Quantitative MRI by nonlinear inversion of the Bloch equations

Abstract

Purpose: Development of a generic model-based reconstruction framework for multiparametric quantitative MRI that can be used with data from different pulse sequences. Methods: Generic nonlinear model-based reconstruction for quantitative MRI estimates parametric maps directly from the acquired k-space by numerical optimization. This requires numerically accurate and efficient methods to solve the Bloch equations and their partial derivatives. In this work, we combine direct sensitivity analysis and pre-computed state-transition matrices into a generic framework for calibrationless model-based reconstruction that can be applied to different pulse sequences. As a proof-of-concept, the method is implemented and validated for quantitative T 1 and T 2 mapping with single-shot inversion-recovery (IR) FLASH and IR bSSFP sequences in simulations, phantoms, and the human brain. Results: The direct sensitivity analysis enables a highly accurate and numerically stable calculation of the derivatives. The state-transition matrices efficiently exploit repeating patterns in pulse sequences, speeding up the calculation by a factor of 10 for the examples considered in this work, while preserving the accuracy of native ordinary differential equations solvers. The generic model-based method reproduces quantitative results of previous model-based reconstructions based on the known analytical solutions for radial IR FLASH. For IR bSFFP it produces accurate T 1 and T 2 maps for the National Insitute of Standards and Technology (NIST) phantom in numerical simulations and experiments. Feasibility is also shown for human brain, although results are affected by magnetization transfer effects. Conclusion: By developing efficient tools for numerical optimizations using the Bloch equations as forward model, this work enables generic model-based reconstruction for quantitative MRI.

Latent signal models: Learning compact representations of signal evolution for improved time‐resolved, multi‐contrast MRI

“…In comparison to auto‐differentiating through the EPG simulations, our proposed approach reduced reconstruction time by at least an order of magnitude. Thus, we envision our approach being advantageous when differentiation through the signal simulation requires significant computation, like isochromat‐based simulations 28,62 . On the other hand, the latent signal model auto‐encoders need to be retrained for varying acquisitions and sequence parameters, whereas Bloch equation–based auto‐differentiation only requires a differentiable implementation of new sequences of interest.…”

“…Some techniques model signals with an analytic formula and then resolve the underlying tissue parameters that characterize this model, 21–26 introducing a nonlinear optimization problem that may not account for slice‐profile effects, stimulated echoes, and B1+ inhomogeneity 27 . To model these effects, more complicated techniques build the Bloch equations into the forward model and solve for the underlying parameters governing the model 28–30 but require extensive computation or approximation of gradients.…”

A fast and practical computation method for magnetic resonance simulators

“…When processing subsequences with RF pulses, a known method for reducing computational cost is to precompute each combined transition 12–14 . Computation of combined transitions were also used in another simulator, 15 image reconstruction, 16 the design of RF pulses, 17 and relaxation and exchange processes in more complex multi‐compartment models using eigenvectors of transitions 18,19,20 …”