Neural Networks for parameter estimation in microstructural MRI: a study with a high-dimensional diffusion-relaxation model of white matter microstructure

Specific features of white-matter microstructure can be investigated by using biophysical models to interpret relaxation-diffusion MRI brain data. Although more intricate models have the potential to reveal more details of the tissue, they also incur time-consuming parameter estimation that may con-verge to inaccurate solutions due to a prevalence of local minima in a degenerate fitting landscape. Machine-learning fitting algorithms have been proposed to accelerate the parameter estimation and increase the robustness of the attained estimates. So far, learning-based fitting approaches have been restricted to lower-dimensional microstructural models where dense sets of training data are easy to generate. Moreover, the degree to which machine learning can alleviate the degeneracy problem is poorly understood. For conventional least-squares solvers, it has been shown that degeneracy can be avoided by acquisition with optimized relaxation-diffusion-correlation protocols that include tensor-valued diffusion encoding; whether machine-learning techniques can offset these acquisition require-ments remains to be tested. In this work, we employ deep neural networks to vastly accelerate the fitting of a recently introduced high-dimensional relaxation-diffusion model of tissue microstructure. We also develop strategies for assessing the accuracy and sensitivity of function fitting networks and use those strategies to explore the impact of acquisition protocol design on the performance of the network. The developed learning-based fitting pipelines were tested on relaxation-diffusion data acquired with optimized and sub-sampled acquisition protocols. We found no evidence that machine-learning algorithms can by themselves replace a careful design of the acquisition protocol or correct for a degenerate fitting landscape.