Parameter estimation for WMTI-Watson model of white matter using encoder-decoder recurrent neural network

Biophysical modelling of the diffusion MRI signal provides estimates of specific microstructural tissue properties. Model parameters estimates can be obtained by fitting the model to the measured signal. Although nonlinear optimization such as non-linear least squares (NLLS) is the most widespread method for model estimation, it suffers from local minima, high computational cost and uncertain accuracy. Deep Learning approaches are steadily replacing NL fitting, but come with the limitation that the model needs to be retrained for each acquisition protocol and noise level. The White Matter Tract Integrity (WMTI)- Watson model was proposed as an implementation of the Standard Model of diffusion in white matter that estimates model parameters from the diffusion and kurtosis tensors (DKI), thereby overcoming fitting the model signal equation. Here we proposed a deep learning approach based on the encoder-decoder recurrent neural network (RNN) to increase the robustness and accelerate the parameter estimation of WMTI-Watson. We use an embedding approach to render the model insensitive to potential differences in distributions between training data and experimental data. This RNN-based solver thus has the advantage of being highly efficient in computation and more readily translatable to other datasets, irrespective of acquisition protocol and underlying parameter distributions as long as diffusion and kurtosis tensors (or their typical derived scalars) were pre-computed from the data. In this study, we evaluated the performance of NLLS, the RNN-based method and a baseline DL architecture based on multilayer perceptron (MLP) on synthetic and in vivo datasets of rat and human brain. We showed that the proposed RNN-based fitting approach had the advantage of highly reduced computation time over NLLS (from hours to seconds), with similar accuracy and precision but improved robustness, and superior translatability to new datasets over MLP, irrespective of acquisition protocol or species being rat or human. Keywords Diffusion MRI, white matter, WMTI-Watson, model fitting, deep learning 1. Introduction Diffusion magnetic resonance imaging (dMRI) which encodes information about brain white matter (WM) microstructure in diffusion-weighted signal has emerged in recent years as a highly promising technique to provide specific information about microstructure features.