machine learning techniques, including deep neural networks (DNNs), have been proposed as robust alternatives to NLLS. Here we present a deep learning implementation of qMRI model fitting, which uses DNNs to perform the inversion of the forward signal model. We compare two DNN training strategies, based on two alternative definitions of the loss function, since at present it is not known which definition leads to the most accurate, precise and robust parameter estimation. In strategy 1 we define the loss as the l2-norm of tissue parameter prediction errors, while in strategy 2 as the l2-norm of MRI signal prediction errors. We compare the two approaches on synthetic and 3T in vivo saturation inversion recovery (SIR) diffusion-weighted (DW) MRI data, using a model for joint diffusion-T1 mapping. Strategy 1 leads to lower tissue parameter root mean squared errors (RMSEs) when realistic noise distributions are considered (e.g. Rician vs Gaussian). However, strategy 2 offers lower signal reconstruction RMSE, and allows training to be performed on both synthetic and actual in vivo MRI measurements. In conclusion, both strategies are valid choices for DNN-based fitting. Strategy 2 is more practical, as it does not require pre-computation of reference tissue parameters, but may lead to worse parameter estimation.