Physics-informed optimization of saturation-transfer MRI protocols using non-differentiable Bloch models

Saturation transfer MR fingerprinting (ST-MRF) is a quantitative molecular MRI method that simultaneously estimates parameters of free water, solute, and semisolid macromolecule protons. The accuracy of these quantification is highly dependent on the choice of acquisition parameters, and thus, the optimization of the data acquisition schedule is crucial to improve acquisition efficiency and quantification accuracy. Herein, we developed a learning-based optimization framework for ST-MRF, incorporating a deep Bloch equation simulator as a surrogate model for the forward Bloch equation solver to enable rapid simulations. Notably, the deep Bloch equation simulator overcomes the non-differentiability of the original model by enabling gradient computation during backpropagation within the physics-informed optimization framework, thereby allowing iterative updates of the acquisition schedule to minimize quantification error. In addition, the proposed method estimated an accurate ΔB₀map with the inclusion of a minimal number of scans to address B₀inhomogeneity. B₁inhomogeneity was corrected by providing a relative<i>B</i>₁map as an input to the quantification network. We validated our approach using Bloch-McConnell equation-based digital phantoms and further evaluated the performance of the proposed optimized ST-MRF framework in<i>in vivo</i>experiments. Our results showed that the optimal ST-MRF schedule outperformed other data acquisition schedules with regard to quantification accuracy. In addition, we enhanced the<i>in vivo</i>quantitative maps by correcting motion artifacts and suppressing noise using self-supervised learning techniques. The optimal ST-MRF approach could generate accurate and reliable multi-tissue parameter maps within a clinically acceptable time.