“Select and retrieve via direct upsampling” network (SARDU-Net): a data-driven, model-free, deep learning approach for quantitative MRI protocol design

Purpose We introduce “Select and retrieve via direct upsampling” network (SARDU-Net), a data-driven framework for model-free quantitative MRI (qMRI) protocol design, and demonstrate it on in vivo brain and prostate diffusion-relaxation imaging (DRI). Methods SARDU-Net selects subsets of informative measurements within lengthy pilot scans, without the requirement to identify tissue parameters for which to optimise for. The algorithm consists of a selector , identifying measurement subsets, and a predictor , estimating fully-sampled signals from the subsets. We implement both using deep neural networks, which are trained jointly end-to-end. We demonstrate the algorithm on brain (32 diffusion-/T1-weightings) and prostate (16 diffusion-/T2-weightings) DRI scans acquired on 3 healthy volunteers on two separate 3T Philips systems each. We used SARDU-Net to identify sub-protocols of fixed size, assessing the reproducibility of the procedure and testing sub-protocols for their potential to inform multi-contrast analyses via T1-weighted spherical mean diffusion tensor (T1-SMDT, brain) and hybrid multi-dimensional MRI (HM-MRI, prostate) modelling. Results In both brain and prostate, SARDU-Net identifies sub-protocols that maximise information content in a reproducible manner across training instantiations. The sub-protocols enable multi-contrast modelling for which they were not optimised explicitly, providing robust T1-SMDT and HM-MRI maps and goodness-of-fit in the top 5% against extensive sub-protocol comparisons. Conclusions SARDU-Net gives new opportunities to identify economical but informative qMRI protocols from a subset of the pilot scans that can be used for acquisition-time-sensitive applications. The simple architecture makes the algorithm easy to train when exhaustive searches are intractable, and applicable to a variety of anatomical contexts. ### Competing Interest Statement Francesco Grussu is supported by PREdICT, a study co-funded by AstraZeneca in Spain. Torben Schneider is an employee of Deep Spin (Germany) and previously worked for Philips (UK).